Engineering students approaching the mathematics textbook as a potential learning tool – opportunities and constraints

OpenAIRE

Randahl, Mira

2016-01-01

Doktorgradsavhandling It is usually assumed that the students at tertiary level work intensively and individually with the new mathematical concepts (Wood, 2001). In this context the mathematics textbook might be an important learning tool. This thesis addresses the issue of what factors might influence the role of the mathematics textbook as a learning tool. The study is situated in the context of the basic mathematics course taken by first-year engineering students. A b...

Making Culturally Responsive Mathematics Teaching Explicit: A Lesson Analysis Tool

Science.gov (United States)

Aguirre, Julia M.; Zavala, Maria del Rosario

2013-01-01

In the United States, there is a need for pedagogical tools that help teachers develop essential pedagogical content knowledge and practices to meet the mathematical education needs of a growing culturally and linguistically diverse student population. In this article, we introduce an innovative lesson analysis tool that focuses on integrating…

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…

5th Conference on Advanced Mathematical and Computational Tools in Metrology

CERN Document Server

Cox, M G; Filipe, E; Pavese, F; Richter, D

2001-01-01

Advances in metrology depend on improvements in scientific and technical knowledge and in instrumentation quality, as well as on better use of advanced mathematical tools and development of new ones. In this volume, scientists from both the mathematical and the metrological fields exchange their experiences. Industrial sectors, such as instrumentation and software, will benefit from this exchange, since metrology has a high impact on the overall quality of industrial products, and applied mathematics is becoming more and more important in industrial processes.This book is of interest to people

Discrete mathematics using a computer

CERN Document Server

Hall, Cordelia

2000-01-01

Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica­ tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools su...

Mathematical tools for data mining set theory, partial orders, combinatorics

CERN Document Server

Simovici, Dan A

2014-01-01

Data mining essentially relies on several mathematical disciplines, many of which are presented in this second edition of this book. Topics include partially ordered sets, combinatorics, general topology, metric spaces, linear spaces, graph theory. To motivate the reader a significant number of applications of these mathematical tools are included ranging from association rules, clustering algorithms, classification, data constraints, logical data analysis, etc. The book is intended as a reference for researchers and graduate students. The current edition is a significant expansion of the firs

Mathematical tool from corn stover TGA to determine its composition.

Science.gov (United States)

Freda, Cesare; Zimbardi, Francesco; Nanna, Francesco; Viola, Egidio

2012-08-01

Corn stover was treated by steam explosion process at four different temperatures. A fraction of the four exploded matters was extracted by water. The eight samples (four from steam explosion and four from water extraction of exploded matters) were analysed by wet chemical way to quantify the amount of cellulose, hemicellulose and lignin. Thermogravimetric analysis in air atmosphere was executed on the eight samples. A mathematical tool was developed, using TGA data, to determine the composition of corn stover in terms of cellulose, hemicellulose and lignin. It uses the biomass degradation temperature as multiple linear function of the cellulose, hemicellulose and lignin content of the biomass with interactive terms. The mathematical tool predicted cellulose, hemicellulose and lignin contents with average absolute errors of 1.69, 5.59 and 0.74 %, respectively, compared to the wet chemical method.

Learning Mathematics by Designing, Programming, and Investigating with Interactive, Dynamic Computer-Based Objects

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Marshall, Neil; Buteau, Chantal

2014-01-01

As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…

Teachers' Use of Computational Tools to Construct and Explore Dynamic Mathematical Models

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Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron

2011-01-01

To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the…

INTEGRATING CORPUS-BASED RESOURCES AND NATURAL LANGUAGE PROCESSING TOOLS INTO CALL

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Pascual Cantos Gomez

2002-06-01

Full Text Available This paper ainis at presenting a survey of computational linguistic tools presently available but whose potential has been neither fully considered not exploited to its full in modern CALL. It starts with a discussion on the rationale of DDL to language learning, presenting typical DDL-activities. DDL-software and potential extensions of non-typical DDL-software (electronic dictionaries and electronic dictionary facilities to DDL . An extended section is devoted to describe NLP-technology and how it can be integrated into CALL, within already existing software or as stand alone resources. A range of NLP-tools is presentcd (MT programs, taggers, lemn~atizersp, arsers and speech technologies with special emphasis on tagged concordancing. The paper finishes with a number of reflections and ideas on how language technologies can be used efficiently within the language learning context and how extensive exploration and integration of these technologies might change and extend both modern CAI,I, and the present language learning paradigiii..

Dynamic principle for ensemble control tools.

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Samoletov, A; Vasiev, B

2017-11-28

Dynamical equations describing physical systems in contact with a thermal bath are commonly extended by mathematical tools called "thermostats." These tools are designed for sampling ensembles in statistical mechanics. Here we propose a dynamic principle underlying a range of thermostats which is derived using fundamental laws of statistical physics and ensures invariance of the canonical measure. The principle covers both stochastic and deterministic thermostat schemes. Our method has a clear advantage over a range of proposed and widely used thermostat schemes that are based on formal mathematical reasoning. Following the derivation of the proposed principle, we show its generality and illustrate its applications including design of temperature control tools that differ from the Nosé-Hoover-Langevin scheme.

Discrete Mathematics Re "Tooled."

Science.gov (United States)

Grassl, Richard M.; Mingus, Tabitha T. Y.

1999-01-01

Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)

Material tools and meaning formation in mathematics

DEFF Research Database (Denmark)

Johansen, Mikkel Willum; Misfeldt, Morten

revealed several new aspects. For this presentation we will especially focus on how mathematicians use external representations as a way to familiarize themselves with, or ascribe meaning to the mathematical objects they are working with, and how this process plays an important role in the heuristic...... for several different purposes and different tools are used at different stages of the working process. In our talk we will focus on the use of external representations such as symbols, figures and diagrams, and we will explain the role played by such representations in the cognitive practice of working...

Mathematical modeling of physiological systems: an essential tool for discovery.

Science.gov (United States)

Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J

2014-08-28

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.

Mathematical support for automated geometry analysis of lathe machining of oblique peakless round-nose tools

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Filippov, A. V.; Tarasov, S. Yu; Podgornyh, O. A.; Shamarin, N. N.; Filippova, E. O.

2017-01-01

Automatization of engineering processes requires developing relevant mathematical support and a computer software. Analysis of metal cutting kinematics and tool geometry is a necessary key task at the preproduction stage. This paper is focused on developing a procedure for determining the geometry of oblique peakless round-nose tool lathe machining with the use of vector/matrix transformations. Such an approach allows integration into modern mathematical software packages in distinction to the traditional analytic description. Such an advantage is very promising for developing automated control of the preproduction process. A kinematic criterion for the applicable tool geometry has been developed from the results of this study. The effect of tool blade inclination and curvature on the geometry-dependent process parameters was evaluated.

Challenges of Blended E-Learning Tools in Mathematics: Students' Perspectives University of Uyo

Science.gov (United States)

Umoh, Joseph B.; Akpan, Ekemini T.

2014-01-01

An in-depth knowledge of pedagogical approaches can help improve the formulation of effective and efficient pedagogy, tools and technology to support and enhance the teaching and learning of Mathematics in higher institutions. This study investigated students' perceptions of the challenges of blended e-learning tools in the teaching and learning…

FPGA Implementation of Blue Whale Calls Classifier Using High-Level Programming Tool

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Mohammed Bahoura

2016-02-01

Full Text Available In this paper, we propose a hardware-based architecture for automatic blue whale calls classification based on short-time Fourier transform and multilayer perceptron neural network. The proposed architecture is implemented on field programmable gate array (FPGA using Xilinx System Generator (XSG and the Nexys-4 Artix-7 FPGA board. This high-level programming tool allows us to design, simulate and execute the compiled design in Matlab/Simulink environment quickly and easily. Intermediate signals obtained at various steps of the proposed system are presented for typical blue whale calls. Classification performances based on the fixed-point XSG/FPGA implementation are compared to those obtained by the floating-point Matlab simulation, using a representative database of the blue whale calls.

Experimental and Mathematical Modeling for Prediction of Tool Wear on the Machining of Aluminium 6061 Alloy by High Speed Steel Tools

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Okokpujie Imhade Princess

2017-12-01

Full Text Available In recent machining operation, tool life is one of the most demanding tasks in production process, especially in the automotive industry. The aim of this paper is to study tool wear on HSS in end milling of aluminium 6061 alloy. The experiments were carried out to investigate tool wear with the machined parameters and to developed mathematical model using response surface methodology. The various machining parameters selected for the experiment are spindle speed (N, feed rate (f, axial depth of cut (a and radial depth of cut (r. The experiment was designed using central composite design (CCD in which 31 samples were run on SIEG 3/10/0010 CNC end milling machine. After each experiment the cutting tool was measured using scanning electron microscope (SEM. The obtained optimum machining parameter combination are spindle speed of 2500 rpm, feed rate of 200 mm/min, axial depth of cut of 20 mm, and radial depth of cut 1.0mm was found out to achieved the minimum tool wear as 0.213 mm. The mathematical model developed predicted the tool wear with 99.7% which is within the acceptable accuracy range for tool wear prediction.

Experimental and Mathematical Modeling for Prediction of Tool Wear on the Machining of Aluminium 6061 Alloy by High Speed Steel Tools

Science.gov (United States)

Okokpujie, Imhade Princess; Ikumapayi, Omolayo M.; Okonkwo, Ugochukwu C.; Salawu, Enesi Y.; Afolalu, Sunday A.; Dirisu, Joseph O.; Nwoke, Obinna N.; Ajayi, Oluseyi O.

2017-12-01

In recent machining operation, tool life is one of the most demanding tasks in production process, especially in the automotive industry. The aim of this paper is to study tool wear on HSS in end milling of aluminium 6061 alloy. The experiments were carried out to investigate tool wear with the machined parameters and to developed mathematical model using response surface methodology. The various machining parameters selected for the experiment are spindle speed (N), feed rate (f), axial depth of cut (a) and radial depth of cut (r). The experiment was designed using central composite design (CCD) in which 31 samples were run on SIEG 3/10/0010 CNC end milling machine. After each experiment the cutting tool was measured using scanning electron microscope (SEM). The obtained optimum machining parameter combination are spindle speed of 2500 rpm, feed rate of 200 mm/min, axial depth of cut of 20 mm, and radial depth of cut 1.0mm was found out to achieved the minimum tool wear as 0.213 mm. The mathematical model developed predicted the tool wear with 99.7% which is within the acceptable accuracy range for tool wear prediction.

Rescheduling nursing shifts: scoping the challenge and examining the potential of mathematical model based tools.

Science.gov (United States)

Clark, Alistair; Moule, Pam; Topping, Annie; Serpell, Martin

2015-05-01

To review research in the literature on nursing shift scheduling / rescheduling, and to report key issues identified in a consultation exercise with managers in four English National Health Service trusts to inform the development of mathematical tools for rescheduling decision-making. Shift rescheduling is unrecognised as an everyday time-consuming management task with different imperatives from scheduling. Poor rescheduling decisions can have quality, cost and morale implications. A systematic critical literature review identified rescheduling issues and existing mathematic modelling tools. A consultation exercise with nursing managers examined the complex challenges associated with rescheduling. Minimal research exists on rescheduling compared with scheduling. Poor rescheduling can result in greater disruption to planned nursing shifts and may impact negatively on the quality and cost of patient care, and nurse morale and retention. Very little research examines management challenges or mathematical modelling for rescheduling. Shift rescheduling is a complex and frequent management activity that is more challenging than scheduling. Mathematical modelling may have potential as a tool to support managers to minimise rescheduling disruption. The lack of specific methodological support for rescheduling that takes into account its complexity, increases the likelihood of harm for patients and stress for nursing staff and managers. © 2013 John Wiley & Sons Ltd.

Easy as π? an introduction to higher mathematics

CERN Document Server

Ivanov, O A

1999-01-01

The present book is rare, even unique of its kind, at least among mathematics texts published in Russian. You have before you neither a textbook nor a monograph, although these selected chapters from elementary mathematics certainly constitute a fine educational tool. It is my opinion that this is more than just another book about mathematics and the art of teaching that subject. Without considering the actual topics treated (the author himself has described these in sufficient detail in of the book as a whole, the Introduction), I shall attempt to convey a general idea and describe the impressions it makes on the reader. Almost every chapter begins by considering well-known problems of elementary mathematics. Now, every worthwhile elementary problem has hidden behind its diverting formulation what might be called "higher mathematics," or, more simply, mathematics, and it is this that the author demonstrates to the reader in this book. It is thus to be expected that every chapter should contain subject matter...

Bottle Caps as Prekindergarten Mathematical Tools

Science.gov (United States)

Raisor, Jill M.; Hudson, Rick A.

2018-01-01

Early childhood provides a time of crucial growth in all developmental domains. Prekindergarten is an optimal time for young children to use objects of play as a medium to explore new cognitive concepts, including mathematical structure. Mathematical structure plays an important role in providing students a means to reason about mathematics,…

Mathematical tool to size rural digesters

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Florentino Helenice de Oliveira

2003-01-01

Full Text Available Anaerobic digesters have been highlighted due to the current energy crisis and its consequent search for alternative energy sources, allied to the intense process of livestock farming and agriculture modernization, which besides demanding a lot of energy, produces a great amount of crop and animal residues, most of the times generating sanitary problems. The aim of this work is to provide a mathematical tool to establish parameters for projects of construction of rural digesters, considering the response to energy demand, the suitability of the dimensions of the systems, yield factors and the guarantee of functionality. Non-linear optimization models, of easy resolution, for the three main types of rural digesters were formulated in this way. With the resolution of these models one can determine the height and the diameter that lead to a minimum volume for each type, so reducing the necessary amount of masonry and, consequently, diminishing the cost.

