A Framework for Mathematical Thinking: The Case of Linear Algebra

Science.gov (United States)

Stewart, Sepideh; Thomas, Michael O. J.

2009-01-01

Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…

ACER: A framework on the use of mathematics in upper-division physics

Science.gov (United States)

Caballero, Marcos D.; Wilcox, Bethany R.; Pepper, Rachel E.; Pollock, Steven J.

2013-01-01

At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics, electromagnetism, and quantum mechanics. Unsurprisingly, a number of difficulties are related to students' use of mathematical tools (e.g., approximation methods). Previous work has documented a number of challenges that students must overcome to use mathematical tools fluently in introductory physics (e.g., mapping meaning onto mathematical symbols). We have developed a theoretical framework to facilitate connecting students' difficulties to challenges with specific mathematical and physical concepts. In this paper, we motivate the need for this framework and demonstrate its utility for both researchers and course instructors by applying it to frame results from interview data on students' use of Taylor approximations.

A Framework for Describing Mathematics Discourse in Instruction and Interpreting Differences in Teaching

Science.gov (United States)

Adler, Jill; Ronda, Erlina

2015-01-01

We describe and use an analytical framework to document mathematics discourse in instruction (MDI), and interpret differences in mathematics teaching. MDI is characterised by four interacting components in the teaching of a mathematics lesson: exemplification (occurring through a sequence of examples and related tasks), explanatory talk (talk that…

The relationship between learning mathematics and general cognitive ability in primary school.

Science.gov (United States)

Cowan, Richard; Hurry, Jane; Midouhas, Emily

2018-06-01

Three relationships between learning mathematics and general cognitive ability have been hypothesized: The educational hypothesis that learning mathematics develops general cognitive skills, the psychometric hypothesis that differences in general cognitive ability cause differences in mathematical attainment, and the reciprocal influence hypothesis that developments in mathematical ability and general cognitive ability influence each other. These hypotheses are assessed with a sample of 948 children from the Twins Early Development Study who were assessed at 7, 9, and 10 years on mathematics, English, and general cognitive ability. A cross-lagged path analysis with mathematics and general cognitive ability measures supports the reciprocal influence hypothesis between 7 and 9 and between 9 and 10. A second analysis including English assessments only provides evidence of a reciprocal relationship between 7 and 9. Statement of Contribution What is already known on this subject? The correlations between mathematical attainment, literacy, and measures of general cognitive skills are well established. The role of literacy in developing general cognitive skills is emerging. What the present study adds? Mathematics contributes to the development of general cognitive skills. General cognitive ability contributes to mathematical development between 7 and 10. These findings support the hypothesis of reciprocal influence between mathematics and general cognitive ability, at least between 7 and 9. © 2017 The British Psychological Society.

Conceptual and mathematical advances in the search for a unified framework

CERN Document Server

Müller, Olaf; Nardmann, Marc; Tolksdorf, Jürgen; Zeidler, Eberhard; Quantum field theory and gravity

2012-01-01

One of the most challenging problems of contemporary theoretical physics is the mathematically rigorous construction of a theory which describes gravitation and the other fundamental physical interactions within a common framework. The physical ideas which grew from attempts to develop such a theory require highly advanced mathematical methods and radically new physical concepts. This book presents different approaches to a rigorous unified description of quantum fields and gravity. It contains a carefully selected cross-section of lively discussions which took place in autumn 2010 at the fifth conference "Quantum field theory and gravity - Conceptual and mathematical advances in the search for a unified framework" in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicis...

A cognitive framework for analyzing and describing introductory students' use and understanding of mathematics in physics

Science.gov (United States)

Tuminaro, Jonathan

Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics. In this thesis I propose a theoretical framework to analyze and describe students' mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events. The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework. Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of

Adapting Technological Pedagogical Content Knowledge Framework to Teach Mathematics

Science.gov (United States)

Getenet, Seyum Tekeher

2017-01-01

The technological pedagogical content knowledge framework is increasingly in use by educational technology researcher as a generic description of the knowledge requirements for teachers using technology in all subjects. This study describes the development of a mathematics specific variety of the technological pedagogical content knowledge…

New Avenues for History in Mathematics Education: Mathematical Competencies and Anchoring

DEFF Research Database (Denmark)

Jankvist, U. T.; Kjeldsen, T. H.

2011-01-01

. The first scenario occurs when history is used as a ‘tool’ for the learning and teaching of mathematics, the second when history of mathematics as a ‘goal’ is pursued as an integral part of mathematics education. We introduce a multiple-perspective approach to history, and suggest that research on history......The paper addresses the apparent lack of impact of ‘history in mathematics education’ in mathematics education research in general, and proposes new avenues for research. We identify two general scenarios of integrating history in mathematics education that each gives rise to different problems...... in mathematics education follows one of two different avenues in dealing with these scenarios. The first is to focus on students’ development of mathematical competencies when history is used a tool for the learning of curriculum-dictated mathematical in-issues. A framework for this is described. Secondly, when...

The Importance of Theoretical Frameworks and Mathematical Constructs in Designing Digital Tools

Science.gov (United States)

Trinter, Christine

2016-01-01

The increase in availability of educational technologies over the past few decades has not only led to new practice in teaching mathematics but also to new perspectives in research, methodologies, and theoretical frameworks within mathematics education. Hence, the amalgamation of theoretical and pragmatic considerations in digital tool design…

The mathematical theory of general relativity

CERN Document Server

Katkar, L N

2014-01-01

This book is prepared for M. Sc. Students of Mathematics and Physics. The aim of writing this book is to give the reader a feeling for the necessity and beauty of the laws of general relativity. The contents of the book will attract both mathematicians and physicists which provides motivation and applications of many ideas and powerful mathematical methods of modern analysis and differential geometry. An attempt has been made to make the presentation comprehensive, rigorous and yet simple. Most calculations and transformations have been carried out in great detail. KEY FEATURE: Numerous solved examples using the well known mathematical techniques viz., the tensors and the differential forms in each chapter.

Motivation and engagement in mathematics: a qualitative framework for teacher-student interactions

Science.gov (United States)

Durksen, Tracy L.; Way, Jennifer; Bobis, Janette; Anderson, Judy; Skilling, Karen; Martin, Andrew J.

2017-02-01

We started with a classic research question (How do teachers motivate and engage middle year students in mathematics?) that is solidly underpinned and guided by an integration of two theoretical and multidimensional models. In particular, the current study illustrates how theory is important for guiding qualitative analytical approaches to motivation and engagement in mathematics. With little research on how teachers of mathematics are able to maintain high levels of student motivation and engagement, we focused on developing a qualitative framework that highlights the influence of teacher-student interactions. Participants were six teachers (upper primary and secondary) that taught students with higher-than-average levels of motivation and engagement in mathematics. Data sources included one video-recorded lesson and associated transcripts from pre- and post-lesson interviews with each teacher. Overall, effective classroom organisation stood out as a priority when promoting motivation and engagement in mathematics. Results on classroom organisation revealed four key indicators within teacher-student interactions deemed important for motivation and engagement in mathematics—confidence, climate, contact, and connection. Since much of the effect of teachers on student learning relies on interactions, and given the universal trend of declining mathematical performance during the middle years of schooling, future research and intervention studies might be assisted by our qualitative framework.

Visual Processing in Generally Gifted and Mathematically Excelling Adolescents

Science.gov (United States)

Paz-Baruch, Nurit; Leikin, Roza; Leikin, Mark

2016-01-01

Little empirical data are available concerning the cognitive abilities of gifted individuals in general and especially those who excel in mathematics. We examined visual processing abilities distinguishing between general giftedness (G) and excellence in mathematics (EM). The research population consisted of 190 students from four groups of 10th-…

A Framework for Proofs and Refutations in School Mathematics: Increasing Content by Deductive Guessing

Science.gov (United States)

Komatsu, Kotaro

2016-01-01

The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

Alignment between South African mathematics assessment standards and the TIMSS assessment frameworks

Directory of Open Access Journals (Sweden)

Mdutshekelwa Ndlovu

2012-12-01

Full Text Available South Africa’s performance in international benchmark tests is a major cause for concern amongst educators and policymakers, raising questions about the effectiveness of the curriculum reform efforts of the democratic era. The purpose of the study reported in this article was to investigate the degree of alignment between the TIMSS 2003 Grade 8 Mathematics assessment frameworks and the Revised National Curriculum Statements (RNCS assessment standards for Grade 8 Mathematics, later revised to become the Curriculum and Assessment Policy Statements (CAPS. Such an investigation could help to partly shed light on why South African learners do not perform well and point out discrepancies that need to be attended to. The methodology of document analysis was adopted for the study, with the RNCS and the TIMSS 2003 Grade 8 Mathematics frameworks forming the principal documents. Porter’s moderately complex index of alignment was adopted for its simplicity. The computed index of 0.751 for the alignment between the RNCS assessment standards and the TIMSS assessment objectives was found to be significantly statistically low, at the alpha level of 0.05, according to Fulmer’s critical values for 20 cells and 90 or 120 standard points. The study suggests that inadequate attention has been paid to the alignment of the South African mathematics curriculum to the successive TIMSS assessment frameworks in terms of the cognitive level descriptions. The study recommends that participation in TIMSS should rigorously and critically inform ongoing curriculum reform efforts.

Market valuation in the framework of modern life insurance mathematics

Directory of Open Access Journals (Sweden)

Maja Petrač

2013-12-01

Full Text Available In the traditional actuarial life insurance mathematics, liabilities to beneficiaries (technical reserves are calculated based on conservative assumptions of mortality and interest rates. However, this approach was found to be incomplete since it does not contain the market component which has become essential due to the development of the financial market. Since about 80% of total liabilities of life insurance companies are made up of technical reserves, this issue has a major impact on the overall performance of insuran - ce companies. The introduction of financial components into the actuarial valuation resulted in actuarial mathematics using more and more the elements of financial mathematics thus creating new, modern life insurance mathematics. Using a simple example, this paper compares the traditional and market approaches to valuation. For this purpose, one of the principles of modern life insurance mathematics, the principle of equivalence, was observed. The above market approach to valuation, together with operational risk management, forms the basis of Solvency II Directive, the new legislative and regulatory framework for insurance and reinsurance companies in the European Union.

Elementary General and Special Education Teachers' Mathematics Skills and Efficacy

Science.gov (United States)

Flores, Margaret M.; Thornton, Jennifer; Franklin, Toni M.; Hinton, Vanessa M.; Strozier, Shaunita

2014-01-01

The purpose of this study was to extend the literature regarding elementary teachers' beliefs about mathematics instruction to include special education teachers by surveying special education and general education teachers' mathematics teaching efficacy. In addition, the researchers' surveyed teachers' mathematics skills. The participants (n =…

Molecular Phylogenetics: Mathematical Framework and Unsolved Problems

Science.gov (United States)

Xia, Xuhua

Phylogenetic relationship is essential in dating evolutionary events, reconstructing ancestral genes, predicting sites that are important to natural selection, and, ultimately, understanding genomic evolution. Three categories of phylogenetic methods are currently used: the distance-based, the maximum parsimony, and the maximum likelihood method. Here, I present the mathematical framework of these methods and their rationales, provide computational details for each of them, illustrate analytically and numerically the potential biases inherent in these methods, and outline computational challenges and unresolved problems. This is followed by a brief discussion of the Bayesian approach that has been recently used in molecular phylogenetics.

Development of a General Purpose Gamification Framework

OpenAIRE

Vea, Eivind

2016-01-01

This report describes the design and implementation of a general purpose gamification framework developed in JavaScript on the Metor platform. Gamification is described as the use of game elements in none-game contexts. The purpose is to encourage and change user behaviour. Examples of existing gamification use cases and frameworks are described. A demo game shows how a general purpose framework can be used.

An initial framework for the language of higher-order thinking mathematics practices

Science.gov (United States)

Staples, Megan E.; Truxaw, Mary P.

2012-09-01

This article presents an examination of the language demands of cognitively demanding tasks and proposes an initial framework for the language demands of higher-order mathematics thinking practices. We articulate four categories for this framework: language of generalisation, language of comparison, language of proportional reasoning, and language of analysing impact. These categories were developed out of our collaborative work to design and implement higher-order thinking tasks with a group of Grade 9 (14- and 15-year-olds) teachers teaching in a linguistically diverse setting; analyses of student work samples on these tasks; and our knowledge of the literature. We describe each type of language demand and then analyse student work in each category to reveal linguistic challenges facing students as they engage these mathematical tasks. Implications for teaching and professional development are discussed.

Teachers' Use of a Pedagogical Framework for Improvement in Mathematics Teaching: Case Studies from YuMi Deadly Maths

Science.gov (United States)

Carter, Merilyn; Cooper, Tom; Anderson, Robyn

2016-01-01

This paper describes the pedagogical framework used by YuMi Deadly Maths, a school change process used to improve mathematics teaching and thus enhance employment and life chances for socially disadvantaged students. The framework, called the RAMR cycle, is capable of being used by mathematics teachers for planning and delivering lessons and units…

A general framework of automorphic inflation

International Nuclear Information System (INIS)

Schimmrigk, Rolf

2016-01-01

Automorphic inflation is an application of the framework of automorphic scalar field theory, based on the theory of automorphic forms and representations. In this paper the general framework of automorphic and modular inflation is described in some detail, with emphasis on the resulting stratification of the space of scalar field theories in terms of the group theoretic data associated to the shift symmetry, as well as the automorphic data that specifies the potential. The class of theories based on Eisenstein series provides a natural generalization of the model of j-inflation considered previously.

A general framework of automorphic inflation

Energy Technology Data Exchange (ETDEWEB)

Schimmrigk, Rolf [Department of Physics, Indiana University at South Bend,1700 Mishawaka Ave. South Bend, IN 46634 (United States)

2016-05-24

Automorphic inflation is an application of the framework of automorphic scalar field theory, based on the theory of automorphic forms and representations. In this paper the general framework of automorphic and modular inflation is described in some detail, with emphasis on the resulting stratification of the space of scalar field theories in terms of the group theoretic data associated to the shift symmetry, as well as the automorphic data that specifies the potential. The class of theories based on Eisenstein series provides a natural generalization of the model of j-inflation considered previously.

Mathematical Modeling of Biofilm Structures Using COMSTAT Data

DEFF Research Database (Denmark)

Verotta, Davide; Haagensen, Janus Anders Juul; Spormann, Alfred M.

2017-01-01

Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data...... in terms of few parameters and the capability to (i) compare different experiments and exposures to different agents, (ii) test different hypotheses regarding biofilm growth and interaction with different agents, and (iii) simulate arbitrary administrations of agents. The mathematical framework is divided...... to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We...

Toward Nexus Equation: A Conceptual and Mathematical Framework for Water- Energy-Food Nexus

Science.gov (United States)

Abou Najm, Majdi; Higgins, Chad

2016-04-01

Water, energy, and agriculture are highly interdependent that attempts to achieve sustainability in any of those three domains will directly impact the others. These interdependencies, collectively known as the Water-Energy-Food Nexus, become more complex and more critical as the climate changes, the population grows, habits and lifestyles alternate, and the prices of water, energy, and food increase. However, and despite several attempts to incorporate the nexus, the global research community continues to focus on different subsets of the problem with limited holistic attempts to address the full problem. At best, interactions between two of the three domains were studied, often neglecting the impact of such interaction on the third domain. For example, agricultural researchers tracked water costs by applying concepts like virtual water or water footprint, or using large-scale system models to investigate food and water security, ignoring most often the corresponding energy footprint. Similarly, investigators quantified water-energy tradeoffs in the highly engineered, centralized systems of water and power management, paying no attention to water diversion from agriculture. Most nexus initiatives focused on reviews and data collection of existing knowledge and relevant facts, but unfortunately lacked a conceptual and mathematical framework that can integrate all the gathered knowledge and account for multiple interactions, feedbacks, or natural processes that occur across all three domains of the nexus. Here, we present an integrated conceptual and mathematical framework (roadmap) for the nexus. This framework is driven by spatiotemporal demands for water, energy, and food to be satisfied by resource management of the three domains, envisioned as a stepwise process, with each step requiring inputs from the three nexus domains and creating waste products. The efficiency of each step, combined with mass balances, create the linkages and feedback loops within the

University Students' Metacognitive Failures in Mathematical Proving Investigated Based on the Framework of Assimilation and Accommodation

Science.gov (United States)

Huda, Nizlel; Subanji; Nusantar, Toto; Susiswo; Sutawidjaja, Akbar; Rahardjo, Swasono

2016-01-01

This study aimed to determine students' metacognitive failure in Mathematics Education Program of FKIP in Jambi University investigated based on assimilation and accommodation Mathematical framework. There were 35 students, five students did not answer the question, three students completed the questions correctly and 27 students tried to solve…

A general-purpose process modelling framework for marine energy systems

International Nuclear Information System (INIS)

Dimopoulos, George G.; Georgopoulou, Chariklia A.; Stefanatos, Iason C.; Zymaris, Alexandros S.; Kakalis, Nikolaos M.P.

2014-01-01

Highlights: • Process modelling techniques applied in marine engineering. • Systems engineering approaches to manage the complexity of modern ship machinery. • General purpose modelling framework called COSSMOS. • Mathematical modelling of conservation equations and related chemical – transport phenomena. • Generic library of ship machinery component models. - Abstract: High fuel prices, environmental regulations and current shipping market conditions impose ships to operate in a more efficient and greener way. These drivers lead to the introduction of new technologies, fuels, and operations, increasing the complexity of modern ship energy systems. As a means to manage this complexity, in this paper we present the introduction of systems engineering methodologies in marine engineering via the development of a general-purpose process modelling framework for ships named as DNV COSSMOS. Shifting the focus from components – the standard approach in shipping- to systems, widens the space for optimal design and operation solutions. The associated computer implementation of COSSMOS is a platform that models, simulates and optimises integrated marine energy systems with respect to energy efficiency, emissions, safety/reliability and costs, under both steady-state and dynamic conditions. DNV COSSMOS can be used in assessment and optimisation of design and operation problems in existing vessels, new builds as well as new technologies. The main features and our modelling approach are presented and key capabilities are illustrated via two studies on the thermo-economic design and operation optimisation of a combined cycle system for large bulk carriers, and the transient operation simulation of an electric marine propulsion system

ELPSA as A Lesson Design Framework

Directory of Open Access Journals (Sweden)

Tom Lowrie

2015-07-01

Full Text Available This paper offers a framework for mathematics lesson design that is consistent with the way we learn about, and discover, most things in life. In addition, the framework provides a structure for identifying how mathematical concepts and understanding are acquired and developed. This framework is called ELPSA and represents five learning components, namely: Experience, Language, Pictorial, Symbolic and Applications. This framework has been used in developing lessons and teacher professional programs in Indonesia since 2012 in cooperation with the World Bank. This paper describes the theory that underlines the framework in general and in relation to each inter-connected component. Two explicit learning sequences for classroom practice are described, associated with Pythagoras theorem and probability. This paper then concludes with recommendations for using ELPSA in various institutional contexts.

Mathematical framework for fast and rigorous track fit for the ZEUS detector

Energy Technology Data Exchange (ETDEWEB)

Spiridonov, Alexander

2008-12-15

In this note we present a mathematical framework for a rigorous approach to a common track fit for trackers located in the inner region of the ZEUS detector. The approach makes use of the Kalman filter and offers a rigorous treatment of magnetic field inhomogeneity, multiple scattering and energy loss. We describe mathematical details of the implementation of the Kalman filter technique with a reduced amount of computations for a cylindrical drift chamber, barrel and forward silicon strip detectors and a forward straw drift chamber. Options with homogeneous and inhomogeneous field are discussed. The fitting of tracks in one ZEUS event takes about of 20ms on standard PC. (orig.)

Application and the Identity of Mathematics

DEFF Research Database (Denmark)

Jensen, Kasper Bjering Søby

In the paper a conceptual framework for discussing the identity of mathematics as a school subject is constructed with particular emphasize on application of mathematics. The framework is used to analyze the identity of mathematics, as it appears on two different kinds of domains: the political s...... system and the teachers. At the end it is discussed whether this frameworks gives us new insights into mathematics teaching. It is concluded that the framework can articulates important aspects.......In the paper a conceptual framework for discussing the identity of mathematics as a school subject is constructed with particular emphasize on application of mathematics. The framework is used to analyze the identity of mathematics, as it appears on two different kinds of domains: the political...

ELPSA AS A LESSON DESIGN FRAMEWORK

Directory of Open Access Journals (Sweden)

Tom Lowrie

2015-07-01

Full Text Available This paper offers a framework for mathematics lesson design that is consistent with the way we learn about, and discover, most things in life. In addition, the framework provides a structure for identifying how mathematical concepts and understanding are acquired and developed. This framework is called ELPSA and represents five learning components, namely: Experience, Language, Pictorial, Symbolic and Applications. This framework has been used in developing lessons and teacher professional programs in Indonesia since 2012 in cooperation with the World Bank. This paper describes the theory that underlines the framework in general and in relation to each inter-connected component. Two explicit learning sequences for classroom practice are described, associated with Pythagoras theorem and probability. This paper then concludes with recommendations for using ELPSA in various institutional contexts.Keywords: ELPSA, lesson design framework, Pythagoras theorem, probability DOI: dx.doi.org/10.22342/jme.62.77

Oriented matroid theory as a mathematical framework for M-theory

OpenAIRE

Nieto, J. A.

2006-01-01

We claim that $M$(atroid) theory may provide a mathematical framework for an underlying description of $M$-theory. Duality is the key symmetry which motivates our proposal. The definition of an oriented matroid in terms of the Farkas property plays a central role in our formalism. We outline how this definition may be carried over $M$-theory. As a consequence of our analysis we find a new type of action for extended systems which combines dually the $p$-brane and its dual $p^{\\perp}$-brane.

Mathematical Methods of Game and Economic Theory

CERN Document Server

Aubin, J-P

1982-01-01

This book presents a unified treatment of optimization theory, game theory and a general equilibrium theory in economics in the framework of nonlinear functional analysis. It not only provides powerful and versatile tools for solving specific problems in economics and the social sciences but also serves as a unifying theme in the mathematical theory of these subjects as well as in pure mathematics itself.

Mathematical Modeling of Biofilm Structures Using COMSTAT Data

Directory of Open Access Journals (Sweden)

Davide Verotta

2017-01-01

Full Text Available Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data in terms of few parameters and the capability to (i compare different experiments and exposures to different agents, (ii test different hypotheses regarding biofilm growth and interaction with different agents, and (iii simulate arbitrary administrations of agents. The mathematical framework is divided to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We demonstrate the application of (some of the models using confocal microscopy data obtained using the computer program COMSTAT.

Aspects of Theories, Frameworks and Paradigms in Mathematics Education Research

Science.gov (United States)

Stoilescu, Dorian

2016-01-01

This article discusses major theoretical debates and paradigms from the last decades in general education and their specific influences in mathematics education contexts. Behaviourism, cognitive science, constructivism, situated cognition, critical theory, place-based learning, postmodernism and poststructuralism and their significant aspects in…

Deep graphs—A general framework to represent and analyze heterogeneous complex systems across scales

Science.gov (United States)

Traxl, Dominik; Boers, Niklas; Kurths, Jürgen

2016-06-01

Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. Particularly in recent years, a great progress has been made by augmenting "traditional" network theory in order to account for the multiplex nature of many networks, multiple types of connections between objects, the time-evolution of networks, networks of networks and other intricacies. However, existing network representations still lack crucial features in order to serve as a general data analysis tool. These include, most importantly, an explicit association of information with possibly heterogeneous types of objects and relations, and a conclusive representation of the properties of groups of nodes as well as the interactions between such groups on different scales. In this paper, we introduce a collection of definitions resulting in a framework that, on the one hand, entails and unifies existing network representations (e.g., network of networks and multilayer networks), and on the other hand, generalizes and extends them by incorporating the above features. To implement these features, we first specify the nodes and edges of a finite graph as sets of properties (which are permitted to be arbitrary mathematical objects). Second, the mathematical concept of partition lattices is transferred to the network theory in order to demonstrate how partitioning the node and edge set of a graph into supernodes and superedges allows us to aggregate, compute, and allocate information on and between arbitrary groups of nodes. The derived partition lattice of a graph, which we denote by deep graph, constitutes a concise, yet comprehensive representation that enables the expression and analysis of heterogeneous properties, relations, and interactions on all scales of a complex system in a self-contained manner. Furthermore, to be able to utilize existing network-based methods and models, we derive different representations of

The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering

International Nuclear Information System (INIS)

Stakhov, A.P.

2005-01-01

The 'Dichotomy Principle' and the classical 'Golden Section Principle' are two of the most important principles of Nature, Science and also Art. The Generalized Principle of the Golden Section that follows from studying the diagonal sums of the Pascal triangle is a sweeping generalization of these important principles. This underlies the foundation of 'Harmony Mathematics', a new proposed mathematical direction. Harmony Mathematics includes a number of new mathematical theories: an algorithmic measurement theory, a new number theory, a new theory of hyperbolic functions based on Fibonacci and Lucas numbers, and a theory of the Fibonacci and 'Golden' matrices. These mathematical theories are the source of many new ideas in mathematics, philosophy, botanic and biology, electrical and computer science and engineering, communication systems, mathematical education as well as theoretical physics and physics of high energy particles

Toward the Nexus Equation: A Conceptual and Mathematical Framework for Energy-Water-Food Nexus Analysis

Science.gov (United States)

Higgins, C. W.; Abou Najm, M.

2015-12-01

Water, energy, and agriculture depend on each other so strongly that attempts to achieve sustainability in any of those three domains will directly impact the others. These interdependencies, collectively known as the Water-Energy-Food Nexus, become more complex and more critical as the climate changes, the population grows, habits and lifestyle alternatives, and the prices of water, energy, and food increase. The U.S. National Intelligence Council has identified the nexus of water, energy, food, and climate change as one of four overarching megatrends that will shape the world in 2030. However, the global research community has rarely addressed the full problem and focused instead on different subsets of the problem. For example, interactions between two of the three domains were studied, often neglecting the impact of such interaction on the third domain. Investigators have quantified water-energy tradeoffs in the highly engineered, centralized systems of water and power management. Agricultural researchers have tracked water costs by applying the concept of virtual water (the total volume of water needed to produce and process a commodity or service) or using large-scale system models to investigate food and water security. Integrative nexus initiatives have focused on reviews and data collection of existing knowledge and relevant facts. They unfortunately lack a conceptual and mathematical framework that can integrate all the gathered knowledge and account for multiple interactions, feedbacks, or natural processes that occur across all three domains of the nexus. Here, we present an integrated conceptual and mathematical framework (roadmap) for the nexus. This framework is driven by spatiotemporal demands for water, energy, and food to be satisfied by resource management of the three domains, envisioned as a stepwise process, with each step requiring inputs from the three nexus domains and creating waste products. The efficiency of each step, combined with mass

The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering

Energy Technology Data Exchange (ETDEWEB)

Stakhov, A.P. [International Club of the Golden Section, 6 McCreary Trail, Bolton, ON, L7E 2C8 (Canada)] e-mail: goldenmuseum@rogers.com

2005-10-01

The 'Dichotomy Principle' and the classical 'Golden Section Principle' are two of the most important principles of Nature, Science and also Art. The Generalized Principle of the Golden Section that follows from studying the diagonal sums of the Pascal triangle is a sweeping generalization of these important principles. This underlies the foundation of 'Harmony Mathematics', a new proposed mathematical direction. Harmony Mathematics includes a number of new mathematical theories: an algorithmic measurement theory, a new number theory, a new theory of hyperbolic functions based on Fibonacci and Lucas numbers, and a theory of the Fibonacci and 'Golden' matrices. These mathematical theories are the source of many new ideas in mathematics, philosophy, botanic and biology, electrical and computer science and engineering, communication systems, mathematical education as well as theoretical physics and physics of high energy particles.

A general framework for reasoning on inconsistency

CERN Document Server

Martinez, Maria Vanina; Subrahmanian, VS; Amgoud, Leila

2013-01-01

This SpringerBrief proposes a general framework for reasoning about inconsistency in a wide variety of logics, including inconsistency resolution methods that have not yet been studied.  The proposed framework allows users to specify preferences on how to resolve inconsistency when there are multiple ways to do so. This empowers users to resolve inconsistency in data leveraging both their detailed knowledge of the data as well as their application needs. The brief shows that the framework is well-suited to handle inconsistency in several logics, and provides algorithms to compute preferred opt

Promoting Student Learning and Productive Persistence in Developmental Mathematics: Research Frameworks Informing the Carnegie Pathways

Science.gov (United States)

Edwards, Ann R.; Beattie, Rachel L.

2016-01-01

This paper focuses on two research-based frameworks that inform the design of instruction and promote student success in accelerated, developmental mathematics pathways. These are Learning Opportunities--productive struggle on challenging and relevant tasks, deliberate practice, and explicit connections, and Productive Persistence--promoting…

GENERAL TASKS OF MATHEMATICAL EDUCATION DEVELOPMENT

Directory of Open Access Journals (Sweden)

V. A. Testov

2014-01-01

Full Text Available The paper discusses basic implementation aspects of the Mathematical Education Development Concept, adopted by the Russian Government in 2013. According to the above document, the main problems of mathematical education include: low motivation of secondary and higher school students for studying the discipline, resulted from underestimation of mathematical knowledge; and outdated educational content, overloaded by technical elements. In the author’s opinion, a number of important new mathematical fields, developed over the last years, - the graph theory, discrete mathematics, encoding theory, fractal geometry, etc – have a large methodological and applied educational potential. However, these new subdisciplines have very little representation both in the secondary and higher school mathematical curricula. As a solution for overcoming the gap between the latest scientific achievements and pedagogical practices, the author recommends integration of the above mentioned mathematical disciplines in educational curricula instead of some outdated technical issues. In conclusion, the paper emphasizes the need for qualified mathematical teachers’ training for solving the problems of students’ motivation development and content updates.

Developing and Validating a Competence Framework for Secondary Mathematics Student Teachers through a Delphi Method

Science.gov (United States)

Muñiz-Rodríguez, Laura; Alonso, Pedro; Rodríguez-Muñiz, Luis J.; Valcke, Martin

2017-01-01

Initial teacher education programmes provide student teachers with the desired competences to develop themselves as teachers. Although a generic framework for teaching competences is available covering all school subjects in Spain, the initial teacher education programmes curriculum does not specify which competences secondary mathematics student…

Experimental Validation of Mathematical Framework for Fast Switching Valves used in Digital Hydraulic Machines

DEFF Research Database (Denmark)

Nørgård, Christian; Roemer, Daniel Beck; Bech, Michael Møller

2015-01-01

of 10 kW during switching (mean of approximately 250 W) and a pressure loss below 0.5 bar at 600 l/min. The main goal of this article is validate parts of the mathematical framework based on a series of experiments. Furthermore, this article aims to document the experience gained from the experimental...

Generalized dynamics of soft-matter quasicrystals mathematical models and solutions

CERN Document Server

Fan, Tian-You

2017-01-01

The book systematically introduces the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (SMQ). It provides methods for solving the initial-boundary value problems in these systems. The solutions obtained demonstrate the distribution, deformation and motion of the soft-matter quasicrystals, and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. Mathematical solutions for solid and soft-matter quasicrystals are compared, to help readers to better understand the featured properties of SMQ.

A note on stability of stationary points in mathematical programs with generalized complementarity constraints

Czech Academy of Sciences Publication Activity Database

Červinka, Michal

2016-01-01

Roč. 65, č. 5 (2016), s. 1049-1060 ISSN 0233-1934 R&D Projects: GA ČR GAP402/12/1309 Institutional support: RVO:67985556 Keywords : parameter-dependent mathematical programs with generalized equilibrium constraints * M-stationarity * C-stationarity * isolated calmness * Aubin property Subject RIV: BA - General Mathematics Impact factor: 0.943, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/cervinka-0461163.pdf

A case study of pedagogy of mathematics support tutors without a background in mathematics education

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Walsh, Richard

2017-01-01

This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to these tutors' provision of mathematics support to first and second year undergraduate engineering students and second year undergraduate science students. It was found that tutors are lacking in various pedagogical skills which are needed for high-quality learning amongst service mathematics students (e.g. engineering/science/technology students), a demographic which have low levels of mathematics upon entering university. Tutors teach their support classes in a very fast didactic way with minimal opportunities for students to ask questions or to attempt problems. It was also found that this teaching method is even more so exaggerated in mandatory departmental mathematics tutorials that students take as part of their mathematics studies at tertiary level. The implications of the findings on mathematics tutor training at tertiary level are also discussed.

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

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Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

Sample Grade Level Benchmarks, Grades 5-8, Based on the 1998 Arkansas State Mathematics Framework.

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Arkansas State Dept. of Education, Little Rock.

This document presents the application and use of mathematics learning proposed by the Arkansas curriculum frameworks for grades 5-8. The standards are presented in chart form and organized into five strands: (1) number sense, properties, and operations; (2) geometry and spatial sense; (3) measurement; (4) data analysis, statistics, and…

A General Framework for Reviewing Dictionaries

DEFF Research Database (Denmark)

Nielsen, Sandro

2013-01-01

in specific types of situations in the real (extra-lexicographic) world. I propose a basis for a framework that contains an outline of general theoretical and practical principles that underlie the true nature of dictionary reviews, and places the reviews in a lexicographic universe with the dictionary...... and lexicography at its centre. This seems to be in line with the modern understanding of lexicography as a separate academic discipline concerned with the compilation, design, evaluation and use of dictionaries. Moreover, a set of generally applicable principles may lead the discourse community to accept...

Mathematical grammar of biology

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Yamagishi, Michel Eduardo Beleza

2017-01-01

This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called “Chargaff’s grammar of biology” by providing the conceptual theoretical framework necessary to generalize Chargaff’s rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties.

A general framework for updating belief distributions.

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Bissiri, P G; Holmes, C C; Walker, S G

2016-11-01

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. For instance, when the object of interest is low dimensional, such as a mean or median, it is cumbersome to have to achieve this via a complete model for the whole data distribution. More importantly, there are settings where the parameter of interest does not directly index a family of density functions and thus the Bayesian approach to learning about such parameters is currently regarded as problematic. Our framework uses loss functions to connect information in the data to functionals of interest. The updating of beliefs then follows from a decision theoretic approach involving cumulative loss functions. Importantly, the procedure coincides with Bayesian updating when a true likelihood is known yet provides coherent subjective inference in much more general settings. Connections to other inference frameworks are highlighted.

An Analysis on Eight Grade Mathematics Textbook of New Indonesian Curriculum (K-13 Based on Pisa’s Framework

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Sarlita Murdaningsih

2016-01-01

Full Text Available This study aims to analyze and describe the mathematics problems in the eighth grade mathematics textbook of new Indonesian curriculum (K-13 based on The Programme for International Student Assesment (PISA frameworks. The object of this study was the the revised version textbooks of the eighth grade mathematics student’s book published by The Ministry of Education and Culture (Kemendikbud in 2014. The framework of the analysis in this study was the PISA components consisting of process, content, and context with its categories. The research method was descriptive quantitative. The data was collected by observing the contents of the textbook and interviewing the students and the teachers in SMP Negeri 2 Rembang. The analysis showed that the contents of the textbook were in accordance to the PISA components. The result also indicated that in both semester of the students’ book, the problems involving the process of employing mathematical concepts, facts, procedures, and reasoning were more dominant than others. Moreover, in the contexts, the problems were dominated by the personal context. Furthermore, the first semester students’ books were dominated by the change and relationships contents while the second semester books were dominated by the space and shape contents.

Mathematical Modeling of a Moving Planar Payload Pendulum on Flexible Portal Framework

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Edwar Yazid

2012-03-01

Full Text Available Mathematical modeling of a moving planar payload pendulum on elastic portal framework is presented in this paper. The equations of motion of such a system are obtained by modeling the portal frame using finite element in conjunction with moving finite element method and moving planar payload pendulum by using Lagrange’s equations. The generated equations indicate the presence of nonlinear coupling between dynamics of portal framework and the payload pendulum. The combinational direct numerical integration technique, namely Newmarkand fourth-order Runge-Kutta method, is then proposed to solve the coupled equations of motion. Several numerical simulations are performed and the results are verified with several benchmarks. The results indicate that the amplitude and frequency of the payload pendulum swing angle are greatly affected by flexibility of structure and the cable in term of carriage speed. 

Universal Basic Education and the Provision of Quality Mathematics in Southern Africa

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Kazima, Mercy

2014-01-01

In this paper, I discuss Universal Basic Education (UBE) in relation to the teaching and learning of mathematics in Southern Africa. I present the status of UBE for all countries in the region and then use 3 selected examples: Botswana, Malawi, and Zambia, to illustrate the provision of mathematics in the general framework of UBE in the countries.…

Mathematical Formulation of Multilayer Networks

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De Domenico, Manlio; Solé-Ribalta, Albert; Cozzo, Emanuele; Kivelä, Mikko; Moreno, Yamir; Porter, Mason A.; Gómez, Sergio; Arenas, Alex

2013-10-01

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing “traditional” network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion—for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.

Development of an explanatory framework for the solution of electricity problems

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Reuben D. Koontse

2017-11-01

Full Text Available Problem solving is considered a higher order thinking skill and is included as one of the 21st century’s core competencies. To demonstrate how students’ use of a specific mathematical approach leads to a particular type of understanding when solving problems in electricity, an interpretive framework was developed. This interpretive framework combined two extensively used frameworks, namely Mathematical Resources (MR and Extended Semantic Model (ESM and was rationalised in electricity subtopics namely electric circuit, electric force and electric field. An interpretivist research paradigm was chosen to explain and derive meaning from fifteen first year physics students’ mathematical approaches in solving electricity problems. In general, students were found to be more inclined to activate formal mathematical rules, even when the use of basic or everyday mathematics that require activation of intuitive knowledge elements and reasoning primitives, would be more efficient. The need for a qualitative approach to solving physics problems rather than a quantitative one was presented and this has implications for future approaches to teaching science.

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

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Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

The quest for a new modelling framework in mathematical biology. Comment on "On the interplay between mathematics and biology: Hallmarks towards a new systems biology" by N. Bellomo et al.

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Eftimie, Raluca

2015-03-01

One of the main unsolved problems of modern physics is finding a "theory of everything" - a theory that can explain, with the help of mathematics, all physical aspects of the universe. While the laws of physics could explain some aspects of the biology of living systems (e.g., the phenomenological interpretation of movement of cells and animals), there are other aspects specific to biology that cannot be captured by physics models. For example, it is generally accepted that the evolution of a cell-based system is influenced by the activation state of cells (e.g., only activated and functional immune cells can fight diseases); on the other hand, the evolution of an animal-based system can be influenced by the psychological state (e.g., distress) of animals. Therefore, the last 10-20 years have seen also a quest for a "theory of everything"-approach extended to biology, with researchers trying to propose mathematical modelling frameworks that can explain various biological phenomena ranging from ecology to developmental biology and medicine [1,2,6]. The basic idea behind this approach can be found in a few reviews on ecology and cell biology [6,7,9-11], where researchers suggested that due to the parallel between the micro-scale dynamics and the emerging macro-scale phenomena in both cell biology and in ecology, many mathematical methods used for ecological processes could be adapted to cancer modelling [7,9] or to modelling in immunology [11]. However, this approach generally involved the use of different models to describe different biological aspects (e.g., models for cell and animal movement, models for competition between cells or animals, etc.).

A general framework for intelligent recommender systems

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Jose Aguilar

2017-07-01

Full Text Available In this paper, we propose a general framework for an intelligent recommender system that extends the concept of a knowledge-based recommender system. The intelligent recommender system exploits knowledge, learns, discovers new information, infers preferences and criticisms, among other things. For that, the framework of an intelligent recommender system is defined by the following components: knowledge representation paradigm, learning methods, and reasoning mechanisms. Additionally, it has five knowledge models about the different aspects that we can consider during a recommendation: users, items, domain, context and criticisms. The mix of the components exploits the knowledge, updates it and infers, among other things. In this work, we implement one intelligent recommender system based on this framework, using Fuzzy Cognitive Maps (FCMs. Next, we test the performance of the intelligent recommender system with specialized criteria linked to the utilization of the knowledge in order to test the versatility and performance of the framework.

A mathematical framework for multiscale science and engineering: the variational multiscale method and interscale transfer operators

International Nuclear Information System (INIS)

Shadid, John Nicolas; Lehoucq, Richard B.; Christon, Mark Allen; Slepoy, Alexander; Bochev, Pavel Blagoveston; Collis, Samuel Scott; Wagner, Gregory John

2004-01-01

Existing approaches in multiscale science and engineering have evolved from a range of ideas and solutions that are reflective of their original problem domains. As a result, research in multiscale science has followed widely diverse and disjoint paths, which presents a barrier to cross pollination of ideas and application of methods outside their application domains. The status of the research environment calls for an abstract mathematical framework that can provide a common language to formulate and analyze multiscale problems across a range of scientific and engineering disciplines. In such a framework, critical common issues arising in multiscale problems can be identified, explored and characterized in an abstract setting. This type of overarching approach would allow categorization and clarification of existing models and approximations in a landscape of seemingly disjoint, mutually exclusive and ad hoc methods. More importantly, such an approach can provide context for both the development of new techniques and their critical examination. As with any new mathematical framework, it is necessary to demonstrate its viability on problems of practical importance. At Sandia, lab-centric, prototype application problems in fluid mechanics, reacting flows, magnetohydrodynamics (MHD), shock hydrodynamics and materials science span an important subset of DOE Office of Science applications and form an ideal proving ground for new approaches in multiscale science.

A General Framework for Probabilistic Characterizing Formulae

DEFF Research Database (Denmark)

Sack, Joshua; Zhang, Lijun

2012-01-01

Recently, a general framework on characteristic formulae was proposed by Aceto et al. It offers a simple theory that allows one to easily obtain characteristic formulae of many non-probabilistic behavioral relations. Our paper studies their techniques in a probabilistic setting. We provide...... a general method for determining characteristic formulae of behavioral relations for probabilistic automata using fixed-point probability logics. We consider such behavioral relations as simulations and bisimulations, probabilistic bisimulations, probabilistic weak simulations, and probabilistic forward...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Appl. 175 (1993) 458), to establish mathematically, the existence of hydrodynamic instability in single diffusive bottom heavy systems, when considered in the more general framework of the boundary conditions of the type specified by Beavers and Joseph (J. Fluid Mech. 30 (1967) 197), in the parameter regime T 0 2 > 1 ...

Conceptualising inquiry based education in mathematics

DEFF Research Database (Denmark)

Blomhøj, Morten; Artigue, Michéle

2013-01-01

of inquiry as a pedagogical concept in the work of Dewey (e.g. 1916, 1938) to analyse and discuss its migration to science and mathematics education. For conceptualizing inquiry-based mathematics education (IBME) it is important to analyse how this concept resonates with already well-established theoretical...... frameworks in mathematics education. Six such frameworks are analysed from the perspective of inquiry: the problem-solving tradition, the Theory of Didactical Situations, the Realistic Mathematics Education programme, the mathematical modelling perspective, the Anthropological Theory of Didactics...

An Emergent Framework: Views of Mathematical Processes

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Sanchez, Wendy B.; Lischka, Alyson E.; Edenfield, Kelly W.; Gammill, Rebecca

2015-01-01

The findings reported in this paper were generated from a case study of teacher leaders at a state-level mathematics conference. Investigation focused on how participants viewed the mathematical processes of communication, connections, representations, problem solving, and reasoning and proof. Purposeful sampling was employed to select nine…

NetMOD Version 2.0 Mathematical Framework

Energy Technology Data Exchange (ETDEWEB)

Merchant, Bion J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Young, Christopher J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Chael, Eric P. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-08-01

NetMOD ( Net work M onitoring for O ptimal D etection) is a Java-based software package for conducting simulation of seismic, hydroacoustic and infrasonic networks. Network simulations have long been used to study network resilience to station outages and to determine where additional stations are needed to reduce monitoring thresholds. NetMOD makes use of geophysical models to determine the source characteristics, signal attenuation along the path between the source and station, and the performance and noise properties of the station. These geophysical models are combined to simulate the relative amplitudes of signal and noise that are observed at each of the stations. From these signal-to-noise ratios (SNR), the probabilities of signal detection at each station and event detection across the network of stations can be computed given a detection threshold. The purpose of this document is to clearly and comprehensively present the mathematical framework used by NetMOD, the software package developed by Sandia National Laboratories to assess the monitoring capability of ground-based sensor networks. Many of the NetMOD equations used for simulations are inherited from the NetSim network capability assessment package developed in the late 1980s by SAIC (Sereno et al., 1990).

Quantum generalized observables framework for psychological data: a case of preference reversals in US elections

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Khrennikova, Polina; Haven, Emmanuel

2017-10-01

Politics is regarded as a vital area of public choice theory, and it is strongly relying on the assumptions of voters' rationality and as such, stability of preferences. However, recent opinion polls and real election outcomes in the USA have shown that voters often engage in `ticket splitting', by exhibiting contrasting party support in Congressional and Presidential elections (cf. Khrennikova 2014 Phys. Scripta T163, 014010 (doi:10.1088/0031-8949/2014/T163/014010); Khrennikova & Haven 2016 Phil. Trans. R. Soc. A 374, 20150106 (doi:10.1098/rsta.2015.0106); Smith et al. 1999 Am. J. Polit. Sci. 43, 737-764 (doi:10.2307/2991833)). Such types of preference reversals cannot be mathematically captured via the formula of total probability, thus showing that voters' decision making is at variance with the classical probabilistic information processing framework. In recent work, we have shown that quantum probability describes well the violation of Bayesian rationality in statistical data of voting in US elections, through the so-called interference effects of probability amplitudes. This paper is proposing a novel generalized observables framework of voting behaviour, by using the statistical data collected and analysed in previous studies by Khrennikova (Khrennikova 2015 Lect. Notes Comput. Sci. 8951, 196-209) and Khrennikova & Haven (Khrennikova & Haven 2016 Phil. Trans. R. Soc. A 374, 20150106 (doi:10.1098/rsta.2015.0106)). This framework aims to overcome the main problems associated with the quantum probabilistic representation of psychological data, namely the non-double stochasticity of transition probability matrices. We develop a simplified construction of generalized positive operator valued measures by formulating special non-orthonormal bases with respect to these operators. This article is part of the themed issue `Second quantum revolution: foundational questions'.

Retrofitting Non-Cognitive-Diagnostic Reading Assessment under the Generalized DINA Model Framework

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Chen, Huilin; Chen, Jinsong

2016-01-01

Cognitive diagnosis models (CDMs) are psychometric models developed mainly to assess examinees' specific strengths and weaknesses in a set of skills or attributes within a domain. By adopting the Generalized-DINA model framework, the recently developed general modeling framework, we attempted to retrofit the PISA reading assessments, a…

Model-Based Policymaking: A Framework to Promote Ethical “Good Practice” in Mathematical Modeling for Public Health Policymaking

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Boden, Lisa A.; McKendrick, Iain J.

2017-01-01

Mathematical models are increasingly relied upon as decision support tools, which estimate risks and generate recommendations to underpin public health policies. However, there are no formal agreements about what constitutes professional competencies or duties in mathematical modeling for public health. In this article, we propose a framework to evaluate whether mathematical models that assess human and animal disease risks and control strategies meet standards consistent with ethical “good practice” and are thus “fit for purpose” as evidence in support of policy. This framework is derived from principles of biomedical ethics: independence, transparency (autonomy), beneficence/non-maleficence, and justice. We identify ethical risks associated with model development and implementation and consider the extent to which scientists are accountable for the translation and communication of model results to policymakers so that the strengths and weaknesses of the scientific evidence base and any socioeconomic and ethical impacts of biased or uncertain predictions are clearly understood. We propose principles to operationalize a framework for ethically sound model development and risk communication between scientists and policymakers. These include the creation of science–policy partnerships to mutually define policy questions and communicate results; development of harmonized international standards for model development; and data stewardship and improvement of the traceability and transparency of models via a searchable archive of policy-relevant models. Finally, we suggest that bespoke ethical advisory groups, with relevant expertise and access to these resources, would be beneficial as a bridge between science and policy, advising modelers of potential ethical risks and providing overview of the translation of modeling advice into policy. PMID:28424768

A general framework and review of scatter correction methods in cone beam CT. Part 2: Scatter estimation approaches

International Nuclear Information System (INIS)

Ruehrnschopf and, Ernst-Peter; Klingenbeck, Klaus

2011-01-01

The main components of scatter correction procedures are scatter estimation and a scatter compensation algorithm. This paper completes a previous paper where a general framework for scatter compensation was presented under the prerequisite that a scatter estimation method is already available. In the current paper, the authors give a systematic review of the variety of scatter estimation approaches. Scatter estimation methods are based on measurements, mathematical-physical models, or combinations of both. For completeness they present an overview of measurement-based methods, but the main topic is the theoretically more demanding models, as analytical, Monte-Carlo, and hybrid models. Further classifications are 3D image-based and 2D projection-based approaches. The authors present a system-theoretic framework, which allows to proceed top-down from a general 3D formulation, by successive approximations, to efficient 2D approaches. A widely useful method is the beam-scatter-kernel superposition approach. Together with the review of standard methods, the authors discuss their limitations and how to take into account the issues of object dependency, spatial variance, deformation of scatter kernels, external and internal absorbers. Open questions for further investigations are indicated. Finally, the authors refer on some special issues and applications, such as bow-tie filter, offset detector, truncated data, and dual-source CT.

Helping Children Learn Mathematics through Multiple Intelligences and Standards for School Mathematics.

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Adams, Thomasenia Lott

2001-01-01

Focuses on the National Council of Teachers of Mathematics 2000 process-oriented standards of problem solving, reasoning and proof, communication, connections, and representation as providing a framework for using the multiple intelligences that children bring to mathematics learning. Presents ideas for mathematics lessons and activities to…

A General Framework for Portfolio Theory—Part I: Theory and Various Models

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Stanislaus Maier-Paape

2018-05-01

Full Text Available Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two-dimensional space of utility and risk. This is a rather general pattern. The modern portfolio theory of Markowitz (1959 and the capital market pricing model Sharpe (1964, are special cases of our general framework when the risk measure is taken to be the standard deviation and the utility function is the identity mapping. Using our general framework, we also recover and extend the results in Rockafellar et al. (2006, which were already an extension of the capital market pricing model to allow for the use of more general deviation measures. This generalized capital asset pricing model also applies to e.g., when an approximation of the maximum drawdown is considered as a risk measure. Furthermore, the consideration of a general utility function allows for going beyond the “additive” performance measure to a “multiplicative” one of cumulative returns by using the log utility. As a result, the growth optimal portfolio theory Lintner (1965 and the leverage space portfolio theory Vince (2009 can also be understood and enhanced under our general framework. Thus, this general framework allows a unification of several important existing portfolio theories and goes far beyond. For simplicity of presentation, we phrase all for a finite underlying probability space and a one period market model, but generalizations to more complex structures are straightforward.

The Rights of the Learner: A Framework for Promoting Equity through Formative Assessment in Mathematics Education

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Kalinec-Craig, Crystal A.

2017-01-01

An elementary mathematics teacher once argued that she and her students held four Rights of the Learner in the classroom: (1) the right to be confused; (2) the right to claim a mistake; (3) the right to speak, listen and be heard; and (4) the right to write, do, and represent only what makes sense. Written as an emerging framework to promote…

Understanding mathematical proof

CERN Document Server

Taylor, John

2014-01-01

Introduction The need for proof The language of mathematics Reasoning Deductive reasoning and truth Example proofs Logic and ReasoningIntroduction Propositions, connectives, and truth tables Logical equivalence and logical implication Predicates and quantification Logical reasoning Sets and Functions Introduction Sets and membership Operations on setsThe Cartesian product Functions and composite functions Properties of functions The Structure of Mathematical ProofsIntroduction Some proofs dissected An informal framework for proofs Direct proof A more formal framework Finding Proofs Direct proo

Student and Teacher Interventions: A Framework for Analysing Mathematical Discourse in the Classroom

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Drageset, Ove Gunnar

2015-01-01

Mathematical discourse in the classroom has been conceptualised in several ways, from relatively general patterns such as initiation-response-evaluation (Cazden in "Classroom discourse: the language of teaching and learning," Heinemann, London, 1988; Mehan in "Learning lessons: social organization in the classroom." Cambridge,…

Identifying Domain-General and Domain-Specific Predictors of Low Mathematics Performance: A Classification and Regression Tree Analysis

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David J. Purpura

2017-12-01

Full Text Available Many children struggle to successfully acquire early mathematics skills. Theoretical and empirical evidence has pointed to deficits in domain-specific skills (e.g., non-symbolic mathematics skills or domain-general skills (e.g., executive functioning and language as underlying low mathematical performance. In the current study, we assessed a sample of 113 three- to five-year old preschool children on a battery of domain-specific and domain-general factors in the fall and spring of their preschool year to identify Time 1 (fall factors associated with low performance in mathematics knowledge at Time 2 (spring. We used the exploratory approach of classification and regression tree analyses, a strategy that uses step-wise partitioning to create subgroups from a larger sample using multiple predictors, to identify the factors that were the strongest classifiers of low performance for younger and older preschool children. Results indicated that the most consistent classifier of low mathematics performance at Time 2 was children’s Time 1 mathematical language skills. Further, other distinct classifiers of low performance emerged for younger and older children. These findings suggest that risk classification for low mathematics performance may differ depending on children’s age.

Mathematical marriages: intercourse between mathematics and Semiotic choice.

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Wagner, Roy

2009-04-01

This paper examines the interaction between Semiotic choices and the presentation and solution of a family of contemporary mathematical problems centred around the so-called 'stable marriage problem'. I investigate how a socially restrictive choice of signs impacts mathematical production both in terms of problem formation and of solutions. I further note how the choice of gendered language ends up constructing a reality, which duplicates the very structural framework that it imported into mathematical analysis in the first place. I go on to point out some semiotic lines of flight from this interlocking grip of mathematics and gendered language.

A general consumer-resource population model

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Lafferty, Kevin D.; DeLeo, Giulio; Briggs, Cheryl J.; Dobson, Andrew P.; Gross, Thilo; Kuris, Armand M.

2015-01-01

Food-web dynamics arise from predator-prey, parasite-host, and herbivore-plant interactions. Models for such interactions include up to three consumer activity states (questing, attacking, consuming) and up to four resource response states (susceptible, exposed, ingested, resistant). Articulating these states into a general model allows for dissecting, comparing, and deriving consumer-resource models. We specify this general model for 11 generic consumer strategies that group mathematically into predators, parasites, and micropredators and then derive conditions for consumer success, including a universal saturating functional response. We further show how to use this framework to create simple models with a common mathematical lineage and transparent assumptions. Underlying assumptions, missing elements, and composite parameters are revealed when classic consumer-resource models are derived from the general model.

A Computational Framework for Bioimaging Simulation

Science.gov (United States)

Watabe, Masaki; Arjunan, Satya N. V.; Fukushima, Seiya; Iwamoto, Kazunari; Kozuka, Jun; Matsuoka, Satomi; Shindo, Yuki; Ueda, Masahiro; Takahashi, Koichi

2015-01-01

Using bioimaging technology, biologists have attempted to identify and document analytical interpretations that underlie biological phenomena in biological cells. Theoretical biology aims at distilling those interpretations into knowledge in the mathematical form of biochemical reaction networks and understanding how higher level functions emerge from the combined action of biomolecules. However, there still remain formidable challenges in bridging the gap between bioimaging and mathematical modeling. Generally, measurements using fluorescence microscopy systems are influenced by systematic effects that arise from stochastic nature of biological cells, the imaging apparatus, and optical physics. Such systematic effects are always present in all bioimaging systems and hinder quantitative comparison between the cell model and bioimages. Computational tools for such a comparison are still unavailable. Thus, in this work, we present a computational framework for handling the parameters of the cell models and the optical physics governing bioimaging systems. Simulation using this framework can generate digital images of cell simulation results after accounting for the systematic effects. We then demonstrate that such a framework enables comparison at the level of photon-counting units. PMID:26147508

A Computational Framework for Bioimaging Simulation.

Science.gov (United States)

Watabe, Masaki; Arjunan, Satya N V; Fukushima, Seiya; Iwamoto, Kazunari; Kozuka, Jun; Matsuoka, Satomi; Shindo, Yuki; Ueda, Masahiro; Takahashi, Koichi

2015-01-01

Using bioimaging technology, biologists have attempted to identify and document analytical interpretations that underlie biological phenomena in biological cells. Theoretical biology aims at distilling those interpretations into knowledge in the mathematical form of biochemical reaction networks and understanding how higher level functions emerge from the combined action of biomolecules. However, there still remain formidable challenges in bridging the gap between bioimaging and mathematical modeling. Generally, measurements using fluorescence microscopy systems are influenced by systematic effects that arise from stochastic nature of biological cells, the imaging apparatus, and optical physics. Such systematic effects are always present in all bioimaging systems and hinder quantitative comparison between the cell model and bioimages. Computational tools for such a comparison are still unavailable. Thus, in this work, we present a computational framework for handling the parameters of the cell models and the optical physics governing bioimaging systems. Simulation using this framework can generate digital images of cell simulation results after accounting for the systematic effects. We then demonstrate that such a framework enables comparison at the level of photon-counting units.

A Computational Framework for Bioimaging Simulation.

Directory of Open Access Journals (Sweden)

Masaki Watabe

Full Text Available Using bioimaging technology, biologists have attempted to identify and document analytical interpretations that underlie biological phenomena in biological cells. Theoretical biology aims at distilling those interpretations into knowledge in the mathematical form of biochemical reaction networks and understanding how higher level functions emerge from the combined action of biomolecules. However, there still remain formidable challenges in bridging the gap between bioimaging and mathematical modeling. Generally, measurements using fluorescence microscopy systems are influenced by systematic effects that arise from stochastic nature of biological cells, the imaging apparatus, and optical physics. Such systematic effects are always present in all bioimaging systems and hinder quantitative comparison between the cell model and bioimages. Computational tools for such a comparison are still unavailable. Thus, in this work, we present a computational framework for handling the parameters of the cell models and the optical physics governing bioimaging systems. Simulation using this framework can generate digital images of cell simulation results after accounting for the systematic effects. We then demonstrate that such a framework enables comparison at the level of photon-counting units.

Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics

NARCIS (Netherlands)

Sweller, John; Clark, Richard; Kirschner, Paul A.

2010-01-01

Sweller, J., Clark, R., & Kirschner, P. A. (2010). Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics. Notices of the American Mathematical Society, 57, 1303-1304.

Generalized Intelligent Framework for Tutoring (GIFT) Cloud/Virtual Open Campus Quick Start Guide (Revision 1)

Science.gov (United States)

2017-06-01

ARL-CR-0816 ● JUNE 2017 US Army Research Laboratory Generalized Intelligent Framework for Tutoring (GIFT) Cloud/Virtual Open...to the originator. ARL-CR-0816 ● JUNE 2017 US Army Research Laboratory Generalized Intelligent Framework for Tutoring (GIFT...January 2017 4. TITLE AND SUBTITLE Generalized Intelligent Framework for Tutoring (GIFT) Cloud/Virtual Open Campus Quick-Start Guide (Revision 1

The (Mathematical) Modeling Process in Biosciences.

Science.gov (United States)

Torres, Nestor V; Santos, Guido

2015-01-01

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

A Framework for Teachers' Knowledge of Mathematical Reasoning

Science.gov (United States)

Herbert, Sandra

2014-01-01

Exploring and developing primary teachers' understanding of mathematical reasoning was the focus of the "Mathematical Reasoning Professional Learning Research Program." Twenty-four primary teachers were interviewed after engagement in the first stage of the program incorporating demonstration lessons focused on reasoning conducted in…

Mathematical competencies and the role of mathematics in physics education: A trend analysis of TIMSS Advanced 1995 and 2008

Directory of Open Access Journals (Sweden)

Trude Nilsen

2013-10-01

Full Text Available As students advance in their learning of physics over the course of their education, the requirement of mathematical applications in physics-related tasks increases, especially so in upper secondary school and in higher education. Yet there is little empirical work (particularly large-scale or longitudinal on the application of mathematics in physics education compared with the research related to the conceptual knowledge of physics. In order to clarify the nature of mathematics in physics education, we developed a theoretical framework for mathematical competencies pertinent to various physics tasks based on theoretical frameworks from mathematics and physics education. We used this synthesis of frameworks as a basis to create a model for physics competence. The framework also served as a tool for analyzing and categorizing trend items from the international large-scale survey, TIMSS Advanced 1995 and 2008. TIMSS Advanced assessed students in upper secondary school with special preparation in advanced physics and mathematics. We then investigated the changes in achievements on these categorized items across time for nations who participated in both surveys. The results from our analysis indicate that students whose overall physics achievement declined struggled the most with items requiring mathematics, especially items requiring them to handle symbols, such as manipulating equations. This finding suggests the importance of collaboration between mathematics and physics education as well as the importance of traditional algebra for physics education.

Generalized network improvement and packing problems

CERN Document Server

Holzhauser, Michael

2016-01-01

Michael Holzhauser discusses generalizations of well-known network flow and packing problems by additional or modified side constraints. By exploiting the inherent connection between the two problem classes, the author investigates the complexity and approximability of several novel network flow and packing problems and presents combinatorial solution and approximation algorithms. Contents Fractional Packing and Parametric Search Frameworks Budget-Constrained Minimum Cost Flows: The Continuous Case Budget-Constrained Minimum Cost Flows: The Discrete Case Generalized Processing Networks Convex Generalized Flows Target Groups Researchers and students in the fields of mathematics, computer science, and economics Practitioners in operations research and logistics The Author Dr. Michael Holzhauser studied computer science at the University of Kaiserslautern and is now a research fellow in the Optimization Research Group at the Department of Mathematics of the University of Kaiserslautern.

The Contributions of Domain-General and Numerical Factors to Third-Grade Arithmetic Skills and Mathematical Learning Disability

Science.gov (United States)

Cowan, Richard; Powell, Daisy

2014-01-01

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed, and oral language) and numerical factors that include single-digit processing efficiency and multidigit skills…

A mathematical framework for modelling and evaluating natural gas pipeline networks under hydrogen injection

Energy Technology Data Exchange (ETDEWEB)

Tabkhi, F.; Azzaro-Pantel, C.; Pibouleau, L.; Domenech, S. [Laboratoire de Genie Chimique, UMR5503 CNRS/INP/UPS, 5 rue Paulin Talabot F-BP1301, 31106 Toulouse Cedex 1 (France)

2008-11-15

This article presents the framework of a mathematical formulation for modelling and evaluating natural gas pipeline networks under hydrogen injection. The model development is based on gas transport through pipelines and compressors which compensate for the pressure drops by implying mainly the mass and energy balances on the basic elements of the network. The model was initially implemented for natural gas transport and the principle of extension for hydrogen-natural gas mixtures is presented. The objective is the treatment of the classical fuel minimizing problem in compressor stations. The optimization procedure has been formulated by means of a nonlinear technique within the General Algebraic Modelling System (GAMS) environment. This work deals with the adaptation of the current transmission networks of natural gas to the transport of hydrogen-natural gas mixtures. More precisely, the quantitative amount of hydrogen that can be added to natural gas can be determined. The studied pipeline network, initially proposed in [1] is revisited here for the case of hydrogen-natural gas mixtures. Typical quantitative results are presented, showing that the addition of hydrogen to natural gas decreases significantly the transmitted power: the maximum fraction of hydrogen that can be added to natural gas is around 6 mass% for this example. (author)

IAEA Director General Comments on Cooperation Framework with Iran

International Nuclear Information System (INIS)

2013-01-01

Full text: The following are remarks by the Director General of the International Atomic Energy Agency, Yukiya Amano, at a News Conference after he signed a Joint Statement on a Framework for Cooperation with the Islamic Republic of Iran: ''The International Atomic Energy Agency and the Islamic Republic of Iran have just issued the Joint Statement on a Framework for Cooperation. ''Under the Framework, Iran and the IAEA will cooperate further with respect to verification activities to be undertaken by the IAEA to resolve all present and past issues. The practical measures contained in the Annex are substantive measures and will be implemented in three months starting from today. ''This is an important step forward to start with, but much more needs to be done. ''The outstanding issues that are not contained in the Annex to the Framework for Cooperation, including those in my previous reports to the Board of Governors, will be addressed in the subsequent steps under the Framework for Cooperation. ''The IAEA is firmly committed to resolving all outstanding issues through dialogue and cooperation . (IAEA)

Generalized framework for context-specific metabolic model extraction methods

Directory of Open Access Journals (Sweden)

Semidán eRobaina Estévez

2014-09-01

Full Text Available Genome-scale metabolic models are increasingly applied to investigate the physiology not only of simple prokaryotes, but also eukaryotes, such as plants, characterized with compartmentalized cells of multiple types. While genome-scale models aim at including the entirety of known metabolic reactions, mounting evidence has indicated that only a subset of these reactions is active in a given context, including: developmental stage, cell type, or environment. As a result, several methods have been proposed to reconstruct context-specific models from existing genome-scale models by integrating various types of high-throughput data. Here we present a mathematical framework that puts all existing methods under one umbrella and provides the means to better understand their functioning, highlight similarities and differences, and to help users in selecting a most suitable method for an application.

The Impact of a "Framework"-Aligned Science Professional Development Program on Literacy and Mathematics Achievement of K-3 Students

Science.gov (United States)

Paprzycki, Peter; Tuttle, Nicole; Czerniak, Charlene M.; Molitor, Scott; Kadervaek, Joan; Mendenhall, Robert

2017-01-01

This study investigates the effect of a Framework-aligned professional development program at the PreK-3 level. The NSF funded program integrated science with literacy and mathematics learning and provided teacher professional development, along with materials and programming for parents to encourage science investigations and discourse around…

Mathematics education for social justice

Science.gov (United States)

Suhendra

2016-02-01

Mathematics often perceived as a difficult subject with many students failing to understand why they learn mathematics. This situation has been further aggravated by the teaching and learning processes used, which is mechanistic without considering students' needs. The learning of mathematics tends to be just a compulsory subject, in which all students have to attend its classes. Social justice framework facilitates individuals or groups as a whole and provides equitable approaches to achieving equitable outcomes by recognising disadvantage. Applying social justice principles in educational context is related to how the teachers treat their students, dictates that all students the right to equal treatment regardless of their background and completed with applying social justice issues integrated with the content of the subject in order to internalise the principles of social justice simultaneously the concepts of the subject. The study examined the usefulness of implementing the social justice framework as a means of improving the quality of mathematics teaching in Indonesia involved four teacher-participants and their mathematics classes. The study used action research as the research methodology in which the teachers implemented and evaluated their use of social justice framework in their teaching. The data were collected using multiple research methods while analysis and interpretation of the data were carried out throughout the study. The findings of the study indicated that there were a number of challengesrelated to the implementation of the social justice framework. The findings also indicated that, the teachers were provided with a comprehensive guide that they could draw on to make decisions about how they could improve their lessons. The interactions among students and between the teachers and the students improved, they became more involved in teaching and learning process. Using social justice framework helped the teachers to make mathematics more

A mathematical programming framework for early stage design of wastewater treatment plants

DEFF Research Database (Denmark)

Bozkurt, Hande; Quaglia, Alberto; Gernaey, Krist

2015-01-01

The increasing number of alternative wastewater treatment technologies and stricter effluent requirements make the optimal treatment process selection for wastewater treatment plant design a complicated problem. This task, defined as wastewater treatment process synthesis, is currently based on e...... the design problem is formulated as a Mixed Integer (Non)linear Programming problem e MI(N)LP e and solved. A case study is formulated and solved to highlight the application of the framework. © 2014 Elsevier Ltd. All rights reserved....... on expert decisions and previous experiences. This paper proposes a new approach based on mathematical programming to manage the complexity of the problem. The approach generates/identifies novel and optimal wastewater treatment process selection, and the interconnection between unit operations to create...

Mathematics at University

DEFF Research Database (Denmark)

Winsløw, Carl

2015-01-01

Mathematics is studied in universities by a large number of students. At the same time it is a field of research for a (smaller) number of university teachers. What relations, if any, exist between university research and teaching of mathematics? Can research “support” teaching? What research...... and what teaching? In this presentation we propose a theoretical framework to study these questions more precisely, based on the anthropological theory of didactics. As a main application, the links between the practices of mathematical research and university mathematics teaching are examined...

Mathematics in India

CERN Document Server

Plofker, Kim

2009-01-01

Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic sc

Mathematical model for biomolecular quantification using surface-enhanced Raman spectroscopy based signal intensity distributions

DEFF Research Database (Denmark)

Palla, Mirko; Bosco, Filippo Giacomo; Yang, Jaeyoung

2015-01-01

This paper presents the development of a novel statistical method for quantifying trace amounts of biomolecules by surface-enhanced Raman spectroscopy (SERS) using a rigorous, single molecule (SM) theory based mathematical derivation. Our quantification framework could be generalized for planar...

Mathematical modelling

DEFF Research Database (Denmark)

Blomhøj, Morten

2004-01-01

Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...

Generalized Intelligent Framework for Tutoring (GIFT) Cloud/Virtual Open Campus Quick-Start Guide

Science.gov (United States)

2016-03-01

The GIFT Account allows users to log into GIFT Cloud , manage their personal storage in GIFT Cloud , download GIFT Local, and access resources...ARL-CR-0796 ● MAR 2016 US Army Research Laboratory Generalized Intelligent Framework for Tutoring (GIFT) Cloud / Virtual Open...originator. ARL-CR-0796 ● MAR 2016 US Army Research Laboratory Generalized Intelligent Framework for Tutoring (GIFT) Cloud / Virtual

A General Framework for Setting Quantitative Population Objectives for Wildlife Conservation

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Kristen E. Dybala

2017-03-01

Full Text Available https://doi.org/10.15447/sfews.2017v15iss1art8Quantitative population objectives are necessary to successfully achieve conservation goals of secure or robust wildlife populations. However, existing methods for setting quantitative population objectives commonly require extensive species-specific population viability data, which are often unavailable or are based on estimates of historical population sizes, which may no longer represent feasible objectives. Conservation practitioners require an alternative, science-based method for setting long-term quantitative population objectives. We reviewed conservation biology literature to develop a general conceptual framework that represents conservation biology principles and identifies key milestones a population would be expected to pass in the process of becoming a recovered or robust population. We then synthesized recent research to propose general hypotheses for the orders of magnitude at which most populations would be expected to reach each milestone. The framework is structured as a hierarchy of four population sizes, ranging from very small populations at increased risk of inbreeding depression and extirpation (< 1,000 adults to large populations with minimized risk of extirpation (> 50,000 adults, along with additional modifiers describing steeply declining and resilient populations. We also discuss the temporal and geographic scales at which this framework should be applied. To illustrate the application of this framework to conservation planning, we outline our use of the framework to set long-term population objectives for a multi-species regional conservation plan, and discuss additional considerations in applying this framework to other systems. This general framework provides a transparent, science-based method by which conservation practitioners and stakeholders can agree on long-term population objectives of an appropriate magnitude, particularly when the alternative approaches are

A Generalized Cauchy Distribution Framework for Problems Requiring Robust Behavior

Directory of Open Access Journals (Sweden)

Carrillo RafaelE

2010-01-01

Full Text Available Statistical modeling is at the heart of many engineering problems. The importance of statistical modeling emanates not only from the desire to accurately characterize stochastic events, but also from the fact that distributions are the central models utilized to derive sample processing theories and methods. The generalized Cauchy distribution (GCD family has a closed-form pdf expression across the whole family as well as algebraic tails, which makes it suitable for modeling many real-life impulsive processes. This paper develops a GCD theory-based approach that allows challenging problems to be formulated in a robust fashion. Notably, the proposed framework subsumes generalized Gaussian distribution (GGD family-based developments, thereby guaranteeing performance improvements over traditional GCD-based problem formulation techniques. This robust framework can be adapted to a variety of applications in signal processing. As examples, we formulate four practical applications under this framework: (1 filtering for power line communications, (2 estimation in sensor networks with noisy channels, (3 reconstruction methods for compressed sensing, and (4 fuzzy clustering.

Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity Frameworks

Directory of Open Access Journals (Sweden)

Heng-you Lan

2013-01-01

Full Text Available We introduce and study a new notion of relatively A-maximal m-relaxed monotonicity framework and discuss some properties of a new class of generalized relatively resolvent operator associated with the relatively A-maximal m-relaxed monotone operator and the new generalized Yosida approximations based on relatively A-maximal m-relaxed monotonicity framework. Furthermore, we give some remarks to show that the theory of the new generalized relatively resolvent operator and Yosida approximations associated with relatively A-maximal m-relaxed monotone operators generalizes most of the existing notions on (relatively maximal monotone mappings in Hilbert as well as Banach space and can be applied to study variational inclusion problems and first-order evolution equations as well as evolution inclusions.

Understanding general practice: a conceptual framework developed from case studies in the UK NHS.

Science.gov (United States)

Checkland, Kath

2007-01-01

General practice in the UK is undergoing a period of rapid and profound change. Traditionally, research into the effects of change on general practice has tended to regard GPs as individuals or as members of a professional group. To understand the impact of change, general practices should also be considered as organisations. To use the organisational studies literature to build a conceptual framework of general practice organisations, and to test and develop this empirically using case studies of change in practice. This study used the implementation of National Service Frameworks (NSFs) and the new General Medical Services (GMS) contract as incidents of change. In-depth, qualitative case studies. The design was iterative: each case study was followed by a review of the theoretical ideas. The final conceptual framework was the result of the dynamic interplay between theory and empirical evidence. Five general practices in England, selected using purposeful sampling. Semi-structured interviews with all clinical and managerial personnel in each practice, participant and nonparticipant observation, and examination of documents. A conceptual framework was developed that can be used to understand how and why practices respond to change. This framework enabled understanding of observed reactions to the introduction of NSFs and the new GMS contract. Important factors for generating responses to change included the story that the practice members told about their practice, beliefs about what counted as legitimate work, the role played by the manager, and previous experiences of change. Viewing general practices as small organisations has generated insights into factors that influence responses to change. Change tends to occur from the bottom up and is determined by beliefs about organisational reality. The conceptual framework suggests some questions that can be asked of practices to explain this internal reality.

A Generalized DRM Architectural Framework

Directory of Open Access Journals (Sweden)

PATRICIU, V. V.

2011-02-01

Full Text Available Online digital goods distribution environment lead to the need for a system to protect digital intellectual property. Digital Rights Management (DRM is the system born to protect and control distribution and use of those digital assets. The present paper is a review of the current state of DRM, focusing on architectural design, security technologies, and important DRM deployments. The paper primarily synthesizes DRM architectures within a general framework. We also present DRM ecosystem as providing a better understanding of what is currently happening to content rights management from a technological point of view. This paper includes conclusions of several DRM initiative studies, related to rights management systems with the purpose of identifying and describing the most significant DRM architectural models. The basic functions and processes of the DRM solutions are identified.

Curriculum Framework (CF) Implementation Conference. Report of the Regional Educational Laboratory Network Program and the National Network of Eisenhower Mathematics and Science Regional Consortia (Hilton Head Island, South Carolina, January 26-27, 1995).

Science.gov (United States)

Palmer, Jackie; Powell, Mary Jo

The Laboratory Network Program and the National Network of Eisenhower Mathematics and Science Regional Consortia, operating as the Curriculum Frameworks Task Force, jointly convened a group of educators involved in implementing state-level mathematics or science curriculum frameworks (CF). The Hilton Head (South Carolina) conference had a dual…

Linking Teaching in Mathematics and the Subjects of Natural Science

DEFF Research Database (Denmark)

Michelsen, Claus

2017-01-01

teaching programs. This is partly due to the lack of a framework for integrating productive ideas across the disciplines. This paper focus on how to grasp the challenges of an interdisciplinary approach to teaching in mathematics and the subjects of natural science. Based on contemporary mathematics...... and science education we design a didactical framework for interdisciplinary teaching centered on modeling activities across mathematics and the disciplines of natural science. To exemplify the potential of the framework we present a case study of an intensive in-service teacher-training program...... for mathematics and biology teachers. The teachers were presented to the didactical framework and in pairs of two, one mathematics teacher and one biology teacher; they designed and implemented interdisciplinary mathematicsbiology teaching sequences. The teachers’ reports on their development and implementation...

The Principle of General Tovariance

Science.gov (United States)

Heunen, C.; Landsman, N. P.; Spitters, B.

2008-06-01

We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining these ideas is topos theory, a framework earlier proposed for physics by Isham and collaborators. Our principle of general tovariance states that any mathematical structure appearing in the laws of physics must be definable in an arbitrary topos (with natural numbers object) and must be preserved under so-called geometric morphisms. This principle identifies geometric logic as the mathematical language of physics and restricts the constructions and theorems to those valid in intuitionism: neither Aristotle's principle of the excluded third nor Zermelo's Axiom of Choice may be invoked. Subsequently, our equivalence principle states that any algebra of observables (initially defined in the topos Sets) is empirically equivalent to a commutative one in some other topos.

Mathematical models of bipolar disorder

Science.gov (United States)

Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.

2009-07-01

We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.

Moments Based Framework for Performance Analysis of One-Way/Two-Way CSI-Assisted AF Relaying

KAUST Repository

Xia, Minghua

2012-09-01

When analyzing system performance of conventional one-way relaying or advanced two-way relaying, these two techniques are always dealt with separately and, thus, their performance cannot be compared efficiently. Moreover, for ease of mathematical tractability, channels considered in such studies are generally assumed to be subject to Rayleigh fading or to be Nakagami-$m$ channels with integer fading parameters, which is impractical in typical urban environments. In this paper, we propose a unified moments-based framework for general performance analysis of channel-state-information (CSI) assisted amplify-and-forward (AF) relaying systems. The framework is applicable to both one-way and two-way relaying over arbitrary Nakagami-$m$ fading channels, and it includes previously reported results as special cases. Specifically, the mathematical framework is firstly developed under the umbrella of the weighted harmonic mean of two Gamma-distributed variables in conjunction with the theory of Pad\\\\\\'e approximants. Then, general expressions for the received signal-to-noise ratios of the users in one-way/two-way relaying systems and the corresponding moments, moment generation function, and cumulative density function are established. Subsequently, the mathematical framework is applied to analyze, compare, and gain insights into system performance of one-way and two-way relaying techniques, in terms of outage probability, average symbol error probability, and achievable data rate. All analytical results are corroborated by simulation results as well as previously reported results whenever available, and they are shown to be efficient tools to evaluate and compare system performance of one-way and two-way relaying.

Analysis of the production stability of mixed grasslands. II. A mathematical framework for the quantification of production stability of grassland ecosystems

NARCIS (Netherlands)

Schulte, R.P.O.

2003-01-01

The analysis of the intrinsic properties and processes of ecosystems, which regulate the production stability of mixed grasslands, has been complicated by the environmental noise caused by stochastic weather fluctuations. A mathematical framework is presented to deduct the actual, the extrinsic and

Mathematical Education for Geographers

Science.gov (United States)

Wilson, Alan

1978-01-01

Outlines mathematical topics of use to college geography students identifies teaching methods for mathematical techniques in geography at the University of Leeds; and discusses problem of providing students with a framework for synthesizing all content of geography education. For journal availability, see SO 506 593. (Author/AV)

Use of Interactive Whiteboard in the Mathematics Classroom: Students' Perceptions within the Framework of the Technology Acceptance Model

Science.gov (United States)

Önal, Nezih

2017-01-01

The purpose of the present research was to reveal students' perceptions regarding the use of the interactive whiteboard in the mathematics classroom within the framework of the Technology Acceptance Model. Semi-structured interviews were performed with 58 secondary school students (5th, 6th, 7th, and 8th grades) to collect data. The data obtained…

Dispositions and changing teacher practice in mathematics

DEFF Research Database (Denmark)

Meaney, Tamsin; Lange, Troels; Valero, Paola

2009-01-01

We explore how different interpretations of learning can be integrated to form a theoretical framework for exploring teachers' perceptions of professional learning about mathematics teaching. Although it is possible to identify the separate, contributing factors that operate in mathematics...... experiences of limited value to them. Work done in mathematics education by Skovsmose and Valero combined with Kemmis and Grootenboer's work on academic architectures provide a theoretical framework that enables this complexity to be unpacked. Skovsmose considered learning to involve ascribing meaning...

An Exemplar-Based Multi-View Domain Generalization Framework for Visual Recognition.

Science.gov (United States)

Niu, Li; Li, Wen; Xu, Dong; Cai, Jianfei

2018-02-01

In this paper, we propose a new exemplar-based multi-view domain generalization (EMVDG) framework for visual recognition by learning robust classifier that are able to generalize well to arbitrary target domain based on the training samples with multiple types of features (i.e., multi-view features). In this framework, we aim to address two issues simultaneously. First, the distribution of training samples (i.e., the source domain) is often considerably different from that of testing samples (i.e., the target domain), so the performance of the classifiers learnt on the source domain may drop significantly on the target domain. Moreover, the testing data are often unseen during the training procedure. Second, when the training data are associated with multi-view features, the recognition performance can be further improved by exploiting the relation among multiple types of features. To address the first issue, considering that it has been shown that fusing multiple SVM classifiers can enhance the domain generalization ability, we build our EMVDG framework upon exemplar SVMs (ESVMs), in which a set of ESVM classifiers are learnt with each one trained based on one positive training sample and all the negative training samples. When the source domain contains multiple latent domains, the learnt ESVM classifiers are expected to be grouped into multiple clusters. To address the second issue, we propose two approaches under the EMVDG framework based on the consensus principle and the complementary principle, respectively. Specifically, we propose an EMVDG_CO method by adding a co-regularizer to enforce the cluster structures of ESVM classifiers on different views to be consistent based on the consensus principle. Inspired by multiple kernel learning, we also propose another EMVDG_MK method by fusing the ESVM classifiers from different views based on the complementary principle. In addition, we further extend our EMVDG framework to exemplar-based multi-view domain

Generalizing Backtrack-Free Search: A Framework for Search-Free Constraint Satisfaction

Science.gov (United States)

Jonsson, Ari K.; Frank, Jeremy

2000-01-01

Tractable classes of constraint satisfaction problems are of great importance in artificial intelligence. Identifying and taking advantage of such classes can significantly speed up constraint problem solving. In addition, tractable classes are utilized in applications where strict worst-case performance guarantees are required, such as constraint-based plan execution. In this work, we present a formal framework for search-free (backtrack-free) constraint satisfaction. The framework is based on general procedures, rather than specific propagation techniques, and thus generalizes existing techniques in this area. We also relate search-free problem solving to the notion of decision sets and use the result to provide a constructive criterion that is sufficient to guarantee search-free problem solving.

A Categorization Model for Educational Values of the History of Mathematics. An Empirical Study

Science.gov (United States)

Wang, Xiao-qin; Qi, Chun-yan; Wang, Ke

2017-11-01

There is not a clear consensus on the categorization framework of the educational values of the history of mathematics. By analyzing 20 Chinese teaching cases on integrating the history of mathematics into mathematics teaching based on the relevant literature, this study examined a new categorization framework of the educational values of the history of mathematics by combining the objectives of high school mathematics curriculum in China. This framework includes six dimensions: the harmony of knowledge, the beauty of ideas or methods, the pleasure of inquiries, the improvement of capabilities, the charm of cultures, and the availability of moral education. The results show that this framework better explained the all-educational values of the history of mathematics that all teaching cases showed. Therefore, the framework can guide teachers to better integrate the history of mathematics into teaching.

Ratio Analysis: Where Investments Meet Mathematics.

Science.gov (United States)

Barton, Susan D.; Woodbury, Denise

2002-01-01

Discusses ratio analysis by which investments may be evaluated. Requires the use of fundamental mathematics, problem solving, and a comparison of the mathematical results within the framework of industry. (Author/NB)

The Mathematical State of the World

DEFF Research Database (Denmark)

Christensen, Ole Ravn; Skovsmose, Ole; Yasukawa, Keiko

2009-01-01

the concepts of “mathematical description” and “mathematical model” are inadequate to evaluate the use of mathematics in decision-making processes. As a result we develop a conceptual framework that is complex enough to match what goes on in scenarios involving applications of mathematics.......In this article we try to analyse the conditions for describing the world mathematically. We consider the role played by mathematics in discussing and analysing “the state of the world.” We use this discussion to clarify what it means to use a mathematical description. We illustrate why...

A unified MGF-based capacity analysis of diversity combiners over generalized fading channels

KAUST Repository

Yilmaz, Ferkan

2012-03-01

Unified exact ergodic capacity results for L-branch coherent diversity combiners including equal-gain combining (EGC) and maximal-ratio combining (MRC) are not known. This paper develops a novel generic framework for the capacity analysis of L-branch EGC/MRC over generalized fading channels. The framework is used to derive new results for the gamma-shadowed generalized Nakagami-m fading model which can be a suitable model for the fading environments encountered by high frequency (60 GHz and above) communications. The mathematical formalism is illustrated with some selected numerical and simulation results confirming the correctness of our newly proposed framework. © 2012 IEEE.

Generalized frameworks for first-order evolution inclusions based on Yosida approximations

Directory of Open Access Journals (Sweden)

Ram U. Verma

2011-04-01

Full Text Available First, general frameworks for the first-order evolution inclusions are developed based on the A-maximal relaxed monotonicity, and then using the Yosida approximation the solvability of a general class of first-order nonlinear evolution inclusions is investigated. The role the A-maximal relaxed monotonicity is significant in the sense that it not only empowers the first-order nonlinear evolution inclusions but also generalizes the existing Yosida approximations and its characterizations in the current literature.

Arche papers on the mathematics of abstraction

CERN Document Server

Cook, Roy T

2007-01-01

This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Gottlob Frege's original logicist project was, in effect, refuted by Russell's paradox. Crispin Wright has recently revived Frege's enterprise, however, providing a philosophical and technical framework within which a reconstruction of arithmetic is possible. While the Neo-Fregean project has recieved extensive attention and discussion, the present volume is unique in pre

An Evaluation of the Generalized Intelligent Framework for Tutoring (GIFT) from an Author’s Perspective

Science.gov (United States)

2014-12-01

An Evaluation of the Generalized Intelligent Framework for Tutoring (GIFT) from an Author’s Perspective by Robert A Sottilare, Keith W...Intelligent Framework for Tutoring (GIFT) from an Author’s Perspective Robert A Sottilare and Keith W Brawner Human Research and Engineering...SUBTITLE An Evaluation of the Generalized Intelligent Framework for Tutoring (GIFT) from an Author’s Perspective 5a. CONTRACT NUMBER 5b. GRANT

Domain General Mediators of the Relation between Kindergarten Number Sense and First-Grade Mathematics Achievement

Science.gov (United States)

Hassinger-Das, Brenna; Jordan, Nancy C.; Glutting, Joseph; Irwin, Casey; Dyson, Nancy

2013-01-01

Domain general skills that mediate the relation between kindergarten number sense and first-grade mathematics skills were investigated. Participants were 107 children who displayed low number sense in the fall of kindergarten. Controlling for background variables, multiple regression analyses showed that attention problems and executive functioning both were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance while executive functioning was more important for predicting first-grade performance on applied problems. Moreover, both executive functioning and attention problems were unique partial mediators of the relationship between kindergarten and first-grade mathematics skills. The results provide empirical support for developing interventions that target executive functioning and attention problems in addition to instruction in number skills for kindergartners with initial low number sense. PMID:24237789

The generalized zero-mode supersymmetry scheme and the confluent algorithm

Energy Technology Data Exchange (ETDEWEB)

Contreras-Astorga, Alonso, E-mail: aloncont@iun.edu [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary IN 46408 (United States); Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary IN 46408 (United States); Department of Physics, Indiana University Northwest, 3400 Broadway, Gary IN 46408 (United States)

2015-03-15

We show the relationship between the mathematical framework used in recent papers by Rosu et al. (2014) [1–3] and the second-order confluent supersymmetric quantum mechanics. In addition, we point out several immediate generalizations of the approach taken in the latter references. Furthermore, it is shown how to apply the generalized scheme to the Dirac and to the Fokker–Planck equation.

The generalized zero-mode supersymmetry scheme and the confluent algorithm

International Nuclear Information System (INIS)

Contreras-Astorga, Alonso; Schulze-Halberg, Axel

2015-01-01

We show the relationship between the mathematical framework used in recent papers by Rosu et al. (2014) [1–3] and the second-order confluent supersymmetric quantum mechanics. In addition, we point out several immediate generalizations of the approach taken in the latter references. Furthermore, it is shown how to apply the generalized scheme to the Dirac and to the Fokker–Planck equation

Mathematical Abstraction: Constructing Concept of Parallel Coordinates

Science.gov (United States)

Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

2017-09-01

Mathematical abstraction is an important process in teaching and learning mathematics so pre-service mathematics teachers need to understand and experience this process. One of the theoretical-methodological frameworks for studying this process is Abstraction in Context (AiC). Based on this framework, abstraction process comprises of observable epistemic actions, Recognition, Building-With, Construction, and Consolidation called as RBC + C model. This study investigates and analyzes how pre-service mathematics teachers constructed and consolidated concept of Parallel Coordinates in a group discussion. It uses AiC framework for analyzing mathematical abstraction of a group of pre-service teachers consisted of four students in learning Parallel Coordinates concepts. The data were collected through video recording, students’ worksheet, test, and field notes. The result shows that the students’ prior knowledge related to concept of the Cartesian coordinate has significant role in the process of constructing Parallel Coordinates concept as a new knowledge. The consolidation process is influenced by the social interaction between group members. The abstraction process taken place in this group were dominated by empirical abstraction that emphasizes on the aspect of identifying characteristic of manipulated or imagined object during the process of recognizing and building-with.

General framework and key technologies of national nuclear emergency system

International Nuclear Information System (INIS)

Yuan Feng; Li Xudong; Zhu Guangying; Song Yafeng; Zeng Suotian; Shen Lifeng

2014-01-01

Nuclear emergency is the important safeguard for the sustainable development of nuclear energy, and is the significant part of national public crisis management. The paper gives the definition of nuclear emergency system explicitly based on the analysis of the characteristics of the nuclear emergency, and through the research of the structure and general framework, the general framework of the national nuclear emergency management system (NNEMS) is obtained, which is constructed in four parts, including one integrative platform, six layers, eight applications and two systems, then the paper indicate that the architecture of national emergency system that should be laid out by three-tiers, i.e. national, provincial and organizations with nuclear facilities, and also describe the functions of the NNEMS on the nuclear emergency's workflow. Finally, the paper discuss the key technology that NNIEMS needed, such as WebGIS, auxiliary decision-making, digitalized preplan and the conformity and usage of resources, and analyze the technical principle in details. (authors)

Equivalence of the generalized and complex Kohn variational methods

Energy Technology Data Exchange (ETDEWEB)

Cooper, J N; Armour, E A G [School of Mathematical Sciences, University Park, Nottingham NG7 2RD (United Kingdom); Plummer, M, E-mail: pmxjnc@googlemail.co [STFC Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD (United Kingdom)

2010-04-30

For Kohn variational calculations on low energy (e{sup +} - H{sub 2}) elastic scattering, we prove that the phase shift approximation, obtained using the complex Kohn method, is precisely equal to a value which can be obtained immediately via the real-generalized Kohn method. Our treatment is sufficiently general to be applied directly to arbitrary potential scattering or single open channel scattering problems, with exchange if required. In the course of our analysis, we develop a framework formally to describe the anomalous behaviour of our generalized Kohn calculations in the regions of the well-known Schwartz singularities. This framework also explains the mathematical origin of the anomaly-free singularities we reported in a previous article. Moreover, we demonstrate a novelty: that explicit solutions of the Kohn equations are not required in order to calculate optimal phase shift approximations. We relate our rigorous framework to earlier descriptions of the Kohn-type methods.

Equivalence of the generalized and complex Kohn variational methods

International Nuclear Information System (INIS)

Cooper, J N; Armour, E A G; Plummer, M

2010-01-01

For Kohn variational calculations on low energy (e + - H 2 ) elastic scattering, we prove that the phase shift approximation, obtained using the complex Kohn method, is precisely equal to a value which can be obtained immediately via the real-generalized Kohn method. Our treatment is sufficiently general to be applied directly to arbitrary potential scattering or single open channel scattering problems, with exchange if required. In the course of our analysis, we develop a framework formally to describe the anomalous behaviour of our generalized Kohn calculations in the regions of the well-known Schwartz singularities. This framework also explains the mathematical origin of the anomaly-free singularities we reported in a previous article. Moreover, we demonstrate a novelty: that explicit solutions of the Kohn equations are not required in order to calculate optimal phase shift approximations. We relate our rigorous framework to earlier descriptions of the Kohn-type methods.

Utilizing the National Research Council's (NRC) Conceptual Framework for the Next Generation Science Standards (NGSS): A Self-Study in My Science, Engineering, and Mathematics Classroom

Science.gov (United States)

Corvo, Arthur Francis

Given the reality that active and competitive participation in the 21 st century requires American students to deepen their scientific and mathematical knowledge base, the National Research Council (NRC) proposed a new conceptual framework for K--12 science education. The framework consists of an integration of what the NRC report refers to as the three dimensions: scientific and engineering practices, crosscutting concepts, and core ideas in four disciplinary areas (physical, life and earth/spaces sciences, and engineering/technology). The Next Generation Science Standards (NGSS ), which are derived from this new framework, were released in April 2013 and have implications on teacher learning and development in Science, Technology, Engineering, and Mathematics (STEM). Given the NGSS's recent introduction, there is little research on how teachers can prepare for its release. To meet this research need, I implemented a self-study aimed at examining my teaching practices and classroom outcomes through the lens of the NRC's conceptual framework and the NGSS. The self-study employed design-based research (DBR) methods to investigate what happened in my secondary classroom when I designed, enacted, and reflected on units of study for my science, engineering, and mathematics classes. I utilized various best practices including Learning for Use (LfU) and Understanding by Design (UbD) models for instructional design, talk moves as a tool for promoting discourse, and modeling instruction for these designed units of study. The DBR strategy was chosen to promote reflective cycles, which are consistent with and in support of the self-study framework. A multiple case, mixed-methods approach was used for data collection and analysis. The findings in the study are reported by study phase in terms of unit planning, unit enactment, and unit reflection. The findings have implications for science teaching, teacher professional development, and teacher education.

Official pedagogic identities from South African policy – some implications for mathematics teacher education practice

Directory of Open Access Journals (Sweden)

Diane Parker

2006-10-01

Full Text Available In South Africa the National Curriculum Statement for Grades 10 – 12 (General: Mathematics (DoE, 2003 together with the Norms and Standards for Educators (DoE, 2000a are key policy documents that provide the official basis for mathematics education reform and for the construction of new pedagogic identities. In this paper I use a framework based on the work of Bernstein (1996, 2000 to theorise the construction of pedagogic identities. I use this to build on Graven’s (2002 description of the new official pedagogic identity of the South African mathematics teacher, and on Adler et al. (2002 and others to raise questions related to teacher knowledge and the challenges  of developing specialist mathematics teacher identities through initial teacher education programmes.

Domain-general mediators of the relation between kindergarten number sense and first-grade mathematics achievement.

Science.gov (United States)

Hassinger-Das, Brenna; Jordan, Nancy C; Glutting, Joseph; Irwin, Casey; Dyson, Nancy

2014-02-01

Domain-general skills that mediate the relation between kindergarten number sense and first-grade mathematics skills were investigated. Participants were 107 children who displayed low number sense in the fall of kindergarten. Controlling for background variables, multiple regression analyses showed that both attention problems and executive functioning were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance, whereas executive functioning was more important for predicting first-grade performance on applied problems. Moreover, both executive functioning and attention problems were unique partial mediators of the relationship between kindergarten and first-grade mathematics skills. The results provide empirical support for developing interventions that target executive functioning and attention problems in addition to instruction in number skills for kindergartners with initial low number sense. Copyright © 2013 Elsevier Inc. All rights reserved.

The role of mathematics for physics teaching and understanding

International Nuclear Information System (INIS)

Pospiech, G; Geyer, M.A.; Eylon, B.; Bagno, E.; Lehavi, Y.

2015-01-01

That mathematics is the “language of physics” implies that both areas are deeply interconnected, such that often no separation between “pure” mathematics and “pure” physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers’ background and experiences. The results fit well into the derived model of PCK.

The role of mathematics for physics teaching and understanding

Science.gov (United States)

Pospiech, Gesche; Eylon, BatSheva; Bagno, Esther; Lehavi, Yaron; Geyer, Marie-Annette

2016-05-01

-1That mathematics is the "language of physics" implies that both areas are deeply interconnected, such that often no separation between "pure" mathematics and "pure" physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers' background and experiences. The results fit well into the derived model of PCK.

A General Solution Framework for Component-Commonality Problems

Directory of Open Access Journals (Sweden)

Nils Boysen

2009-05-01

Full Text Available Component commonality - the use of the same version of a component across multiple products - is being increasingly considered as a promising way to offer high external variety while retaining low internal variety in operations. However, increasing commonality has both positive and negative cost effects, so that optimization approaches are required to identify an optimal commonality level. As components influence to a greater or lesser extent nearly every process step along the supply chain, it is not surprising that a multitude of diverging commonality problems is being investigated in literature, each of which are developing a specific algorithm designed for the respective commonality problem being considered. The paper on hand aims at a general framework which is flexible and efficient enough to be applied to a wide range of commonality problems. Such a procedure based on a two-stage graph approach is presented and tested. Finally, flexibility of the procedure is shown by customizing the framework to account for different types of commonality problems.

Deflected Mirage Mediation: A Phenomenological Framework for Generalized Supersymmetry Breaking

International Nuclear Information System (INIS)

Everett, Lisa L.; Kim, Ian-Woo; Ouyang, Peter; Zurek, Kathryn M.

2008-01-01

We present a general phenomenological framework for dialing between gravity mediation, gauge mediation, and anomaly mediation. The approach is motivated from recent developments in moduli stabilization, which suggest that gravity mediated terms can be effectively loop suppressed and thus comparable to gauge and anomaly mediated terms. The gauginos exhibit a mirage unification behavior at a ''deflected'' scale, and gluinos are often the lightest colored sparticles. The approach provides a rich setting in which to explore generalized supersymmetry breaking at the CERN Large Hadron Collider

National Service Frameworks and UK general practitioners: street-level bureaucrats at work?

Science.gov (United States)

Checkland, Kath

2004-11-01

This paper argues that the past decade has seen significant changes in the nature of medical work in general practice in the UK. Increasing pressure to use normative clinical guidelines and the move towards explicit quantitative measures of performance together have the potential to alter the way in which health care is delivered to patients. Whilst it is possible to view these developments from the well-established sociological perspectives of deprofessionalisation and proletarianisation, this paper takes a view of general practice as work, and uses the ideas of Lipsky to analyse practice-level responses to some of these changes. In addition to evidence-based clinical guidelines, National Service Frameworks, introduced by the UK government in 1997, also specify detailed models of service provision that health care providers are expected to follow. As part of a larger study examining the impact of National Service Frameworks in general practice, the response of three practices to the first four NSFs were explored. The failure of NSFs to make a significant impact is compared to the practices' positive responses to purely clinical guidelines such as those developed by the British Hypertension Society. Lipsky's concept of public service workers as 'street-level bureaucrats' is discussed and used as a framework within which to view these findings.

The interrogation decision-making model: A general theoretical framework for confessions.

Science.gov (United States)

Yang, Yueran; Guyll, Max; Madon, Stephanie

2017-02-01

This article presents a new model of confessions referred to as the interrogation decision-making model . This model provides a theoretical umbrella with which to understand and analyze suspects' decisions to deny or confess guilt in the context of a custodial interrogation. The model draws upon expected utility theory to propose a mathematical account of the psychological mechanisms that not only underlie suspects' decisions to deny or confess guilt at any specific point during an interrogation, but also how confession decisions can change over time. Findings from the extant literature pertaining to confessions are considered to demonstrate how the model offers a comprehensive and integrative framework for organizing a range of effects within a limited set of model parameters. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

A general nonlinear evolution equation for irreversible conservative approach to stable equilibrium

International Nuclear Information System (INIS)

Beretta, G.P.

1986-01-01

This paper addresses a mathematical problem relevant to the question of nonequilibrium and irreversibility, namely, that of ''designing'' a general evolution equation capable of describing irreversible but conservative relaxtion towards equilibrium. The objective is to present an interesting mathematical solution to this design problem, namely, a new nonlinear evolution equation that satisfies a set of very stringent relevant requirements. Three different frameworks are defined from which the new equation could be adopted, with entirely different interpretations. Some useful well-known mathematics involving Gram determinants are presented and a nonlinear evolution equation is given which meets the stringent design specifications

Novice Mathematics Teachers Create Themselves

Science.gov (United States)

Schatz Oppenheimer, Orna; Dvir, Nurit

2018-01-01

This study presents a qualitative research based on three narratives written by novice mathematics teachers. We examine their unique professional world during their first year of work. The methodology of narrative framework, on which this article is based, helps to gain better understanding of the need for novice mathematics teachers to have…

Domain-Specific and Domain-General Training to Improve Kindergarten Children’s Mathematics

Directory of Open Access Journals (Sweden)

Geetha B. Ramani

2017-12-01

Full Text Available Ensuring that kindergarten children have a solid foundation in early numerical knowledge is of critical importance for later mathematical achievement. In this study, we targeted improving the numerical knowledge of kindergarteners (n = 81 from primarily low-income backgrounds using two approaches: one targeting their conceptual knowledge, specifically, their understanding of numerical magnitudes; and the other targeting their underlying cognitive system, specifically, their working memory. Both interventions involved playing game-like activities on tablet computers over the course of several sessions. As predicted, both interventions improved children’s numerical magnitude knowledge as compared to a no-contact control group, suggesting that both domain-specific and domain-general interventions facilitate mathematical learning. Individual differences in effort during the working memory game, but not the number knowledge training game predicted children’s improvements in number line estimation. The results demonstrate the potential of using a rapidly growing technology in early childhood classrooms to promote young children’s numerical knowledge.

Developing a framework of, and quality indicators for, general practice management in Europe.

NARCIS (Netherlands)

Engels, Y.M.P.; Campbell, S.M.; Dautzenberg, M.G.H.; Hombergh, P. van den; Brinkmann, H.; Szecsenyi, J.; Falcoff, H.; Seuntjens, L.; Kuenzi, B.; Grol, R.P.T.M.

2005-01-01

OBJECTIVES: To develop a framework for general practice management made up of quality indicators shared by six European countries. METHODS: Two-round postal Delphi questionnaire in the setting of general practice in Belgium, France, Germany, The Netherlands, Switzerland and the United Kingdom. Six

Contemplating Symbolic Literacy of First Year Mathematics Students

Science.gov (United States)

Bardini, Caroline; Pierce, Robyn; Vincent, Jill

2015-01-01

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

Parallelization of mathematical library for generalized eigenvalue problem for real band matrices

International Nuclear Information System (INIS)

Tanaka, Yasuhisa.

1997-05-01

This research has focused on a parallelization of the mathematical library for a generalized eigenvalue problem for real band matrices on IBM SP and Hitachi SR2201. The origin of the library is LASO (Lanczos Algorithm with Selective Orthogonalization), which was developed on the basis of Block Lanczos method for standard eigenvalue problem for real band matrices at Texas University. We adopted D.O.F. (Degree Of Freedom) decomposition method for a parallelization of this library, and evaluated its parallel performance. (author)

Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

OpenAIRE

Motsepa, Tanki; Khalique, Chaudry Masood; Molati, Motlatsi

2014-01-01

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant so...

A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic engineering.

Science.gov (United States)

Klamt, Steffen; Müller, Stefan; Regensburger, Georg; Zanghellini, Jürgen

2018-02-07

The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing. We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small

Mathematics Education in Singapore--An Insider's Perspective

Science.gov (United States)

Kaur, Berinderjeet

2014-01-01

Singapore's Education System has evolved over time and so has Mathematics Education in Singapore. The present day School Mathematics Curricula can best be described as one that caters for the needs of every child in school. It is based on a framework that has mathematical problem solving as its primary focus. The developments from 1946 to 2012…

Creating opportunities to learn in mathematics education: a sociocultural perspective

Science.gov (United States)

Goos, Merrilyn

2014-09-01

The notion of `opportunities to learn in mathematics education' is open to interpretation from multiple theoretical perspectives, where the focus may be on cognitive, social or affective dimensions of learning, curriculum and assessment design, issues of equity and access, or the broad policy and political contexts of learning and teaching. In this paper, I conceptualise opportunities to learn from a sociocultural perspective. Beginning with my own research on the learning of students and teachers of mathematics, I sketch out two theoretical frameworks for understanding this learning. One framework extends Valsiner's zone theory of child development, and the other draws on Wenger's ideas about communities of practice. My aim is then to suggest how these two frameworks might help us understand the learning of others who have an interest in mathematics education, such as mathematics teacher educator-researchers and mathematicians. In doing so, I attempt to move towards a synthesis of ideas to inform mathematics education research and development.

Connecting Mathematics Learning through Spatial Reasoning

Science.gov (United States)

Mulligan, Joanne; Woolcott, Geoffrey; Mitchelmore, Michael; Davis, Brent

2018-01-01

Spatial reasoning, an emerging transdisciplinary area of interest to mathematics education research, is proving integral to all human learning. It is particularly critical to science, technology, engineering and mathematics (STEM) fields. This project will create an innovative knowledge framework based on spatial reasoning that identifies new…

Enhancing student engagement to positively impact mathematics anxiety, confidence and achievement for interdisciplinary science subjects

Science.gov (United States)

Everingham, Yvette L.; Gyuris, Emma; Connolly, Sean R.