Elementary mathematical and computational tools for electrical and computer engineers using Matlab

CERN Document Server

Manassah, Jamal T

2013-01-01

Ideal for use as a short-course textbook and for self-study Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB fills that gap. Accessible after just one semester of calculus, it introduces the many practical analytical and numerical tools that are essential to success both in future studies and in professional life. Sharply focused on the needs of the electrical and computer engineering communities, the text provides a wealth of relevant exercises and design problems. Changes in MATLAB's version 6.0 are included in a special addendum.

Capturing student mathematical engagement through differently enacted classroom practices: applying a modification of Watson's analytical tool

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Patahuddin, Sitti Maesuri; Puteri, Indira; Lowrie, Tom; Logan, Tracy; Rika, Baiq

2018-04-01

This study examined student mathematical engagement through the intended and enacted lessons taught by two teachers in two different middle schools in Indonesia. The intended lesson was developed using the ELPSA learning design to promote mathematical engagement. Based on the premise that students will react to the mathematical tasks in the forms of words and actions, the analysis focused on identifying the types of mathematical engagement promoted through the intended lesson and performed by students during the lesson. Using modified Watson's analytical tool (2007), students' engagement was captured from what the participants' did or said mathematically. We found that teachers' enacted practices had an influence on student mathematical engagement. The teacher who demonstrated content in explicit ways tended to limit the richness of the engagement; whereas the teacher who presented activities in an open-ended manner fostered engagement.

The Multimedia Case as a Tool for Professional Development: An Analysis of Online and Face-to-Face Interaction among Mathematics Pre-Service Teachers, In-Service Teachers, Mathematicians, and Mathematics Teacher Educators

Science.gov (United States)

McGraw, Rebecca; Lynch, Kathleen; Koc, Yusuf; Budak, Ayfer; Brown, Catherine A.

2007-01-01

In this study, we consider the potential of multimedia cases as tools for teacher professional development. Specifically, we examined online and face-to-face discussions that occurred within groups composed of pre-service mathematics teachers, in-service mathematics teachers, mathematicians, and mathematics teacher educators. Discussions within…

a Discrete Mathematical Model to Simulate Malware Spreading

Science.gov (United States)

Del Rey, A. Martin; Sánchez, G. Rodriguez

2012-10-01

With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.

A mathematical framework for agent based models of complex biological networks.

Science.gov (United States)

Hinkelmann, Franziska; Murrugarra, David; Jarrah, Abdul Salam; Laubenbacher, Reinhard

2011-07-01

Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models, it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis. This mathematical framework can also accommodate other model types such as Boolean networks and the more general logical models, as well as Petri nets.

Finite Mathematics and Discrete Mathematics: Is There a Difference?

Science.gov (United States)

Johnson, Marvin L.

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

Short report The DeDiMa battery: a tool for identifying students’ mathematical learning profiles

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Giannis Karagiannakis

2014-10-01

Full Text Available Background The DeDiMa battery is designed for assessing students’ mathematical learning profiles, and it has been used to validate a 4-dimensional model for classifying mathematical learning difficulties. The model arises from existing hypotheses in the cognitive psychology and neuroscience literature, while the DeDiMa battery provides a reliable set of mathematical tasks that help to match characteristics of students’ mathematical performances to their more basic learning difficulties. Participants and procedure In this report we address the question of how these tools can help sketch out a student’s mathematical learning profile. The participants are 5th and 6th grade students. Results We compare the emerging profiles of two students with mathematical learning difficulties (MLD matched for age, performance on a standardized test, non-verbal IQ, and educational experiences. The profiles are very different. Conclusions We believe that this approach can inform the design of individualized remedial interventions for MLD students.

Evo-SETI: A Mathematical Tool for Cladistics, Evolution, and SETI

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Claudio Maccone

2017-04-01

Full Text Available The discovery of new exoplanets makes us wonder where each new exoplanet stands along its way to develop life as we know it on Earth. Our Evo-SETI Theory is a mathematical way to face this problem. We describe cladistics and evolution by virtue of a few statistical equations based on lognormal probability density functions (pdf in the time. We call b-lognormal a lognormal pdf starting at instant b (birth. Then, the lifetime of any living being becomes a suitable b-lognormal in the time. Next, our “Peak-Locus Theorem” translates cladistics: each species created by evolution is a b-lognormal whose peak lies on the exponentially growing number of living species. This exponential is the mean value of a stochastic process called “Geometric Brownian Motion” (GBM. Past mass extinctions were all-lows of this GBM. In addition, the Shannon Entropy (with a reversed sign of each b-lognormal is the measure of how evolved that species is, and we call it EvoEntropy. The “molecular clock” is re-interpreted as the EvoEntropy straight line in the time whenever the mean value is exactly the GBM exponential. We were also able to extend the Peak-Locus Theorem to any mean value other than the exponential. For example, we derive in this paper for the first time the EvoEntropy corresponding to the Markov-Korotayev (2007 “cubic” evolution: a curve of logarithmic increase.

THE CASE STUDY TASKS AS A BASIS FOR THE FUND OF THE ASSESSMENT TOOLS AT THE MATHEMATICAL ANALYSIS FOR THE DIRECTION 01.03.02 APPLIED MATHEMATICS AND COMPUTER SCIENCE

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Dina Aleksandrovna Kirillova

2015-12-01

Full Text Available The modern reform of the Russian higher education involves the implementation of competence-based approach, the main idea of which is the practical orientation of education. Mathematics is a universal language of description, modeling and studies of phenomena and processes of different nature. Therefore creating the fund of assessment tools for mathematical disciplines based on the applied problems is actual. The case method is the most appropriate mean of monitoring the learning outcomes, it is aimed at bridging the gap between theory and practice.The aim of the research is the development of methodical materials for the creating the fund of assessment tools that are based on the case-study for the mathematical analisis for direction «Applied Mathematics and Computer Science». The aim follows from the contradiction between the need for the introduction of case-method in the educational process in high school and the lack of study of the theoretical foundations of using of this method as applied to mathematical disciplines, insufficient theoretical basis and the description of the process of creating case-problems for use their in the monitoring of the learning outcomes.

The Magic of Mathematics Discovering the Spell of Mathematics

CERN Document Server

Pappas, Theoni

2011-01-01

Delves into the world of ideas, explores the spell mathematics casts on our lives, and helps you discover mathematics where you least expect it. Be spellbound by the mathematical designs found in nature. Learn how knots may untie the mysteries of life. Be mesmerized by the computer revolution. Discover how the hidden forces of mathematics hold architectural structures together connect your telephone calls help airplanes get off the ground solve the mysteries of the living cell. See how some artists use a mathematical palette in their works and how many writers draw upon the wealth of its ideas

How Mockups, a Key Engineering Tool, Help to Promote Science, Technology, Engineering, and Mathematics Education

Science.gov (United States)

McDonald, Harry E.

2010-01-01

The United States ranking among the world in science, technology, engineering, and mathematics (STEM) education is decreasing. To counteract this problem NASA has made it part of its mission to promote STEM education among the nation s youth. Mockups can serve as a great tool when promoting STEM education in America. The Orion Cockpit Working Group has created a new program called Students Shaping America s Next Space Craft (SSANS) to outfit the Medium Fidelity Orion Mockup. SSANS will challenge the students to come up with unique designs to represent the flight design hardware. There are two main types of project packages created by SSANS, those for high school students and those for university students. The high school projects will challenge wood shop, metal shop and pre-engineering classes. The university projects are created mainly for senior design projects and will require the students to perform finite element analysis. These projects will also challenge the undergraduate students in material selection and safety requirements. The SSANS program will help NASA in its mission to promote STEM education, and will help to shape our nations youth into the next generation of STEM leaders.

Why Is the Learning of Elementary Arithmetic Concepts Difficult? Semiotic Tools for Understanding the Nature of Mathematical Objects

Science.gov (United States)

Godino, Juan D.; Font, Vicenc; Wilhelmi, Miguel R.; Lurduy, Orlando

2011-01-01

The semiotic approach to mathematics education introduces the notion of "semiotic system" as a tool to describe mathematical activity. The semiotic system is formed by the set of signs, the production rules of signs and the underlying meaning structures. In this paper, we present the notions of system of practices and configuration of objects and…

Mathematical marriages: intercourse between mathematics and Semiotic choice.

Science.gov (United States)

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.

Use of mathematical modeling in nuclear measurements projects

International Nuclear Information System (INIS)

Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A.; Chany, P.; Devita, A.

2011-01-01

Mathematical modeling of nuclear measurement systems is not a new concept. The response of the measurement system is described using a pre-defined mathematical model that depends on a set of parameters. These parameters are determined using a limited set of experimental measurement points e.g. efficiency curve, dose rates... etc. The model that agrees with the few experimental points is called an experimentally validated model. Once these models have been validated, we use mathematical interpolation to find the parameters of interest. Sometimes, when measurements are not practical or are impossible extrapolation is implemented but with care. CANBERRA has been extensively using mathematical modeling for the design and calibration of large and sophisticated systems to create and optimize designs that would be prohibitively expensive with only experimental tools. The case studies that will be presented here are primarily performed with MCNP, CANBERRA's MERCURAD/PASCALYS and ISOCS (In Situ Object Counting Software). For benchmarking purposes, both Monte Carlo and ray-tracing based codes are inter-compared to show models consistency and add a degree of reliability to modeling results. (authors)

E-learning materials in mathematics education

OpenAIRE

Fajfar, Tina

2012-01-01

When studying mathematics, most pupils and students need mathematical tools, along with the teachers' explanation. The updated curriculum for mathematics in primary and secondary education also recommends using materials connected to information and communication technology. Although e-learning materials are not directly mentioned in a curricula as a tool for learning mathematics, they should, nevertheless, be considered as a tool which can be used in a class with the help of a teacher or ind...

Learning Behaviours of Low-Achieving Children's Mathematics Learning in Using of Helping Tools in a Synchronous Peer-Tutoring System

Science.gov (United States)

Tsuei, Mengping

2017-01-01

This study examined the effects of low-achieving children's use of helping tools in a synchronous mathematics peer-tutoring system on the children's mathematics learning and their learning behaviours. In a remedial class, 16 third-grade students in a remedial class engaged in peer tutoring in a face-to-face synchronous online environment during a…

Heap: a highly sensitive and accurate SNP detection tool for low-coverage high-throughput sequencing data

KAUST Repository

Kobayashi, Masaaki; Ohyanagi, Hajime; Takanashi, Hideki; Asano, Satomi; Kudo, Toru; Kajiya-Kanegae, Hiromi; Nagano, Atsushi J.; Tainaka, Hitoshi; Tokunaga, Tsuyoshi; Sazuka, Takashi; Iwata, Hiroyoshi; Tsutsumi, Nobuhiro; Yano, Kentaro

2017-01-01

and GP depends on not only their mathematical models, but the quality and quantity of variants employed in the analysis. In NGS single nucleotide polymorphism (SNP) calling, conventional tools ideally require more reads for higher SNP sensitivity

Making the Learning of Mathematics More Meaningful

Science.gov (United States)

Ward, Robin A.

1998-01-01

In the early 1980's, the National Commission on Excellence in Education responded to the call for reform in the teaching and learning of mathematics. In particular, the Commission developed a document addressing the consensus that all students need to learn more, and often different, mathematics and that instruction in mathematics must be significantly revised. In a response to these calls for mathematics education reform, the National Council of Teachers of Mathematics (NCTM) developed its Curriculum and Evaluation Standards (1989) with a two-fold purpose: 1) to create a coherent vision of what it means to be mathematically literate in a world that relies on calculators and computers, and 2) to create a set of standards to guide the revisions of school mathematics curriculum.

The effects of a digital formative assessment tool on mathematics achievement and student motivation : Results of a randomized experiment

NARCIS (Netherlands)

Faber, Janke; Luyten, Johannes W.; Visscher, Arend J.

2017-01-01

In this study a randomized experimental design was used to examine the effects of a digital formative assessment tool on mathematics achievement and motivation in grade three primary education (n schools = 79, n students = 1808). Experimental schools used a digital formative assessment tool whereas

Effects of a Mathematics Fluency Program on Mathematics Performance of Students with Challenging Behaviors

Science.gov (United States)

Whitney, Todd; Hirn, Regina G.; Lingo, Amy S.