2017-11-01

Contemporary science educators must equip their students with the knowledge and practical know-how to connect multiple disciplines like mathematics, computing and the natural sciences to gain a richer and deeper understanding of a scientific problem. However, many biology and earth science students are prejudiced against mathematics due to negative emotions like high mathematical anxiety and low mathematical confidence. Here, we present a theoretical framework that investigates linkages between student engagement, mathematical anxiety, mathematical confidence, student achievement and subject mastery. We implement this framework in a large, first-year interdisciplinary science subject and monitor its impact over several years from 2010 to 2015. The implementation of the framework coincided with an easing of anxiety and enhanced confidence, as well as higher student satisfaction, retention and achievement. The framework offers interdisciplinary science educators greater flexibility and confidence in their approach to designing and delivering subjects that rely on mathematical concepts and practices.

Policy implementation in practice: the case of national service frameworks in general practice.

Science.gov (United States)

Checkland, Kath; Harrison, Stephen

2004-10-01

National Service Frameworks are an integral part of the government's drive to 'modernise' the NHS, intended to standardise both clinical care and the design of the services used to deliver that clinical care. This article uses evidence from qualitative case studies in three general practices to illustrate the difficulties associated with the implementation of such top-down guidelines and models of service. In these studies it was found that, while there had been little explicit activity directed at implementation overall, the National Service Framework for coronary heart disease had in general fared better than that for older people. Gunn's notion of 'perfect implementation' is used to make sense of the findings.

A general multiscale framework for the emergent effective elastodynamics of metamaterials

Science.gov (United States)

Sridhar, A.; Kouznetsova, V. G.; Geers, M. G. D.

2018-02-01

This paper presents a general multiscale framework towards the computation of the emergent effective elastodynamics of heterogeneous materials, to be applied for the analysis of acoustic metamaterials and phononic crystals. The generality of the framework is exemplified by two key characteristics. First, the underlying formalism relies on the Floquet-Bloch theorem to derive a robust definition of scales and scale separation. Second, unlike most homogenization approaches that rely on a classical volume average, a generalized homogenization operator is defined with respect to a family of particular projection functions. This yields a generalized macro-scale continuum, instead of the classical Cauchy continuum. This enables (in a micromorphic sense) to homogenize the rich dispersive behavior resulting from both Bragg scattering and local resonance. For an arbitrary unit cell, the homogenization projection functions are constructed using the Floquet-Bloch eigenvectors obtained in the desired frequency regime at select high symmetry points, which effectively resolves the emergent phenomena dominating that regime. Furthermore, a generalized Hill-Mandel condition is proposed that ensures power consistency between the homogenized and full-scale model. A high-order spatio-temporal gradient expansion is used to localize the multiscale problem leading to a series of recursive unit cell problems giving the appropriate micro-mechanical corrections. The developed multiscale method is validated against standard numerical Bloch analysis of the dispersion spectra of example unit cells encompassing multiple high-order branches generated by local resonance and/or Bragg scattering.

Science, technology, engineering, mathematics (STEM) as mathematics learning approach in 21st century

Science.gov (United States)

Milaturrahmah, Naila; Mardiyana, Pramudya, Ikrar

2017-08-01

This 21st century demands competent human resources in science, technology, engineering design and mathematics so that education is expected to integrate the four disciplines. This paper aims to describe the importance of STEM as mathematics learning approach in Indonesia in the 21st century. This paper uses a descriptive analysis research method, and the method reveals that STEM education growing in developed countries today can be a framework for innovation mathematics in Indonesia in the 21st century. STEM education integrate understanding of science, math skills, and the available technology with the ability to perform engineering design process. Implementation of mathematics learning with STEM approach makes graduates trained in using of mathematics knowledge that they have to create innovative products that are able to solve the problems that exist in society.

Middle School Mathematics Teachers Panel Perspectives of Instructional Practicess

Science.gov (United States)

Ziegler, Cindy

2017-01-01

In a local middle school, students were not meeting standards on the state mathematics tests. The purpose of this qualitative study was to explore mathematics teachers' perspectives on effective mathematics instruction vis-a-vis the principles of the National Council of Teachers of Mathematics (NCTM). Within this framework, the 6 principles in the…

A Mathematical Approach to Establishing Constitutive Models for Geomaterials

Directory of Open Access Journals (Sweden)

Guang-hua Yang

2013-01-01

Full Text Available The mathematical foundation of the traditional elastoplastic constitutive theory for geomaterials is presented from the mathematical point of view, that is, the expression of stress-strain relationship in principal stress/strain space being transformed to the expression in six-dimensional space. A new framework is then established according to the mathematical theory of vectors and tensors, which is applicable to establishing elastoplastic models both in strain space and in stress space. Traditional constitutive theories can be considered as its special cases. The framework also enables modification of traditional constitutive models.

Mathematical models of viscous friction

CERN Document Server

Buttà, Paolo; Marchioro, Carlo

2015-01-01

In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force. We investigate this topic in the framework of mathematical physics by focusing mainly on the class of purely Hamiltonian systems, for which very few results are available. We discuss two cases: when the medium is a gas and when it is a fluid. In the first case, the aim is to obtain microscopic models of viscous friction. In the second, we seek to underline some non-trivial features of the motion. Far from giving a general survey on the subject, which is very rich and complex from both a phenomenological and theoretical point of view, we focus on some fairly simple models that can be studied rigorously, thus providing a first step towards a mathematical description of viscous friction. In some cases, we restrict ourselves to studying the problem at a heuristic level, or we present the main ideas, discussing only some as...

How Are Questions That Students Ask in High Level Mathematics Classes Linked to General Giftedness?

Science.gov (United States)

Leikin, Roza; Koichu, Boris; Berman, Avi; Dinur, Sariga

2017-01-01

This paper presents a part of a larger study, in which we asked "How are learning and teaching of mathematics at high level linked to students' general giftedness?" We consider asking questions, especially student-generated questions, as indicators of quality of instructional interactions. In the part of the study presented in this…

General systems theory mathematical foundations

CERN Document Server

Mesarovic, Mihajlo D

1975-01-01

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

Mathematics Education in Singapore - an Insider's Perspective

OpenAIRE

Kaur, Berinderjeet

2014-01-01

Singapore's Education System has evolved over time and so has Mathematics Education in Singapore. The present day School Mathematics Curricula can best be described as one that caters for the needs of every child in school. It is based on a framework that has mathematical problem solving as its primary focus. The developments from 1946 to 2012 that have shaped the present School Mathematics Curricula in Singapore are direct consequences of developments in the Education System of Singapore dur...

Understanding Understanding Mathematics. Artificial Intelligence Memo No. 488.

Science.gov (United States)

Michener, Edwina Rissland

This document is concerned with the important extra-logical knowledge that is often outside of traditional discussions in mathematics, and looks at some of the ingredients and processes involved in the understanding of mathematics. The goal is to develop a conceptual framework in which to talk about mathematical knowledge and to understand the…

Mathematical foundations of image processing and analysis

CERN Document Server

Pinoli, Jean-Charles

2014-01-01

Mathematical Imaging is currently a rapidly growing field in applied mathematics, with an increasing need for theoretical mathematics. This book, the second of two volumes, emphasizes the role of mathematics as a rigorous basis for imaging sciences. It provides a comprehensive and convenient overview of the key mathematical concepts, notions, tools and frameworks involved in the various fields of gray-tone and binary image processing and analysis, by proposing a large, but coherent, set of symbols and notations, a complete list of subjects and a detailed bibliography. It establishes a bridg

A general theoretical framework for decoherence in open and closed systems

International Nuclear Information System (INIS)

Castagnino, Mario; Fortin, Sebastian; Laura, Roberto; Lombardi, Olimpia

2008-01-01

A general theoretical framework for decoherence is proposed, which encompasses formalisms originally devised to deal just with open or closed systems. The conditions for decoherence are clearly stated and the relaxation and decoherence times are compared. Finally, the spin-bath model is developed in detail from the new perspective

Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

Directory of Open Access Journals (Sweden)

Tanki Motsepa

2014-01-01

Full Text Available We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.

The nature of mathematical enrichment: a case study of implementation

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Jennifer Susan Piggott

2007-12-01

Full Text Available This paper reports a framework for describing the nature of mathematics enrichment that emerged from a case study based on the work of the NRICH Project (www.nrich.maths.org team when producing “mathematics enrichment trails” (an ordered set of related mathematics problems and support materials. A range of data sources, including the trails, trail development sessions, related literature and the views of colleagues were used to inform the findings. The data were analysed using NVivo and involved the development of two complementary coding systems. One, drawn from the data itself, gave evidence of views of the content aspects of mathematical enrichment. The other, specifically designed and informed by the literature, was used to aid the analysis of the roles of teaching and learning inherent in views of enrichment described by participants. The framework describes the content of an enrichment curriculum as well as implications for teaching and learning, the experiences of learners and the features of settings where this occurs. To support this, some detail is provided on the role, nature and purpose of problem-solving and what constitutes a good problem. While emerging from a particular context, the framework highlights the need for debate concerning the audience for mathematics enrichment, particularly in questioning the commonly held belief that its value is in supporting the needs of the mathematically most able. The framework also has potential value through offering a focus for debate within the wider community concerning the nature of mathematics enrichment and as a reference point for evaluating the potential of existing or new curriculum to deliver mathematics enrichment.

Working memory and language: skill-specific or domain-general relations to mathematics?

Science.gov (United States)

Purpura, David J; Ganley, Colleen M

2014-06-01

Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the specific relations of these two non-mathematical factors to individual aspects of early mathematics. Thus, the focus of this study was to determine whether working memory and language were related to only individual aspects of early mathematics or related to many components of early mathematics skills. A total of 199 4- to 6-year-old preschool and kindergarten children were assessed on a battery of early mathematics tasks as well as measures of working memory and language. Results indicated that working memory has a specific relation to only a few-but critically important-early mathematics skills and language has a broad relation to nearly all early mathematics skills. Copyright © 2014 Elsevier Inc. All rights reserved.

Enhancing Mathematics Communication using Critical Aspects and Dimensions of Variation

Science.gov (United States)

Olteanu, Constanta; Olteanu, Lucian

2013-01-01

This article deals with two prominent topics in the field of mathematics education: the communication in mathematics and its teaching and learning and the continuous professional development of mathematics teachers. In this article, a framework is proposed for analysing the effectiveness of communication in mathematics classrooms. The presentation…

Connecting mathematics learning through spatial reasoning

Science.gov (United States)

Mulligan, Joanne; Woolcott, Geoffrey; Mitchelmore, Michael; Davis, Brent

2018-03-01

Spatial reasoning, an emerging transdisciplinary area of interest to mathematics education research, is proving integral to all human learning. It is particularly critical to science, technology, engineering and mathematics (STEM) fields. This project will create an innovative knowledge framework based on spatial reasoning that identifies new pathways for mathematics learning, pedagogy and curriculum. Novel analytical tools will map the unknown complex systems linking spatial and mathematical concepts. It will involve the design, implementation and evaluation of a Spatial Reasoning Mathematics Program (SRMP) in Grades 3 to 5. Benefits will be seen through development of critical spatial skills for students, increased teacher capability and informed policy and curriculum across STEM education.

TIMSS Advanced 2015 Assessment Frameworks

Science.gov (United States)

Mullis, Ina V. S., Ed.; Martin, Michael O., Ed.

2014-01-01

The "TIMSS Advanced 2015 Assessment Frameworks" provides the foundation for the two international assessments to take place as part of the International Association for the Evaluation of Educational Achievement's TIMSS (Trends in International Mathematics and Science Study) Advanced 2015--Advanced Mathematics and Physics. Chapter 1 (Liv…

Applied Mathematical Problems in Engineering

Directory of Open Access Journals (Sweden)

Carlos Llopis-Albert

2016-10-01

Full Text Available There is a close relationship between engineering and mathematics, which has led to the development of new techniques in recent years. Likewise the developments in technology and computers have led to new ways of teaching mathematics for engineering students and the use of modern techniques and methods.  This research aims to provide insight on how to deal with mathematical problems for engineering students. This is performed by means of a fuzzy set/Qualitative Comparative Analysis applied to conflict resolution of Public Participation Projects in support to the EU Water Framework Directive.

Relationships of Mathematics Anxiety, Mathematics Self-Efficacy and Mathematics Performance of Adult Basic Education Students

Science.gov (United States)

Watts, Beverly Kinsey

2011-01-01

Competent mathematical skills are needed in the workplace as well as in the college setting. Adults in Adult Basic Education classes and programs generally perform below high school level competency, but very few studies have been performed investigating the predictors of mathematical success for adults. The current study contributes to the…

Weak Quantum Theory: Formal Framework and Selected Applications

International Nuclear Information System (INIS)

Atmanspacher, Harald; Filk, Thomas; Roemer, Hartmann

2006-01-01

Two key concepts of quantum theory, complementarity and entanglement, are considered with respect to their significance in and beyond physics. An axiomatically formalized, weak version of quantum theory, more general than the ordinary quantum theory of physical systems, is described. Its mathematical structure generalizes the algebraic approach to ordinary quantum theory. The crucial formal feature leading to complementarity and entanglement is the non-commutativity of observables.The ordinary Hilbert space quantum mechanics can be recovered by stepwise adding the necessary features. This provides a hierarchy of formal frameworks of decreasing generality and increasing specificity. Two concrete applications, more specific than weak quantum theory and more general than ordinary quantum theory, are discussed: (i) complementarity and entanglement in classical dynamical systems, and (ii) complementarity and entanglement in the bistable perception of ambiguous stimuli

A Categorization Model for Educational Values of the History of Mathematics: An Empirical Study

Science.gov (United States)

Wang, Xiao-qin; Qi, Chun-yan; Wang, Ke

2017-01-01

There is not a clear consensus on the categorization framework of the educational values of the history of mathematics. By analyzing 20 Chinese teaching cases on integrating the history of mathematics into mathematics teaching based on the relevant literature, this study examined a new categorization framework of the educational values of the…

A general science-based framework for dynamical spatio-temporal models

Science.gov (United States)

Wikle, C.K.; Hooten, M.B.

2010-01-01

Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially-explicit processes that evolve over time. Correspondingly, in recent years there has been a significant amount of research on new statistical methodology for such models. Although descriptive models that approach the problem from the second-order (covariance) perspective are important, and innovative work is being done in this regard, many real-world processes are dynamic, and it can be more efficient in some cases to characterize the associated spatio-temporal dependence by the use of dynamical models. The chief challenge with the specification of such dynamical models has been related to the curse of dimensionality. Even in fairly simple linear, first-order Markovian, Gaussian error settings, statistical models are often over parameterized. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters. In addition, this framework has allowed for the specification of science based parameterizations (and associated prior distributions) in which classes of deterministic dynamical models (e. g., partial differential equations (PDEs), integro-difference equations (IDEs), matrix models, and agent-based models) are used to guide specific parameterizations. Most of the focus for the application of such models in statistics has been in the linear case. The problems mentioned above with linear dynamic models are compounded in the case of nonlinear models. In this sense, the need for coherent and sensible model parameterizations is not only helpful, it is essential. Here, we present an overview of a framework for incorporating scientific information to motivate dynamical spatio-temporal models. First, we illustrate the methodology with the linear case. We then develop a general nonlinear spatio-temporal framework that we call general quadratic

Didactic use of cinema in Mathematics

Directory of Open Access Journals (Sweden)

Pablo BELTRÁN PELLICER

2014-10-01

Full Text Available The use of cinema as didactical resource in the Mathematics classroom has interested several authors and teachers during the last years, mainly because of its power to motivate students. On this point, suggestive compilations of scenes containing mathematical references, detailed analysis of movies closely related to Mathematics and even didactical materials to be used in the classroom have been developed. This article proposes a theoretical framework for designing classroom sequences based on the didactical situation which can arise from movies or fiction series scenes. In order to develop such a framework, we follow a didactical engineering process, taking into account some specific characteristics, as the one related to the didactical transposition, as it is required to consider the mathematic knowledge within the chosen scene, overall the way it appears. As well, a classroom experience is described, designed following the mentioned guidelines and implemented in the course of a collaborative project between two secondary education centers, where a significant motivation increase has been detected, due to using mathematical situations from the real world (or from fictional contexts but which can be easily assimilated by the students. There was also evidence about the fact that the designed didactical sequences allow to reduce the cognitive gap required to acquire certain mathematical concepts, because of the scenes provide additional information within an extra-mathematical context. Therefore, our proposal establishes some basic considerations in order to efficiently design didactical sequences using movie scenes as a resource, underlining its power to motivate as well as its facilitating ability when introducing new mathematical concepts to our students.

Mathematics University Teachers' Perception of Pedagogical Content Knowledge (PCK)

Science.gov (United States)

Khakbaz, Azimehsadat

2016-01-01

Teaching mathematics in university levels is one of the most important fields of research in the area of mathematics education. Nevertheless, there is little information about teaching knowledge of mathematics university teachers. Pedagogical content knowledge (PCK) provides a suitable framework to study knowledge of teachers. The purpose of this…

A Mathematics Software Database Update.

Science.gov (United States)

Cunningham, R. S.; Smith, David A.

1987-01-01

Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)

Relationship of Mathematics Olympiad Performance of Gifted Students with IQ and Mathematics Achievement

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Ali İhsan BORAN

2015-04-01

Full Text Available The purpose of this study is to investigate relationship of mathematics Olympiad (analysis-algebra and geometry scores of gifted students with IQ scores (verbal, performance and general and mathematics achievement scores of the gifted students. Study group of the study included 64 gifted students (27 girls and 37 boys who took courses from one Science and Art Center. Data of study involved scores of the participants on mathematics Olympiad exam, WISC-R test and school mathematics achievement. For analysis of the data Pearson correlation analysis, Spearman correlation analysis, independent groups’ t-test and Mann Whitney U test were utilized. The findings showed that there was no significant relationship between the Olympiad scores on analysis-algebra and geometry and IQ scores (general, performance and verbal. But the Olympiad scores on analysis-algebra and geometry factors were significantly related to school mathematics achievement. Comparing IQ scores of highest and lowest scorer groups on the Olympiad scores showed that there were no significant differences between IQ scores (general, performance and verbal of the groups. However school mathematics scores of the participants significantly differed in terms of groups determined based on analysis-algebra and geometry scores.

An Evaluation of the Generalized Intelligent Framework for Tutoring (GIFT) from a Researcher’s or Analyst’s Perspective

Science.gov (United States)

2014-12-01

An Evaluation of the Generalized Intelligent Framework for Tutoring (GIFT) from a Researcher’s or Analyst’s Perspective by Robert A...Generalized Intelligent Framework for Tutoring (GIFT) from a Researcher’s or Analyst’s Perspective Robert A Sottilare and Anne M Sinatra Human...2014 4. TITLE AND SUBTITLE An Evaluation of the Generalized Intelligent Framework for Tutoring (GIFT) from a Researcher’s or Analyst’s Perspective

An MGF-based unified framework to determine the joint statistics of partial sums of ordered i.n.d. random variables

KAUST Repository

Nam, Sungsik; Yang, Hongchuan; Alouini, Mohamed-Slim; Kim, Dongin

2014-01-01

framework to determine the joint statistics of partial sums of ordered i.n.d. RVs. Our mathematical formalism is illustrated with an application on the exact performance analysis of the capture probability of generalized selection combining (GSC)-based RAKE

Promoting Mathematical Connections Using Three-Dimensional Manipulatives

Science.gov (United States)

Safi, Farshid; Desai, Siddhi

2017-01-01

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

Forum of Mathematics for Industry 2013

CERN Document Server

Anderssen, Robert; Cheng, Jin; Fukumoto, Yasuhide; McKibbin, Robert; Polthier, Konrad; Takagi, Tsuyoshi; Toh, Kim-Chuan

2014-01-01

This book is a collection of papers presented at the Forum “The Impact of Applications on Mathematics” in October 2013. It describes an appropriate framework in which to highlight how real-world problems, over the centuries and today, have influenced and are influencing the development of mathematics and, thereby, how mathematics is reshaped, in order to advance mathematics and its application. The contents of this book address productive and successful interaction between industry and mathematicians, as well as the cross-fertilization and collaboration that result when mathematics is involved with the advancement of science and technology.

Visualization and mathematics III

CERN Document Server

Polthier, Konrad

2003-01-01

This research book on Mathematical Visualization contains state of the art presentations on visualization problems in mathematics, on fundamental mathematical research in computer graphics, and on software frameworks for the application of visualization to real-world problems. All contributions were written by leading experts in the field and peer-refereed by an international editorial team. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin. The themes of the book cover important recent developments on - Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology - Geometric Modelling - Image Based Visualization - Software Environments and Applications - Education and Communication The variety of topics makes the book a suitable resource for researchers, lecturers, and practitioners; http://www-sfb288.math.tu-berlin.de/vismath/

Teacher's Guide to Secondary Mathematics.

Science.gov (United States)

Duval County Schools, Jacksonville, FL.

This is a teacher's guide to secondary school mathematics. Developed for use in the Duval County Public Schools, Jacksonville, Florida. Areas of mathematics covered are algebra, analysis, calculus, computer literacy, computer science, geometry, analytic geometry, general mathematics, consumer mathematics, pre-algebra, probability and statistics,…

Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

Science.gov (United States)

Schaid, Daniel J

2010-01-01

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.

Modeling framework for crew decisions during accident sequences

International Nuclear Information System (INIS)

Lukic, Y.D.; Worledge, D.H.; Hannaman, G.W.; Spurgin, A.J.

1986-01-01

The ability to model the average behavior of operating crews in the course of accident sequences is vital in learning on how to prevent damage to power plants and to maintain safety. This paper summarizes the work carried out in support of a Human Reliability Model framework. This work develops the mathematical framework of the model and identifies the parameters which could be measured in some way, e.g., through simulator experience and/or small scale tests. Selected illustrative examples are presented, of the numerical experiments carried out in order to understand the model sensitivity to parameter variation. These examples ar discussed with the objective of deriving insights of general nature regarding operating of the model which may lead to enhanced understanding of man/machine interactions

Teachers' Understanding of Algebraic Generalization

Science.gov (United States)

Hawthorne, Casey Wayne

Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby teachers respond to and build upon the ideas that arise from students' explorations of these activities. Although more and more teachers are engaging their students in such generalizing tasks, little is known about teachers' understanding of generalization and their understanding of students' mathematical thinking in this domain. In this work, I addressed this gap, exploring the understanding of algebraic generalization of 4 exemplary 8th-grade teachers from multiple perspectives. A significant feature of this investigation is an examination of teachers' understanding of the generalization process, including the use of algebraic symbols. The research consisted of two phases. Phase I was an examination of the teachers' understandings of the underlying quantities and quantitative relationships represented by algebraic notation. In Phase II, I observed the instruction of 2 of these teachers. Using the lens of professional noticing of students' mathematical thinking, I explored the teachers' enacted knowledge of algebraic generalization, characterizing how it supported them to effectively respond to the needs and queries of their students. Results indicated that teachers predominantly see these figural patterns as enrichment activities, disconnected from course content. Furthermore, in my analysis, I identified conceptual difficulties teachers experienced when solving generalization tasks, in particular, connecting multiple symbolic representations with the quantities in the figures. Moreover, while the teachers strived to overcome the challenges of connecting different representations, they invoked both productive and unproductive

Mathematical stereochemistry

CERN Document Server

Fujita, Shinsaku

2015-01-01

Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. A new stereoisogram approach, developed by the author, is introduced in this book, providing a theoretical framework for mathematical aspects of modern stereochemistry. The discussion covers point-groups and permutation symmetry and exemplifies the concepts using organic molecules and inorganic complexes.

Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction

Science.gov (United States)

Li, Shu-Nan; Cao, Bing-Yang

2017-09-01

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

Understanding the Chinese Approach to Creative Teaching in Mathematics Classrooms

Science.gov (United States)

Niu, Weihua; Zhou, Zheng; Zhou, Xinlin

2017-01-01

Using Amabile's componential theory of creativity as a framework, this paper analyzes how Chinese mathematics teachers achieve creative teaching through acquiring in-depth domain-specific knowledge in mathematics, developing creativity-related skills, as well as stimulating student interest in learning mathematics, through well-crafted,…

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

International Nuclear Information System (INIS)

Carretero-González, R; Frantzeskakis, D J; Kevrekidis, P G

2008-01-01

The aim of this review is to introduce the reader to some of the physical notions and the mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyse some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g. the linear or the nonlinear limit or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools. (invited article)

Obstacle problems in mathematical physics

CERN Document Server

Rodrigues, J-F

1987-01-01

The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.

A general framework for performance guaranteed green data center networking

OpenAIRE

Wang, Ting; Xia, Yu; Muppala, Jogesh; Hamdi, Mounir; Foufou, Sebti

2014-01-01

From the perspective of resource allocation and routing, this paper aims to save as much energy as possible in data center networks. We present a general framework, based on the blocking island paradigm, to try to maximize the network power conservation and minimize sacrifices of network performance and reliability. The bandwidth allocation mechanism together with power-aware routing algorithm achieve a bandwidth guaranteed tighter network. Besides, our fast efficient heuristics for allocatin...

The tools of mathematical reasoning

CERN Document Server

Lakins, Tamara J

2016-01-01

This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.

CHI: A General Agent Communication Framework

Energy Technology Data Exchange (ETDEWEB)

Goldsmith, S.Y.; Phillips, L.R.; Spires, S.V.

1998-12-17

We have completed and exercised a communication framework called CHI (CLOS to HTML Interface) by which agents can communicate with humans. CHI follows HTTP (HyperText Transfer Protocol) and produces HTML (HyperText Markup Language) for use by WWW (World-Wide Web) browsers. CHI enables the rapid and dynamic construction of interface mechanisms. The essence of CHI is automatic registration of dynamically generated interface elements to named objects in the agent's internal environment. The agent can access information in these objects at will. State is preserved, so an agent can pursue branching interaction sequences, activate failure recovery behaviors, and otherwise act opportunistically to maintain a conversation. The CHI mechanism remains transparent in multi-agent, multi-user environments because of automatically generated unique identifiers built into the CHI mechanism. In this paper we discuss design, language, implementation, and extension issues, and, by way of illustration, examine the use of the general CHI/HCHI mechanism in a specific international electronic commerce system. We conclude that the CHI mechanism is an effective, efficient, and extensible means of the agent/human communication.

Speed mathematics

CERN Document Server

Handley, Bill

2012-01-01

This new, revised edition of the bestselling Speed Mathematics features new chapters on memorising numbers and general information, calculating statistics and compound interest, square roots, logarithms and easy trig calculations. Written so anyone can understand, this book teaches simple strategies that will enable readers to make lightning-quick calculations. People who excel at mathematics use better strategies than the rest of us; they are not necessarily more intelligent. With Speed Mathematics you'll discover methods to make maths easy and fun. This book is perfect for stud

DETERMINATION ALGORITHM OF OPTIMAL GEOMETRICAL PARAMETERS FOR COMPONENTS OF FREIGHT CARS ON THE BASIS OF GENERALIZED MATHEMATICAL MODELS

Directory of Open Access Journals (Sweden)

O. V. Fomin

2013-10-01

Full Text Available Purpose. Presentation of features and example of the use of the offered determination algorithm of optimum geometrical parameters for the components of freight cars on the basis of the generalized mathematical models, which is realized using computer. Methodology. The developed approach to search for optimal geometrical parameters can be described as the determination of optimal decision of the selected set of possible variants. Findings. The presented application example of the offered algorithm proved its operation capacity and efficiency of use. Originality. The determination procedure of optimal geometrical parameters for freight car components on the basis of the generalized mathematical models was formalized in the paper. Practical value. Practical introduction of the research results for universal open cars allows one to reduce container of their design and accordingly to increase the carrying capacity almost by100 kg with the improvement of strength characteristics. Taking into account the mass of their park this will provide a considerable economic effect when producing and operating. The offered approach is oriented to the distribution of the software packages (for example Microsoft Excel, which are used by technical services of the most enterprises, and does not require additional capital investments (acquisitions of the specialized programs and proper technical staff training. This proves the correctness of the research direction. The offered algorithm can be used for the solution of other optimization tasks on the basis of the generalized mathematical models.

Early Career Mathematics Teachers' General Pedagogical Knowledge and Skills: Do Teacher Education, Teaching Experience, and Working Conditions Make a Difference?

Science.gov (United States)

König, Johannes; Blömeke, Sigrid; Kaiser, Gabriele

2015-01-01

We examined several facets of general pedagogical knowledge and skills of early career mathematics teachers, asking how they are associated with characteristics of teacher education, teaching experience, and working conditions. Declarative general pedagogical knowledge (GPK) was assessed via a paper-and-pencil test, while early career teachers'…

Mathematics for physical chemistry

CERN Document Server

Mortimer, Robert G

2013-01-01

Mathematics for Physical Chemistry is the ideal supplementary text for practicing chemists and students who want to sharpen their mathematics skills while enrolled in general through physical chemistry courses. This book specifically emphasizes the use of mathematics in the context of physical chemistry, as opposed to being simply a mathematics text. This 4e includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The early chapters are constructed around a sequence of mathematical topics, wit

Creativity for teaching mathematics. A diagnosis of secondary school professionals

Directory of Open Access Journals (Sweden)

Lapa, Zenobia

2013-01-01

Full Text Available This paper presents the results of a research completed at junior high school in Lima, Peru, involving teachers of mathematics during 2010. The objective was to assess the level of creativity of teachers of mathematics for the sake of enlarging it. Theoretical methods were used to construct a general framework; likewise interviews and observation were used and processed statistically. Motivation, originality and flexibility were considered as dimensions of creativity. The results show that 80 % of interviewed teachers self-evaluate their level of creativity as high. However, according to observations only 40 % of teacher creativity reaches a mid-level, and only a fifth of those assessed by their own pupils attained such mid-levels and show potentials for team work and initiative to elaborate or look for material aids generating a pleasant learning atmosphere.

The Open-Ended Approach Framework

Science.gov (United States)

Munroe, Lloyd

2015-01-01

This paper describes a pedagogical framework that teachers can use to support students who are engaged in solving open-ended problems, by explaining how two Japanese expert teachers successfully apply open-ended problems in their mathematics class. The Open-Ended Approach (OPA) framework consists of two main sections: Understanding Mathematical…

Mathematics 2

CERN Document Server

Kodaira, Kunihiko

1996-01-01

This is the translation from the Japanese textbook for the grade 11 course, "General Mathematics". It is part of the easier of the three elective courses in mathematics offered at this level and is taken by about 40% of students. The book covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.

Experiences of Student Mathematics-Teachers in Computer-Based Mathematics Learning Environment

Science.gov (United States)

Karatas, Ilhan

2011-01-01

Computer technology in mathematics education enabled the students find many opportunities for investigating mathematical relationships, hypothesizing, and making generalizations. These opportunities were provided to pre-service teachers through a faculty course. At the end of the course, the teachers were assigned project tasks involving…

Quantum Networks: General theory and applications

International Nuclear Information System (INIS)

Bisio, A.; D'Ariano, G. M.; Perinotti, P.; Chiribella, G.

2011-01-01

In this work we present a general mathematical framework to deal with Quantum Networks, i.e. networks resulting from the interconnection of elementary quantum circuits. The cornerstone of our approach is a generalization of the Choi isomorphism that allows one to efficiently represent any given Quantum Network in terms of a single positive operator. Our formalism allows one to face and solve many quantum information processing problems that would be hardly manageable otherwise, the most relevant of which are reviewed in this work: quantum process tomography, quantum cloning and learning of transformations, inversion of a unitary gate, information-disturbance tradeoff in estimating a unitary transformation, cloning and learning of a measurement device (Authors)

High school mathematics teachers' perspectives on the purposes of mathematical proof in school mathematics

Science.gov (United States)

Dickerson, David S.; Doerr, Helen M.

2014-12-01

Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were transferable to other fields of endeavor. We found teachers were divided on the characteristics (or features) of proofs that would serve these purposes. Teachers with less experience tended to believe that proofs in the high school should adhere to strict standards of language and reasoning while teachers with more experience tended to believe that proofs based on concrete or visual features were well suited for high school mathematics. This study has implications for teacher preparation because it appears that there is a wide variation in how teachers think about proof. It seems likely that students would experience proof very differently merely because they were seated in different classrooms.

A mathematical framework for functional mapping of complex phenotypes using delay differential equations.

Science.gov (United States)

Fu, Guifang; Wang, Zhong; Li, Jiahan; Wu, Rongling

2011-11-21

All biological phenomena occurring at different levels of organization from cells to organisms can be modeled as a dynamic system, in which the underlying components interact dynamically to comprehend its biological function. Such a systems modeling approach facilitates the use of biochemically and biophysically detailed mathematical models to describe and quantify "living cells," leading to an in-depth and precise understanding of the behavior, development and function of a biological system. Here, we illustrate how this approach can be used to map genes or quantitative trait loci (QTLs) that control a complex trait using the example of the circadian rhythm system which has been at the forefront of analytical mathematical modeling for many years. We integrate a system of biologically meaningful delay differential equations (DDEs) into functional mapping, a statistical model designed to map dynamic QTLs involved in biological processes. The DDEs model the ability of circadian rhythm to generate autonomously sustained oscillations with a period close to 24h, in terms of time-varying mRNA and protein abundances. By incorporating the Runge-Kutta fourth order algorithm within the likelihood-based context of functional mapping, we estimated the genetic parameters that define the periodic pattern of QTL effects on time-varying mRNA and protein abundances and their dynamic association as well as the linkage disequilibrium of the QTL and a marker. We prove theorems about how to choose appropriate parameters to guarantee periodic oscillations. We further used simulation studies to investigate how a QTL influences the period and the amplitude of circadian oscillations through changing model parameters. The model provides a quantitative framework for assessing the interplay between genetic effects of QTLs and rhythmic responses. Copyright © 2011 Elsevier Ltd. All rights reserved.

Introduction to General Relativity and Black Holes (5/5)

CERN Multimedia

CERN. Geneva

2001-01-01

Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.

Introduction to General Relativity and Black Holes (3/5)

CERN Multimedia

CERN. Geneva

2001-01-01

Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.

Introduction to General Relativity and Black Holes (1/5)

CERN Multimedia

CERN. Geneva

2001-01-01

Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.

Introduction to General Relativity and Black Holes (2/5)

CERN Multimedia

CERN. Geneva

2001-01-01

Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.

Introduction to General Relativity and Black Holes (4/5)

CERN Multimedia

CERN. Geneva

2001-01-01

Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.

Mathematical literacy of school leaving pupils in South Africa

NARCIS (Netherlands)

Howie, S.; Plomp, T.

2002-01-01

This paper discusses some results of South African (SA) grade 12 pupils on an international test of mathematical literacy, administered in the framework of the Third International Mathematics and Science Study (TIMSS) under the auspices of the International Association for the Evaluation of

Gravitation. [Book on general relativity

Science.gov (United States)

Misner, C. W.; Thorne, K. S.; Wheeler, J. A.

1973-01-01

This textbook on gravitation physics (Einstein's general relativity or geometrodynamics) is designed for a rigorous full-year course at the graduate level. The material is presented in two parallel tracks in an attempt to divide key physical ideas from more complex enrichment material to be selected at the discretion of the reader or teacher. The full book is intended to provide competence relative to the laws of physics in flat space-time, Einstein's geometric framework for physics, applications with pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, gravitational waves, experimental tests of Einstein's theory, and mathematical concepts of differential geometry.

Musings on multiplication tables and associated mathematics and teaching practices

Directory of Open Access Journals (Sweden)

Faaiz Gierdien

2009-09-01

Full Text Available This paper is based on my reflections on a deceptively simple tabular representation of a combined 12×12 multiplication table showing multiplier and multiplicand,starting at a time when I taught mathematics full time at a primary (elementary school through to my presentteaching of mathematics education modules to prospective teachers. A historically–motivated framework on the importance of tables as expressions of complex information in two–dimensional form is used to gain insight into and understand multiplication tables. Through this framework it is shown that the modal practice of “knowing one’s tables” in the primary grade levels is really about knowing sequenced and separated lists of whole number multiplications. In contrast, tabular multiplication sequences in a combined multiplication table can, through appropriate teaching practices, enable the discovery of multiple relationships beyond multiplication or arithmetic, resulting in significant mathematics that spans the grade levels. Implications for mathematics teacher education practice with its current focus mathematical knowledge for teaching, are considered.

A Bivariate Generalized Linear Item Response Theory Modeling Framework to the Analysis of Responses and Response Times.

Science.gov (United States)

Molenaar, Dylan; Tuerlinckx, Francis; van der Maas, Han L J

2015-01-01

A generalized linear modeling framework to the analysis of responses and response times is outlined. In this framework, referred to as bivariate generalized linear item response theory (B-GLIRT), separate generalized linear measurement models are specified for the responses and the response times that are subsequently linked by cross-relations. The cross-relations can take various forms. Here, we focus on cross-relations with a linear or interaction term for ability tests, and cross-relations with a curvilinear term for personality tests. In addition, we discuss how popular existing models from the psychometric literature are special cases in the B-GLIRT framework depending on restrictions in the cross-relation. This allows us to compare existing models conceptually and empirically. We discuss various extensions of the traditional models motivated by practical problems. We also illustrate the applicability of our approach using various real data examples, including data on personality and cognitive ability.

Mathematical biology

CERN Document Server

Murray, James D

1993-01-01

The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...

The contribution of several Nobel Laureates in the development of the Theory of general economic equilibrium

OpenAIRE

Florentina Xhelili Krasniqi; Rahmie Topxhiu; Donat Rexha

2016-01-01

Nobel Laureates with their contributions to the development of the theory of general equilibrium have enabled this theory to be one of the most important for theoretical and practical analysis of the overall economy and the efficient use of economic resources. Results of the research showing that contributions of Nobel Laureates in the economy belong to two main frameworks of development of the general equilibrium theory: one was the mathematical model of general equilibrium developed by J...

Children thinking mathematically beyond authoritative identities

Science.gov (United States)

MacMillan, Agnes

1995-10-01

A study into the mathematics-related interactions and developing attitudes of young children during the transition period between pre-school and school is reported. Transcripts of interactions during a six-week observation period in one of two preschool sites are coded according to the classifications defined within a theoretical framework. Two separate episodes of construction play were analysed and one of these is used to examine the mathematical nature of the children's interactions within an emerging model of autonomous learning. The results of the analysis indicate that access to self-regulatory social relations is very closely linked to the accessibility of mathematical meanings.

Mathematics, Language, and Learning: A Longitudinal Study of Elementary Teachers and Their Mathematics Teaching Practices

OpenAIRE

Yeh, Cathery

2016-01-01

Elementary school mathematics has gained increased attention in the last few decades. A growing field of research has studied the programmatic design and development of elementary mathematics teaching in teacher education, however, few studies have examined longitudinally the mathematics teaching of novice elementary teachers. Existing longitudinal studies on elementary mathematics teaching have generally focused on the effects of teacher preparation on their beginning practices and have exam...

Basics of modern mathematical statistics

CERN Document Server

Spokoiny, Vladimir

2015-01-01

This textbook provides a unified and self-contained presentation of the main approaches to and ideas of mathematical statistics. It collects the basic mathematical ideas and tools needed as a basis for more serious studies or even independent research in statistics. The majority of existing textbooks in mathematical statistics follow the classical asymptotic framework. Yet, as modern statistics has changed rapidly in recent years, new methods and approaches have appeared. The emphasis is on finite sample behavior, large parameter dimensions, and model misspecifications. The present book provides a fully self-contained introduction to the world of modern mathematical statistics, collecting the basic knowledge, concepts and findings needed for doing further research in the modern theoretical and applied statistics. This textbook is primarily intended for graduate and postdoc students and young researchers who are interested in modern statistical methods.

Modelling Framework and Assistive Device for Peripheral Intravenous Injections

Science.gov (United States)

Kam, Kin F.; Robinson, Martin P.; Gilbert, Mathew A.; Pelah, Adar

2016-02-01

Intravenous access for blood sampling or drug administration that requires peripheral venepuncture is perhaps the most common invasive procedure practiced in hospitals, clinics and general practice surgeries.We describe an idealised mathematical framework for modelling the dynamics of the peripheral venepuncture process. Basic assumptions of the model are confirmed through motion analysis of needle trajectories during venepuncture, taken from video recordings of a skilled practitioner injecting into a practice kit. The framework is also applied to the design and construction of a proposed device for accurate needle guidance during venepuncture administration, assessed as consistent and repeatable in application and does not lead to over puncture. The study provides insights into the ubiquitous peripheral venepuncture process and may contribute to applications in training and in the design of new devices, including for use in robotic automation.

Generalization of Einstein's gravitational field equations

Science.gov (United States)

Moulin, Frédéric

2017-12-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

A synthesis of mathematical and cognitive performances of students with mathematics learning disabilities.

Science.gov (United States)

Shin, Mikyung; Bryant, Diane Pedrotty

2015-01-01

The purpose of this study was to synthesize the findings from 23 articles that compared the mathematical and cognitive performances of students with mathematics learning disabilities (LD) to (a) students with LD in mathematics and reading, (b) age- or grade-matched students with no LD, and (c) mathematical-ability-matched younger students with no LD. Overall results revealed that students with mathematics LD exhibited higher word problem-solving abilities and no significant group differences on working memory, long-term memory, and metacognition measures compared to students with LD in mathematics and reading. Findings also revealed students with mathematics LD demonstrated significantly lower performance compared to age- or grade-matched students with no LD on both mathematical and cognitive measures. Comparison between students with mathematics LD and younger students with no LD revealed mixed outcomes on mathematical measures and generally no significant group differences on cognitive measures. © Hammill Institute on Disabilities 2013.

Mathematical Modelling of the Evaporating Liquid Films on the Basis of the Generalized Interface Conditions

Directory of Open Access Journals (Sweden)

Goncharova Olga

2016-01-01

Full Text Available The two-dimensional films, flowing down an inclined, non-uniformly heated substrate are studied. The results contain the new mathematical models developed with the help of the long-wave approximation of the Navier-Stokes and heat transfer equations or Oberbeck-Boussinesq equations in the case, when the generalized conditions are formulated at thermocapillary interface. The evolution equations for the film thickness include the effects of gravity, viscosity, capillarity, thermocapillarity, additional stress effects and evaporation.

A proximal point algorithm with generalized proximal distances to BEPs

OpenAIRE

Bento, G. C.; Neto, J. X. Cruz; Lopes, J. O.; Soares Jr, P. A.; Soubeyran, A.

2014-01-01

We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of the sequences generated by the algorithm. This class of problems is very interesting because it covers mathematical programs and optimization problems under equilibrium constraints. As an application, we consider the problem of the stability and change dyna...

Courses on the Beauty of Mathematics: Our Version of General Education Mathematics Courses

Science.gov (United States)

Rash, Agnes M.; Fillebrown, Sandra

2016-01-01

This article describes various courses designed to incorporate mathematical proofs into courses for non-math and non-science majors. These courses, nicknamed "math beauty" courses, are designed to discuss one topic in-depth rather than to introduce many topics at a superficial level. A variety of courses, each requiring students to…

A generalized coherence framework for detecting and characterizing nonlinear interactions in the nervous system

NARCIS (Netherlands)

Yang, Y.; Solis Escalante, T.; van der Helm, F.C.T.; Schouten, A.C.

2016-01-01

Objective: This paper introduces a generalized coherence framework for detecting and characterizing nonlinear interactions in the nervous system, namely cross-spectral coherence (CSC). CSC can detect different types of nonlinear interactions including harmonic and intermodulation coupling as present

Students’ logical-mathematical intelligence profile

Science.gov (United States)

Arum, D. P.; Kusmayadi, T. A.; Pramudya, I.

2018-04-01

One of students’ characteristics which play an important role in learning mathematics is logical-mathematical intelligence. This present study aims to identify profile of students’ logical-mathematical intelligence in general and specifically in each indicator. It is also analyzed and described based on students’ sex. This research used qualitative method with case study strategy. The subjects involve 29 students of 9th grade that were selected by purposive sampling. Data in this research involve students’ logical-mathematical intelligence result and interview. The results show that students’ logical-mathematical intelligence was identified in the moderate level with the average score is 11.17 and 51.7% students in the range of the level. In addition, the level of both male and female students are also mostly in the moderate level. On the other hand, both male and female students’ logical-mathematical intelligence is strongly influenced by the indicator of ability to classify and understand patterns and relationships. Furthermore, the ability of comparison is the weakest indicator. It seems that students’ logical-mathematical intelligence is still not optimal because more than 50% students are identified in moderate and low level. Therefore, teachers need to design a lesson that can improve students’ logical-mathematical intelligence level, both in general and on each indicator.

The language of mathematics: investigating the ways language counts for children's mathematical development.

Science.gov (United States)

Vukovic, Rose K; Lesaux, Nonie K

2013-06-01

This longitudinal study examined how language ability relates to mathematical development in a linguistically and ethnically diverse sample of children from 6 to 9 years of age. Study participants were 75 native English speakers and 92 language minority learners followed from first to fourth grades. Autoregression in a structural equation modeling (SEM) framework was used to evaluate the relation between children's language ability and gains in different domains of mathematical cognition (i.e., arithmetic, data analysis/probability, algebra, and geometry). The results showed that language ability predicts gains in data analysis/probability and geometry, but not in arithmetic or algebra, after controlling for visual-spatial working memory, reading ability, and sex. The effect of language on gains in mathematical cognition did not differ between language minority learners and native English speakers. These findings suggest that language influences how children make meaning of mathematics but is not involved in complex arithmetical procedures whether presented with Arabic symbols as in arithmetic or with abstract symbols as in algebraic reasoning. The findings further indicate that early language experiences are important for later mathematical development regardless of language background, denoting the need for intensive and targeted language opportunities for language minority and native English learners to develop mathematical concepts and representations. Copyright © 2013. Published by Elsevier Inc.

MOOSE: A parallel computational framework for coupled systems of nonlinear equations

International Nuclear Information System (INIS)

Gaston, Derek; Newman, Chris; Hansen, Glen; Lebrun-Grandie, Damien

2009-01-01

Systems of coupled, nonlinear partial differential equations (PDEs) often arise in simulation of nuclear processes. MOOSE: Multiphysics Object Oriented Simulation Environment, a parallel computational framework targeted at the solution of such systems, is presented. As opposed to traditional data-flow oriented computational frameworks, MOOSE is instead founded on the mathematical principle of Jacobian-free Newton-Krylov (JFNK). Utilizing the mathematical structure present in JFNK, physics expressions are modularized into 'Kernels,' allowing for rapid production of new simulation tools. In addition, systems are solved implicitly and fully coupled, employing physics-based preconditioning, which provides great flexibility even with large variance in time scales. A summary of the mathematics, an overview of the structure of MOOSE, and several representative solutions from applications built on the framework are presented.

Factors Considered by Elementary Teachers When Developing and Modifying Mathematical Tasks to Support Children's Mathematical Thinking

Science.gov (United States)

Fredenberg, Michael Duane

The idea that problems and tasks play a pivotal role in a mathematics lesson has a long standing in mathematics education research. Recent calls for teaching reform appeal for training teachers to better understand how students learn mathematics and to employ students' mathematical thinking as the basis for pedagogy (CCSSM, 2010; NCTM, 2000; NRC 1999). The teaching practices of (a) developing a task for a mathematics lesson and, (b) modifying the task for students while enacting the lesson fit within the scope of supporting students' mathematical thinking. Surprisingly, an extensive search of the literature did not yield any research aimed to identify and refine the constituent parts of the aforementioned teaching practices in the manner called for by Grossman and xiii colleagues (2009). Consequently, my research addresses the two questions: (a) what factors do exemplary elementary teachers consider when developing a task for a mathematics lesson? (b) what factors do they consider when they modify a task for a student when enacting a lesson? I conducted a multiple case study involving three elementary teachers, each with extensive training in the area of Cognitively Guided Instruction (CGI), as well as several years experience teaching mathematics following the principles of CGI (Carpenter et al., 1999). I recorded video of three mathematics lessons with each participant and after each lesson I conducted a semi-structured stimulated recall interview. A subsequent follow-up clinical interview was conducted soon thereafter to further explore the teacher's thoughts (Ginsberg, 1997). In addition, my methodology included interjecting myself at select times during a lesson to ask the teacher to explain her reasoning. Qualitative analysis led to a framework that identified four categories of influencing factors and seven categories of supporting objectives for the development of a task. Subsets of these factors and objectives emerged as particularly relevant when the

In the Middle of Nowhere: How a Textbook Can Position the Mathematics Learner

Science.gov (United States)

Herbel-Eisenmann, Beth; Wagner, David

2005-01-01

We outline a framework for investigating how a mathematics textbook positions the mathematics learner. We use tools and concepts from discourse analysis, a field of linguistic scholarship, to illustrate the ways in which a textbook can position people in relation to mathematics and how the text can position the mathematics learner in relation to…

Mathematical Physics Framework SustainingNatural Anticipation and Selection of Attention

Directory of Open Access Journals (Sweden)

Alfons Salden

2005-04-01

Full Text Available An ambient intelligent environment is definitely a prerequisite for anticipating the needs and catching the attention of systems. But how to endow such an environment with natural anticipatory and attentive features is still a hardly ever properly addressed question. Before providing a roadmap towards such an ambient intelligent environment we first give cognitive-ergonomic accounts for how natural anticipation and selection of attention (NASA emerge in living organisms. In particular, we describe why, when and how exploratory and goal-directed acts by living organisms are controlled while optimizing their changing and limited structural and functional capabilities of multimodal sensor, cognitive and actuator systems. Next, we describe how NASA can be embedded and embodied in sustainable intelligent multimodal systems (SIMS. Such systems allow an ambient intelligent environment to (self- interact taking its contexts into account. In addition, collective intelligent agents (CIA distribute, store, extend, maintain, optimize, diversify and sustain the NASA embedded and embodied in the ambient intelligent environment. Finally, we present the basic ingredients of a mathematical-physical framework for empirically modeling and sustaining NASA within SIMS by CIA in an ambient intelligent environment. An environment which is modeled this way, robustly and reliably over time aligns multi-sensor detection and fusion; multimodal fusion, dialogue planning and fission; multi actuator fission, rendering and presentation schemes. NASA residing in such an environment are then active within every phase of perception-decision-action cycles, and are gauged and renormalized to its physics. After determining and assessing across several evolutionary dynamic scales appropriate fitness, utility and measures, NASA can be realized by reinforcement learning and self-organization.

Episodes in the mathematics of medieval Islam

CERN Document Server

Berggren, J L

1986-01-01

From the reviews: The book is, in spite of the author's more modest claims, an introductory survey of main developments in those disciplines which were particularly important in Medieval Islamic mathematics...No knowledge of mathematics (or of the history of mathematics) beyond normal high-school level is presupposed, and everything required beyond that (be it Apollonian theory of conics or the definitions of celestial circles) is explained carefully and clearly. Scattered throughout the work are a number of lucid remarks on the character of Islamic mathematics or of mathematical work in general. The book will hence not only be an excellent textbook for the teaching of the history of mathematics but also for the liberal art aspect of mathematics teaching in general. - Jens Høyrup, Mathematical Reviews ...as a textbook, this work is highly commendable...It is definitely the product of a skillful mathematician who has collected over the years a reasonably large number of interesting problems from medieval Arab...

Developing a Multi-Dimensional Early Elementary Mathematics Screener and Diagnostic Tool: The Primary Mathematics Assessment.

Science.gov (United States)

Brendefur, Jonathan L; Johnson, Evelyn S; Thiede, Keith W; Strother, Sam; Severson, Herb H

2018-01-01

There is a critical need to identify primary level students experiencing difficulties in mathematics to provide immediate and targeted instruction that remediates their deficits. However, most early math screening instruments focus only on the concept of number, resulting in inadequate and incomplete information for teachers to design intervention efforts. We propose a mathematics assessment that screens and provides diagnostic information in six domains that are important to building a strong foundation in mathematics. This article describes the conceptual framework and psychometric qualities of a web-based assessment tool, the Primary Math Assessment (PMA). The PMA includes a screener to identify students at risk for poor math outcomes and a diagnostic tool to provide a more in-depth profile of children's specific strengths and weaknesses in mathematics. The PMA allows teachers and school personnel to make better instructional decisions by providing more targeted analyses.

Gender, culture, and mathematics performance

OpenAIRE

Hyde, Janet S.; Mertz, Janet E.

2009-01-01

Using contemporary data from the U.S. and other nations, we address 3 questions: Do gender differences in mathematics performance exist in the general population? Do gender differences exist among the mathematically talented? Do females exist who possess profound mathematical talent? In regard to the first question, contemporary data indicate that girls in the U.S. have reached parity with boys in mathematics performance, a pattern that is found in some other nations as well. Focusing on the ...

An analytical framework for mathematics teacher education from a ...

African Journals Online (AJOL)

Whereas there has been considerable advancement in the last few decades with regard to theories and practices in mathematics education from a critical perspective, very little is known about what it means to prepare teachers for such approaches. In this article I undertake a retrospective, reflexive analysis of my praxis as ...

Programming-Languages as a Conceptual Framework for Teaching Mathematics

Science.gov (United States)

Feurzeig, Wallace; Papert, Seymour A.

2011-01-01

Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively…

The Reinvention of General Relativity: A Historiographical Framework for Assessing One Hundred Years of Curved Space-time.

Science.gov (United States)

Blum, Alexander; Lalli, Roberto; Renn, M Jürgen

2015-09-01

The history of the theory of general relativity presents unique features. After its discovery, the theory was immediately confirmed and rapidly changed established notions of space and time. The further implications of general relativity, however, remained largely unexplored until the mid 1950s, when it came into focus as a physical theory and gradually returned to the mainstream of physics. This essay presents a historiographical framework for assessing the history of general relativity by taking into account in an integrated narrative intellectual developments, epistemological problems, and technological advances; the characteristics of post-World War II and Cold War science; and newly emerging institutional settings. It argues that such a framework can help us understand this renaissance of general relativity as a result of two main factors: the recognition of the untapped potential of general relativity and an explicit effort at community building, which allowed this formerly disparate and dispersed field to benefit from the postwar changes in the scientific landscape.

Physical mathematics

CERN Document Server

Cahill, Kevin

2013-01-01

Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.

Mathematical concepts

CERN Document Server

Jost, Jürgen

2015-01-01

The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: ·         simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure ·         by itself as a first introduction to abstract mathematics ·         together with existing textbooks, to put their results into a more general perspective ·         to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detaile...

Dyslexia, Dyspraxia and Mathematics.

Science.gov (United States)

Yeo, Dorian

This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…

Evaluating and optimizing the operation of the hydropower system in the Upper Yellow River: A general LINGO-based integrated framework.

Science.gov (United States)

Si, Yuan; Li, Xiang; Yin, Dongqin; Liu, Ronghua; Wei, Jiahua; Huang, Yuefei; Li, Tiejian; Liu, Jiahong; Gu, Shenglong; Wang, Guangqian

2018-01-01

The hydropower system in the Upper Yellow River (UYR), one of the largest hydropower bases in China, plays a vital role in the energy structure of the Qinghai Power Grid. Due to management difficulties, there is still considerable room for improvement in the joint operation of this system. This paper presents a general LINGO-based integrated framework to study the operation of the UYR hydropower system. The framework is easy to use for operators with little experience in mathematical modeling, takes full advantage of LINGO's capabilities (such as its solving capacity and multi-threading ability), and packs its three layers (the user layer, the coordination layer, and the base layer) together into an integrated solution that is robust and efficient and represents an effective tool for data/scenario management and analysis. The framework is general and can be easily transferred to other hydropower systems with minimal effort, and it can be extended as the base layer is enriched. The multi-objective model that represents the trade-off between power quantity (i.e., maximum energy production) and power reliability (i.e., firm output) of hydropower operation has been formulated. With equivalent transformations, the optimization problem can be solved by the nonlinear programming (NLP) solvers embedded in the LINGO software, such as the General Solver, the Multi-start Solver, and the Global Solver. Both simulation and optimization are performed to verify the model's accuracy and to evaluate the operation of the UYR hydropower system. A total of 13 hydropower plants currently in operation are involved, including two pivotal storage reservoirs on the Yellow River, which are the Longyangxia Reservoir and the Liujiaxia Reservoir. Historical hydrological data from multiple years (2000-2010) are provided as input to the model for analysis. The results are as follows. 1) Assuming that the reservoirs are all in operation (in fact, some reservoirs were not operational or did not

The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children.

Science.gov (United States)

Träff, Ulf

2013-10-01

This study examined the relative contributions of general cognitive abilities and number abilities to word problem solving, calculation, and arithmetic fact retrieval in a sample of 134 children aged 10 to 13 years. The following tasks were administered: listening span, visual matrix span, verbal fluency, color naming, Raven's Progressive Matrices, enumeration, number line estimation, and digit comparison. Hierarchical multiple regressions demonstrated that number abilities provided an independent contribution to fact retrieval and word problem solving. General cognitive abilities contributed to problem solving and calculation. All three number tasks accounted for a similar amount of variance in fact retrieval, whereas only the number line estimation task contributed unique variance in word problem solving. Verbal fluency and Raven's matrices accounted for an equal amount of variance in problem solving and calculation. The current findings demonstrate, in accordance with Fuchs and colleagues' developmental model of mathematical learning (Developmental Psychology, 2010, Vol. 46, pp. 1731-1746), that both number abilities and general cognitive abilities underlie 10- to 13-year-olds' proficiency in problem solving, whereas only number abilities underlie arithmetic fact retrieval. Thus, the amount and type of cognitive contribution to arithmetic proficiency varies between the different aspects of arithmetic. Furthermore, how closely linked a specific aspect of arithmetic is to the whole number representation systems is not the only factor determining the amount and type of cognitive contribution in 10- to 13-year-olds. In addition, the mathematical complexity of the task appears to influence the amount and type of cognitive support. Copyright © 2013 Elsevier Inc. All rights reserved.

Data assimilation a mathematical introduction

CERN Document Server

Law, Kody; Zygalakis, Konstantinos

2015-01-01

This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a sy...

On a Generalized Hankel Type Convolution of Generalized Functions

Indian Academy of Sciences (India)

Generalized Hankel type transformation; Parserval relation; generalized ... The classical generalized Hankel type convolution are defined and extended to a class of generalized functions. ... Proceedings – Mathematical Sciences | News.

Mathematics and biology

International Nuclear Information System (INIS)

Khan, I.A.

1991-06-01

In India and in so many other countries, the science students are generally separated into two main streams: one opting mathematical sciences, the other studying biological sciences. As a result, medicos and biologists have no adequate knowledge of mathematical sciences. It causes a great drawback to them in order to be perfect and updated in their profession, due to the tremendous application of mathematics in bio-sciences, now-a-days. The main aim of this article is to emphasize on the need of the time to produce the mathematico-biologists in abundance for the better service of mankind. (author)

Game Design and Development as Mathematical Activities

DEFF Research Database (Denmark)

Jensen, Erik Ottar; Hanghøj, Thorkild; Misfeldt, Morten

2016-01-01

education which have mostly been tied to students making learning games involving specific mathematical content. Game design activities are reported to have a motivational pull for students. A challenge seems to be that the students are mostly motivated by the game design or the programming activities...... between user and goal through the computational artifacts being used. The framework serves as a lens for making sense of computer game design as a context for learning mathematics....

Subjective and Objective Assessment of Mathematics Anxiety Levels among College Students

OpenAIRE

Baloğlu, Mustafa

2015-01-01

The study investigated the relationship between college students’ subjective and objective assessment of mathematics anxiety levels. Students rated their general and current mathematics anxiety levels, mathematical ability levels, and confidence in doing mathematics. The Revised Mathematics Anxiety Rating Scale was used as an objective measure of their mathematics anxiety levels. Participants were 559 students, 406 (72.6%) women and 151 (27.0%) men. Results showed that perceived general mathe...

General System Theory: Toward a Conceptual Framework for Science and Technology Education for All.

Science.gov (United States)

Chen, David; Stroup, Walter

1993-01-01

Suggests using general system theory as a unifying theoretical framework for science and technology education for all. Five reasons are articulated: the multidisciplinary nature of systems theory, the ability to engage complexity, the capacity to describe system dynamics, the ability to represent the relationship between microlevel and…

Stirring the Pot: Supporting and Challenging General Education Science, Technology, Engineering, and Mathematics Faculty to Change Teaching and Assessment Practice

Science.gov (United States)

Stieha, Vicki; Shadle, Susan E.; Paterson, Sharon

2016-01-01

Evidence-based instructional practices (ebips) have been associated with positive student outcomes; however, institutions struggle to catalyze widespread adoption of these practices in general education science, technology, engineering, and mathematics (stem) courses. Further, linking ebips with integrated learning assessment is rarely discussed…

Using fuzzy mathematics for decision making in economics

Directory of Open Access Journals (Sweden)

Pavkov Ivan

2012-01-01

Full Text Available Traditionally, economic models are based on classical mathematics and Aristotelian two-valued logic. Nevertheless, fuzzy mathematics, as a tool for modeling some types of uncertainties and incomplete phenomena, is a more appropriate framework for modeling in economics. New approach has resulted in approximate reasoning and fuzzy control systems, which proved to be an efficient tool for decision making in fuzzy environment.

Rethinking the mathematics curriculum

CERN Document Server

Hoyles, Celia; Woodhouse, Geoffrey

1998-01-01

At a time when political interest in mathematics education is at its highest, this book demonstrates that the issues are far from straightforward. A wide range of international contributors address such questions as: What is mathematics, and what is it for? What skills does mathematics education need to provide as technology advances? What are the implications for teacher education? What can we learn from past attempts to change the mathematics curriculum? Rethinking the Mathematics Curriculum offers stimulating discussions, showing much is to be learnt from the differences in culture, national expectations, and political restraints revealed in the book. This accessible book will be of particular interest to policy makers, curriculum developers, educators, researchers and employers as well as the general reader.

MATHEMATICAL MODEL MANIPULATOR ROBOTS

Directory of Open Access Journals (Sweden)

O. N. Krakhmalev

2015-12-01

Full Text Available A mathematical model to describe the dynamics of manipulator robots. Mathematical model are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical model make it possible to determine the elastic deviations of manipulator robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. Mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by model are compared to the example of a two-link manipulator system. The considered model can be used when performing investigations of the mathematical accuracy of the manipulator robots.

Mathematical modeling of biological processes

CERN Document Server

Friedman, Avner

2014-01-01

This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.

Profile of mathematics anxiety of 7th graders

Science.gov (United States)

Udil, Patrisius Afrisno; Kusmayadi, Tri Atmojo; Riyadi

2017-08-01

Mathematics anxiety is one of the important factors affect students mathematics achievement. This present research investigates profile of students' mathematics anxiety. This research focuses on analysis and description of students' mathematics anxiety level generally and its dominant domain and aspect. Qualitative research with case study strategy was used in this research. Subject in this research involved 15 students of 7th grade chosen with purposive sampling. Data in this research were students' mathematics anxiety scale result, interview record, and observation result during both mathematics learning activity and test. They were asked to complete mathematics anxiety scale before interviewed and observed. The results show that generally students' mathematics anxiety was identified in the moderate level. In addition, students' mathematics anxiety during mathematics test was identified in the high level, but it was in the moderate level during mathematics learning process. Based on the anxiety domain, students have a high mathematics anxiety on cognitive domain, while it was in the moderate level for psychological and physiological domains. On the other hand, it was identified in low level for psychological domain during mathematics learning process. Therefore, it can be concluded that students have serious and high anxiety regarding mathematics on the cognitive domain and mathematics test aspect.

Realizing rigor in the mathematics classroom

CERN Document Server

Hull, Ted H (Henry); Balka, Don S

2014-01-01

Rigor put within reach! Rigor: The Common Core has made it policy-and this first-of-its-kind guide takes math teachers and leaders through the process of making it reality. Using the Proficiency Matrix as a framework, the authors offer proven strategies and practical tools for successful implementation of the CCSS mathematical practices-with rigor as a central objective. You'll learn how to Define rigor in the context of each mathematical practice Identify and overcome potential issues, including differentiating instruction and using data

Mathematical tapas

CERN Document Server

Hiriart-Urruty, Jean-Baptiste

This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something interesting, challenge the reader to solve and learn, and may have surprising results. This first volume of Mathematical Tapas will appeal to mathematicians, motivated undergraduate students from science-based areas, and those generally interested in mathematics.

A mathematical modelling framework for linked within-host and between-host dynamics for infections with free-living pathogens in the environment.

Science.gov (United States)

Garira, Winston; Mathebula, Dephney; Netshikweta, Rendani

2014-10-01

In this study we develop a mathematical modelling framework for linking the within-host and between-host dynamics of infections with free-living pathogens in the environment. The resulting linked models are sometimes called immuno-epidemiological models. However, there is still no generalised framework for linking the within-host and between-host dynamics of infectious diseases. Furthermore, for infections with free-living pathogens in the environment, there is an additional stumbling block in that there is a gap in knowledge on how environmental factors (through water, air, soil, food, fomites, etc.) alter many aspects of such infections including susceptibility to infective dose, persistence of infection, pathogen shedding and severity of the disease. In this work, we link the two subsystems (within-host and between-host models) by identifying the within-host and between-host variables and parameters associated with the environmental dynamics of the pathogen and then design a feedback of the variables and parameters across the within-host and between-host models using human schistosomiasis as a case study. We study the mathematical properties of the linked model and show that the model is epidemiologically well-posed. Using results from the analysis of the endemic equilibrium expression, the disease reproductive number R0, and numerical simulations of the full model, we adequately account for the reciprocal influence of the linked within-host and between-host models. In particular, we illustrate that for human schistosomiasis, the outcome of infection at the individual level determines if, when and how much the individual host will further transmit the infectious agent into the environment, eventually affecting the spread of the infection in the host population. We expect the conceptual modelling framework developed here to be applicable to many infectious disease with free-living pathogens in the environment beyond the specific disease system of human

Mathematics for Maths Anxious Tertiary Students: Integrating the cognitive and affective domains using interactive multimedia

Directory of Open Access Journals (Sweden)

Janet Taylor

2011-04-01

Full Text Available Today, commencing university students come from a diversity of backgrounds and have a broad range of abilities and attitudes. It is well known that attitudes towards mathematics, especially mathematics anxiety, can affect students’ performance to the extent that mathematics is often seen as a barrier to success by many. This paper reports on the design, development and evaluation of an interactive multimedia resource designed to explicitly address students’ beliefs and attitudes towards mathematics by following five characters as they progress through the highs and low of studying a preparatory mathematics course. The resource was built within two theoretical frameworks, one related to effective numeracy teaching (Marr and Helme 1991 and the other related to effective educational technology development (Laurillard 2002. Further, it uses a number of multimedia alternatives (video, audio, animations, diarying, interactive examples and self assessment to encourage students to feel part of a group, to reflect on their feelings and beliefs about mathematics, to expose students to authentic problem solving and generally build confidence through practice and self-assessment. Evaluation of the resource indicated that it encouraged students to value their own mathematical ability and helped to build confidence, while developing mathematical problem solving skills. The evaluation clearly demonstrated that it is possible to address the affective domain through multimedia initiatives and that this can complement the current focus on computer mediated communication as the primary method of addressing affective goals within the online environment.

On Mathematical Anti-Evolutionism

Science.gov (United States)

Rosenhouse, Jason

2016-03-01

The teaching of evolution in American high schools has long been a source of controversy. The past decade has seen an important shift in the rhetoric of anti-evolutionists, toward arguments of a strongly mathematical character. These mathematical arguments, while different in their specifics, follow the same general program and rely on the same underlying model of evolution. We shall discuss the nature and history of this program and model and describe general reasons for skepticism with regard to any anti-evolutionary arguments based upon them. We shall then survey the major arguments used by anti-evolutionists, to show how our general considerations make it possible to quickly identify their weakest points.

Cognitive correlates of performance in advanced mathematics.

Science.gov (United States)

Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

2012-03-01

Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.

Visual Representations in Mathematics Teaching: An Experiment with Students

Science.gov (United States)

Debrenti, Edith

2015-01-01

General problem-solving skills are of central importance in school mathematics achievement. Word problems play an important role not just in mathematical education, but in general education as well. Meaningful learning and understanding are basic aspects of all kinds of learning and it is even more important in the case of learning mathematics. In…

A hypothetical history of Old Babylonian mathematics

DEFF Research Database (Denmark)

Høyrup, Jens

2012-01-01

Most general standard histories of mathematics speak indiscriminately of “Babylonian” mathematics, presenting together the mathematics of the Old Babylonian and the Seleucid period (respectively 2000–1600 and 300–100 BCE) and neglecting the rest. Specialist literature has always known...

Quantifying heterogeneity attributable to polythetic diagnostic criteria: theoretical framework and empirical application.

Science.gov (United States)

Olbert, Charles M; Gala, Gary J; Tupler, Larry A

2014-05-01

Heterogeneity within psychiatric disorders is both theoretically and practically problematic: For many disorders, it is possible for 2 individuals to share very few or even no symptoms in common yet share the same diagnosis. Polythetic diagnostic criteria have long been recognized to contribute to this heterogeneity, yet no unified theoretical understanding of the coherence of symptom criteria sets currently exists. A general framework for analyzing the logical and mathematical structure, coherence, and diversity of Diagnostic and Statistical Manual diagnostic categories (DSM-5 and DSM-IV-TR) is proposed, drawing from combinatorial mathematics, set theory, and information theory. Theoretical application of this framework to 18 diagnostic categories indicates that in most categories, 2 individuals with the same diagnosis may share no symptoms in common, and that any 2 theoretically possible symptom combinations will share on average less than half their symptoms. Application of this framework to 2 large empirical datasets indicates that patients who meet symptom criteria for major depressive disorder and posttraumatic stress disorder tend to share approximately three-fifths of symptoms in common. For both disorders in each of the datasets, pairs of individuals who shared no common symptoms were observed. Any 2 individuals with either diagnosis were unlikely to exhibit identical symptomatology. The theoretical and empirical results stemming from this approach have substantive implications for etiological research into, and measurement of, psychiatric disorders.

Mathematics Teaching as Problem Solving: A Framework for Studying Teacher Metacognition Underlying Instructional Practice in Mathematics.

Science.gov (United States)

Artzt, Alice F.; Armour-Thomas, Eleanor

1998-01-01

Uses a "teaching as problem solving" perspective to examine the components of metacognition underlying the instructional practice of seven experienced and seven beginning secondary-school mathematics teachers. Data analysis of observations, lesson plans, videotapes, and audiotapes of structured interviews suggests that the metacognition of…

Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory

CERN Document Server

Yushkevich, A

1992-01-01

This multi-authored effort, Mathematics of the nineteenth century (to be fol­ lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics fram antiquity to the early nineteenth century, published in three 1 volumes from 1970 to 1972. For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as weIl. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend...