2016-01-01

In the present study, we examined the effects of a fluency-building mathematics program called Great Leaps Math on fluency of basic addition mathematics facts zero to nine and word problem solving using a multiple probe design across participants. Three elementary students with challenging behaviors and mathematics difficulty participated in the…

Identifying Professional Development Needs in Mathematics: A Planning Tool for Grades 3-7. Second Edition

Science.gov (United States)

Taylor, Mary Jo; Dimino, Joseph A.; Gellar, Leanne Ketterlin; Koontz, Trish

2010-01-01

This document offers a planning tool for grades 3-7 that can be used by regional comprehensive centers, other technical assistance centers, and state departments of education to plan professional development for teachers. It is based on the "National Mathematics Advisory Panel Report" which was published in 2008. The panel synthesized its final…

Cluster algebras in mathematical physics

International Nuclear Information System (INIS)

Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2014-01-01

This special issue of Journal of Physics A: Mathematical and Theoretical contains reviews and original research articles on cluster algebras and their applications to mathematical physics. Cluster algebras were introduced by S Fomin and A Zelevinsky around 2000 as a tool for studying total positivity and dual canonical bases in Lie theory. Since then the theory has found diverse applications in mathematics and mathematical physics. Cluster algebras are axiomatically defined commutative rings equipped with a distinguished set of generators (cluster variables) subdivided into overlapping subsets (clusters) of the same cardinality subject to certain polynomial relations. A cluster algebra of rank n can be viewed as a subring of the field of rational functions in n variables. Rather than being presented, at the outset, by a complete set of generators and relations, it is constructed from the initial seed via an iterative procedure called mutation producing new seeds successively to generate the whole algebra. A seed consists of an n-tuple of rational functions called cluster variables and an exchange matrix controlling the mutation. Relations of cluster algebra type can be observed in many areas of mathematics (Plücker and Ptolemy relations, Stokes curves and wall-crossing phenomena, Feynman integrals, Somos sequences and Hirota equations to name just a few examples). The cluster variables enjoy a remarkable combinatorial pattern; in particular, they exhibit the Laurent phenomenon: they are expressed as Laurent polynomials rather than more general rational functions in terms of the cluster variables in any seed. These characteristic features are often referred to as the cluster algebra structure. In the last decade, it became apparent that cluster structures are ubiquitous in mathematical physics. Examples include supersymmetric gauge theories, Poisson geometry, integrable systems, statistical mechanics, fusion products in infinite dimensional algebras, dilogarithm

SACA: Software Assisted Call Analysis--an interactive tool supporting content exploration, online guidance and quality improvement of counseling dialogues.

Science.gov (United States)

Trinkaus, Hans L; Gaisser, Andrea E

2010-09-01

Nearly 30,000 individual inquiries are answered annually by the telephone cancer information service (CIS, KID) of the German Cancer Research Center (DKFZ). The aim was to develop a tool for evaluating these calls, and to support the complete counseling process interactively. A novel software tool is introduced, based on a structure similar to a music score. Treating the interaction as a "duet", guided by the CIS counselor, the essential contents of the dialogue are extracted automatically. For this, "trained speech recognition" is applied to the (known) counselor's part, and "keyword spotting" is used on the (unknown) client's part to pick out specific items from the "word streams". The outcomes fill an abstract score representing the dialogue. Pilot tests performed on a prototype of SACA (Software Assisted Call Analysis) resulted in a basic proof of concept: Demographic data as well as information regarding the situation of the caller could be identified. The study encourages following up on the vision of an integrated SACA tool for supporting calls online and performing statistics on its knowledge database offline. Further research perspectives are to check SACA's potential in comparison with established interaction analysis systems like RIAS. Copyright (c) 2010 Elsevier Ireland Ltd. All rights reserved.

Women in Mathematics: A Nested Approach

Science.gov (United States)

Köse, Emek; Johnson, Angela C.

2016-01-01

In this article, we present a case study of a course called Women in Mathematics. Students in the course studied the lives and the mathematical contributions of women mathematicians throughout history, as well as current gender equity issues in the study of mathematics and in mathematical careers. They also mentored 20 middle school girls…

Explorations in Elementary Mathematical Modeling

Directory of Open Access Journals (Sweden)

Mazen Shahin

2010-06-01

Full Text Available In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and cooperative learning into this inquiry-based learning course where students work in small groups on carefully designed activities and utilize available software to support problem solving and understanding of real life situations. We emphasize the use of graphical and numerical techniques, rather than theoretical techniques, to investigate and analyze the behavior of the solutions of the difference equations.As an illustration of our approach, we will show a nontraditional and efficient way of introducing models from finance and economics. We will also present an interesting model of supply and demand with a lag time, which is called the cobweb theorem in economics. We introduce a sample of a research project on a technique of removing chaotic behavior from a chaotic system.

International Conference on $p$-Adic Mathematical Physics and its Applications

CERN Document Server

2015-01-01

Since 1987, there have been many interesting and promissing applications of p-adic (non-Archimedean, ultrametric) analysis to some problems of modern mathematical and theoretical physics, and also to some other related fields of sciences. As a result, it emerged a new field of research called p-adic mathematical physics. During this time, there has been permanent interest in investigation of relevant mathematical tools, as well as of possible applications -- from strings to the universe as a whole. In particular, there have been remarkable achievements in some complex biosystems with hierarchy. Enthusiastic researchers believe that application of p-adic analysis and ultrametric methods becomes one of scientific challenges of the 21st century. For the progress in this field in period 1987-2008 one can see review paper http://arxiv.org/abs/0904.4205. For an insight to investigations after 2008 one can look at publications of the journal p-Adic Numbers, Ultrametric Analysis and Applications. To promote this fiel...

Mathematics a simple tool for geologists

CERN Document Server

Waltham, D, D

1994-01-01

Uses geological examples to illustrate mathematical ideas. Contains a large number of worked examples, and problems for students to attempt themselves. Answers to all the questions are given at the end of the book.

THE TEACHING OF MATHEMATICS WITH MEDIATING TOOLS: MOODLE WITH GEOGEBRA AND WEBQUEST FOR THE LEARNING OF MATHEMATICAL KNOWLEDGE

Directory of Open Access Journals (Sweden)

Graciela Aluizio Reali

2013-07-01

Full Text Available Much has been thought through about how to make the teaching and learning of scientific content more significant in order to collaborate with education. In this sense, it is up to the teacher to know aspects of human behavior to mediate and facilitate the interpretation of incoming information to students so that this information is transformed into knowledge. Therefore, the educator has seen its role as a transmitter of information turning into a facilitator of the transformation of this information into knowledge, a process that depends on both the teacher and the student. Thus, this work presents some aspects related to the teaching and learning of mathematics, highlighting the use of information and communication technologies (ICTs as mediating and helpful tools of learning. It also presents a virtual learning environment, Moodle, which comprehends Geogebra software, presented in a WebQuest so that together they may be used in the future for the teaching and learning of mathematics in Ourinhos- Fatec Technology College, São Paulo- - Brazil. It is expected, by means of this work, to contribute to discussions and reflections on some emblematic issues of this new practice and mode, as well as disseminate and encourage the use of Geogebra application.

Prospects of application structural mathematical constructs as bases tool conceptualization the subject domain of sociology (statement of a problem

Directory of Open Access Journals (Sweden)

E. V. Maslennikov

2016-01-01

Full Text Available In article the approach to the decision of a problem of conceptual integration of sociology as the set of theoretical knowledge belonging to type - conceptually difficult - the big theories. Development of theoretical sociology with use of forms of the mathematical theory is considered as a private problem in relation to more general problem of development of theoretical knowledge with use of forms of the mathematical theory. Development the theoretical sociology is offered to carry out with use of forms of the mathematical theory on the basis of properties structural mathematical constructs and with application the mathematical methods developed in a scientific direction “The Conceptual analysis and designing”[40] . In the given direction it is used not only a paradigm of structuralism, but also a principle of an ascention from abstract to concrete in the knowledge, realized in procedure of synthesis of formal theories with use of the device of structural mathematics. The system analysis, the theory of systems and the theory of structures of N. Burbaki concerns to sources of occurrence of a method of the conceptual analysis. The method is intended for the analysis of subject domains of a high level of complexity, realization of conceptual modeling of objects from these subject domains and reception of new knowledge about essence of subject domains and their relations. Conceptual complexity of phenomena is understood as complexity of the structures expressing the relations and interrelations between concepts, describing interesting area from the point of view of solved tasks. For a subject domain conceptual complexity is potentially established by quantity of basic sets on which scales of sets and the steps belonging to them representing definitions of developed theory of a subject domain are constructed. In article is exposed to the analysis role structural mathematical constructs device in expansion integrating tool conceptualization

Reorganizing Freshman Business Mathematics II: Authentic Assessment in Mathematics through Professional Memos

Science.gov (United States)

Green, Kris; Emerson, Allen

2008-01-01

The first part of this two-part paper [see EJ787497] described the development of a new freshman business mathematics (FBM) course at our college. In this paper, we discuss our assessment tool, the business memo, as a venue for students to apply mathematical skills, via mathematical modelling, to realistic business problems. These memos have…

An introduction to mathematical cryptography

CERN Document Server

Hoffstein, Jeffrey; Silverman, Joseph H

2014-01-01

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cr...

Mathematical physics applied mathematics for scientists and engineers

CERN Document Server

Kusse, Bruce R

2006-01-01

What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations

Panel Debate: Technics and technology in mathematics and mathematics education

DEFF Research Database (Denmark)

Misfeldt, Morten

2015-01-01

The use of computer technology for teaching and learning of mathematics has several consequences and does sometimes give rise to both controversies and misunderstandings. We address these problems by both a philosophical and a historical approach, investigating what it actually is that goes on when...... guidelines and conclusions regarding the use of computer technology in mathematics education....... new technologies enter mathematics as a discipline and mathematics education as a societal practice. Our analysis suggests a focus on continuities in time and place in the sense that it is necessary to understand the history of “tool use” in mathematics and the various ways that scholastic and non...

Mathematics in Engineering - Part I

Indian Academy of Sciences (India)

tion of mathematics to engineering problems; to provide a taste of some ... for organizations like ISRO or DRDO are called scien- tists. ... analysis and development of measurable physical data, using .... Any serious discussion of mathematics in modern engi- neering .... A simple way to solve this problem computationally is.

Research on Mathematics Teachers as Partners in Task Design

Science.gov (United States)

Jones, Keith; Pepin, Birgit

2016-01-01

Mathematical tasks and tools, including tasks in the form of digital tools, are key resources in mathematics teaching and in mathematics teacher education. Even so, the "design" of mathematical tasks is perceived in different ways: sometimes seen as something distinct from the teaching and learning process, and sometimes as integral to…

Mathematics and engineering in real life through mathematical competitions

Science.gov (United States)

More, M.

2018-02-01

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

Mathematics Teachers' Response to the Reform Agenda: Results of the 1993 National Survey of Science and Mathematics Education.

Science.gov (United States)

Weiss, Iris R.

The NCTM Standards call for the introduction of challenging mathematics content for all students beginning in the early grades. If teachers are to guide students in their exploration of mathematics concepts, they must themselves have a firm grasp of powerful mathematics concepts. This paper uses data from the 1993 National Survey of Science and…

Research on Team-teaching in Mathematics Education

OpenAIRE

重松, 敬一; 井戸野, 佐知子; 勝美, 芳雄

1995-01-01

Recently, there are many classes in which at least two teachers teach mathematics in elementary and lower secondary schools. We call that kind of teaching team-teaching. In some countries, it is called co-operative teaching. In this paper, we investigate the concept of team-teaching in mathematics education implementing a questionnaire, interviews or observing classroom lessons. Today, team-teaching has been administratively systematized. For example, additive teachers are sent to local schoo...

Reassembling mathematical practices: a philosophicalanthropological approach

Directory of Open Access Journals (Sweden)

Karen François

2016-06-01

Full Text Available In this paper we first explore how Wittgenstein’s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein’s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics (Wittgenstein 1973. We will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics. The central philosophical investigation concerns Wittgenstein’s shift to abandoning the essentialist concept of language and therefore denying the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—are immersed in a form of life, in a cultural or social formation and are embedded in the totality of communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure-making and sand drawing, to illustrate Wittgenstein’s ideas. Based on an ethnomathematical comparative analysis, we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality, as expressed in both string figure-making and sand drawing practices, from one society to another. Finally, we suggest that a philosophical-anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cultures. Philosophical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better characterize mathematical

Mathematical Representation of VoIP Connection Delay

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M. Halas

2007-09-01

Full Text Available The main topic of this article is to define mathematical formulation of VoIP connection delay model. It handles about all partial delay components, the mechanism of their generation, facilities and their mathematical formulation. Thereafter based on mathematical formulation of all partial delay components, the final mathematical model of whole VoIP call delay is created. In conclusion of this article the results of the designed mathematical model are compared with the experimentally gained results.

Problems of Mathematical Finance by Stochastic Control Methods

Science.gov (United States)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

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.

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...

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

Directory of Open Access Journals (Sweden)

María F. Ayllón

2016-04-01

Full Text Available This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas, flexibility (range of ideas, novelty (unique idea and elaboration (idea development. These factors contribute, among others, to the fact that schoolchildren are competent in mathematics. The problem solving and posing are a very powerful evaluation tool that shows the mathematical reasoning and creative level of a person. Creativity is part of the mathematics education and is a necessary ingredient to perform mathematical assignments. This contribution presents some important research works about problem posing and solving related to the development of mathematical knowledge and creativity. To that end, it is based on various beliefs reflected in the literature with respect to notions of creativity, problem solving and posing.

Hidden Dimensions in the So-Called Reality of a Mathematics Classroom.