LIMES Large Infrastructure in Mathematics - Enhanced Services

CERN Document Server

Fachinformationszentrum Energie, Physik, Mathematik. Karlsruhe

The Large Infrastructure in Mathematics - Enhanced Services (LIMES) Project is a RTD project within the Fifth (EC) Framework Programme - Horizontal Programme "Improving human research potential and the socio-economic knowledge base", Access to Resear The objective of this project is to upgrade the existing database Zentralblatt-MATH into a European based world class database for mathematics (pure and applied) by a process of technical improvement and wide Europeanisation, improving the present distribuited system. The goal is to make Zentralblatt MATH a world reference database, offering full coverage of the mathematics literature worldwide ncluding bibliographic data, peer reviews and/or abstracts, indexing, classification and search,

A general CFD framework for fault-resilient simulations based on multi-resolution information fusion

Science.gov (United States)

Lee, Seungjoon; Kevrekidis, Ioannis G.; Karniadakis, George Em

2017-10-01

We develop a general CFD framework for multi-resolution simulations to target multiscale problems but also resilience in exascale simulations, where faulty processors may lead to gappy, in space-time, simulated fields. We combine approximation theory and domain decomposition together with statistical learning techniques, e.g. coKriging, to estimate boundary conditions and minimize communications by performing independent parallel runs. To demonstrate this new simulation approach, we consider two benchmark problems. First, we solve the heat equation (a) on a small number of spatial "patches" distributed across the domain, simulated by finite differences at fine resolution and (b) on the entire domain simulated at very low resolution, thus fusing multi-resolution models to obtain the final answer. Second, we simulate the flow in a lid-driven cavity in an analogous fashion, by fusing finite difference solutions obtained with fine and low resolution assuming gappy data sets. We investigate the influence of various parameters for this framework, including the correlation kernel, the size of a buffer employed in estimating boundary conditions, the coarseness of the resolution of auxiliary data, and the communication frequency across different patches in fusing the information at different resolution levels. In addition to its robustness and resilience, the new framework can be employed to generalize previous multiscale approaches involving heterogeneous discretizations or even fundamentally different flow descriptions, e.g. in continuum-atomistic simulations.

The Relevance of Mathematics: Leaders and Teachers as Gatekeeper for Queensland Senior Calculus Mathematics

Science.gov (United States)

Easey, Michael; Gleeson, Jim

2016-01-01

The aim of the larger study, of which this paper is a part, is to investigate the decline in Year 10 male students' participation in senior calculus mathematics courses at an independent boys' school located in metropolitan Queensland. This paper draws on Sealey and Noyes's (2010) relevance framework to conduct document analysis and interviews…

A generalized adjoint framework for sensitivity and global error estimation in time-dependent nuclear reactor simulations

International Nuclear Information System (INIS)

Stripling, H.F.; Anitescu, M.; Adams, M.L.

2013-01-01

Highlights: ► We develop an abstract framework for computing the adjoint to the neutron/nuclide burnup equations posed as a system of differential algebraic equations. ► We validate use of the adjoint for computing both sensitivity to uncertain inputs and for estimating global time discretization error. ► Flexibility of the framework is leveraged to add heat transfer physics and compute its adjoint without a reformulation of the adjoint system. ► Such flexibility is crucial for high performance computing applications. -- Abstract: We develop a general framework for computing the adjoint variable to nuclear engineering problems governed by a set of differential–algebraic equations (DAEs). The nuclear engineering community has a rich history of developing and applying adjoints for sensitivity calculations; many such formulations, however, are specific to a certain set of equations, variables, or solution techniques. Any change or addition to the physics model would require a reformulation of the adjoint problem and substantial difficulties in its software implementation. In this work we propose an abstract framework that allows for the modification and expansion of the governing equations, leverages the existing theory of adjoint formulation for DAEs, and results in adjoint equations that can be used to efficiently compute sensitivities for parametric uncertainty quantification. Moreover, as we justify theoretically and demonstrate numerically, the same framework can be used to estimate global time discretization error. We first motivate the framework and show that the coupled Bateman and transport equations, which govern the time-dependent neutronic behavior of a nuclear reactor, may be formulated as a DAE system with a power constraint. We then use a variational approach to develop the parameter-dependent adjoint framework and apply existing theory to give formulations for sensitivity and global time discretization error estimates using the adjoint

MONTO: A Machine-Readable Ontology for Teaching Word Problems in Mathematics

Science.gov (United States)

Lalingkar, Aparna; Ramnathan, Chandrashekar; Ramani, Srinivasan

2015-01-01

The Indian National Curriculum Framework has as one of its objectives the development of mathematical thinking and problem solving ability. However, recent studies conducted in Indian metros have expressed concern about students' mathematics learning. Except in some private coaching academies, regular classroom teaching does not include problem…

Quantitative Literacy at Michigan State University, 3: Designing General Education Mathematics Courses

Directory of Open Access Journals (Sweden)

Samuel L. Tunstall

2016-07-01

Full Text Available In this paper, we describe the process at Michigan State University whereby we have created two courses, Math 101 and 102, designed to foster numeracy and alleviate mathematics anxiety. The courses--which are not sequential--provide a means of satisfying the University's general education requirement without taking college algebra or calculus, among other options. They are context-driven and broken into modules such as "The World and Its People" and "Health and Risk." They have been highly successful thus far, with students providing positive feedback on their interest in the material and the utility they see of it in their daily lives. We include background on the courses' history, their current status, and present and future challenges, ending with suggestions for others as they attempt to implement quantitative literacy courses at their own institution.

General existence principles for Stieltjes differential equations with applications to mathematical biology

Science.gov (United States)

López Pouso, Rodrigo; Márquez Albés, Ignacio

2018-04-01

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper.

A Framework for Generalized Conjugate Gradient Methods - with Special Emphasis on Contributions by Rüdiger Weiss

Czech Academy of Sciences Publication Activity Database

Gutknecht, M. H.; Rozložník, Miroslav

2002-01-01

Roč. 41, - (2002), s. 7-22 ISSN 0168-9274 R&D Projects: GA AV ČR IAA1030103; GA ČR GA101/00/1035 Institutional research plan: AV0Z1030915 Keywords : sparse linear systems * Krylov space method * orthogonal residual method * minimal residual method * conjugate gradient method * residual smoothing * CG * CGNE * CGNR * CR * FOM * GMRES * PRES Subject RIV: BA - General Mathematics Impact factor: 0.504, year: 2002

Mathematical Models of Breast and Ovarian Cancers

Science.gov (United States)

Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron

2016-01-01

Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, since answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible, in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. PMID:27259061

Development of Mathematics Learning Strategy Module, Based on Higher Order Thinking Skill (Hots) To Improve Mathematic Communication And Self Efficacy On Students Mathematics Department

Science.gov (United States)

Andriani, Ade; Dewi, Izwita; Halomoan, Budi

2018-03-01

In general, this research is conducted to improve the quality of lectures on mathematics learning strategy in Mathematics Department. The specific objective of this research is to develop learning instrument of mathematics learning strategy based on Higher Order Thinking Skill (HOTS) that can be used to improve mathematical communication and self efficacy of mathematics education students. The type of research is development research (Research & Development), where this research aims to develop a new product or improve the product that has been made. This development research refers to the four-D Model, which consists of four stages: defining, designing, developing, and disseminating. The instrument of this research is the validation sheet and the student response sheet of the instrument.

Fractions Learning in Children With Mathematics Difficulties.

Science.gov (United States)

Tian, Jing; Siegler, Robert S

Learning fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of children with MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind their TA peers in fraction understanding and fall further behind during middle school. In contrast, Chinese children, who like the MD children in the United States score in the bottom one third of the distribution in their country, possess reasonably good fraction understanding. We interpret these findings within the framework of the integrated theory of numerical development. By emphasizing the importance of fraction magnitude knowledge for numerical understanding in general, the theory proved useful for understanding differences in fraction knowledge between MD and TA children and for understanding how knowledge can be improved. Several interventions demonstrated the possibility of improving fraction magnitude knowledge and producing benefits that generalize to fraction arithmetic learning among children with MD. The reasonably good fraction understanding of Chinese children with MD and several successful interventions with U.S. students provide hope for the improvement of fraction knowledge among American children with MD.

Description of a comprehensive mathematical model

DEFF Research Database (Denmark)

Li, Xiyan; Yin, Chungen

2017-01-01

Biomass gasification is still a promising technology after over 30 years’ research and development and has success only in a few niche markets. In this paper, a comprehensive mathematical model for biomass particle gasification is developed within a generic particle framework, assuming the feed...

A Bayesian framework for parameter estimation in dynamical models.

Directory of Open Access Journals (Sweden)

Flávio Codeço Coelho

Full Text Available Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.

Mathematical models in radiogeochronology

International Nuclear Information System (INIS)

Abril, J.M.; Garcia Leon, M.

1991-01-01

The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)

Generalization of Einstein's gravitational field equations

International Nuclear Information System (INIS)

Moulin, Frederic

2017-01-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)

Generalization of Einstein's gravitational field equations

Energy Technology Data Exchange (ETDEWEB)

Moulin, Frederic [Ecole Normale Superieure Paris-Saclay, Departement de Physique, Cachan (France)

2017-12-15

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)

Feasibility Study of a Generalized Framework for Developing Computer-Aided Detection Systems-a New Paradigm.

Science.gov (United States)

Nemoto, Mitsutaka; Hayashi, Naoto; Hanaoka, Shouhei; Nomura, Yukihiro; Miki, Soichiro; Yoshikawa, Takeharu

2017-10-01

We propose a generalized framework for developing computer-aided detection (CADe) systems whose characteristics depend only on those of the training dataset. The purpose of this study is to show the feasibility of the framework. Two different CADe systems were experimentally developed by a prototype of the framework, but with different training datasets. The CADe systems include four components; preprocessing, candidate area extraction, candidate detection, and candidate classification. Four pretrained algorithms with dedicated optimization/setting methods corresponding to the respective components were prepared in advance. The pretrained algorithms were sequentially trained in the order of processing of the components. In this study, two different datasets, brain MRA with cerebral aneurysms and chest CT with lung nodules, were collected to develop two different types of CADe systems in the framework. The performances of the developed CADe systems were evaluated by threefold cross-validation. The CADe systems for detecting cerebral aneurysms in brain MRAs and for detecting lung nodules in chest CTs were successfully developed using the respective datasets. The framework was shown to be feasible by the successful development of the two different types of CADe systems. The feasibility of this framework shows promise for a new paradigm in the development of CADe systems: development of CADe systems without any lesion specific algorithm designing.

Establishing a mathematical Lesson Study culture in Danish teacher education

DEFF Research Database (Denmark)

Skott, Charlotte Krog; Østergaard, Camilla Hellsten

Bridging theory and practice is a general challenge in mathematics teacher education. Research shows that Lesson Study (LS) is an effective way for prospective mathematics teachers to build relations between course work and field experiences......Bridging theory and practice is a general challenge in mathematics teacher education. Research shows that Lesson Study (LS) is an effective way for prospective mathematics teachers to build relations between course work and field experiences...

Mathematical aspects of field quantization. Quantum electrodynamics

International Nuclear Information System (INIS)

Bongaarts, P.J.M.

1983-01-01

Fundamental mathematical aspects of quantum field theory are discussed. A brief review of various approaches to mathematical problems of quantum electrodynamics is given, preceded by a more extensive account of the development of ideas on the mathematical nature of quantum fields in general, providing an appropriate historical context. (author)

A general framework for sensor-based human activity recognition.

Science.gov (United States)

Köping, Lukas; Shirahama, Kimiaki; Grzegorzek, Marcin

2018-04-01

Today's wearable devices like smartphones, smartwatches and intelligent glasses collect a large amount of data from their built-in sensors like accelerometers and gyroscopes. These data can be used to identify a person's current activity and in turn can be utilised for applications in the field of personal fitness assistants or elderly care. However, developing such systems is subject to certain restrictions: (i) since more and more new sensors will be available in the future, activity recognition systems should be able to integrate these new sensors with a small amount of manual effort and (ii) such systems should avoid high acquisition costs for computational power. We propose a general framework that achieves an effective data integration based on the following two characteristics: Firstly, a smartphone is used to gather and temporally store data from different sensors and transfer these data to a central server. Thus, various sensors can be integrated into the system as long as they have programming interfaces to communicate with the smartphone. The second characteristic is a codebook-based feature learning approach that can encode data from each sensor into an effective feature vector only by tuning a few intuitive parameters. In the experiments, the framework is realised as a real-time activity recognition system that integrates eight sensors from a smartphone, smartwatch and smartglasses, and its effectiveness is validated from different perspectives such as accuracies, sensor combinations and sampling rates. Copyright © 2018 Elsevier Ltd. All rights reserved.

Mathematical Sciences Institute Workshop

CERN Document Server

Scott, Philip

1990-01-01

A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions ...

A history of mathematics

CERN Document Server

Boyer, Carl B

1989-01-01

"Boyer and Merzbach distill thousands of years of mathematics into this fascinating chronicle. From the Greeks to Godel, the mathematics is brilliant; the cast of characters is distinguished; the ebb and flow of ideas is everywhere evident. And, while tracing the development of European mathematics, the authors do not overlook the contributions of Chinese, Indian, and Arabic civilizations. Without doubt, this is--and will long remain--a classic one-volume history of mathematics and mathematicians who create it." --William Dunham Author, Journey Through Genius, The Great Theorems of Mathematics "When we read a book like A History of Mathematics, we get the picture of a mounting structure, ever taller and broader and more beautiful and magnificent--and with a foundation, moreover, that is as untainted and as functional now as it was when Thales worked out the first geometrical theorems nearly 26 centuries ago." --From the Foreword by Isaac Asimov "One of the most useful and comprehensive general introductions t...

Translation Accommodations Framework for Testing English Language Learners in Mathematics

Science.gov (United States)

Solano-Flores, Guillermo

2012-01-01

The present framework is developed under contract with the Smarter Balanced Assessment Consortium (SBAC) as a conceptual and methodological tool for guiding the reasonings and actions of contractors in charge of developing and providing test translation accommodations for English language learners. The framework addresses important challenges in…

Integrating Universal Design and Response to Intervention in Methods Courses for General Education Mathematics Teachers

Science.gov (United States)

Buchheister, Kelley; Jackson, Christa; Taylor, Cynthia E.

2014-01-01

Traditionally, teacher education programs have placed little emphasis on preparing mathematics teachers to work with students who struggle in mathematics. Therefore, it is crucial that mathematics teacher educators explicitly prepare prospective teachers to instruct students who struggle with mathematics by providing strategies and practices that…

A Graphical User Interface to Generalized Linear Models in MATLAB

Directory of Open Access Journals (Sweden)

Peter Dunn

1999-07-01

Full Text Available Generalized linear models unite a wide variety of statistical models in a common theoretical framework. This paper discusses GLMLAB-software that enables such models to be fitted in the popular mathematical package MATLAB. It provides a graphical user interface to the powerful MATLAB computational engine to produce a program that is easy to use but with many features, including offsets, prior weights and user-defined distributions and link functions. MATLAB's graphical capacities are also utilized in providing a number of simple residual diagnostic plots.

Adapting the Mathematical Task Framework to Design Online Didactic Objects

Science.gov (United States)

Bowers, Janet; Bezuk, Nadine; Aguilar, Karen

2011-01-01

Designing didactic objects involves imagining how students can conceive of specific mathematical topics and then imagining what types of classroom discussions could support these mental constructions. This study investigated whether it was possible to design Java applets that might serve as didactic objects to support online learning where…

Where is the bigger picture in the teaching and learning of mathematics?

Directory of Open Access Journals (Sweden)

Satsope Maoto

2016-11-01

Full Text Available This article presents an interpretive analysis of three different mathematics teaching cases to establish where the bigger picture should lie in the teaching and learning of mathematics. We use pre-existing data collected through pre-observation and post-observation interviews and passive classroom observation undertaken by the third author in two different Grade 11 classes taught by two different teachers at one high school. Another set of data was collected through participant observation of the second author’s Year 2 University class. We analyse the presence or absence of the bigger picture, especially, in the teachers’ questioning strategies and their approach to content, guided by Tall’s framework of three worlds of mathematics, namely the ‘conceptual-embodied’ world, the ‘proceptual-symbolic’ world and the ‘axiomatic-formal’ world. Within this broad framework we acknowledge Pirie and Kieren’s notion of folding back towards the attainment of an axiomatic-formal world. We argue that the teaching and learning of mathematics should remain anchored in the bigger picture and, in that way, mathematics is meaningful, accessible, expandable and transferable.

Calculating observables in inhomogeneous cosmologies. Part I: general framework

Science.gov (United States)

Hellaby, Charles; Walters, Anthony

2018-02-01

We lay out a general framework for calculating the variation of a set of cosmological observables, down the past null cone of an arbitrarily placed observer, in a given arbitrary inhomogeneous metric. The observables include redshift, proper motions, area distance and redshift-space density. Of particular interest are observables that are zero in the spherically symmetric case, such as proper motions. The algorithm is based on the null geodesic equation and the geodesic deviation equation, and it is tailored to creating a practical numerical implementation. The algorithm provides a method for tracking which light rays connect moving objects to the observer at successive times. Our algorithm is applied to the particular case of the Szekeres metric. A numerical implementation has been created and some results will be presented in a subsequent paper. Future work will explore the range of possibilities.

Parallel Boltzmann machines : a mathematical model

NARCIS (Netherlands)

Zwietering, P.J.; Aarts, E.H.L.

1991-01-01

A mathematical model is presented for the description of parallel Boltzmann machines. The framework is based on the theory of Markov chains and combines a number of previously known results into one generic model. It is argued that parallel Boltzmann machines maximize a function consisting of a

Irish Mathematics Teachers' Attitudes towards Inclusion

Science.gov (United States)

Whitty, Elaine; Clarke, Marie

2012-01-01

This paper through the theoretical framework of constructive attitude theory explores mathematics teachers' attitudes and pedagogical strategies with reference to inclusive practice. The authors argue that though teachers may have formed positive inclusive attitudes, the translation of these into practice does not always occur and poses…

Abstract Radio Resource Management Framework for System Level Simulations in LTE-A Systems

DEFF Research Database (Denmark)

Fotiadis, Panagiotis; Viering, Ingo; Zanier, Paolo

2014-01-01

This paper provides a simple mathematical model of different packet scheduling policies in Long Term Evolution- Advanced (LTE-A) systems, by investigating the performance of Proportional Fair (PF) and the generalized cross-Component Carrier scheduler from a theoretical perspective. For that purpose......, an abstract Radio Resource Management (RRM) framework has been developed and tested for different ratios of users with Carrier Aggregation (CA) capabilities. The conducted system level simulations confirm that the proposed model can satisfactorily capture the main properties of the aforementioned scheduling...

(m,n-Semirings and a Generalized Fault-Tolerance Algebra of Systems

Directory of Open Access Journals (Sweden)

Syed Eqbal Alam

2013-01-01

Full Text Available We propose a new class of mathematical structures called (m,n-semirings (which generalize the usual semirings and describe their basic properties. We define partial ordering and generalize the concepts of congruence, homomorphism, and so forth, for (m,n-semirings. Following earlier work by Rao (2008, we consider systems made up of several components whose failures may cause them to fail and represent the set of such systems algebraically as an (m,n-semiring. Based on the characteristics of these components, we present a formalism to compare the fault-tolerance behavior of two systems using our framework of a partially ordered (m,n-semiring.

Mathematics-Literacy Checklists: A Pedagogical Innovation to Support Teachers as They Implement the Common Core

Science.gov (United States)

del Prado Hill, Pixita; Friedland, Ellen S.; McMillen, Susan

2016-01-01

This article presents two innovative tools--the Mathematics-Literacy Planning Framework and Mathematics-Literacy Implementation Checklist--which are designed to help instructional coaches and specialists support teachers to meet the challenges of the mathematics-literacy integration goals of the Common Core. Developed with teacher input, these…

Evaluating and optimizing the operation of the hydropower system in the Upper Yellow River: A general LINGO-based integrated framework

Science.gov (United States)

Si, Yuan; Liu, Ronghua; Wei, Jiahua; Huang, Yuefei; Li, Tiejian; Liu, Jiahong; Gu, Shenglong; Wang, Guangqian

2018-01-01

The hydropower system in the Upper Yellow River (UYR), one of the largest hydropower bases in China, plays a vital role in the energy structure of the Qinghai Power Grid. Due to management difficulties, there is still considerable room for improvement in the joint operation of this system. This paper presents a general LINGO-based integrated framework to study the operation of the UYR hydropower system. The framework is easy to use for operators with little experience in mathematical modeling, takes full advantage of LINGO’s capabilities (such as its solving capacity and multi-threading ability), and packs its three layers (the user layer, the coordination layer, and the base layer) together into an integrated solution that is robust and efficient and represents an effective tool for data/scenario management and analysis. The framework is general and can be easily transferred to other hydropower systems with minimal effort, and it can be extended as the base layer is enriched. The multi-objective model that represents the trade-off between power quantity (i.e., maximum energy production) and power reliability (i.e., firm output) of hydropower operation has been formulated. With equivalent transformations, the optimization problem can be solved by the nonlinear programming (NLP) solvers embedded in the LINGO software, such as the General Solver, the Multi-start Solver, and the Global Solver. Both simulation and optimization are performed to verify the model’s accuracy and to evaluate the operation of the UYR hydropower system. A total of 13 hydropower plants currently in operation are involved, including two pivotal storage reservoirs on the Yellow River, which are the Longyangxia Reservoir and the Liujiaxia Reservoir. Historical hydrological data from multiple years (2000–2010) are provided as input to the model for analysis. The results are as follows. 1) Assuming that the reservoirs are all in operation (in fact, some reservoirs were not operational or did

Evaluating and optimizing the operation of the hydropower system in the Upper Yellow River: A general LINGO-based integrated framework.

Directory of Open Access Journals (Sweden)

Yuan Si

Full Text Available The hydropower system in the Upper Yellow River (UYR, one of the largest hydropower bases in China, plays a vital role in the energy structure of the Qinghai Power Grid. Due to management difficulties, there is still considerable room for improvement in the joint operation of this system. This paper presents a general LINGO-based integrated framework to study the operation of the UYR hydropower system. The framework is easy to use for operators with little experience in mathematical modeling, takes full advantage of LINGO's capabilities (such as its solving capacity and multi-threading ability, and packs its three layers (the user layer, the coordination layer, and the base layer together into an integrated solution that is robust and efficient and represents an effective tool for data/scenario management and analysis. The framework is general and can be easily transferred to other hydropower systems with minimal effort, and it can be extended as the base layer is enriched. The multi-objective model that represents the trade-off between power quantity (i.e., maximum energy production and power reliability (i.e., firm output of hydropower operation has been formulated. With equivalent transformations, the optimization problem can be solved by the nonlinear programming (NLP solvers embedded in the LINGO software, such as the General Solver, the Multi-start Solver, and the Global Solver. Both simulation and optimization are performed to verify the model's accuracy and to evaluate the operation of the UYR hydropower system. A total of 13 hydropower plants currently in operation are involved, including two pivotal storage reservoirs on the Yellow River, which are the Longyangxia Reservoir and the Liujiaxia Reservoir. Historical hydrological data from multiple years (2000-2010 are provided as input to the model for analysis. The results are as follows. 1 Assuming that the reservoirs are all in operation (in fact, some reservoirs were not operational

Mathematics Education in Singapore – An Insider’s Perspective

Directory of Open Access Journals (Sweden)

Berinderjeet Kaur

2014-07-01

Full Text Available Singapore’s Education System has evolved over time and so has Mathematics Education in Singapore. The present day School Mathematics Curricula can best be described as one that caters for the needs of every child in school. It is based on a framework that has mathematical problem solving as its primary focus. The developments from 1946 to 2012 that have shaped the present School Mathematics Curricula in Singapore are direct consequences of developments in the Education System of Singapore during the same period. The curriculum, teachers, leaners and the learning environment may be said to contribute towards Singapore’s performance in international benchmark studies such as TIMSS and PISA.

Mathematical Optimiation in Economics

CERN Document Server

De Finetti, Bruno

2011-01-01

Preface by B. de Finetti.- G.Th. Guilbaud: Les equilibres dans les modeles economiques.-H.W. Kuhn: Locational problems and mathematical programming.- M. Morishima: The multi-sectoral theory of economic growth.- B. Martos, J. Kornai: Experiments in Hungary with industry-wide and economy wide programming.- A. Prekopa: Probability distribution problems concerning stochastic programming problems.- R. Frisch: General principles and mathematical techniques of macroeconomic programming.

Optimization and mathematical modeling in computer architecture

CERN Document Server

Sankaralingam, Karu; Nowatzki, Tony

2013-01-01

In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t

15th International Congress on Mathematical Physics

CERN Document Server

New Trends in Mathematical Physics

2009-01-01

This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad ov...

Techtalk: Mobile Apps and College Mathematics

Science.gov (United States)

Hoang, Theresa V.; Caverly, David C.

2013-01-01

In this column, the authors discuss apps useful in developing mathematical reasoning. They place these into a theoretical framework, suggesting how they could be used in an instructional model such as the Algorithmic Instructional Technique (AIT) developed by Vasquez (2003). This model includes four stages: modeling, practice, transition, and…

Validity-Supporting Evidence of the Self-Efficacy for Teaching Mathematics Instrument

Science.gov (United States)

McGee, Jennifer R.; Wang, Chuang

2014-01-01

The purpose of this study is to provide evidence of reliability and validity of the Self-Efficacy for Teaching Mathematics Instrument (SETMI). Self-efficacy, as defined by Bandura, was the theoretical framework for the development of the instrument. The complex belief systems of mathematics teachers, as touted by Ernest provided insights into the…

Negative probability in the framework of combined probability

OpenAIRE

Burgin, Mark

2013-01-01

Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of conventional probability. So, it is natural that negative probability also has different axiomatic frameworks. In the previous publications (Burgin, 2009; 2010), negative probability was mathematically formalized and rigorously interpreted in the context of extende...

Explanation, Motivation and Question Posing Routines in University Mathematics Teachers' Pedagogical Discourse: A Commognitive Analysis

Science.gov (United States)

Viirman, Olov

2015-01-01

This paper investigates the teaching practices used by university mathematics teachers when lecturing, a topic within university mathematics education research which is gaining an increasing interest. In the study, a view of mathematics teaching as a discursive practice is taken, and Sfard's commognitive framework is used to investigate the…

Cognitive science and mathematics education

CERN Document Server

Schoenfeld, Alan H

1987-01-01

This volume is a result of mathematicians, cognitive scientists, mathematics educators, and classroom teachers combining their efforts to help address issues of importance to classroom instruction in mathematics. In so doing, the contributors provide a general introduction to fundamental ideas in cognitive science, plus an overview of cognitive theory and its direct implications for mathematics education. A practical, no-nonsense attempt to bring recent research within reach for practicing teachers, this book also raises many issues for cognitive researchers to consider.

Secondary Schools Curriculum Guide, Mathematics, Grades 10-12. Revised.

Science.gov (United States)

Cranston School Dept., RI.

Behavioral objectives for grades 10 through 12 are specified for plane geometry, algebra, general mathematics, computer mathematics, slide rule mathematics, basic college mathematics, trigonometry, analytic geometry, calculus and probability. Most sections present material in terms of portions of a school year. At least one major objective is…

Four (Algorithms) in One (Bag): An Integrative Framework of Knowledge for Teaching the Standard Algorithms of the Basic Arithmetic Operations

Science.gov (United States)

Raveh, Ira; Koichu, Boris; Peled, Irit; Zaslavsky, Orit

2016-01-01

In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic…

Testing general relativity with compact-body orbits: a modified Einstein–Infeld–Hoffmann framework

Science.gov (United States)

Will, Clifford M.

2018-04-01

We describe a general framework for analyzing orbits of systems containing compact objects (neutron stars or black holes) in a class of Lagrangian-based alternative theories of gravity that also admit a global preferred reference frame. The framework is based on a modified Einstein–Infeld–Hoffmann (EIH) formalism developed by Eardley and by Will, generalized to include the possibility of Lorentz-violating, preferred-frame effects. It uses a post-Newtonian N-body Lagrangian with arbitrary parameters that depend on the theory of gravity and on ‘sensitivities’ that encode the effects of the bodies’ internal structure on their motion. We determine the modified EIH parameters for the Einstein-Æther and Khronometric vector-tensor theories of gravity. We find the effects of motion relative to a preferred universal frame on the orbital parameters of binary systems containing neutron stars, such as a class of ultra-circular pulsar-white dwarf binaries; the amplitudes of the effects depend upon ‘strong-field’ preferred-frame parameters \\hatα1 and \\hatα2 , which we relate to the fundamental modified EIH parameters. We also determine the amplitude of the ‘Nordtvedt effect’ in a triple system containing the pulsar J0337+1715 in terms of the modified EIH parameters.

The contribution of general cognitive abilities and approximate number system to early mathematics.

Science.gov (United States)

Passolunghi, Maria Chiara; Cargnelutti, Elisa; Pastore, Massimiliano

2014-12-01

Math learning is a complex process that entails a wide range of cognitive abilities to be fulfilled. There is sufficient evidence that both general and specific cognitive skills assume a fundamental role, despite the absence of shared consensus about the relative extent of their involvement. Moreover, regarding general abilities, there is no agreement about the recruitment of the different memory components or of intelligence. In relation to specific factors, great debate subsists regarding the role of the approximate number system (ANS). Starting from these considerations, we wanted to conduct a wide assessment of memory components and ANS, by controlling for the effects associated with intelligence and also exploring possible relationships between all precursors. To achieve this purpose, a sample of 157 children was tested at both beginning and end of their Grade 1. Both general (memory and intelligence) and specific (ANS) precursors were evaluated by a wide battery of tests and put in relation to concurrent and subsequent math skills. Memory was explored in passive and active aspects involving both verbal and visuo-spatial components. Path analysis results demonstrated that memory, and especially the more active processes, and intelligence were the strongest precursors in both assessment times. ANS had a milder role which lost significance by the end of the school year. Memory and ANS seemed to influence early mathematics almost independently. Both general and specific precursors seemed to have a crucial role in early math competences, despite the lower involvement of ANS. © 2014 The British Psychological Society.

Patterns of motivation and emotion in mathematics classrooms

OpenAIRE

Lewis , Gareth

2015-01-01

International audience; A case is made that the study of state, as opposed to trait, is necessary to give a more rounded picture of affective aspects of students' experience of learning mathematics. This paper is based on a study of disaffection with school mathematics. The study was a primarily qualitative study conducted from a constructivist and interpre-tivist perspective, using Reversal Theory as the main design and interpretive framework. The paper reports findings of some patterns in t...

Generalized Garvan's formulas

Czech Academy of Sciences Publication Activity Database

Zuevsky, Alexander

2016-01-01

Roč. 8, č. 3 (2016), s. 225-231 ISSN 1942-5600 Institutional support: RVO:67985840 Keywords : modular discriminant * Fay's trisecant identities * modular forms Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics

Framework of synchromodal transportation problems

NARCIS (Netherlands)

Juncker, M.A.M. de; Huizing, D.; Vecchyo, M.R.O. del; Phillipson, F.; Sangers, A.

2017-01-01

Problem statements and solution methods in mathematical synchromodal transportation problems depend greatly on a set of model choices for which no rule of thumb exists. In this paper, a framework is introduced with which the model choices in synchromodal transportation problems can be classified,

Framework of Synchromodal Transportation Problems

NARCIS (Netherlands)

Huncker, M.A.M. de; Huizing, D.; Ortega del Vecchyo, M.R.; Phillipson, F.; Sangers, A.

2017-01-01

Problem statements and solution methods in mathematical synchromodal transportation problems depend greatly on a set of model choices for which no rule of thumb exists. In this paper, a framework is introduced with which the model choices in synchromodal transportation problems can be classified,

Developing a framework of, and quality indicators for, general practice management in Europe.

Science.gov (United States)

Engels, Yvonne; Campbell, Stephen; Dautzenberg, Maaike; van den Hombergh, Pieter; Brinkmann, Henrik; Szécsényi, Joachim; Falcoff, Hector; Seuntjens, Luc; Kuenzi, Beat; Grol, Richard

2005-04-01

To develop a framework for general practice management made up of quality indicators shared by six European countries. Two-round postal Delphi questionnaire in the setting of general practice in Belgium, France, Germany, The Netherlands, Switzerland and the United Kingdom. Six national expert panels, each consisting of 10 members, primarily primary care practitioners and experts in the field of quality in primary care participated in the study. The main outcome measures were: (a) a European framework with indicators for the organization of primary care; and (b) ratings of the face validity of the usefulness of the indicators by expert panels in six countries. Agreement was reached about a definition of practice management across five domains (infrastructure, staff, information, finance, and quality and safety), and a common set of indicators for the organization of general practice. The panellist response rate was 95%. Sixty-two indicators (37%) were rated face valid by all six panels. Examples include out of hours service, accessibility, the content of doctors' bags and staff involvement in quality improvement. No indicators were rated invalid by all six panels. It proved to be possible to develop a European set of indicators for assessing the quality of practice management, despite the differences in health care systems and cultures in the six different countries. These indicators will now be used in a quality assessment procedure of practice management in nine European countries. While organizational indicators are part of the new GMS contract in the UK, this research shows that many practice management issues within primary care are also of relevance in other European countries.

Coaching in Early Mathematics.

Science.gov (United States)

Germeroth, Carrie; Sarama, Julie

2017-01-01

Falling scores in math have prompted a renewed interest in math instruction at early ages. By their own admission, early childhood educators are generally underprepared and not always comfortable teaching math. Professional development (PD) in early mathematics is widely considered a main way to increase teachers' skills and efficacy (e.g., Guskey, 2000; Hyson & Woods, 2014; Munby, Russell, & Martin, 2001; Piasta, Logan, Pelatti, Capps, & Petrill, 2015; Richardson & Placier, 2001; Sarama, Clements, Wolfe, & Spitler, 2016; Sarama & DiBiase, 2004; Zaslow, 2014). However, it has been documented that stand-alone PD is not as effective in changing practice (e.g., Biancarosa & Bryk, 2011; Garet et al., 2008; Guskey, 2000; Hyson & Woods, 2014; Institute of Medicine and National Research Council, 2015; Joyce & Showers, 2002; Zaslow, 2014). Site-embedded ongoing support in the form of coaching or mentoring has been shown to be critical for successful implementation (Neuman & Cunningham, 2009; Powell, Diamond, Burchinal, & Koehler, 2010). In this chapter, we describe coaching models and abstract characteristics of effective coaching from the research. With this background, we provide an in-depth view of the coaching aspect of two large empirical studies in early mathematics. We introduce the theoretical framework from which the coaching models for these projects were developed and describe the research on which they were based. We then summarize how the planned models were instantiated and challenges to their implementation within each project. In the final section, we summarize what we have learned and described implications and challenges for the field. © 2017 Elsevier Inc. All rights reserved.

Images of Italian Mathematics in France from Risorgimento to Fascism

CERN Document Server

Jouve, Guillaume; Mazliak, Laurent; Tazzioli, Rossana

2016-01-01

The contributions in this proceedings volume offer a new perspective on the mathematical ties between France and Italy, and reveal how mathematical developments in these two countries affected one another. The focus is above all on the Peninsula’s influence on French mathematicians, counterbalancing the historically predominant perception that French mathematics was a model for Italian mathematicians. In the process, the book details a subtle network of relations between the two countries, where mathematical exchanges fit into the changing and evolving framework of Italian political and academic structures. It reconsiders the issue of nationalities in all of its complexity, an aspect often neglected in research on the history of mathematics. The works in this volume are selected contributions from a conference held in Lille and Lens (France) in November 2013 on Images of Italian Mathematics in France from Risorgimento to Fascism. The authors include respected historians of mathematics, philosophers of scien...

Early mathematics intervention in a Danish municipality

DEFF Research Database (Denmark)

Lindenskov, Lena; Weng, Peter

2013-01-01

We describe a pilot project 2009 – 2010 about early intervention in second grade mathematics (about 8 years old) in Frederiksberg, a Danish urban municipality. We shortly describe the background of the pilot project, aims and organisation in four design cycles. We explore the pilot teachers......' feedback during the pilot process, how pilot teacher feedback was applied in material production, and the relations between the feedback and the project’s theoretical basis. The project is based on original theory (Math Holes theory), but international frameworks, like Mathematics Recovery, serve...

How to Make Mathematical eContent Travel Well

OpenAIRE

Caprotti, Olga; Pauna, Matti; Seppälä, Mika

2009-01-01

Electronic content produced for education travels well when it can be reused across national borders and in different curricular frameworks. In this article, we discuss what features of mathematical e-content contribute to making it travel well.

Encouraging Students to Read Mathematics

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Shepherd, Mary D.

2005-01-01

It is generally agreed that the ability to read mathematics is an important skill--one that few of our students possess. A number of people have published some suggestions for helping students learn to read their mathematics textbooks. What these have in common is suggestions for getting students more active while reading. Using these resources as…

Mathematics for physicists

CERN Document Server

Dennery, Philippe

1967-01-01

""A fine example of how to present 'classical' physical mathematics."" - American ScientistWritten for advanced undergraduate and graduate students, this volume provides a thorough background in the mathematics needed to understand today's more advanced topics in physics and engineering. Without sacrificing rigor, the authors develop the theoretical material at length, in a highly readable, and, wherever possible, in an intuitive manner. Each abstract idea is accompanied by a very simple, concrete example, showing the student that the abstraction is merely a generalization from easily understo

On the complex interaction between mathematics and the sciences of living systems. Comment on "Move me, astonish me...delight my eyes and brain: The Vienna Integrated Model of top-down and bottom-up processes in Art Perception (VIMAP) and corresponding affective, evaluative, and neurophysiological correlates" by Matthew Pelowski et al.

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Bellomo, Nicola; Outada, Nisrine

2017-07-01

Cultural framework: Our comment looks at the general framework given by the interactions between the so-called ;soft; and ;hard; sciences. Specifically, it looks at the development of a mathematics for living systems. Our comment aims at showing how the interesting survey [11] can contribute to the aforementioned challenging task.

Mathematics of aperiodic order

CERN Document Server

Lenz, Daniel; Savinien, Jean

2015-01-01

What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomolog...

A general framework for thermodynamically consistent parameterization and efficient sampling of enzymatic reactions.

Directory of Open Access Journals (Sweden)

Pedro Saa

2015-04-01

Full Text Available Kinetic models provide the means to understand and predict the dynamic behaviour of enzymes upon different perturbations. Despite their obvious advantages, classical parameterizations require large amounts of data to fit their parameters. Particularly, enzymes displaying complex reaction and regulatory (allosteric mechanisms require a great number of parameters and are therefore often represented by approximate formulae, thereby facilitating the fitting but ignoring many real kinetic behaviours. Here, we show that full exploration of the plausible kinetic space for any enzyme can be achieved using sampling strategies provided a thermodynamically feasible parameterization is used. To this end, we developed a General Reaction Assembly and Sampling Platform (GRASP capable of consistently parameterizing and sampling accurate kinetic models using minimal reference data. The former integrates the generalized MWC model and the elementary reaction formalism. By formulating the appropriate thermodynamic constraints, our framework enables parameterization of any oligomeric enzyme kinetics without sacrificing complexity or using simplifying assumptions. This thermodynamically safe parameterization relies on the definition of a reference state upon which feasible parameter sets can be efficiently sampled. Uniform sampling of the kinetics space enabled dissecting enzyme catalysis and revealing the impact of thermodynamics on reaction kinetics. Our analysis distinguished three reaction elasticity regions for common biochemical reactions: a steep linear region (0> ΔGr >-2 kJ/mol, a transition region (-2> ΔGr >-20 kJ/mol and a constant elasticity region (ΔGr <-20 kJ/mol. We also applied this framework to model more complex kinetic behaviours such as the monomeric cooperativity of the mammalian glucokinase and the ultrasensitive response of the phosphoenolpyruvate carboxylase of Escherichia coli. In both cases, our approach described appropriately not only

The Mathematics of "Star Trek"--An Honors Colloquium

Science.gov (United States)

Karls, Michael A.

2011-01-01

After the success of a course on cryptography for a general audience, based on Simon Singh's "The Code Book" [49], I decided to try again and create a mathematics course for a general audience based on "The Physics of Star Trek" by Lawrence Krauss [32]. This article looks at the challenges of designing a physics-based mathematics course "from…

Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})

Energy Technology Data Exchange (ETDEWEB)

Roche, Ph., E-mail: philippe.roche@univ-montp2.fr [Université Montpellier 2, CNRS, L2C, IMAG, Montpellier (France)

2016-03-15

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

Commognitive Analysis of Undergraduate Mathematics Students' First Encounter with the Subgroup Test

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Ioannou, Marios

2018-01-01

This study analyses learning aspects of undergraduate mathematics students' first encounter with the subgroup test, using the commognitive theoretical framework. It focuses on students' difficulties as these are related to the object-level and metalevel mathematical learning in group theory, and, when possible, highlights any commognitive…

Foundational aspects of non standard mathematics

CERN Document Server

Ballard, David

1994-01-01

This work proposes a major new extension of "non"standard mathematics. Addressed to a general mathematical audience, the book is intended to be philosophically provocative. The model theory on which "non"standard mathematics has been based is first reformulated within point set topology, which facilitates proofs and adds perspective. These topological techniques are then used to give new, uniform conservativity proofs for the various versions of "non"standard mathematics proposed by Nelson, Hrbáček, and Kawai. The proofs allow for sharp comparison. Addressing broader issues, Ballard then argues that what is novel in these forms of "non"standard mathematics is the introduction, however tentative, of relativity in one's mathematical environment. This hints at the possibility of a mathematical environment which is radically relativistic. The work's major and final feature is to present and prove conservative a version of "non"standard mathematics which, for the first time, illustrates this full radical relativ...

A Mathematical Experience Involving Defining Processes: In-Action Definitions and Zero-Definitions

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Ouvrier-Buffet, Cecile

2011-01-01

In this paper, a focus is made on defining processes at stake in an unfamiliar situation coming from discrete mathematics which brings surprising mathematical results. The epistemological framework of Lakatos is questioned and used for the design and the analysis of the situation. The cognitive background of Vergnaud's approach enriches the study…

Developing a Framework of Outcomes for Mathematics Teacher Learning: Three Mathematics Educators Engage in Collaborative Self-Study

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Bahr, Damon L.; Monroe, Eula Ewing; Mantilla, Jodi

2018-01-01

This article synthesizes the literature on what it means to teach mathematics and science to ELLs and abstract from it a set of knowledge and skills teachers might need to teach ELLs effectively. To this end, the article brings together the sociocultural and linguistic perspectives identifying three areas of effective teaching practice. One…

Phenomenology and Mathematics

CERN Document Server

Hartimo, Mirja

2010-01-01

During Edmund Husserl,s lifetime, modern logic and mathematics rapidly developed toward their current outlook and Husserl,s writings can be fruitfully compared and contrasted with both 19th century figures (Boole, Schroder, Weierstrass) as well as the 20th century characters (Heyting, Zermelo, Godel). Besides the more historical studies, the internal ones on Husserl alone and the external ones attempting to clarify his role in the more general context of the developing mathematics and logic, Husserl,s phenomenology offers also a systematically rich but little researched area of investigation.

A Framework for Analyzing the Collaborative Construction of Arguments and Its Interplay with Agency

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Mueller, Mary; Yankelewitz, Dina; Maher, Carolyn

2012-01-01

In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem solving, we introduce three types of collaboration and…

TIMSS Advanced 2015 and Advanced Placement Calculus & Physics. A Framework Analysis. Research in Review 2016-1

Science.gov (United States)

Lazzaro, Christopher; Jones, Lee; Webb, David C.; Grover, Ryan; Di Giacomo, F. Tony; Marino, Katherine Adele

2016-01-01

This report will determine to what degree the AP Physics 1 and 2 and AP Calculus AB and BC frameworks are aligned with the Trends in International Mathematics and Science Study (TIMSS) Advanced Physics and Mathematics frameworks. This will enable an exploration of any differences in content coverage and levels of complexity, and will set the stage…

New generalized functions and multiplication of distributions

International Nuclear Information System (INIS)

Colombeau, J.F.

1984-01-01

Since its conception, Quantum Field Theory is based on 'heuristic' computations (in particular products of distributions) that, despite lots of effort, remained meaningless from a mathematical viewpoint. In this book the author presents a new mathematical theory giving a rigorous mathematical sense to these heuristic computations and, from a mathematical viewpoint, to all products of distributions. This new mathematical theory is a new theory of Generalized Functions defined on any open subset Ω of Rsup(n), which are much more general than the distributions on Ω. (Auth.)

Adaptation and extension of the framework of reducing abstraction in the case of differential equations

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Raychaudhuri, Debasree

2014-01-01

Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of reducing abstraction maps the abstract nature of mathematics to the nature of knowledge construction by offering three interpretations of how students reduce abstraction while learning mathematical concepts. We apply this framework to explain students' cognition processes as they construct the concept of solution to differential equations and related concepts during a semester long study. Additionally, we refine and extend the framework to elucidate various nuances of the interplay between mathematical structures and human thoughts.

Mathematics education, democracy and development: Exploring connections

Directory of Open Access Journals (Sweden)

Renuka Vithal

2012-12-01

Full Text Available Mathematics education and its links to democracy and development are explored in this article, with specific reference to the case of South Africa. This is done by engaging four key questions. Firstly, the question of whether mathematics education can be a preparation for democracy and include a concern for development, is discussed by drawing on conceptual tools of critical mathematics education and allied areas in a development context. Secondly, the question of how mathematics education is distributed in society and participates in shaping educational possibilities in addressing its development needs and goals is used to examine the issues emerging from mathematics performance in international studies and the national Grade 12 examination; the latter is explored specifically in respect of the South African mathematics curriculum reforms and teacher education challenges. Thirdly, the question of whether a mathematics classroom can be a space for democratic living and learning that equally recognises the importance of issues of development in contexts like South Africa, as a post-conflict society still healing from its apartheid wounds, continuing inequality and poverty, is explored through pedagogies of conflict, dialogue and forgiveness. Finally the question of whether democracy and development can have anything to do with mathematics content matters, is discussed by appropriating, as a metaphor, South Africa’s Truth and Reconciliation Commission’s framework of multiple ‘truths’, to seek links within and across the various forms and movements in mathematics and mathematics education that have emerged in the past few decades.

Toward a model framework of generalized parallel componential processing of multi-symbol numbers.

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Huber, Stefan; Cornelsen, Sonja; Moeller, Korbinian; Nuerk, Hans-Christoph

2015-05-01

In this article, we propose and evaluate a new model framework of parallel componential multi-symbol number processing, generalizing the idea of parallel componential processing of multi-digit numbers to the case of negative numbers by considering the polarity signs similar to single digits. In a first step, we evaluated this account by defining and investigating a sign-decade compatibility effect for the comparison of positive and negative numbers, which extends the unit-decade compatibility effect in 2-digit number processing. Then, we evaluated whether the model is capable of accounting for previous findings in negative number processing. In a magnitude comparison task, in which participants had to single out the larger of 2 integers, we observed a reliable sign-decade compatibility effect with prolonged reaction times for incompatible (e.g., -97 vs. +53; in which the number with the larger decade digit has the smaller, i.e., negative polarity sign) as compared with sign-decade compatible number pairs (e.g., -53 vs. +97). Moreover, an analysis of participants' eye fixation behavior corroborated our model of parallel componential processing of multi-symbol numbers. These results are discussed in light of concurrent theoretical notions about negative number processing. On the basis of the present results, we propose a generalized integrated model framework of parallel componential multi-symbol processing. (c) 2015 APA, all rights reserved).

Understanding Mathematics and Culture in Rural Contexts. ERIC Digest.

Science.gov (United States)

Bush, William S.

This ERIC Digest provides an overview of concepts, writers, and tenets associated with the study of mathematics and culture and offers researchers a framework for the field, particularly with regard to rural contexts. (Author)

International Conference on Quantum Mathematical Physics : a Bridge between Mathematics and Physics

CERN Document Server

Kleiner, Johannes; Röken, Christian; Tolksdorf, Jürgen

2016-01-01

Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fu...

Strengthening the Conceptualization of Mathematics Pedagogical Content Knowledge for International Studies: A Taiwanese Perspective

Science.gov (United States)

Hsieh, Feng-Jui

2013-01-01

This paper discusses different conceptual frameworks for measuring mathematics pedagogical content knowledge (MPCK) in international comparison studies. Two large-scale international comparative studies, "Mathematics Teaching in the Twenty-First Century" (MT21; Schmidt et al., 2011) and the "Teacher Education and Development Study…

Becoming a Reflective Mathematics Teacher: A Guide for Observations and Self-Assessment. Studies in Mathematical Thinking and Learning Series.

Science.gov (United States)

Artzt, Alice F.; Armour-Thomas, Eleanor

This activity-oriented book for preservice mathematics teachers who are taking methods courses or who have been student teaching offers a framework for teacher reflection and self- assessment. It supplies detailed observation instruments for observing other teachers, reflective activities, and guidelines and instruments for supervisors. There are…

A Cognitive Analysis of Students’ Mathematical Problem Solving Ability on Geometry

Science.gov (United States)

Rusyda, N. A.; Kusnandi, K.; Suhendra, S.

2017-09-01

The purpose of this research is to analyze of mathematical problem solving ability of students in one of secondary school on geometry. This research was conducted by using quantitative approach with descriptive method. Population in this research was all students of that school and the sample was twenty five students that was chosen by purposive sampling technique. Data of mathematical problem solving were collected through essay test. The results showed the percentage of achievement of mathematical problem solving indicators of students were: 1) solve closed mathematical problems with context in math was 50%; 2) solve the closed mathematical problems with the context beyond mathematics was 24%; 3) solving open mathematical problems with contexts in mathematics was 35%; And 4) solving open mathematical problems with contexts outside mathematics was 44%. Based on the percentage, it can be concluded that the level of achievement of mathematical problem solving ability in geometry still low. This is because students are not used to solving problems that measure mathematical problem solving ability, weaknesses remember previous knowledge, and lack of problem solving framework. So the students’ ability of mathematical problems solving need to be improved with implement appropriate learning strategy.

Framework for utilizing computational devices within simulation

Directory of Open Access Journals (Sweden)

Miroslav Mintál

2013-12-01

Full Text Available Nowadays there exist several frameworks to utilize a computation power of graphics cards and other computational devices such as FPGA, ARM and multi-core processors. The best known are either low-level and need a lot of controlling code or are bounded only to special graphic cards. Furthermore there exist more specialized frameworks, mainly aimed to the mathematic field. Described framework is adjusted to use in a multi-agent simulations. Here it provides an option to accelerate computations when preparing simulation and mainly to accelerate a computation of simulation itself.

A general framework for predicting delayed responses of ecological communities to habitat loss.

Science.gov (United States)

Chen, Youhua; Shen, Tsung-Jen

2017-04-20

Although biodiversity crisis at different spatial scales has been well recognised, the phenomena of extinction debt and immigration credit at a crossing-scale context are, at best, unclear. Based on two community patterns, regional species abundance distribution (SAD) and spatial abundance distribution (SAAD), Kitzes and Harte (2015) presented a macroecological framework for predicting post-disturbance delayed extinction patterns in the entire ecological community. In this study, we further expand this basic framework to predict diverse time-lagged effects of habitat destruction on local communities. Specifically, our generalisation of KH's model could address the questions that could not be answered previously: (1) How many species are subjected to delayed extinction in a local community when habitat is destructed in other areas? (2) How do rare or endemic species contribute to extinction debt or immigration credit of the local community? (3) How will species differ between two local areas? From the demonstrations using two SAD models (single-parameter lognormal and logseries), the predicted patterns of the debt, credit, and change in the fraction of unique species can vary, but with consistencies and depending on several factors. The general framework deepens the understanding of the theoretical effects of habitat loss on community dynamic patterns in local samples.

Using the Scientific Method to Engage Mathematical Modeling: An Investigation of pi

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Archer, Lester A. C.; Ng, Karen E.

2016-01-01

The purpose of this paper is to explain how to use the scientific method as the framework to introduce mathematical model. Two interdisciplinary activities, targeted for students in grade 6 or grade 7, are explained to show the application of the scientific method while building a mathematical model to investigate the relationship between the…

Modellus: Learning Physics with Mathematical Modelling

Science.gov (United States)

Teodoro, Vitor

Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations

A Regularized Linear Dynamical System Framework for Multivariate Time Series Analysis.

Science.gov (United States)

Liu, Zitao; Hauskrecht, Milos

2015-01-01

Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning Multivariate Time Series (MTS). However, in general, it is difficult to set the dimension of an LDS's hidden state space. A small number of hidden states may not be able to model the complexities of a MTS, while a large number of hidden states can lead to overfitting. In this paper, we study learning methods that impose various regularization penalties on the transition matrix of the LDS model and propose a regularized LDS learning framework (rLDS) which aims to (1) automatically shut down LDSs' spurious and unnecessary dimensions, and consequently, address the problem of choosing the optimal number of hidden states; (2) prevent the overfitting problem given a small amount of MTS data; and (3) support accurate MTS forecasting. To learn the regularized LDS from data we incorporate a second order cone program and a generalized gradient descent method into the Maximum a Posteriori framework and use Expectation Maximization to obtain a low-rank transition matrix of the LDS model. We propose two priors for modeling the matrix which lead to two instances of our rLDS. We show that our rLDS is able to recover well the intrinsic dimensionality of the time series dynamics and it improves the predictive performance when compared to baselines on both synthetic and real-world MTS datasets.

Uncovering Hidden Mathematics of the Multiplication Table Using Spreadsheets

Directory of Open Access Journals (Sweden)

Sergei Abramovich

2007-05-01

Full Text Available This paper reveals a number of learning activities emerging from a spreadsheetgenerated multiplication table. These activities are made possible by using such features of the software as conditional formatting, circular referencing, calculation through iteration, scroll bars, and graphing. The paper is a reflection on a mathematics content course designed for prospective elementary teachers using the hidden mathematics curriculum framework. It is written in support of standards for teaching and recommendations for teachers in North America.

Generalized Information Theory Meets Human Cognition: Introducing a Unified Framework to Model Uncertainty and Information Search.

Science.gov (United States)

Crupi, Vincenzo; Nelson, Jonathan D; Meder, Björn; Cevolani, Gustavo; Tentori, Katya

2018-06-17

Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people's goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty and the reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma-Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information-theoretic formalism. Copyright © 2018 Cognitive Science Society, Inc.

Mathematical methods in medicine: neuroscience, cardiology and pathology

Science.gov (United States)

Amigó, José M.

2017-01-01

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’. PMID:28507240

Mathematical methods in medicine: neuroscience, cardiology and pathology.

Science.gov (United States)

Amigó, José M; Small, Michael

2017-06-28

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'. © 2017 The Author(s).

Cognitive predictors of children's development in mathematics achievement: A latent growth modeling approach.

Science.gov (United States)

Xenidou-Dervou, Iro; Van Luit, Johannes E H; Kroesbergen, Evelyn H; Friso-van den Bos, Ilona; Jonkman, Lisa M; van der Schoot, Menno; van Lieshout, Ernest C D M

2018-04-24

Research has identified various domain-general and domain-specific cognitive abilities as predictors of children's individual differences in mathematics achievement. However, research into the predictors of children's individual growth rates, namely between-person differences in within-person change in mathematics achievement is scarce. We assessed 334 children's domain-general and mathematics-specific early cognitive abilities and their general mathematics achievement longitudinally across four time-points within the first and second grades of primary school. As expected, a constellation of multiple cognitive abilities contributed to the children's starting level of mathematical success. Specifically, latent growth modeling revealed that WM abilities, IQ, counting skills, nonsymbolic and symbolic approximate arithmetic and comparison skills explained individual differences in the children's initial status on a curriculum-based general mathematics achievement test. Surprisingly, however, only one out of all the assessed cognitive abilities was a unique predictor of the children's individual growth rates in mathematics achievement: their performance in the symbolic approximate addition task. In this task, children were asked to estimate the sum of two large numbers and decide if this estimated sum was smaller or larger compared to a third number. Our findings demonstrate the importance of multiple domain-general and mathematics-specific cognitive skills for identifying children at risk of struggling with mathematics and highlight the significance of early approximate arithmetic skills for the development of one's mathematical success. We argue the need for more research focus on explaining children's individual growth rates in mathematics achievement. © 2018 John Wiley & Sons Ltd.

Provisional Approaches to Goals for School Mathematics; Cambridge Conference on School Mathematics Feasibility Study No. 37.

Science.gov (United States)

Cambridge Conference on School Mathematics, Newton, MA.

These materials were written with the aim of reflecting the thinking of Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics K-6. In view of the experiences of other curriculum groups and of the general discussions since 1963, the present report initiates the next step in evolving the "Goals".…

Tutorium quantum mechanics. By an experienced tutor for students of physics and mathematics. 2. ed.

International Nuclear Information System (INIS)

Schwindt, Jan-Markus

2016-01-01

The focus of this book lies on the general postulates of quantum mechanics (QM), their interpretation, their fundamental terms, and their mathematical formulation. The first and most comprehensive part of the book is dedicated to this thematics. In the second part an imported special case is treated: The QM of the wave functions in one, two, and three spatial dimensions under the condition, that the Hamiltonian operator consists only of the kinetic term and a timely independent potential. The most important examples hereby are the harmonic oscillator and the hydrogen atom. Also the scattering theory is discussed in this framework. The third part comprehends further themes, which belong to the canonical matter of a QM course: Combination of spin and angular momentum, QM with electromagnetism, perturbation theory, and systems with several particles. Rounded off is the whole by a short explanation of the path-integral term and by the relativistic theory of the electron (Dirac equation). Target group of this book are students of physics, who hear QM in the framework of theoretical physics. By the axiomatically deductive approach and the detailed discussion of the mathematical background it is also very well suited for mathematicians, who want to come to an understanding of QM in the subsidiary subject or in their leisure time.

A Framework for Assessing Reading Comprehension of Geometric Construction Texts

Science.gov (United States)

Yang, Kai-Lin; Li, Jian-Lin

2018-01-01

This study investigates one issue related to reading mathematical texts by presenting a two-dimensional framework for assessing reading comprehension of geometric construction texts. The two dimensions of the framework were formulated by modifying categories of reading literacy and drawing on key elements of geometric construction texts. Three…

Mathematical modelling : a tool for hospital infection control

NARCIS (Netherlands)

Grundmann, H; Hellriegel, B

Health-care-associated infections caused by antibiotic-resistant pathogens have become a menace in hospitals worldwide and infection control measures have lead to vastly different outcomes in different countries. During the past 6 years, a theoretical framework based on mathematical models has

Mathematical modelling: a tool for hospital infection control

NARCIS (Netherlands)

Grundmann, Hajo; Hellriegel, B.

2006-01-01

Health-care-associated infections caused by antibiotic-resistant pathogens have become a menace in hospitals worldwide and infection control measures have lead to vastly different outcomes in different countries. During the past 6 years, a theoretical framework based on mathematical models has

Mathematical modelling: a tool for hospital infection control.

NARCIS (Netherlands)

Grundmann, Hajo; Hellriegel, B

2006-01-01

Health-care-associated infections caused by antibiotic-resistant pathogens have become a menace in hospitals worldwide and infection control measures have lead to vastly different outcomes in different countries. During the past 6 years, a theoretical framework based on mathematical models has

Quantum mechanics as applied mathematical statistics

International Nuclear Information System (INIS)

Skala, L.; Cizek, J.; Kapsa, V.

2011-01-01

Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

Open problems in mathematical physics

Science.gov (United States)

Coley, Alan A.

2017-09-01

We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment (Allen and Lidstrom 2017 Phys. Scr. 92 012501). But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that.

Early predictors of high school mathematics achievement.

Science.gov (United States)

Siegler, Robert S; Duncan, Greg J; Davis-Kean, Pamela E; Duckworth, Kathryn; Claessens, Amy; Engel, Mimi; Susperreguy, Maria Ines; Chen, Meichu

2012-07-01

Identifying the types of mathematics content knowledge that are most predictive of students' long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students' knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students' knowledge of fractions and of division uniquely predicts those students' knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed.

Generalized nuclear Fukui functions in the framework of spin-polarized density-functional theory

International Nuclear Information System (INIS)

Chamorro, E.; Proft, F. de; Geerlings, P.

2005-01-01

An extension of Cohen's nuclear Fukui function is presented in the spin-polarized framework of density-functional theory (SP-DFT). The resulting new nuclear Fukui function indices Φ Nα and Φ Sα are intended to be the natural descriptors for the responses of the nuclei to changes involving charge transfer at constant multiplicity and also the spin polarization at constant number of electrons. These generalized quantities allow us to gain new insights within a perturbative scheme based on DFT. Calculations of the electronic and nuclear SP-DFT quantities are presented within a Kohn-Sham framework of chemical reactivity for a sample of molecules, including H 2 O, H 2 CO, and some simple nitrenes (NX) and phosphinidenes (PX), with X=H, Li, F, Cl, OH, SH, NH 2 , and PH 2 . Results have been interpreted in terms of chemical bonding in the context of Berlin's theorem, which provides a separation of the molecular space into binding and antibinding regions

Theoretical numerical analysis a functional analysis framework

CERN Document Server

Atkinson, Kendall

2005-01-01

This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solu

A flexible framework for process-based hydraulic and water ...

Science.gov (United States)

Background Models that allow for design considerations of green infrastructure (GI) practices to control stormwater runoff and associated contaminants have received considerable attention in recent years. While popular, generally, the GI models are relatively simplistic. However, GI model predictions are being relied upon by many municipalities and State/Local agencies to make decisions about grey vs. green infrastructure improvement planning. Adding complexity to GI modeling frameworks may preclude their use in simpler urban planning situations. Therefore, the goal here was to develop a sophisticated, yet flexible tool that could be used by design engineers and researchers to capture and explore the effect of design factors and properties of the media used in the performance of GI systems at a relatively small scale. We deemed it essential to have a flexible GI modeling tool that is capable of simulating GI system components and specific biophysical processes affecting contaminants such as reactions, and particle-associated transport accurately while maintaining a high degree of flexibly to account for the myriad of GI alternatives. The mathematical framework for a stand-alone GI performance assessment tool has been developed and will be demonstrated.Framework Features The process-based model framework developed here can be used to model a diverse range of GI practices such as green roof, retention pond, bioretention, infiltration trench, permeable pavement and

Examining Individual and Collective Level Mathematical Progress

Science.gov (United States)

Rasmussen, Chris; Wawro, Megan; Zandieh, Michelle

2015-01-01

A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. We contribute to these efforts by expanding the constructs in Cobb and Yackel's (Educational Psychologist 31:175-190, 1996) interpretive framework that allow for coordinating social and individual…

IGCSE core mathematics

CERN Document Server

Wall, Terry

2013-01-01

Give your core level students the support and framework they require to get their best grades with this book dedicated to the core level content of the revised syllabus and written specifically to ensure a more appropriate pace. This title has been written for Core content of the revised Cambridge IGCSE Mathematics (0580) syllabus for first teaching from 2013. ? Gives students the practice they require to deepen their understanding through plenty of practice questions. ? Consolidates learning with unique digital resources on the CD, included free with every book. We are working with Cambridge

General relativity and mathematics; Relatividad General y Matematicas

Energy Technology Data Exchange (ETDEWEB)

Mars, M.

2015-07-01

General relativity is more than a theory of gravity, since any physical process occupies space and lasts for a time, forcing to reconcile that physical theory that describes what the dynamic nature of space-time itself. (Author)

Mathematics for physical chemistry

CERN Document Server

Mortimer, Robert G

2005-01-01

Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data.* Numerous examples and problems interspersed throughout the presentations * Each extensive chapter contains a preview, objectives, and ...

Inevitable randomness in discrete mathematics

CERN Document Server

Beck, Jozsef

2009-01-01

Mathematics has been called the science of order. The subject is remarkably good for generalizing specific cases to create abstract theories. However, mathematics has little to say when faced with highly complex systems, where disorder reigns. This disorder can be found in pure mathematical arenas, such as the distribution of primes, the 3n+1 conjecture, and class field theory. The purpose of this book is to provide examples--and rigorous proofs--of the complexity law: (1) discrete systems are either simple or they exhibit advanced pseudorandomness; (2) a priori probabilities often exist even when there is no intrinsic symmetry. Part of the difficulty in achieving this purpose is in trying to clarify these vague statements. The examples turn out to be fascinating instances of deep or mysterious results in number theory and combinatorics. This book considers randomness and complexity. The traditional approach to complexity--computational complexity theory--is to study very general complexity classes, such as P...

Towards quantum gravity: a framework for probabilistic theories with non-fixed causal structure

International Nuclear Information System (INIS)

Hardy, Lucien

2007-01-01

General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper, we build a framework for probabilistic theories with non-fixed causal structure. This combines the radical elements of general relativity and quantum theory. We adopt an operational methodology for the purposes of theory construction (though without committing to operationalism as a fundamental philosophy). The key idea in the construction is physical compression. A physical theory relates quantities. Thus, if we specify a sufficiently large set of quantities (this is the compressed set), we can calculate all the others. We apply three levels of physical compression. First, we apply it locally to quantities (actually probabilities) that might be measured in a particular region of spacetime. Then we consider composite regions. We find that there is a second level of physical compression for a composite region over and above the first level physical compression for the component regions. Each application of first and second level physical compression is quantified by a matrix. We find that these matrices themselves are related by the physical theory and can therefore be subject to compression. This is the third level of physical compression. The third level of physical compression gives rise to a new mathematical object which we call the causaloid. From the causaloid for a particular physical theory we can calculate everything the physical theory can calculate. This approach allows us to set up a framework for calculating probabilistic correlations in data without imposing a fixed causal structure (such as a background time). We show how to put quantum theory in this framework (thus providing a new formulation of this theory). We indicate how general relativity might be put into this framework and how the framework might be used to construct a theory of quantum gravity

The integration of DVH-based planning aspects into a convex intensity modulated radiation therapy optimization framework

International Nuclear Information System (INIS)

Kratt, Karin; Scherrer, Alexander

2009-01-01

The formulation of intensity modulated radiation therapy (IMRT) planning aspects frequently uses the dose-volume histogram (DVH), whereas plan computations often happen in the more desirable convex IMRT optimization framework. Inspired by a recent publication of Zinchenko et al (2008 Phys. Med. Biol. 53 3231-50), this work addresses the integration of DVH-based planning aspects into this framework from a general point of view. It first provides the basic mathematical requirements on the evaluation functions in order to support such an incorporation. Then it introduces the condition number as a description for how precisely DVH-based planning aspects can be reformulated in terms of evaluation functions. Exemplary numerical studies for the generalized equivalent uniform dose and a physical constraint function show the influence of function parameter values and DVH approximation on the condition number. The work concludes by formulating the aspects that should be taken into account for an appropriate integration of DVH-based planning aspects. (note)

The integration of DVH-based planning aspects into a convex intensity modulated radiation therapy optimization framework

Energy Technology Data Exchange (ETDEWEB)

Kratt, Karin [Faculty of Mathematics, Technical University of Kaiserslautern, Kaiserslautern (Germany); Scherrer, Alexander [Department of Optimization, Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern (Germany)], E-mail: alexander.scherrer@itwm.fraunhofer.de

2009-06-21

The formulation of intensity modulated radiation therapy (IMRT) planning aspects frequently uses the dose-volume histogram (DVH), whereas plan computations often happen in the more desirable convex IMRT optimization framework. Inspired by a recent publication of Zinchenko et al (2008 Phys. Med. Biol. 53 3231-50), this work addresses the integration of DVH-based planning aspects into this framework from a general point of view. It first provides the basic mathematical requirements on the evaluation functions in order to support such an incorporation. Then it introduces the condition number as a description for how precisely DVH-based planning aspects can be reformulated in terms of evaluation functions. Exemplary numerical studies for the generalized equivalent uniform dose and a physical constraint function show the influence of function parameter values and DVH approximation on the condition number. The work concludes by formulating the aspects that should be taken into account for an appropriate integration of DVH-based planning aspects. (note)

Generalized Framework and Algorithms for Illustrative Visualization of Time-Varying Data on Unstructured Meshes

Energy Technology Data Exchange (ETDEWEB)

Alexander S. Rattner; Donna Post Guillen; Alark Joshi

2012-12-01

Photo- and physically-realistic techniques are often insufficient for visualization of simulation results, especially for 3D and time-varying datasets. Substantial research efforts have been dedicated to the development of non-photorealistic and illustration-inspired visualization techniques for compact and intuitive presentation of such complex datasets. While these efforts have yielded valuable visualization results, a great deal of work has been reproduced in studies as individual research groups often develop purpose-built platforms. Additionally, interoperability between illustrative visualization software is limited due to specialized processing and rendering architectures employed in different studies. In this investigation, a generalized framework for illustrative visualization is proposed, and implemented in marmotViz, a ParaView plugin, enabling its use on variety of computing platforms with various data file formats and mesh geometries. Detailed descriptions of the region-of-interest identification and feature-tracking algorithms incorporated into this tool are provided. Additionally, implementations of multiple illustrative effect algorithms are presented to demonstrate the use and flexibility of this framework. By providing a framework and useful underlying functionality, the marmotViz tool can act as a springboard for future research in the field of illustrative visualization.

Modelling Mathematical Reasoning in Physics Education

Science.gov (United States)

Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

2012-04-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Mathematical Methods of Managing Economic Sustainability of the Construction Company

Science.gov (United States)

Kostuchenko, Vasiliy; Zdanov, Andrej; Rodionov, Anatolij

2017-10-01

This article presents a long-term research in developing innovative mathematical techniques of managing the contractor’s economic sustainability proven by some experimental studies. The article aims at presenting some practical results of applying these techniques to the scientific community. This research presents a description of some applied mathematical models, views, and some results of their practical application in the applied field for the purposes of evaluating operational sustainability and minimizing losses in the process of managing the company. The authors have put the technology they have developed to practical use, and the article presents the results of such application. The authors have put the developed technology to practical use. Company management also means the management of power consumption, which is highly vital both for the construction and maintenance of buildings and structures. The articles also dwell on some possible improvements of managing energy consumption within the framework of the general management of company’s economic sustainability, because these phenomena have a tight organic interdependence. The authors continue researching this direction in order to improve the production efficiency of the proposed technologies as well as to eliminate some drawbacks they have spotted.

Market valuation in the framework of modern life insurance mathematics

OpenAIRE

Petrač, Maja

2013-01-01

In the traditional actuarial life insurance mathematics, liabilities to beneficiaries (technical reserves) are calculated based on conservative assumptions of mortality and interest rates. However, this approach was found to be incomplete since it does not contain the market component which has become essential due to the development of the financial market. Since about 80% of total liabilities of life insurance companies are made up of technical reserves, this issue has a major i...

Basic notions in mathematics: On the "graph" in particular and on ontology in general

NARCIS (Netherlands)

Hoede, C.

2003-01-01

This paper contains material presented on 31 January 2002 to staff and students of the Department of Mathematics of the University of Utrecht. The talk was one in a series of lectures titled Basic Notions in Mathematics.