Science.gov (United States)

Bauersfeld, Heinrich

1980-01-01

Teaching and learning mathematics in classrooms is interpreted as human interaction in an institutionalized setting. Using theories and categories from different disciplines, a classroom episode is reanalyzed. Four hidden dimensions in the classroom process and thus deficient areas of research are identified. Consequences for teacher training are…

Re-scheduling nursing shifts: Scoping the challenge and examining the potential of mathematical model based tools

OpenAIRE

Clark, A.; Moule, P.; Topping, A.; Serpell, M.

2015-01-01

Aims: To review research in the literature on nursing shift scheduling/rescheduling, and report key issues identified in a listening exercise with managers in four English NHS trusts to inform the development of mathematical tools for rescheduling decision-making.\\ud Background: Shift rescheduling is unrecognised as an everyday time-consuming management task with different imperatives than scheduling. Poor rescheduling decisions can have quality, cost and morale implications.\\ud Evaluation: A...

Mathematical Tools for Discovery of Nanoporous Materials for Energy Applications

International Nuclear Information System (INIS)

Haranczyk, M; Martin, R L

2015-01-01

Porous materials such as zeolites and metal organic frameworks have been of growing importance as materials for energy-related applications such as CO 2 capture, hydrogen and methane storage, and catalysis. The current state-of-the-art molecular simulations allow for accurate in silico prediction of materials' properties but the computational cost of such calculations prohibits their application in the characterisation of very large sets of structures, which would be required to perform brute-force screening. Our work focuses on the development of novel methodologies to efficiently characterize and explore this complex materials space. In particular, we have been developing algorithms and tools for enumeration and characterisation of porous material databases as well as efficient screening approaches. Our methodology represents a ensemble of mathematical methods. We have used Voronoi tessellation-based techniques to enable high-throughput structure characterisation, statistical techniques to perform comparison and screening, and continuous optimisation to design materials. This article outlines our developments in material design

Mathematical modelling

CERN Document Server

2016-01-01

This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

Mathematical modeling

CERN Document Server

Eck, Christof; Knabner, Peter

2017-01-01

Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

Exploring Kuwaiti mathematics: student-teachers' beliefs toward using Logo and mathematics education

OpenAIRE

Sulaiman, NAJ

2011-01-01

The main objective of this study is to explore the effect of one taught course, a Logo module, on Kuwaiti elementary mathematics student-teachers’ beliefs about Information and Communication Technology (ICT) and Logo. The Logo module incorporated ICT, in particular the Logo programming language, as a cognitive tool, that supports the constructivist perspective for mathematics instruction. The Logo module comprised of 24-sessions (deducted from the hours of the Methods of Teaching Mathematics ...

Tools or Crutches? Apparatus as a Sense-Making Aid in Mathematics Teaching with Children with Moderate Learning Difficulties

Science.gov (United States)

Moscardini, Lio

2009-01-01

This paper challenges a view of concrete materials as artifacts used within a rigid instructional sequence that particular children are perceived to require or not, as the case may be. Focussing on mathematics teaching, it contends that it is more useful to consider the function of these materials as "tools," artefacts used flexibly and…

Mathematics and Computer Science | Argonne National Laboratory

Science.gov (United States)

Extreme Computing Data-Intensive Science Applied Mathematics Science & Engineering Applications Software Extreme Computing Data-Intensive Science Applied Mathematics Science & Engineering Opportunities For Employees Staff Directory Argonne National Laboratory Mathematics and Computer Science Tools

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 ...

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.)

A Mathematical Account of the NEGF Formalism

DEFF Research Database (Denmark)

Cornean, Decebal Horia; Moldoveanu, Valeriu; Pillet, Claude-Alain

2018-01-01

The main goal of this paper is to put on solid mathematical grounds the so-called non-equilibrium Green’s function transport formalism for open systems. In particular, we derive the Jauho–Meir–Wingreen formula for the time-dependent current through an interacting sample coupled to non-interacting......The main goal of this paper is to put on solid mathematical grounds the so-called non-equilibrium Green’s function transport formalism for open systems. In particular, we derive the Jauho–Meir–Wingreen formula for the time-dependent current through an interacting sample coupled to non...

Using the Wonder of Inequalities between Averages for Mathematics Problems Solving

Science.gov (United States)

Shaanan, Rachel Mogilevsky; Gordon, Moshe Stupel

2016-01-01

The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…

Tools of the trade introduction to advanced mathematics

CERN Document Server

Sally, Jr, Paul J

2008-01-01

This book provides a transition from the formula-full aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics. Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such

Mathematical aspects of quantum field theory

CERN Document Server

de Faria, Edson

2010-01-01

Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

Developing Digital Technologies for Undergraduate University Mathematics

DEFF Research Database (Denmark)

Triantafyllou, Eva; Timcenko, Olga

2013-01-01

Our research effort presented in this paper relates with developing digital tools for mathematics education at undergraduate university level. It focuses specifically on studies where mathematics is not a core subject but it is very important in order to cope with core subjects. For our design, we...... requirements for the development of digital tools that support mathematics teaching and learning at university level....... during lectures and exercise time. During these observations we were able to investigate how the applets were used in practice but also to get insight in the challenges that the students face during mathematics learning. These findings together with student feedback inspire the next round of design...

New Challenges in the Teaching of Mathematics.

Science.gov (United States)

Bourguignon, Jean Pierre

The manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematical tools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…

Analytical and empirical mathematics with computers

International Nuclear Information System (INIS)

Wolfram, S.

1986-01-01

In this presentation, some of the practical methodological and theoretical implications of computation for the mathematical sciences are discussed. Computers are becoming an increasingly significant tool for research in the mathematical sciences. This paper discusses some of the fundamental ways in which computers have and can be used to do mathematics

Impact of mobility on call block, call drops and optimal cell size in small cell networks

OpenAIRE

Ramanath , Sreenath; Voleti , Veeraruna Kavitha; Altman , Eitan

2011-01-01

We consider small cell networks and study the impact of user mobility. Assuming Poisson call arrivals at random positions with random velocities, we discuss the characterization of handovers at the boundaries. We derive explicit expressions for call block and call drop probabilities using tools from spatial queuing theory. We also derive expressions for the average virtual server held up time. These expressions are used to derive optimal cell sizes for various profile of velocities in small c...

Advances in mathematical economics

CERN Document Server

Maruyama, Toru

2015-01-01

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

Advances in mathematical economics

CERN Document Server

Maruyama, Toru

2014-01-01

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

Advances in mathematical economics

CERN Document Server

Yamazaki, Akira

2006-01-01

A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.

Advances in mathematical economics

CERN Document Server

Yamazaki, Akira

2006-01-01

A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions.Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.

Advances in mathematical economics

CERN Document Server

Maruyama, Toru

2017-01-01

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

Advances in mathematical economics

CERN Document Server

Maruyama, Toru

2016-01-01

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

Critical relationships between teachers and learners of school mathematics

OpenAIRE

Wright, P.

2017-01-01

This article draws on critical theories and perspectives on mathematics education to explain the tendency of mathematics teaching worldwide to remain focused on developing procedural understanding, despite repeated calls from the mathematics education community for a more relevant and engaging curriculum. It highlights how conventional approaches to teaching mathematics contribute towards alienating a high proportion of learners and reproducing inequities within society. The article reports o...

On Scalar Energy: Mathematical Formulation

International Nuclear Information System (INIS)

Hathout, A.M.

2011-01-01

A new kind of electromagnetic waves (EMW), which exists only in vacuum of the empty space, will be discussed and mathematically formulated in this paper. The mathematical existence of this energy was first proposed in a series of groundbreaking equations by Scottish Mathematician, James Clerk Maxwell, in the mid of 1800 and 39;s. This energy is called scalar energy. It is characterized by both particle and wave like. The waves of this energy are called longitudinal EMW to distinguish them from transverse EM, the kind we are familiar with in our daily life. Teslas name of this energy is scalar energy or zero point energy. It is aimed at this paper to explain more details and to verify the scalar EM concept in vacuum.

Mathematics and Forms of Life

Directory of Open Access Journals (Sweden)

Severin Schroeder

2015-10-01

Full Text Available According to Wittgenstein, mathematics is embedded in, and partly constituting, a form of life. Hence, to imagine different, alternative forms of elementary mathematics, we should have to imagine different practices, different forms of life in which they could play a role. If we tried to imagine a radically different arithmetic we should think either of a strange world (in which objects unaccountably vanish or appear or of people acting and responding in very peculiar ways. If such was their practice, a calculus expressing the norms of representation they applied could not be called false. Rather, our criticism could only be to dismiss such a practice as foolish and to dismiss their norms as too different from ours to be called ‘mathematics’.

Scaffolding Mathematical Modelling with a Solution Plan

Science.gov (United States)

Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

2015-01-01

In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…

Exploring Yellowstone National Park with Mathematical Modeling

Science.gov (United States)

Wickstrom, Megan H.; Carr, Ruth; Lackey, Dacia

2017-01-01

Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

The Princeton companion to mathematics

CERN Document Server

Barrow-Green, June; Leader, Imre

2008-01-01

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more

Lectures in the history of mathematics

CERN Document Server

Bos, Henk J M

1993-01-01

"[These lectures] are about themes of the history of mathematics which, for various reasons, are dear to me. The early differential and integral calculus, the work of Christiaan Huygens, and the concept of construction in seventeenth- and eighteenth-century mathematics are the three themes around which much of my research has concentrated and which continue to fascinate me by the insights they offer in the development of that special human activity called mathematics." -from the Introduction This volume contains eleven lectures ranging over a variety of topics in the history of mathematics. The lectures, presented between 1970 and 1987, were delivered in a variety of venues and appeared only in less accessible publications. Those who teach mathematics, as well as mathematics historians, will appreciate this insightful, wide-ranging book.

Tanglegrams: A Reduction Tool for Mathematical Phylogenetics.

Science.gov (United States)

Matsen, Frederick A; Billey, Sara C; Kas, Arnold; Konvalinka, Matjaz

2018-01-01

Many discrete mathematics problems in phylogenetics are defined in terms of the relative labeling of pairs of leaf-labeled trees. These relative labelings are naturally formalized as tanglegrams, which have previously been an object of study in coevolutionary analysis. Although there has been considerable work on planar drawings of tanglegrams, they have not been fully explored as combinatorial objects until recently. In this paper, we describe how many discrete mathematical questions on trees "factor" through a problem on tanglegrams, and how understanding that factoring can simplify analysis. Depending on the problem, it may be useful to consider a unordered version of tanglegrams, and/or their unrooted counterparts. For all of these definitions, we show how the isomorphism types of tanglegrams can be understood in terms of double cosets of the symmetric group, and we investigate their automorphisms. Understanding tanglegrams better will isolate the distinct problems on leaf-labeled pairs of trees and reveal natural symmetries of spaces associated with such problems.

A bridge to advanced mathematics

CERN Document Server

Sentilles, Dennis

2011-01-01

This helpful workbook-style ""bridge"" book introduces students to the foundations of advanced mathematics, spanning the gap between a practically oriented calculus sequence and subsequent courses in algebra and analysis with a more theoretical slant. Part 1 focuses on logic and number systems, providing the most basic tools, examples, and motivation for the manner, method, and concerns of higher mathematics. Part 2 covers sets, relations, functions, infinite sets, and mathematical proofs and reasoning. Author Dennis Sentilles also discusses the history and development of mathematics as well a

Heap: a highly sensitive and accurate SNP detection tool for low-coverage high-throughput sequencing data

KAUST Repository

Kobayashi, Masaaki

2017-04-20

Recent availability of large-scale genomic resources enables us to conduct so called genome-wide association studies (GWAS) and genomic prediction (GP) studies, particularly with next-generation sequencing (NGS) data. The effectiveness of GWAS and GP depends on not only their mathematical models, but the quality and quantity of variants employed in the analysis. In NGS single nucleotide polymorphism (SNP) calling, conventional tools ideally require more reads for higher SNP sensitivity and accuracy. In this study, we aimed to develop a tool, Heap, that enables robustly sensitive and accurate calling of SNPs, particularly with a low coverage NGS data, which must be aligned to the reference genome sequences in advance. To reduce false positive SNPs, Heap determines genotypes and calls SNPs at each site except for sites at the both ends of reads or containing a minor allele supported by only one read. Performance comparison with existing tools showed that Heap achieved the highest F-scores with low coverage (7X) restriction-site associated DNA sequencing reads of sorghum and rice individuals. This will facilitate cost-effective GWAS and GP studies in this NGS era. Code and documentation of Heap are freely available from https://github.com/meiji-bioinf/heap (29 March 2017, date last accessed) and our web site (http://bioinf.mind.meiji.ac.jp/lab/en/tools.html (29 March 2017, date last accessed)).

Mathematics as a laboratory tool dynamics, delays and noise

CERN Document Server

Milton, John

2014-01-01

The importance of mathematics in the undergraduate biology curriculum is ever increasing, as is the importance of biology within the undergraduate applied mathematics curriculum. This ambitious forward thinking book  strives to make concrete  connections between the two fields at the undergraduate level, bringing in a wide variety of mathematical  methods  such as  signal processing, systems identification, and stochastic differential equations to an undergraduate audience interested in biological dynamics. The presentation stresses a practical hands-on approach: important concepts are introduced using linear first- or second-order differential equations that can be solved using “pencil and paper”; next, these are extended to “real world” applications through the use of computer algorithms written in Scientific Python or similar software. This book developed from a course taught by Professor John Milton at the University of Chicago and developed and continued over many years with Professor Toru O...