Bio mathematical aspects of chronic cardiac electric stimulation

International Nuclear Information System (INIS)

Suarez Antola, R

1984-01-01

In the framework a mathematical model of the electrode-tissue system new several concepts are introduced(global versus local threshold variables,critical region for electric stimulation,mechanical hysteresis amongst others) several well known facts are explained,and some guidelines for electrode design are derived

A framework for grouping nanoparticles based on their measurable characteristics.

Science.gov (United States)

Sayes, Christie M; Smith, P Alex; Ivanov, Ivan V

2013-01-01

There is a need to take a broader look at nanotoxicological studies. Eventually, the field will demand that some generalizations be made. To begin to address this issue, we posed a question: are metal colloids on the nanometer-size scale a homogeneous group? In general, most people can agree that the physicochemical properties of nanomaterials can be linked and related to their induced toxicological responses. The focus of this study was to determine how a set of selected physicochemical properties of five specific metal-based colloidal materials on the nanometer-size scale - silver, copper, nickel, iron, and zinc - could be used as nanodescriptors that facilitate the grouping of these metal-based colloids. The example of the framework pipeline processing provided in this paper shows the utility of specific statistical and pattern recognition techniques in grouping nanoparticles based on experimental data about their physicochemical properties. Interestingly, the results of the analyses suggest that a seemingly homogeneous group of nanoparticles could be separated into sub-groups depending on interdependencies observed in their nanodescriptors. These particles represent an important category of nanomaterials that are currently mass produced. Each has been reputed to induce toxicological and/or cytotoxicological effects. Here, we propose an experimental methodology coupled with mathematical and statistical modeling that can serve as a prototype for a rigorous framework that aids in the ability to group nanomaterials together and to facilitate the subsequent analysis of trends in data based on quantitative modeling of nanoparticle-specific structure-activity relationships. The computational part of the proposed framework is rather general and can be applied to other groups of nanomaterials as well.

Values in the Mathematics Classroom: Supporting Cognitive and Affective Pedagogical Ideas

Science.gov (United States)

Seah, Wee Tiong

2016-01-01

Values are the personal convictions which one finds important. Three different aspects which are associated with mathematics education differently are identified, namely, values through mathematics education, values of mathematics education, and values for mathematics. These are paired with Bishop's (1996) conceptions of general educational,…

Entering into dialogue about the mathematical value of contextual mathematising tasks

Science.gov (United States)

Yoon, Caroline; Chin, Sze Looi; Moala, John Griffith; Choy, Ban Heng

2018-03-01

Our project seeks to draw attention to the rich mathematical thinking that is generated when students work on contextual mathematising tasks. We use a design-based research approach to create ways of reporting that raise the visibility of this rich mathematical thinking while retaining and respecting its complexity. These reports will be aimed for three classroom stakeholders: (1) students, who wish to reflect on and enhance their mathematical learning; (2) teachers, who wish to integrate contextual mathematising tasks into their teaching practice and (3) researchers, who seek rich tasks for generating observable instances of mathematical thinking and learning. We anticipate that these reports and the underlying theoretical framework for creating them will contribute to greater awareness of and appreciation for the mathematical value of contextual mathematising tasks in learning, teaching and research.

Towards the Construction of a Framework to Deal with Routine Problems to Foster Mathematical Inquiry

Science.gov (United States)

Santos-Trigo, Manuel; Camacho-Machin, Matias

2009-01-01

To what extent does the process of solving textbook problems help students develop a way of thinking that is consistent with mathematical practice? Can routine problems be transformed into problem solving activities that promote students' mathematical reflection? These questions are used to outline and discuss features of an inquiry framework…

Selected aspects of proposed new EU general data protection legal framework and the Croatian perspective

Directory of Open Access Journals (Sweden)

Nina GUMZEJ

2013-12-01

Full Text Available Proposed new EU general data protection legal framework profoundly affects a large number of day-to-day business operations of organizations processing personal data and calls for significant effort on their part toward the necessary legal-regulatory compliance. In this paper the author examines key legislative developments towards this new EU frame and impact for the Republic of Croatia as the youngest EU Member State. Following introductory overview, legal analysis of draft EU General Data Protection Regulation as proposed by the European Commission and recently adopted amendments by the European Parliament mainly focuses on selected solutions impacting national data protection supervisory authorities. This is complemented with examination of relevant sources of EU law, including the case law of the Court of Justice of the European Union. Assessment of results of this research is next made with respect to prospects of the data protection legal framework of the Republic of Croatia. The paper is concluded with the author’s critical overview of analyzed EU proposals impacting national data protection supervisory authorities in light of EU pivotal goals, and de lege ferenda proposals to timely address identified obstacles towards more adequate enforcement of data protection legislation in Croatia.

Pedagogical Applications from Real Analysis for Secondary Mathematics Teachers

Science.gov (United States)

Wasserman, Nicholas; Weber, Keith

2017-01-01

In this article, we consider the potential influences of the study of proofs in advanced mathematics on secondary mathematics teaching. Thus far, the literature has highlighted the benefits of applying the conclusions of particular proofs to secondary content and of developing a more general sense of disciplinary practices in mathematics in…

Open problems in mathematical physics

International Nuclear Information System (INIS)

Coley, Alan A

2017-01-01

We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment (Allen and Lidstrom 2017 Phys. Scr . 92 012501). But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that. (invited comment)

A Theoretical Framework for Soft-Information-Based Synchronization in Iterative (Turbo Receivers

Directory of Open Access Journals (Sweden)

Lottici Vincenzo

2005-01-01

Full Text Available This contribution considers turbo synchronization, that is to say, the use of soft data information to estimate parameters like carrier phase, frequency, or timing offsets of a modulated signal within an iterative data demodulator. In turbo synchronization, the receiver exploits the soft decisions computed at each turbo decoding iteration to provide a reliable estimate of some signal parameters. The aim of our paper is to show that such "turbo-estimation" approach can be regarded as a special case of the expectation-maximization (EM algorithm. This leads to a general theoretical framework for turbo synchronization that allows to derive parameter estimation procedures for carrier phase and frequency offset, as well as for timing offset and signal amplitude. The proposed mathematical framework is illustrated by simulation results reported for the particular case of carrier phase and frequency offsets estimation of a turbo-coded 16-QAM signal.

Mathematical Footprints Discovering Mathematics Everywhere

CERN Document Server

Pappas, Theoni

1999-01-01

MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent

Nuclear medicine and mathematics

Energy Technology Data Exchange (ETDEWEB)

Pedroso de Lima, J.J. [Dept. de Biofisica e Proc. de Imagem, IBILI - Faculdade de Medicina, Coimbra (Portugal)

1996-06-01

The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new `allies` of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)

Nuclear medicine and mathematics

International Nuclear Information System (INIS)

Pedroso de Lima, J.J.

1996-01-01

The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new 'allies' of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)

Activity Theory as a framework for understanding teachers ...

African Journals Online (AJOL)

Erna Kinsey

framework for understanding how teachers use technology to mediate the teaching and learning of mathematics in primary ... soon appeared to disadvantage the very students it was constructed to ..... in school D the minority speak English.

A general framework for implementing NLO calculations in shower Monte Carlo programs. The POWHEG BOX

Energy Technology Data Exchange (ETDEWEB)

Alioli, Simone [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Nason, Paolo [INFN, Milano-Bicocca (Italy); Oleari, Carlo [INFN, Milano-Bicocca (Italy); Milano-Bicocca Univ. (Italy); Re, Emanuele [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomenology

2010-02-15

In this work we illustrate the POWHEG BOX, a general computer code framework for implementing NLO calculations in shower Monte Carlo programs according to the POWHEG method. Aim of this work is to provide an illustration of the needed theoretical ingredients, a view of how the code is organized and a description of what a user should provide in order to use it. (orig.)

A general framework for implementing NLO calculations in shower Monte Carlo programs. The POWHEG BOX

International Nuclear Information System (INIS)

Alioli, Simone; Nason, Paolo; Oleari, Carlo; Re, Emanuele

2010-02-01

In this work we illustrate the POWHEG BOX, a general computer code framework for implementing NLO calculations in shower Monte Carlo programs according to the POWHEG method. Aim of this work is to provide an illustration of the needed theoretical ingredients, a view of how the code is organized and a description of what a user should provide in order to use it. (orig.)

Investigations in Pure Mathematics: A Constructivist Perspective.

Science.gov (United States)

Hirst, Keith; Shiu, Christine

1995-01-01

Discusses an investigative, constructivist approach in the context of undergraduate mathematics, with particular reference to pure mathematics, general aims and objectives, assessment strategies, and problems of supervision that affect tutors and lecturers using this approach. Gives students' views on their experiences in this mode of working. (19…

Mathematical modelling of scour: A review

DEFF Research Database (Denmark)

Sumer, B. Mutlu

2007-01-01

A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...

Mathematical Modeling Approaches in Plant Metabolomics.

Science.gov (United States)

Fürtauer, Lisa; Weiszmann, Jakob; Weckwerth, Wolfram; Nägele, Thomas

2018-01-01

The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

Fractal geometry mathematical foundations and applications

CERN Document Server

Falconer, Kenneth

2013-01-01

The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals.  The book introduces and develops the general theory and applica

Tasks that May Occasion Mathematical Creativity: Teachers' Choices

Science.gov (United States)

Levenson, Esther

2013-01-01

Promoting mathematical creativity is one of the aims of mathematics education. This study investigates the tasks teachers chose when their aim was to occasion mathematical creativity in the classroom. Five cases are described in depth, and general trends found among these cases as well as in additional data are discussed. Findings indicated that…

Mathematical foundations of biomechanics.

Science.gov (United States)

Niederer, Peter F

2010-01-01

The aim of biomechanics is the analysis of the structure and function of humans, animals, and plants by means of the methods of mechanics. Its foundations are in particular embedded in mathematics, physics, and informatics. Due to the inherent multidisciplinary character deriving from its aim, biomechanics has numerous connections and overlapping areas with biology, biochemistry, physiology, and pathophysiology, along with clinical medicine, so its range is enormously wide. This treatise is mainly meant to serve as an introduction and overview for readers and students who intend to acquire a basic understanding of the mathematical principles and mechanics that constitute the foundation of biomechanics; accordingly, its contents are limited to basic theoretical principles of general validity and long-range significance. Selected examples are included that are representative for the problems treated in biomechanics. Although ultimate mathematical generality is not in the foreground, an attempt is made to derive the theory from basic principles. A concise and systematic formulation is thereby intended with the aim that the reader is provided with a working knowledge. It is assumed that he or she is familiar with the principles of calculus, vector analysis, and linear algebra.

The ABCs of Math: A Genetic Analysis of Mathematics and Its Links With Reading Ability and General Cognitive Ability

Science.gov (United States)

Hart, Sara A.; Petrill, Stephen A.; Thompson, Lee A.; Plomin, Robert

2009-01-01

The goal of this first major report from the Western Reserve Reading Project Math component is to explore the etiology of the relationship among tester-administered measures of mathematics ability, reading ability, and general cognitive ability. Data are available on 314 pairs of monozygotic and same-sex dizygotic twins analyzed across 5 waves of assessment. Univariate analyses provide a range of estimates of genetic (h2 = .00 –.63) and shared (c2 = .15–.52) environmental influences across math calculation, fluency, and problem solving measures. Multivariate analyses indicate genetic overlap between math problem solving with general cognitive ability and reading decoding, whereas math fluency shares significant genetic overlap with reading fluency and general cognitive ability. Further, math fluency has unique genetic influences. In general, math ability has shared environmental overlap with general cognitive ability and decoding. These results indicate that aspects of math that include problem solving have different genetic and environmental influences than math calculation. Moreover, math fluency, a timed measure of calculation, is the only measured math ability with unique genetic influences. PMID:20157630

The mathematical formula of the intravaginal ejaculation latency time (IELT distribution of lifelong premature ejaculation differs from the IELT distribution formula of men in the general male population

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Paddy K.C. Janssen

2016-03-01

Full Text Available Purpose: To find the most accurate mathematical description of the intravaginal ejaculation latency time (IELT distribution in the general male population. Materials and Methods: We compared the fitness of various well-known mathematical distributions with the IELT distribution of two previously published stopwatch studies of the Caucasian general male population and a stopwatch study of Dutch Caucasian men with lifelong premature ejaculation (PE. The accuracy of fitness is expressed by the Goodness of Fit (GOF. The smaller the GOF, the more accurate is the fitness. Results: The 3 IELT distributions are gamma distributions, but the IELT distribution of lifelong PE is another gamma distribution than the IELT distribution of men in the general male population. The Lognormal distribution of the gamma distributions most accurately fits the IELT distribution of 965 men in the general population, with a GOF of 0.057. The Gumbel Max distribution most accurately fits the IELT distribution of 110 men with lifelong PE with a GOF of 0.179. There are more men with lifelong PE ejaculating within 30 and 60 seconds than can be extrapolated from the probability density curve of the Lognormal IELT distribution of men in the general population. Conclusions: Men with lifelong PE have a distinct IELT distribution, e.g., a Gumbel Max IELT distribution, that can only be retrieved from the general male population Lognormal IELT distribution when thousands of men would participate in a IELT stopwatch study. The mathematical formula of the Lognormal IELT distribution is useful for epidemiological research of the IELT.

The mathematical formula of the intravaginal ejaculation latency time (IELT) distribution of lifelong premature ejaculation differs from the IELT distribution formula of men in the general male population

Science.gov (United States)

Janssen, Paddy K.C.

2016-01-01

Purpose To find the most accurate mathematical description of the intravaginal ejaculation latency time (IELT) distribution in the general male population. Materials and Methods We compared the fitness of various well-known mathematical distributions with the IELT distribution of two previously published stopwatch studies of the Caucasian general male population and a stopwatch study of Dutch Caucasian men with lifelong premature ejaculation (PE). The accuracy of fitness is expressed by the Goodness of Fit (GOF). The smaller the GOF, the more accurate is the fitness. Results The 3 IELT distributions are gamma distributions, but the IELT distribution of lifelong PE is another gamma distribution than the IELT distribution of men in the general male population. The Lognormal distribution of the gamma distributions most accurately fits the IELT distribution of 965 men in the general population, with a GOF of 0.057. The Gumbel Max distribution most accurately fits the IELT distribution of 110 men with lifelong PE with a GOF of 0.179. There are more men with lifelong PE ejaculating within 30 and 60 seconds than can be extrapolated from the probability density curve of the Lognormal IELT distribution of men in the general population. Conclusions Men with lifelong PE have a distinct IELT distribution, e.g., a Gumbel Max IELT distribution, that can only be retrieved from the general male population Lognormal IELT distribution when thousands of men would participate in a IELT stopwatch study. The mathematical formula of the Lognormal IELT distribution is useful for epidemiological research of the IELT. PMID:26981594

El mundo matemático digital: el proyecto WDML (World Digital Mathematics Library

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Macías Virgós, Enrique

2007-06-01

Full Text Available We describe the digitization process of the mathematical literature in the framework of the projects WDML and DML-E.Describimos el proceso de digitalización de la literatura matemática de investigación en el marco del proyecto WDML (World Digital Mathematics Library y del proyecto español DML-E.

STATISTICAL EVALUATION OF EXAMINATION TESTS IN MATHEMATICS FOR ECONOMISTS

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KASPŘÍKOVÁ, Nikola

2012-12-01

Full Text Available Examination results are rather important for many students with regard to their future profession development. Results of exams should be carefully inspected by the teachers to help improve design and evaluation of tests and education process in general. Analysis of examination papers in mathematics taken by students of basic mathematics course at University of Economics in Prague is reported. The first issue addressed is identification of significant dependencies between performance in particular problem areas covered in the test and also between particular items and total score in test or ability level as a latent trait. The assessment is first performed with Spearman correlation coefficient, items in the test are then evaluated within Item Response Theory framework. The second analytical task addressed is a search for groups of students who are similar with respect to performance in test. Cluster analysis is performed using partitioning around medoids method and final model selection is made according to average silhouette width. Results of clustering, which may be also considered in connection with setting of the minimum score for passing the exam, show that two groups of students can be identified. The group which may be called "well-performers" is the more clearly defined one.

Written feedback to mathematics homework

OpenAIRE

Žitko, Urša

2017-01-01

This diploma thesis is about teachers’ feedback to students’ mathematics homework. In the theoretical part I present the purpose and history of homework assignments as well as various classifications of types of homework. In general, homework assignments are intended for students to learn and refresh the subject matter they have learnt in class, to gain further understanding, to practice various mathematical processes, and to prepare the student for a forthcoming subject matter. By doing home...

A Mathematical Analysis of Air Traffic Priority Rules

Science.gov (United States)

Nakawicz, Anthony J.; Munoz, Cesar A.; Maddalon, Jeffrey M.

2012-01-01

This paper analyzes priority rules, such as those in Part 91.113 of the Federal Aviation Regulations. Such rules determine which of two aircraft should maneuver in a given conflict scenario. While the rules in 91.113 are well accepted, other concepts of operation for NextGen, such as self separation, may allow for different priority rules. A mathematical framework is presented that can be used to analyze a general set of priority rules and enables proofs of important properties. Specific properties considered in this paper include safety, effectiveness, and stability. A set of rules is said to be safe if it ensures that it is never the case that both aircraft have priority. They are effective if exactly one aircraft has priority in every situation. Finally, a set of rules is called stable if it produces compatible results even under small changes to input data.

Axiomatic Quantum Field Theory in Terms of Operator Product Expansions: General Framework, and Perturbation Theory via Hochschild Cohomology

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Stefan Hollands

2009-09-01

Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.

Discrete Mathematics Course Supported by CAS MATHEMATICA

Science.gov (United States)

Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.

2017-01-01

In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our…

Mathematical and numerical study of nonlinear hyperbolic equations: model coupling and nonclassical shocks

International Nuclear Information System (INIS)

Boutin, B.

2009-11-01

This thesis concerns the mathematical and numerical study of nonlinear hyperbolic partial differential equations. A first part deals with an emergent problematic: the coupling of hyperbolic equations. The pursued applications are linked with the mathematical coupling of computing platforms, dedicated to an adaptative simulation of multi-scale phenomena. We propose and analyze a new coupling formalism based on extended PDE systems avoiding the geometric treatment of the interfaces. In addition, it allows to formulate the problem in a multidimensional setting, with possible covering of the coupled models. This formalism allows in particular to equip the coupling procedure with viscous regularization mechanisms, useful in the selection of natural discontinuous solutions. We analyze existence and uniqueness in the framework of a parabolic regularization a la Dafermos. Existence of a solution holds true under very general conditions but failure of uniqueness may naturally arise as soon as resonance occurs at the interfaces. Next, we highlight that our extended PDE framework gives rise to another regularization strategy based on thick interfaces. In this setting, we prove existence and uniqueness of the solutions of the Cauchy problem for initial data in L ∞ . The main tool consists in the derivation of a flexible and robust finite volume method for general triangulation which is analyzed in the setting of entropy measure-valued solutions by DiPerna. The second part is devoted to the definition of a finite volume scheme for the computing of nonclassical solutions of a scalar conservation law based on a kinetic relation. This scheme offers the feature to be stricto sensu conservative, in opposition to a Glimm approach that is only statistically conservative. The validity of our approach is illustrated through numerical examples. (author)

Research, statistics and mathematics educators in Nigeria: effect ...

African Journals Online (AJOL)

Over reliance on the perspective of a dichotomous reject or fail-to-reject outcome from a null hypothesis testing framework to answer research questions has become a worrisome issue to research methodologists and statistics experts. Thus, the Journals of Mathematical Association of Nigeria, Abacus (2013 & 2014) were ...

Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction.

Science.gov (United States)

Liu, Yingyi

2017-09-08

Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction. Thirty-five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school. Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later. In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later. Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level. © 2017 The British Psychological Society.

A Hybrid Programming Framework for Modeling and Solving Constraint Satisfaction and Optimization Problems

OpenAIRE

Sitek, Paweł; Wikarek, Jarosław

2016-01-01

This paper proposes a hybrid programming framework for modeling and solving of constraint satisfaction problems (CSPs) and constraint optimization problems (COPs). Two paradigms, CLP (constraint logic programming) and MP (mathematical programming), are integrated in the framework. The integration is supplemented with the original method of problem transformation, used in the framework as a presolving method. The transformation substantially reduces the feasible solution space. The framework a...

Mathematical aspects that extend the notion of scientific notation in the area of Physics of General Middle Education

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Yohan Godoy

2018-01-01

Full Text Available For this work, a constructivist didactic proposal was designed in which the students of the third year of General Media Education can acquire a significant learning in the use of Scientific Notation. The type of research used is among feasible projects with a non-experimental field design. For data collection, the survey technique was used, which was applied to 43 students of the Physics subject of the third year of the Liceo Rosario Almarza Trujillo-Venezuela. The analysis of the results indicated that they present deficiencies in terms of significant numbers and order magnitude, which are essential mathematical aspects for the understanding and use of Scientific Notation in the area of Physics, as well as highlighting the need for Implement other teaching and learning strategies, such as a series of complementary activities for the teacher in the classroom or the student. In view of these results, a didactic guide was carried out using the known mathematical aspects and various ludic activities to extend the notion and use of scientific notation.

Concepts of modern mathematics

CERN Document Server

Stewart, Ian

1995-01-01

Some years ago, ""new math"" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of ""new math"" have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor an

Analysis of students’ mathematical reasoning

Science.gov (United States)

Sukirwan; Darhim; Herman, T.

2018-01-01

The reasoning is one of the mathematical abilities that have very complex implications. This complexity causes reasoning including abilities that are not easily attainable by students. Similarly, studies dealing with reason are quite diverse, primarily concerned with the quality of mathematical reasoning. The objective of this study was to determine the quality of mathematical reasoning based perspective Lithner. Lithner looked at how the environment affects the mathematical reasoning. In this regard, Lithner made two perspectives, namely imitative reasoning and creative reasoning. Imitative reasoning can be memorized and algorithmic reasoning. The Result study shows that although the students generally still have problems in reasoning. Students tend to be on imitative reasoning which means that students tend to use a routine procedure when dealing with reasoning. It is also shown that the traditional approach still dominates on the situation of students’ daily learning.

Towards mathematical philosophy

CERN Document Server

Hendricks, Vincent F

2008-01-01

Logical investigations in cognitive science have successfully utilized methods and systems of belief revision, non-monotonic logic and dynamic epistemic logic. This title deals with focal issues of belief revision. It contains a collection of articles applying methods of logic or, more generally, of mathematics to solve problems.

Development of a Framework to Characterise the Openness of Mathematical Tasks

Science.gov (United States)

Yeo, Joseph B. W.

2017-01-01

Educators usually mean different constructs when they speak of open tasks: some may refer to pure-mathematics investigative tasks while others may have authentic real-life tasks in mind; some may think of the answer being open while others may refer to an open method. On the other hand, some educators use different terms, e.g. open and open-ended,…

Mathematics as a constructive activity learners generating examples

CERN Document Server

Watson, Anne

2005-01-01

Explains and demonstrates the role of examples in the teaching and learning of mathematics, and their place in mathematics generally at all levels. Includes a combination of exercises for the reader, practical applications for teaching, and solid scholarly grounding.

IMPROVING TEACHING MATHEMATICS USING MODERN INFORMATION TECHNOLOGIES IN FORMATION MATHEMATICAL COMPETENCE REQUIRED FUTURE SKIPPERS.

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Elena Gudyreva

2015-10-01

Full Text Available The article is devoted to consideration of issues related to identifying the potential for teaching mathematics using network (Internet technology and the introduction of elements of distance learning into educational process of higher educational establishments of the sea profile, as well as achievement of formation of mathematical competence of students of the University generally, and of the University's Maritime profile, in particular. Based on the analysis of psychological and pedagogical literature highlights the factors that influence the increase of efficiency of independent work of students of higher educational institutions and on the formation of steady skills of self-education that ultimately leads to quality of formation of mathematical competence of a student. Specific features of teaching mathematics at the University of the sea profile. The description of the project (complex sites "KSMA. Higher mathematics navigators", who developed and used in the Kherson state Maritime Academy in the teaching of mathematics and the organization of individual techniques of distance learning, shows the simplicity and accessibility of working with complex sites, as well as the simplicity and accessibility of design "personal website", but in fact complex sites, by a teacher of any discipline of higher education. Shown, also a training process with the use of the project "KSMA. Higher mathematics navigators", analyzes the experience of teaching the course "Higher mathematics" in a higher educational institution of the marine profile with the use of a personal website, a teacher and shown positive results in students mastery of basic mathematical competencies.

Mathematical methods for physical and analytical chemistry

CERN Document Server

Goodson, David Z

2011-01-01

Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton's method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical

Using the general-purpose reactivity indicator: challenging examples.

Science.gov (United States)

Anderson, James S M; Melin, Junia; Ayers, Paul W

2016-03-01

We elucidate the regioselectivity of nucleophilic attack on substituted benzenesulfonates, quinolines, and pyridines using a general-purpose reactivity indicator (GPRI) for electrophiles. We observe that the GPRI is most accurate when the incoming nucleophile resembles a point charge. We further observe that the GPRI often chooses reactive "dead ends" as the most reactive sites as well as sterically hindered reactive sites. This means that care must be taken to remove sites that are inherently unreactive. Generally, among sites where reactions actually occur, the GPRI identifies the sites in the molecule that lead to the kinetically favored product(s). Furthermore, the GPRI can discern which sites react with hard reagents and which sites react with soft reagents. Because it is currently impossible to use the mathematical framework of conceptual DFT to identify sterically inaccessible sites and reactive dead ends, the GPRI is primarily useful as an interpretative, not a predictive, tool.

The proper generalized decomposition for advanced numerical simulations a primer

CERN Document Server

Chinesta, Francisco; Leygue, Adrien

2014-01-01

Many problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom. Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical mod...

Generalized expectation with general kernels on g-semirings and its applications

Czech Academy of Sciences Publication Activity Database

Agahi, H.; Mesiar, Radko; Babakhani, A.

2017-01-01

Roč. 111, č. 3 (2017), s. 863-875 ISSN 1578-7303 Institutional support: RVO:67985556 Keywords : Fractional integral * g-expectation * Jensen’s inequality * Probability theory Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.690, year: 2016 http://library.utia.cas.cz/separaty/2017/E/mesiar-0477104.pdf

VMEXT: A Visualization Tool for Mathematical Expression Trees

OpenAIRE

Schubotz, Moritz; Meuschke, Norman; Hepp, Thomas; Cohl, Howard S.; Gipp, Bela

2017-01-01

Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). Expression trees are an important mechanism for storing and processing mathematical expressions as well as the most frequently used visualization of the structure of mathematical expressions. Typically, researchers and practitioners manually visualize expression trees using general-purpose tools. This approach is labori...

Computing Generalized Matrix Inverse on Spiking Neural Substrate

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Rohit Shukla

2018-03-01

Full Text Available Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines.

Computing Generalized Matrix Inverse on Spiking Neural Substrate

Science.gov (United States)

Shukla, Rohit; Khoram, Soroosh; Jorgensen, Erik; Li, Jing; Lipasti, Mikko; Wright, Stephen

2018-01-01

Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines. PMID:29593483

An efficient heuristic versus a robust hybrid meta-heuristic for general framework of serial-parallel redundancy problem

International Nuclear Information System (INIS)

Sadjadi, Seyed Jafar; Soltani, R.

2009-01-01

We present a heuristic approach to solve a general framework of serial-parallel redundancy problem where the reliability of the system is maximized subject to some general linear constraints. The complexity of the redundancy problem is generally considered to be NP-Hard and the optimal solution is not normally available. Therefore, to evaluate the performance of the proposed method, a hybrid genetic algorithm is also implemented whose parameters are calibrated via Taguchi's robust design method. Then, various test problems are solved and the computational results indicate that the proposed heuristic approach could provide us some promising reliabilities, which are fairly close to optimal solutions in a reasonable amount of time.

LEARNING AND THOUGHT PROCESSES IN REALISTIC MATHEMATICS INSTRUCTION

NARCIS (Netherlands)

Nelissen, J.; Tomic, W.

2008-01-01

This article deals with the various different approaches to mathematics and the influence that these approaches have had on the teaching of this subject. In addition to the three generally known schools of mathematics instruction - the mechanistic, the structuralistic and the empirical - the article

Exact penalty results for mathematical programs with vanishing constraints

Czech Academy of Sciences Publication Activity Database

Hoheisel, T.; Kanzow, Ch.; Outrata, Jiří

2010-01-01

Roč. 72, č. 5 (2010), s. 2514-2526 ISSN 0362-546X R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10750506 Keywords : Mathematical programs with vanishing constraints * Mathematical programs with equilibrium constraints * Exact penalization * Calmness * Subdifferential calculus * Limiting normal cone Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://library.utia.cas.cz/separaty/2010/MTR/outrata-exact penalty results for mathematical programs with vanishing constraints.pdf

Giftedness and Aesthetics: Perspectives of Expert Mathematicians and Mathematically Gifted Students

Science.gov (United States)

Tjoe, Hartono

2015-01-01

Giftedness in mathematics has been characterized by exceptional attributes including strong mathematical memory, formalizing perception, generalization, curtailment, flexibility, and elegance. Focusing on the last attribute, this study examined the following: (a) the criteria which expert mathematicians and mathematically gifted students fleshed…

General framework for studying the dynamics of folded and nonfolded proteins by NMR relaxation spectroscopy and MD simulation

NARCIS (Netherlands)

Prompers, J.J.; Brüschweiler, R.

2002-01-01

A general framework is presented for the interpretation of NMR relaxation data of proteins. The method, termed isotropic reorientational eigenmode dynamics (iRED), relies on a principal component analysis of the isotropically averaged covariance matrix of the lattice functions of the spin

Modelling the Intention to Use Technology for Teaching Mathematics among Pre-Service Teachers in Serbia

Science.gov (United States)

Teo, Timothy; Milutinovic, Verica

2015-01-01

This study aims to examine the variables that influence Serbian pre-service teachers' intention to use technology to teach mathematics. Using the technology acceptance model (TAM) as the framework, we developed a research model to include subjective norm, knowledge of mathematics, and facilitating conditions as external variables to the TAM. In…

[Mathematics - astronomy - astrology special library].

Science.gov (United States)

Gluch, Sibylle

2011-01-01

About 1560 Elector August of Saxony created an unusual library--one distinguished within its period by both its specialization and location. Situated within the Kunstkammer this library was mostly dedicated to the mathematical sciences and related disciplines. It contained works by the most important authors on mathematics, astronomy, and astrology from the classical, medieval, and early modern periods. This essay traces the formation and composition of August's library, and examines its function: What kind of relationship existed between the library and the Kunstkammer? In what way did the library mirror the interests of the Elector, and to what extend does it permit inferences regarding the Elector's knowledge of mathematics? From the analysis August emerges not as a specialist with a deep understanding of mathematics, but as a particular aficionado of mathematical applications. As a practitioner and general follower of the mathematical arts he took part in a far-reaching intellectual network the center of which lay in the University of Wittenberg. Here, Melanchthon had effectively strengthened the importance of the mathematical disciplines within the university curriculum. He regarded mathematics as the foremost science, arguing that before all other disciplines its method enabled man to recognize the harmonic order of the world, and to discern divine providence. Thus, mathematics offered consoling stability and support in an often seemingly chaotic world torn by religious controversies. This kind of esteem for the mathematical sciences did not presuppose expert knowledge. Hence, the fact that August does not appear to have read the mathematical books he collected does not come as a contradiction. On the contrary, for August it sufficed to recognize the potential of the mathematical sciences, which he brought into life through the creation of a specialized library that developed a rhetoric of its own. The collection of his Kunstkammer library spoke of a

GeoFramework: A Modeling Framework for Solid Earth Geophysics

Science.gov (United States)

Gurnis, M.; Aivazis, M.; Tromp, J.; Tan, E.; Thoutireddy, P.; Liu, Q.; Choi, E.; Dicaprio, C.; Chen, M.; Simons, M.; Quenette, S.; Appelbe, B.; Aagaard, B.; Williams, C.; Lavier, L.; Moresi, L.; Law, H.

2003-12-01

As data sets in geophysics become larger and of greater relevance to other earth science disciplines, and as earth science becomes more interdisciplinary in general, modeling tools are being driven in new directions. There is now a greater need to link modeling codes to one another, link modeling codes to multiple datasets, and to make modeling software available to non modeling specialists. Coupled with rapid progress in computer hardware (including the computational speed afforded by massively parallel computers), progress in numerical algorithms, and the introduction of software frameworks, these lofty goals of merging software in geophysics are now possible. The GeoFramework project, a collaboration between computer scientists and geoscientists, is a response to these needs and opportunities. GeoFramework is based on and extends Pyre, a Python-based modeling framework, recently developed to link solid (Lagrangian) and fluid (Eulerian) models, as well as mesh generators, visualization packages, and databases, with one another for engineering applications. The utility and generality of Pyre as a general purpose framework in science is now being recognized. Besides its use in engineering and geophysics, it is also being used in particle physics and astronomy. Geology and geophysics impose their own unique requirements on software frameworks which are not generally available in existing frameworks and so there is a need for research in this area. One of the special requirements is the way Lagrangian and Eulerian codes will need to be linked in time and space within a plate tectonics context. GeoFramework has grown beyond its initial goal of linking a limited number of exiting codes together. The following codes are now being reengineered within the context of Pyre: Tecton, 3-D FE Visco-elastic code for lithospheric relaxation; CitComS, a code for spherical mantle convection; SpecFEM3D, a SEM code for global and regional seismic waves; eqsim, a FE code for dynamic

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences; Volume 115; Issue 4. Large Time Behaviour of Solutions of a System of Generalized Burgers Equation. K T Joseph ... Author Affiliations. K T Joseph1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India ...

Identifying and Using Picture Books with Quality Mathematical Content: Moving beyond "Counting on Frank" and "The Very Hungry Caterpillar"

Science.gov (United States)

Marston, Jennie

2014-01-01

This article by Jennie Marston provides a framework to assist you in selecting appropriate picture books to present mathematical content. Jennie demonstrates the framework by applying three specific examples of picture books to the framework along with examples of activities.

Preservice Teachers' Perceptions of the Integration of Mathematics, Reading, and Writing.

Science.gov (United States)

Reinke, Kathryn; Mokhtari, Kouider; Willner, Elizabeth

1997-01-01

Examined the perceptions of preservice elementary teachers enrolled in reading, mathematics, and integrating reading and mathematics methods courses about integrating mathematics, reading, and writing instruction at the elementary/middle school level. Surveys indicated that all students were generally positive about instructional integration. They…

Mathematical card magic fifty-two new effects

CERN Document Server

Mulcahy, Colm

2013-01-01

Mathematical card effects offer both beginning and experienced magicians an opportunity to entertain with a minimum of props. Featuring mostly original creations, Mathematical Card Magic: Fifty-Two New Effects presents an entertaining look at new mathematically based card tricks. Each chapter contains four card effects, generally starting with simple applications of a particular mathematical principle and ending with more complex ones. Practice a handful of the introductory effects and, in no time, you'll establish your reputation as a "mathemagician." Delve a little deeper into each chapter and the mathematics gets more interesting. The author explains the mathematics as needed in an easy-to-follow way. He also provides additional details, background, and suggestions for further explorations.Suitable for recreational math buffs and amateur card lovers or as a text in a first-year seminar, this color book offers a diverse collection of new mathemagic principles and effects.

Mathematics, curriculum and assessment: The role of taxonomies in the quest for coherence

Directory of Open Access Journals (Sweden)