Mathematics is always invisible, Professor Dowling

Science.gov (United States)

Cable, John

2015-09-01

This article provides a critical evaluation of a technique of analysis, the Social Activity Method, recently offered by Dowling (2013) as a `gift' to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between `expression' and `content') instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between `public' and `esoteric' mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling calls the `myth of participation', which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling's `essentially linguistic' conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.

Mathematics Anxiety and Prevention Strategy: An Attempt to Support Students and Strengthen Mathematics Education

Directory of Open Access Journals (Sweden)

Aweke Shishigu

2018-02-01

Full Text Available In the process of reaching a medium income country, science, mathematics and technology have become an emphasis of Ethiopia. But, currently, students' interest to study mathematics and ability in mathematics is declining. This study therefore aimed to investigate the prevalence of mathematics anxiety and its effect on students' current mathematics achievement. Additionally, by grounding on the literature, some strategies supposed to reduce the negative effects of math anxiety were identified for practice. The study was conducted on five randomly selected public secondary schools of East Shoa Zone in Oromia region. Math anxiety was measured using a validated instrument called Math Anxiety Rating Scale (MARS, whereas students' current mathematics achievement was measured using achievement test. Structural model was developed to examine causal relationship of the variables treated in the study. The finding revealed that there was a significant negative relationship between mathematics anxiety and achievement. There was also a statistically significant gender difference in mathematics anxiety and current math achievement, with effect size small and typical respectively. Based on the findings of the study, imperative implication for practice and future research were made.

FEMME, a flexible environment for mathematically modelling the environment

NARCIS (Netherlands)

Soetaert, K.E.R.; DeClippele, V.; Herman, P.M.J.

2002-01-01

A new, FORTRAN-based, simulation environment called FEMME (Flexible Environment for Mathematically Modelling the Environment), designed for implementing, solving and analysing mathematical models in ecology is presented. Three separate phases in ecological modelling are distinguished: (1) the model

The Mathematical Microscope - Making the inaccessible accessible

DEFF Research Database (Denmark)

Ottesen, Johnny T.

2011-01-01

  In this chapter we introduce a new term, the "Mathematical Microscope", as a method of using mathematics in accessing information about reality when this information is otherwise inaccessible. Furthermore, we discuss how models and experiments are related: none of which are important without th...... of mathematical modeling is discussed for type 1 and type 2 diabetes, depression, cardiovascular diseases and the interactions between the combinations of these, the so-called gray triangle in the metabolic syndrome....

Mathematical modeling and computational intelligence in engineering applications

CERN Document Server

Silva Neto, Antônio José da; Silva, Geraldo Nunes

2016-01-01

This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.

From "five" to 5 for 5 minutes: Arabic number transcoding as a short, specific, and sensitive screening tool for mathematics learning difficulties.

Science.gov (United States)

Moura, Ricardo; Lopes-Silva, Júlia Beatriz; Vieira, Laura Rodrigues; Paiva, Giulia Moreira; Prado, Ana Carolina de Almeida; Wood, Guilherme; Haase, Vitor Geraldi

2015-02-01

Number transcoding (e.g., writing 29 when hearing "twenty-nine") is one of the most basic numerical abilities required in daily life and is paramount for mathematics achievement. The aim of this study is to investigate psychometric properties of an Arabic number-writing task and its capacity to identify children with mathematics difficulties. We assessed 786 children (55% girls) from first to fourth grades, who were classified as children with mathematics difficulties (n = 103) or controls (n = 683). Although error rates were low, the task presented adequate internal consistency (0.91). Analyses revealed effective diagnostic accuracy in first and second school grades (specificity equals to 0.67 and 0.76 respectively, and sensitivity equals to 0.70 and 0.88 respectively). Moreover, items tapping the understanding of place-value syntax were the most sensitive to mathematics achievement. Overall, we propose that number transcoding is a useful tool for the assessment of mathematics abilities in early elementary school. © The Author 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

Science.gov (United States)

Schwerdtfeger, Sara

2017-01-01

This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

A Conversion Tool for Mathematical Expressions in Web XML Files.

Science.gov (United States)

Ohtake, Nobuyuki; Kanahori, Toshihiro

2003-01-01

This article discusses the conversion of mathematical equations into Extensible Markup Language (XML) on the World Wide Web for individuals with visual impairments. A program is described that converts the presentation markup style to the content markup style in MathML to allow browsers to render mathematical expressions without other programs.…

The Maths Arcade: A Tool for Supporting and Stretching Mathematics Undergraduates

OpenAIRE

Bradshaw, Noel-Ann

2017-01-01

The Maths Arcade is an activity which aims simultaneously to support those university mathematics learners who are having difficulties, stretch more confident learners, and encourage the development of a staff-student mathematical community. The first Maths Arcade was set up at the University of Greenwich in September 2010, funded initially by a University grant for innovative teaching and later by the Mathematical Sciences Curriculum Innovation Fund of the UK National Higher Education STEM P...

Mathematical Modeling Activities as a Useful Tool for Values Education

Science.gov (United States)

Doruk, Bekir Kursat

2012-01-01

Values education is crucial since it is one of the factors to reach success in education in broader sense and in mathematics education in particular sense. It is also important for educating next generations of societies. However, previous research showed that expected importance for values education was not given in Mathematics courses. In a few…

Pioneering space research in the USSR and mathematical modeling of large problems of radiation transfer

International Nuclear Information System (INIS)

Sushkevich, T.A.

2011-01-01

This review is to remind scientists of the older generation of some memorable historical pages and of many famous researchers, teachers and colleagues. For the younger researchers and foreign colleagues it will be useful to get to know about pioneer advancements of the Soviet scientists in the field of information and mathematical supply for cosmonautic problems on the eve of the space era. Main attention is paid to the scientific experiments conducted on the piloted space vehicles and the research teams who created the information and mathematical tools for the first space projects. The role of Mstislav Vsevolodovich Keldysh, the Major Theoretician of cosmonautics, is particularly emphasized. He determined for the most part the basic directions of development of space research and remote sensing of the Earth and planets that are shortly called remote sensing

Defining, Developing, and Measuring "Proclivities for Teaching Mathematics"

Science.gov (United States)

Lewis, Jennifer M.; Fischman, Davida; Riggs, Matt

2015-01-01

This article presents a form of teacher reasoning that we call "proclivities for teaching mathematics." We define proclivities for teaching mathematics as the beliefs, knowledge, and dispositions that are actionable in the flow of instruction, and we argue that growth in this area contributes to positive change in mathematics…

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Department of Mathematics, The University of Texas – Pan American, 1201 West University Drive, Edinburg, TX 78539, USA; School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA; Departamento de Matemáticas, Universidad de Antioquia, Calle 67 N◦53-108, Medellín, Colombia, USA ...

The effect of mathematics games to the student perception of mathematics subject: A case study in Sekolah Kebangsaan Bukit Kuda, Klang

Science.gov (United States)

Abdul Hadi, Normi; Mohd Noor, Norlenda; Abd Halim, Suhaila; Alwadood, Zuraida; Khairol Azmi, Nurul Nisa'

2013-04-01

Mathematics is a basic subject in primary and secondary schools. Early exposure to mathematics is very important since it will affect the student perception towards this subject for their entire life. Therefore, a program called 'Mini Hari Matematik' was conducted to expose the basic mathematics concept through some games which fit the knowledge of Standard four and five students. A questionnaire regarding student perception towards this subject was distributed before and after the program. From the analysis, the program has positively changed the student's perception towards mathematics.

Mathematics computer-based training tool for pupils with special educational needs

OpenAIRE

Čeponienė, Lina

2010-01-01

Mathematics has a great influence on the development of world science and education, technology and human culture. Ukeje observes that without mathematics there is no science, without science there is no modern technology and without modern technology there is no modern society. In other words, mathematics is the precursor and the queen of science and technology and the indispensable single element in modern societal development. So, it plays a vital role in developing learners abilities to c...

Reassembling mathematical practices: a philosophical-anthropological approach

Directory of Open Access Journals (Sweden)

Karen François

2016-01-01

Full Text Available In this paper we first explore h ow Wittgenstein ’ s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein ’ s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics ( Wittgenstein 1973 . W e will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics . The central philosophical investigation concerns Wittgenstein’s shift to abandon ing the essentialist concept of language and therefore deny ing the existence of a universal language. Languages — or ‘language games’ as Wittgenstein calls them — are immersed in a form of life, in a cultural or social formation and are embedded in the totality o f communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure - making and sand drawing, to illustrate Wittgenstein ’s ideas . Base d on an ethnomathematical comparative analysis , we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality , as expressed in both string figure - making and sand drawing practices, from one society to another . Finally, w e suggest that a philosop hical - anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cul tures. Philoso phical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better

Developing mathematical modelling competence

DEFF Research Database (Denmark)

Blomhøj, Morten; Jensen, Tomas Højgaard

2003-01-01

In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....

VEDIC MATHEMATICS

Directory of Open Access Journals (Sweden)

Sead Rešić

2015-09-01

Full Text Available It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.

An Integrated Approach to Mathematical Modeling: A Classroom Study.

Science.gov (United States)

Doerr, Helen M.

Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…

A Call for Mathematics Education Colleagues and Stakeholders to Collaboratively Engage with NCTM: In Response to Martin's Commentary

Science.gov (United States)

Briars, Diane J.; Larson, Matt; Strutchens, Marilyn E.; Barnes, David

2015-01-01

In his commentary "The Collective Black and 'Principles to Actions,'" Martin (2015) offers a thought-provoking critique of "Principles to Actions: Ensuring Mathematical Success for All" (National Council of Teachers of Mathematics [NCTM], 2014). Martin (2015) states that the mathematics education community, in general, and the…

Principles of mathematical modeling

CERN Document Server

Dym, Clive

2004-01-01

Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...

Mathematical models and methods for planet Earth

CERN Document Server

Locatelli, Ugo; Ruggeri, Tommaso; Strickland, Elisabetta

2014-01-01

In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.

Reconstruction of the ion plasma parameters from the current measurements: mathematical tool

Directory of Open Access Journals (Sweden)

E. Séran

Full Text Available Instrument d’Analyse du Plasma (IAP is one of the instruments of the newly prepared ionospheric mission Demeter. This analyser was developed to measure flows of thermal ions at the altitude of ~ 750 km and consists of two parts: (i retarding potential analyser (APR, which is utilised to measure the energy distribution of the ion plasma along the sensor look direction, and (ii velocity direction analyser (ADV, which is used to measure the arrival angle of the ion flow with respect to the analyser axis. The necessity to obtain quick and precise estimates of the ion plasma parameters has prompted us to revise the existing mathematical tool and to investigate different instrumental limitations, such as (i finite angular aperture, (ii grid transparency, (iii potential depression in the space between the grid wires, (iv losses of ions during their passage between the entrance diaphragm and the collector. Simple analytical expressions are found to fit the currents, which are measured by the APR and ADV collectors, and show a very good agreement with the numerical solutions. It was proven that the fitting of the current with the model functions gives a possibility to properly resolve even minor ion concentrations and to find the arrival angles of the ion flow in the multi-species plasma. The discussion is illustrated by an analysis of the instrument response in the ionospheric conditions which are predicted by the International Reference Ionosphere (IRI model.

Key words. Ionosphere (plasma convection; instruments and techniques – Space plasma physics (experimental and mathematical techniques

Reconstruction of the ion plasma parameters from the current measurements: mathematical tool

Directory of Open Access Journals (Sweden)

E. Séran

2003-05-01

Full Text Available Instrument d’Analyse du Plasma (IAP is one of the instruments of the newly prepared ionospheric mission Demeter. This analyser was developed to measure flows of thermal ions at the altitude of ~ 750 km and consists of two parts: (i retarding potential analyser (APR, which is utilised to measure the energy distribution of the ion plasma along the sensor look direction, and (ii velocity direction analyser (ADV, which is used to measure the arrival angle of the ion flow with respect to the analyser axis. The necessity to obtain quick and precise estimates of the ion plasma parameters has prompted us to revise the existing mathematical tool and to investigate different instrumental limitations, such as (i finite angular aperture, (ii grid transparency, (iii potential depression in the space between the grid wires, (iv losses of ions during their passage between the entrance diaphragm and the collector. Simple analytical expressions are found to fit the currents, which are measured by the APR and ADV collectors, and show a very good agreement with the numerical solutions. It was proven that the fitting of the current with the model functions gives a possibility to properly resolve even minor ion concentrations and to find the arrival angles of the ion flow in the multi-species plasma. The discussion is illustrated by an analysis of the instrument response in the ionospheric conditions which are predicted by the International Reference Ionosphere (IRI model.Key words. Ionosphere (plasma convection; instruments and techniques – Space plasma physics (experimental and mathematical techniques

The Effect of the Immediate Feedback by the Collaborative Education Tool ViLLE on Learning for Business Mathematics in Higher Education

Science.gov (United States)

Kuikka, Matti; Laakso, Mikko-Jussi; Joshi, Marjo

2016-01-01

This article outlines the effect of the collaborative educational tool ViLLE when learning business mathematics in higher education. ViLLE validates students' answers during the assessment process and provides immediate feedback, enabling students to receive feedback and guidance about the correctness of their answers. The learning results in the…

Investigating CALL in the Classroom: Situational Variables to Consider

Directory of Open Access Journals (Sweden)

Darlene Liutkus

2012-01-01

Full Text Available A new paradigm in second language pedagogy has Computer Assisted Language Learning (CALL playing a significant role. Much of the literature to-date claims that CALL can have a positive impact on students’ second language acquisition (SLA. Mixed method of research produces data to investigate if CALL positively affects student language proficiency, motivation and autonomy. Classroom observation of participants in their natural environment is a qualitative technique used but has situational variables that could skew results if not structured. A questionnaire is a quantitative tool that can offer insight regarding participants’ perception of performance but can contradict what the researcher has observed. This paper will take an in-depth look at variables such as: instructor’s pedagogical application; blending CALL into the curriculum; types of CALL implemented; feedback received and their implications for design of the data collection tools

Mathematics of large eddy simulation of turbulent flows

Energy Technology Data Exchange (ETDEWEB)

Berselli, L.C. [Pisa Univ. (Italy). Dept. of Applied Mathematics ' ' U. Dini' ' ; Iliescu, T. [Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Dept. of Mathematics; Layton, W.J. [Pittsburgh Univ., PA (United States). Dept. of Mathematics

2006-07-01

Large eddy simulation (LES) is a method of scientific computation seeking to predict the dynamics of organized structures in turbulent flows by approximating local, spatial averages of the flow. Since its birth in 1970, LES has undergone an explosive development and has matured into a highly-developed computational technology. It uses the tools of turbulence theory and the experience gained from practical computation. This book focuses on the mathematical foundations of LES and its models and provides a connection between the powerful tools of applied mathematics, partial differential equations and LES. Thus, it is concerned with fundamental aspects not treated so deeply in the other books in the field, aspects such as well-posedness of the models, their energy balance and the connection to the Leray theory of weak solutions of the Navier-Stokes equations. The authors give a mathematically informed and detailed treatment of an interesting selection of models, focusing on issues connected with understanding and expanding the correctness and universality of LES. This volume offers a useful entry point into the field for PhD students in applied mathematics, computational mathematics and partial differential equations. Non-mathematicians will appreciate it as a reference that introduces them to current tools and advances in the mathematical theory of LES. (orig.)

Explorations in Elementary Mathematical Modeling

Science.gov (United States)

Shahin, Mazen

2010-01-01

In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…

International Conference on Applied Mathematics, Modeling and Computational Science & Annual meeting of the Canadian Applied and Industrial Mathematics

CERN Document Server

Bélair, Jacques; Kunze, Herb; Makarov, Roman; Melnik, Roderick; Spiteri, Raymond J

2016-01-01

Focusing on five main groups of interdisciplinary problems, this book covers a wide range of topics in mathematical modeling, computational science and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions between mathematicians, scientists, engineers and representatives from other disciplines. The book offers a valuable source of methods, ideas, and tools developed for a variety of disciplines, including the natural and social sciences, medicine, engineering, and technology. Original results are presented on both the fundamental and applied level, accompanied by an ample number of real-world problems and examples emphasizing the interdisciplinary nature and universality of mathematical modeling, and providing an excellent outline of today’s challenges. Mathematical modeling, with applied and computational methods and tools, plays a fundamental role in modern science a...

Mathematical methods in systems biology.

Science.gov (United States)

Kashdan, Eugene; Duncan, Dominique; Parnell, Andrew; Schattler, Heinz

2016-12-01

The editors of this Special Issue of Mathematical Biosciences and Engineering were the organizers for the Third International Workshop "Mathematical Methods in System Biology" that took place on June 15-18, 2015 at the University College Dublin in Ireland. As stated in the workshop goals, we managed to attract a good mix of mathematicians and statisticians working on biological and medical applications with biologists and clinicians interested in presenting their challenging problems and looking to find mathematical and statistical tools for their solutions.

Some applications of mathematics in theoretical physics - A review

International Nuclear Information System (INIS)

Bora, Kalpana

2016-01-01

Mathematics is a very beautiful subject−very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like−differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.

Some applications of mathematics in theoretical physics - A review

Energy Technology Data Exchange (ETDEWEB)

Bora, Kalpana [Physics Department, Gauhati University, Guwahati-781014, Assam (India)

2016-06-21

Mathematics is a very beautiful subject−very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like−differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.

Some applications of mathematics in theoretical physics - A review

Science.gov (United States)

Bora, Kalpana

2016-06-01

Mathematics is a very beautiful subject-very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like-differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.

Mathematics and electromagnetism

International Nuclear Information System (INIS)

Rodriguez Danta, M.

2000-01-01

Symbiosis between mathematics and electromagnetism is analyzed in a simple and concise manner by taking a historical perspective. The universal tool character of mathematical models allowed the transfer of models from several branches of physics into the realm of electromagnetism by drawing analogies. The mutual interdependence between covariant formulation and tensor calculus is marked. The paper focuses on the guiding idea of field theory and Maxwell's equations. Likewise, geometrization of interactions in connection with gauge fields is also noted. (Author)

The reasonable effectiveness of mathematics in the natural sciences

Science.gov (United States)

Harvey, Alex

2011-12-01

Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism—mathematics exists and is discovered; Logicism—all mathematics may be deduced through pure logic; Formalism—mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism—mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.

A mathematics sampler topics for the liberal arts

CERN Document Server

Berlinghoff, William P; Skrien, Dale

2001-01-01

Now in its fifth edition, A Mathematics Sampler presents mathematics as both science and art, focusing on the historical role of mathematics in our culture. It uses selected topics from modern mathematics-including computers, perfect numbers, and four-dimensional geometry-to exemplify the distinctive features of mathematics as an intellectual endeavor, a problem-solving tool, and a way of thinking about the rapidly changing world in which we live. A Mathematics Sampler also includes unique LINK sections throughout the book, each of which connects mathematical concepts with areas of interest th

"Whys" and "Hows" of Using Philosophy in Mathematics Education

Science.gov (United States)

Jankvist, Uffe Thomas; Iversen, Steffen Møllegaard

2014-01-01

The article elaborates and exemplifies a potential categorization of the reasons for using philosophy, in particular the philosophy of mathematics, in mathematics education and approaches to doing so-the so-called "whys" and "hows". More precisely, the "whys" are divided into the two categories of "philosophy as…

Effects of Online Visual and Interactive Technological Tool (OVITT) on Early Adolescent Students' Mathematics Performance, Math Anxiety and Attitudes toward Math

Science.gov (United States)

Orabuchi, Nkechi

2013-01-01

This study reported the results of a 3-month quasi-experimental study that determined the effectiveness of an online visual and interactive technological tool on sixth grade students' mathematics performance, math anxiety and attitudes towards math. There were 155 sixth grade students from a middle school in the North Texas area who participated…

Ultrasound call detection in capybara

Directory of Open Access Journals (Sweden)

Selene S.C. Nogueira

2012-07-01

Full Text Available The vocal repertoire of some animal species has been considered a non-invasive tool to predict distress reactivity. In rats ultrasound emissions were reported as distress indicator. Capybaras[ vocal repertoire was reported recently and seems to have ultrasound calls, but this has not yet been confirmed. Thus, in order to check if a poor state of welfare was linked to ultrasound calls in the capybara vocal repertoire, the aim of this study was to track the presence of ultrasound emissions in 11 animals under three conditions: 1 unrestrained; 2 intermediately restrained, and 3 highly restrained. The ultrasound track identified frequencies in the range of 31.8±3.5 kHz in adults and 33.2±8.5 kHz in juveniles. These ultrasound frequencies occurred only when animals were highly restrained, physically restrained or injured during handling. We concluded that these calls with ultrasound components are related to pain and restraint because they did not occur when animals were free of restraint. Thus we suggest that this vocalization may be used as an additional tool to assess capybaras[ welfare.

Experiencing Socially Relevant Applications in the High School Mathematics Curriculum: Students' Perspectives on Mathematics as a Tool for Social Inquiry

Science.gov (United States)

Brelias, Anastasia

2009-01-01

The purpose of this study was to examine the use of socially relevant mathematics applications in high school mathematics classrooms and students' views of mathematics in light of their experiences with these applications. Also, the study sought to determine whether inquiries afforded by these applications incorporated features that promoted…

K-12 Mathematics and the Web

Science.gov (United States)

Glazer, Evan

2005-01-01

The Web offers numerous learning resources and opportunities for K-12 mathematics education. This paper discusses those resources and opportunities. Discussion includes (a) asynchronous and synchronous communication tools, (b) the use of data sets to make connections between mathematics concepts and real-world applications, and (c) interactive…

Online Mathematics Homework Increases Student Achievement

Directory of Open Access Journals (Sweden)

Jeremy Roschelle

2016-10-01

Full Text Available In a randomized field trial with 2,850 seventh-grade mathematics students, we evaluated whether an educational technology intervention increased mathematics learning. Assigning homework is common yet sometimes controversial. Building on prior research on formative assessment and adaptive teaching, we predicted that combining an online homework tool with teacher training could increase learning. The online tool ASSISTments (a provides timely feedback and hints to students as they do homework and (b gives teachers timely, organized information about students’ work. To test this prediction, we analyzed data from 43 schools that participated in a random assignment experiment in Maine, a state that provides every seventh-grade student with a laptop to take home. Results showed that the intervention significantly increased student scores on an end-of-the-year standardized mathematics assessment as compared with a control group that continued with existing homework practices. Students with low prior mathematics achievement benefited most. The intervention has potential for wider adoption.

Algorithms in Modern Mathematics and Computer Science.

Science.gov (United States)

1980-01-01

importance, since we will go on doing what we are doing no matter what it is called; after all, other disciplines like Mathematics and Chemistry are no...longer related very strongly to the etymology of their names. However, if I had a chance to vote for the name of my own discipline, I would choose to call

Intuitionism vs. classicism a mathematical attack on classical logic

CERN Document Server

Haverkamp, Nick

2015-01-01

In the early twentieth century, the Dutch mathematician L.E.J. Brouwer launched a powerful attack on the prevailing mathematical methods and theories. He developed a new kind of constructive mathematics, called intuitionism, which seems to allow for a rigorous refutation of widely accepted mathematical assumptions including fundamental principles of classical logic. Following an intense mathematical debate esp. in the 1920s, Brouwer's revolutionary criticism became a central philosophical concern in the 1970s, when Michael Dummett tried to substantiate it with meaning-theoretic considerations.

Virtual Manipulatives: Tools for Teaching Mathematics to Students with Learning Disabilities

Science.gov (United States)

Shin, Mikyung; Bryant, Diane P.; Bryant, Brian R.; McKenna, John W.; Hou, Fangjuan; Ok, Min Wook

2017-01-01

Many students with learning disabilities demonstrate difficulty in developing a conceptual understanding of mathematical topics. Researchers recommend using visual models to support student learning of the concepts and skills necessary to complete abstract and symbolic mathematical problems. Virtual manipulatives (i.e., interactive visual models)…

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

Students' perceptions of the relevance of mathematics in engineering

Science.gov (United States)

Flegg, Jennifer; Mallet, Dann; Lupton, Mandy

2012-09-01

In this article, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society [M. Kirschenman and B. Brenner, Education for Civil Engineering: A Profession of Practice, Leader. Manag. Eng. 10 (2010), p. 54]. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of engineering mathematics curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour and the effectiveness of problem-solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.

Call for new OWSD Fellowships for Early Career Women Scientists ...

International Development Research Centre (IDRC) Digital Library (Canada)

2018-05-03

May 3, 2018 ... Call for new OWSD Fellowships for Early Career Women Scientists now open ... or mathematics; and employed at an academic or scientific research ... research groups that will attract international visitors; and to develop links with ... opportunity to support Canadian-African research teams studying Ebola.

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.

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

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.

The body and playfulness: promising tools for teaching and learning mathematics

Directory of Open Access Journals (Sweden)

Yolanda Rodríguez Manosalva

2017-06-01

Full Text Available This paper will analyze the importance of playfulness as an instrument for learning mathematics, taking into account that the body allows to develop not only motor skills but also intellectual faculties involving high levels of abstraction, such as mathematical operations like addition, subtraction, multiplication and division. The methodology used was action research, through interviews to students, parents and teachers, as well as the systematization of experiences in the classroom by means of a field diary. It was found that traditional –tedious- teaching does not allow students to realize the importance of learning mathematics. It is concluded that it is necessary for the teachers to implement strategies that link playfulness and the body, in order to improve teaching-learning processes, which allows that mathematics do not be considered as something far from reality, but that be granted the status of a knowledge that improves the processes of understanding and reflection, facilitating the solution of practical problems.

COLLEGE STUDENTS’ PERCEPTIONS OF LEARNING MATHEMATICS AND USING COMPUTERS

OpenAIRE

Gok, Tolga

2016-01-01

Mathematics isthe key course to interpret the science and nature. A positive attitude shouldbe improved by learners to comprehend the logic of mathematics. However, mostof the research indicated that they were not interested in learning andstudying mathematics. Instead of understanding the basic principles, manystudents preferred to use sophisticated software packages or graphingcalculators for solving mathematics problems. Thus, these tools prevent theimprovement of their mathematical skills...

The written mathematical communication profile of prospective math teacher in mathematical proving

Science.gov (United States)

Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.

2018-01-01

Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

Modeling life the mathematics of biological systems

CERN Document Server

Garfinkel, Alan; Guo, Yina

2017-01-01

From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. This book develops the mathematical tools essential for students in the life sciences to describe these interacting systems and to understand and predict their behavior. Complex feedback relations and counter-intuitive responses are common in dynamical systems in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models ...

The Impact of Chess Instruction on the Critical Thinking Ability and Mathematical Achievement of Developmental Mathematics Students

Science.gov (United States)

Berkley, Darrin K.

2012-01-01

This sequential explanatory mixed-methods study determined whether the game of chess can be used as an educational tool to improve critical thinking skills of developmental mathematics students and improve mathematics achievement for these students. Five research questions were investigated. These questions were as follows: (a) Is there a…

Computational and mathematical methods in brain atlasing.

Science.gov (United States)

Nowinski, Wieslaw L

2017-12-01

Brain atlases have a wide range of use from education to research to clinical applications. Mathematical methods as well as computational methods and tools play a major role in the process of brain atlas building and developing atlas-based applications. Computational methods and tools cover three areas: dedicated editors for brain model creation, brain navigators supporting multiple platforms, and atlas-assisted specific applications. Mathematical methods in atlas building and developing atlas-aided applications deal with problems in image segmentation, geometric body modelling, physical modelling, atlas-to-scan registration, visualisation, interaction and virtual reality. Here I overview computational and mathematical methods in atlas building and developing atlas-assisted applications, and share my contribution to and experience in this field.

A complementary measure of heterogeneity on mathematical skills

Science.gov (United States)

Fedriani, Eugenio M.; Moyano, Rafael

2012-06-01

Finding educational truths is an inherently multivariate problem. There are many factors affecting each student and their performances. Because of this, both measuring of skills and assessing students are always complex processes. This is a well-known problem, and a number of solutions have been proposed by specialists. One of its ramifications is that the variety of progress levels of students in the Mathematics classroom makes teaching more difficult. We think that a measure of the heterogeneity of the different student groups could be interesting in order to prepare some strategies to deal with these kinds of difficulties. The major aim of this study is to develop new tools, complementary to the statistical ones that are commonly used for these purposes, to study situations related to education (mainly to the detection of levels of mathematical education) in which several variables are involved. These tools are thought to simplify these educational analyses and, through a better comprehension of the topic, to improve our teaching. Several authors in our research group have developed some mathematical, theoretical tools, to deal with multidimensional phenomena, and have applied them to measure poverty and also to other business models. These tools are based on multidigraphs. In this article, we implement these tools using symbolic computational software and apply them to study a specific situation related to mathematical education.

Computational experiment approach to advanced secondary mathematics curriculum

CERN Document Server

Abramovich, Sergei

2014-01-01

This book promotes the experimental mathematics approach in the context of secondary mathematics curriculum by exploring mathematical models depending on parameters that were typically considered advanced in the pre-digital education era. This approach, by drawing on the power of computers to perform numerical computations and graphical constructions, stimulates formal learning of mathematics through making sense of a computational experiment. It allows one (in the spirit of Freudenthal) to bridge serious mathematical content and contemporary teaching practice. In other words, the notion of teaching experiment can be extended to include a true mathematical experiment. When used appropriately, the approach creates conditions for collateral learning (in the spirit of Dewey) to occur including the development of skills important for engineering applications of mathematics. In the context of a mathematics teacher education program, this book addresses a call for the preparation of teachers capable of utilizing mo...

The application of new mathematical structures to safety analysis

International Nuclear Information System (INIS)

Cooper, J.A.; Ross, T.J.

1997-10-01

Probabilistic safety analyses (PSAs) often depend on significant subjectivity. The recent successes of fuzzy logic and fuzzy and hybrid mathematics in portraying subjectivity is a reminder that a selection made from the most applicable mathematical tools is more important than forced adaptation of conventional tools. In this paper, the authors consider new approaches that enhance conventional and fuzzy PSA by improved handling of subjectivity. The most significant of the mathematical structures were have investigated (from a standpoint of safety analysis applications) will be described, and the general types of applications will be outlined

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

Differences in Mathematics Teachers' Perceived Preparedness to Demonstrate Competence in Secondary School Mathematics Content by Teacher Characteristics

Science.gov (United States)

Ng'eno, J. K.; Chesimet, M. C.

2016-01-01

A sample of 300 mathematics teachers drawn from a population of 1500 participated in this study. The participants were selected using systematic random sampling and stratified random sampling (stratified by qualification and gender). The data was collected using self-report questionnaires for mathematics teachers. One tool was used to collect…

Reframing Research on Methods Courses to Inform Mathematics Teacher Educators' Practice

Science.gov (United States)

Kastberg, Signe E.; Tyminski, Andrew M.; Sanchez, Wendy B.

2017-01-01

Calls have been made for the creation of a shared knowledge base in mathematics teacher education with the power to inform the design of scholarly inquiry and mathematics teacher educators' (MTEs) scholarly practices. Focusing on mathematics methods courses, we summarize and contribute to literature documenting activities MTEs use in mathematics…

Mathematical and physical theory of turbulence

CERN Document Server

Cannon, John

2006-01-01

Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence. Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier-Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities a...

Mathematical methods for physicists

CERN Document Server

Arfken, George B

2005-01-01

This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.* Updates the leading graduate-level text in mathematical physics* Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering* Focuses on problem-solving skills and offers a vast array of exercises * Clearly illustrates and proves mathematical relationsNew in the Sixth Edition:* Updated content throughout, based on users'' feedback * More advanced sections, including differential forms and the elegant forms of Maxwell''s equations* A new chapter on probability and statistics* More elementary sections have been deleted

Mathematical grammar of biology

CERN Document Server

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.

Applying an alternative mathematics pedagogy for students with weak mathematics: meta-analysis of alternative pedagogies

Science.gov (United States)

Lake, Warren; Wallin, Margie; Woolcott, Geoff; Boyd, Wendy; Foster, Alan; Markopoulos, Christos; Boyd, William

2017-02-01

Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was undertaken of identified innovations and/or interventions that may lead to improvement in student outcomes for university mathematics-based units of study. The review revealed the importance of understanding the foundations of student performance in higher education mathematics learning, especially in first year. Pre-university mathematics skills were identified as significant in student retention and mathematics success at university, and a specific focus on student pre-university mathematics skill level was found to be more effective in providing help, rather than simply focusing on a particular at-risk group. Diagnostics tools were found to be important in identifying (1) student background and (2) appropriate intervention. The studies highlighted the importance of appropriate and validated interventions in mathematics teaching and learning, and the need to improve the learning model for mathematics-based subjects, communication and technology innovations.

Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call

Directory of Open Access Journals (Sweden)

Maxim A. Dulebenets

2018-03-01

Full Text Available Considering a substantial increase in volumes of the international seaborne trade and drastic climate changes due to carbon dioxide emissions, liner shipping companies have to improve planning of their vessel schedules and improve energy efficiency. This paper presents a novel mixed integer non-linear mathematical model for the green vessel scheduling problem, which directly accounts for the carbon dioxide emission costs in sea and at ports of call. The original non-linear model is linearized and then solved using CPLEX. A set of numerical experiments are conducted for a real-life liner shipping route to reveal managerial insights that can be of importance to liner shipping companies. Results indicate that the proposed mathematical model can serve as an efficient planning tool for liner shipping companies and may assist with evaluation of various carbon dioxide taxation schemes. Increasing carbon dioxide tax may substantially change the design of vessel schedules, incur additional route service costs, and improve the environmental sustainability. However, the effects from increasing carbon dioxide tax on the marine container terminal operations are found to be very limited.

Mathematical analysis II

CERN Document Server

Canuto, Claudio

2015-01-01

The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, ...

Assessing call centers’ success:

Directory of Open Access Journals (Sweden)

Hesham A. Baraka

2013-07-01

This paper introduces a model to evaluate the performance of call centers based on the Delone and McLean Information Systems success model. A number of indicators are identified to track the call center’s performance. Mapping of the proposed indicators to the six dimensions of the D&M model is presented. A Weighted Call Center Performance Index is proposed to assess the call center performance; the index is used to analyze the effect of the identified indicators. Policy-Weighted approach was used to assume the weights with an analysis of different weights for each dimension. The analysis of the different weights cases gave priority to the User satisfaction and net Benefits dimension as the two outcomes from the system. For the input dimensions, higher priority was given to the system quality and the service quality dimension. Call centers decision makers can use the tool to tune the different weights in order to reach the objectives set by the organization. Multiple linear regression analysis was used in order to provide a linear formula for the User Satisfaction dimension and the Net Benefits dimension in order to be able to forecast the values for these two dimensions as function of the other dimensions

Interactive Whiteboards in Mathematics Teaching: A Literature Review

Directory of Open Access Journals (Sweden)

Mauro De Vita

2014-01-01

Full Text Available An interactive whiteboard (IWB is a relatively new tool that provides interesting affordances in the classroom environment, such as multiple visualization and multimedia presentation and ability for movement and animation. These affordances make IWBs an innovative tool with high potential for mathematics instructional environments. IWBs can be used to focus on the development of specific mathematical concepts and to improve mathematical knowledge and understanding. The aim of this paper is to review the existing literature upon the use of interactive whiteboards (IWBs in mathematics classrooms. The reviewed studies offer a wide view of IWBs’ affordances, of the more interesting didactic practices, and of the difficulties of embedding this new technology in the classroom. The capabilities of IWBs to enhance the quality of interaction, and, consequently, to improve conceptual mathematical understanding are broadly recognized. Despite these capabilities, evidence from the studies points to a certain inertia on the part of many teachers to do anything else than use IWBs as large-scale visual blackboards or presentation tools. The emerging view of how to attempt to overcome these obstacles is that there is need for greater attention to the pedagogy associated with IWB use and, more specifically, to stimulate the design of new kinds of learning environments.

Study of Tool Wear Mechanisms and Mathematical Modeling of Flank Wear During Machining of Ti Alloy (Ti6Al4V)

Science.gov (United States)

Chetan; Narasimhulu, A.; Ghosh, S.; Rao, P. V.

2015-07-01

Machinability of titanium is poor due to its low thermal conductivity and high chemical affinity. Lower thermal conductivity of titanium alloy is undesirable on the part of cutting tool causing extensive tool wear. The main task of this work is to predict the various wear mechanisms involved during machining of Ti alloy (Ti6Al4V) and to formulate an analytical mathematical tool wear model for the same. It has been found from various experiments that adhesive and diffusion wear are the dominating wear during machining of Ti alloy with PVD coated tungsten carbide tool. It is also clear from the experiments that the tool wear increases with the increase in cutting parameters like speed, feed and depth of cut. The wear model was validated by carrying out dry machining of Ti alloy at suitable cutting conditions. It has been found that the wear model is able to predict the flank wear suitably under gentle cutting conditions.

Obstacles Related to Structuring for Mathematization Encountered by Students when Solving Physics Problems

DEFF Research Database (Denmark)

Niss, Martin

2017-01-01

This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called structuring for mathematization, where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report...

An applied artificial intelligence approach towards assessing building performance simulation tools

Energy Technology Data Exchange (ETDEWEB)

Yezioro, Abraham [Faculty of Architecture and Town Planning, Technion IIT (Israel); Dong, Bing [Center for Building Performance and Diagnostics, School of Architecture, Carnegie Mellon University (United States); Leite, Fernanda [Department of Civil and Environmental Engineering, Carnegie Mellon University (United States)

2008-07-01

With the development of modern computer technology, a large amount of building energy simulation tools is available in the market. When choosing which simulation tool to use in a project, the user must consider the tool's accuracy and reliability, considering the building information they have at hand, which will serve as input for the tool. This paper presents an approach towards assessing building performance simulation results to actual measurements, using artificial neural networks (ANN) for predicting building energy performance. Training and testing of the ANN were carried out with energy consumption data acquired for 1 week in the case building called the Solar House. The predicted results show a good fitness with the mathematical model with a mean absolute error of 0.9%. Moreover, four building simulation tools were selected in this study in order to compare their results with the ANN predicted energy consumption: Energy{sub 1}0, Green Building Studio web tool, eQuest and EnergyPlus. The results showed that the more detailed simulation tools have the best simulation performance in terms of heating and cooling electricity consumption within 3% of mean absolute error. (author)

Using Maxima in the Mathematics Classroom

Science.gov (United States)

Fedriani, Eugenio M.; Moyano, Rafael

2011-01-01

Coming from the Macsyma system and adapted to the Common Lisp standard, Maxima can be regarded as a tool for a frequent use in the mathematics classroom. The main aim of this work is to show some possibilities of Maxima and its graphical interface through our experience as Mathematics teachers in Business degrees, although it can be easily spread…

Mathematics and the laws of nature

CERN Document Server

Tabak, John

2004-01-01

Examining the pioneering ideas, works, and applications that have made math the language of science, Mathematics and the Laws of Nature looks at the many ways in which so-called ''''pure'''' math has been used in the applied sciences. For example, the volume explores how mathematical theories contributed to the development of Kepler''s laws of planetary motion, as well as to that of combustion modeling and hydrodynamics. Offering many examples showing how nature can be described mathematically and how the physical sciences and math are connected, this attention-holding and easy-to-understand volume gives students an insight into the ways that math is used to explain the world around them.

Tool path in torus tool CNC machining

Directory of Open Access Journals (Sweden)

XU Ying

2016-10-01

Full Text Available This paper is about tool path in torus tool CNC machining.The mathematical model of torus tool is established.The tool path planning algorithm is determined through calculation of the cutter location,boundary discretization,calculation of adjacent tool path and so on,according to the conversion formula,the cutter contact point will be converted to the cutter location point and then these points fit a toolpath.Lastly,the path planning algorithm is implemented by using Matlab programming.The cutter location points for torus tool are calculated by Matlab,and then fit these points to a toolpath.While using UG software,another tool path of free surface is simulated of the same data.It is drew compared the two tool paths that using torus tool is more efficient.

Mathematical control theory

International Nuclear Information System (INIS)

Agrachev, A.A.

2002-01-01

This volume is based on the lecture notes of the minicourses given in the frame of the school on Mathematical Control Theory held at the Abdus Salam ICTP from 3 to 28 September 2001. Mathematical Control Theory is a rapidly growing field which provides strict theoretical and computational tools for dealing with problems arising in electrical and aerospace engineering, automatics, robotics, applied chemistry, and biology etc. Control methods are also involved in questions pertaining to the development of countries in the South, such as wastewater treatment, agronomy, epidemiology, population dynamics, control of industrial and natural bio-reactors. Since most of these natural processes are highly nonlinear, the tools of nonlinear control are essential for the modelling and control of such processes. At present regular courses in Mathematical Control Theory are rarely included in the curricula of universities, and very few researchers receive enough background in the field. Therefore it is important to organize specific activities in the form of schools to provide the necessary background for those embarking on research in this field. The school at the Abdus Salam ICTP consisted of several minicourses intended to provide an introduction to various topics of Mathematical Control Theory, including Linear Control Theory (finite and infinite-dimensional), Nonlinear Control, and Optimal Control. The last week of the school was concentrated on applications of Mathematical Control Theory, in particular, those which are important for the development of non-industrialized countries. The school was intended primarily for mathematicians and mathematically oriented engineers at the beginning of their career. The typical participant was expected to be a graduate student or young post-doctoral researcher interested in Mathematical Control Theory. It was assumed that participants have sufficient background in Ordinary Differential Equations and Advanced Calculus. The volume

Mathematical control theory

Energy Technology Data Exchange (ETDEWEB)

Agrachev, A A [Steklov Mathematical Institute, Moscow (Russian Federation); SISSA, Trieste [Italy; ed.

2002-07-15

This volume is based on the lecture notes of the minicourses given in the frame of the school on Mathematical Control Theory held at the Abdus Salam ICTP from 3 to 28 September 2001. Mathematical Control Theory is a rapidly growing field which provides strict theoretical and computational tools for dealing with problems arising in electrical and aerospace engineering, automatics, tics, applied chemistry, and biology etc. Control methods are also involved in questions pertaining to the development of countries in the South, such as wastewater treatment, agronomy, epidemiology, population dynamics, control of industrial and natural bio-reactors. Since most of these natural processes are highly nonlinear, the tools of nonlinear control are essential for the modelling and control of such processes. At present regular courses in Mathematical Control Theory are rarely included in the curricula of universities, and very few researchers receive enough background in the field. Therefore it is important to organize specific activities in the form of schools to provide the necessary background for those embarking on research in this field. The school at the Abdus Salam ICTP consisted of several minicourses intended to provide an introduction to various topics of Mathematical Control Theory, including Linear Control Theory (finite and infinite-dimensional), Nonlinear Control, and Optimal Control. The last week of the school was concentrated on applications of Mathematical Control Theory, in particular, those which are important for the development of non-industrialized countries. The school was intended primarily for mathematicians and mathematically oriented engineers at the beginning of their career. The typical participant was expected to be a graduate student or young post-doctoral researcher interested in Mathematical Control Theory. It was assumed that participants have sufficient background in Ordinary Differential Equations and Advanced Calculus. The volume contains

Improvement of Word Problem Solving and Basic Mathematics Competencies in Students with Attention Deficit/Hyperactivity Disorder and Mathematical Learning Difficulties

Science.gov (United States)

González-Castro, Paloma; Cueli, Marisol; Areces, Débora; Rodríguez, Celestino; Sideridis, Georgios

2016-01-01

Problem solving represents a salient deficit in students with mathematical learning difficulties (MLD) primarily caused by difficulties with informal and formal mathematical competencies. This study proposes a computerized intervention tool, the integrated dynamic representation (IDR), for enhancing the early learning of basic mathematical…

Illustrating Mathematics using 3D Printers

OpenAIRE

Knill, Oliver; Slavkovsky, Elizabeth

2013-01-01

3D printing technology can help to visualize proofs in mathematics. In this document we aim to illustrate how 3D printing can help to visualize concepts and mathematical proofs. As already known to educators in ancient Greece, models allow to bring mathematics closer to the public. The new 3D printing technology makes the realization of such tools more accessible than ever. This is an updated version of a paper included in book Low-Cost 3D Printing for science, education and Sustainable Devel...

CLEP college mathematics

CERN Document Server

Friedman, Mel

2012-01-01

Earn College Credit with REA's Test Prep for CLEP* College Mathematics Everything you need to pass the exam and get the college credit you deserve.CLEP* is the most popular credit-by-examination program in the country, accepted by more than 2,900 colleges and universities. For over 15 years, REA has helped students pass the CLEP* exam and earn college credit while reducing their tuition costs. Our test prep for CLEP* College Mathematics and the free online tools that come with it, allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your lea

The MATH--Open Source Application for Easier Learning of Numerical Mathematics

Science.gov (United States)

Glaser-Opitz, Henrich; Budajová, Kristina

2016-01-01

The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

Research trends in mathematics teacher education

CERN Document Server

Lo, Jane-Jane; Zoest, Laura RVan

2014-01-01

Research on the preparation and continued development of mathematics teachers is becoming an increasingly important subset of mathematics education research. Such research explores the attributes, knowledge, skills and beliefs of mathematics teachers as well as methods for assessing and developing these critical aspects of teachers and influences on teaching.Research Trends in Mathematics Teacher Education focuses on three major themes in current mathematics teacher education research: mathematical knowledge for teaching, teacher beliefs and identities, and tools and techniques to support teacher learning. Through careful reports of individual research studies and cross-study syntheses of the state of research in these areas, the book provides insights into teachers' learning processes and how these processes can be harnessed to develop effective teachers. Chapters investigate bedrock skills needed for working with primary and secondary learners (writing relevant problems, planning lessons, being attentive to...

Using GeoGebra for Mathematics Education at University Undergraduate Level

DEFF Research Database (Denmark)

Triantafyllou, Eva; Timcenko, Olga

Our research effort presented in this talk relates with developing digital tools for mathematics education at undergraduate university level. It focuses specifically on studies where mathematics is not a core subject but it is very important in order to cope with core subjects. For our design, we...... feedback inspire the next round of design requirements for the development of digital tools that support mathematics teaching and learning at university level....... conducted observations of teachers and students during lectures and exercise time. During these observations we were able to investigate how the applets were used in practice but also to get insight in the challenges that the students face during mathematics learning. These findings together with student...

Towards a Dialogical Pedagogy: Some Characteristics of a Community of Mathematical Inquiry

Science.gov (United States)

Kennedy, Nadia Stoyanova

2009-01-01

This paper discusses a teaching model called community of mathematical inquiry (CMI), characterized by dialogical and inquiry-driven communication and a dynamic structure of intertwined cognitive processes including distributed thinking, mathematical argumentation, integrated reasoning, conceptual transformation, internalization of critical…

Higher-order automatic differentiation of mathematical functions

Science.gov (United States)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

Mathematical literacy teachers' engagement with contextual tasks ...

African Journals Online (AJOL)

This article reports on a study carried out with a group of 108 practising Mathematical Literacy (ML) teachers who participated in an Advanced Certificate in Education (ACE) programme. The purpose of the qualitative study was to identify and describe the teachers' varying levels of engagement with mathematics tools and ...

Type classes for mathematics in type theory

OpenAIRE

Spitters, Bas; Van der Weegen, Eelis

2011-01-01

The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage of their unique features to make practical a particularly flexible approach formerly thought infeasible. Thus, we address both traditional proof engineering challenges as well as new ones resulting from our ambition to build upon this development a library...

Mathematical methods for mechanics a handbook with Matlab experiments

CERN Document Server

Gekeler, Eckart W

2008-01-01

This book introduces all the mathematical tools necessary for solving complex problems in the field of mechanics. It also contains various applications of mathematical and numerical methods for modeling comprehensive mechanical-technical practical problems.

The Preparation Experiences of Elementary Mathematics Specialists: Examining Influences on Beliefs, Content Knowledge, and Teaching Practices

Science.gov (United States)

Swars, Susan L.; Smith, Stephanie Z.; Smith, Marvin E.; Carothers, Jody; Myers, Kayla

2018-01-01

Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for…

Semantic Contamination and Mathematical Proof: Can a Non-Proof Prove?

Science.gov (United States)

Mejia-Ramos, Juan Pablo; Inglis, Matthew

2011-01-01

The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to…

Concepts of mathematical modeling

CERN Document Server

Meyer, Walter J

2004-01-01

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec

Mathematical methods for cancer evolution

CERN Document Server

Suzuki, Takashi

2017-01-01

The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools. The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematica...

Mathematical methods of many-body quantum field theory

CERN Document Server

Lehmann, Detlef

2004-01-01

Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations.Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and wh...

Hipatia: a hypermedia learning environment in mathematics

Directory of Open Access Journals (Sweden)

Marisol Cueli

2016-01-01

Full Text Available Literature revealed the benefits of different instruments for the development of mathematical competence, problem solving, self-regulated learning, affective-motivational aspects and intervention in students with specific difficulties in mathematics. However, no one tool combined all these variables. The aim of this study is to present and describe the design and development of a hypermedia tool, Hipatia. Hypermedia environments are, by definición, adaptive learning systems, which are usually a web-based application program that provide a personalized learning environment. This paper describes the principles on which Hipatia is based as well as a review of available technologies developed in different academic subjects. Hipatia was created to boost self-regulated learning, develop specific math skills, and promote effective problem solving. It was targeted toward fifth and sixth grade students with and without learning difficulties in mathematics. After the development of the tool, we concluded that it aligned well with the logic underlying the principles of self-regulated learning. Future research is needed to test the efficacy of Hipatia with an empirical methodology.

Colombeau algebra as a mathematical tool for investigating step load and step deformation of systems of nonlinear springs and dashpots

Science.gov (United States)

Průša, Vít; Řehoř, Martin; Tůma, Karel

2017-02-01

The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its response is governed by a system of linear ordinary differential equations. In the linear case, the mathematical method of choice for the analysis of the response is the classical theory of distributions. However, if the system contains nonlinear elements, then the classical theory of distributions is of no use, since it is strictly limited to the linear setting. Consequently, a question arises whether it is even possible or reasonable to study the response of nonlinear systems to step inputs. The answer is positive. A mathematical theory that can handle the challenge is the so-called Colombeau algebra. Building on the abstract result by Průša and Rajagopal (Int J Non-Linear Mech 81:207-221, 2016), we show how to use the theory in the analysis of response of nonlinear spring-dashpot and spring-dashpot-mass systems.

Introduction to mathematical physics methods and concepts

CERN Document Server

Wong, Chun Wa

2013-01-01

Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages...

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.

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.

The mathematics behind biological invasions

CERN Document Server

Lewis, Mark A; Potts, Jonathan R

2016-01-01

This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes. Applications to real biological invasions are included throughout. Ultimately, the book imparts a powerful principle: that by bringing ecology and mathematics together, researchers can uncover new understanding of, and effective response strategies to, biological invasions. It is suitable for graduate students and established researchers in mathematical ecolo...

Teach the Mathematics of Mathematicians

Directory of Open Access Journals (Sweden)

Peter Taylor

2018-04-01

Full Text Available The secondary-school mathematics curriculum is narrow in scope and technical in character; this is quite different from the nature of the discipline itself. As a result, it offers little inspiration to both students and teachers, and provides students with poor preparation for university mathematics courses and indeed for life. Over the past century, recently more than ever, there have been calls for change, for a curriculum that is true to the subject of mathematics as the creation and study of patterns and structures. While there are hopeful responses to this at the elementary level, there is almost nothing at the secondary level. Ironically, it is felt that in order to prepare students for university calculus, the secondary curriculum simply has to be what it is. This is a special case of a myth that needs to be destroyed.

Rigorous Mathematical Thinking Approach to Enhance Students’ Mathematical Creative and Critical Thinking Abilities

Science.gov (United States)

Hidayat, D.; Nurlaelah, E.; Dahlan, J. A.

2017-09-01

The ability of mathematical creative and critical thinking are two abilities that need to be developed in the learning of mathematics. Therefore, efforts need to be made in the design of learning that is capable of developing both capabilities. The purpose of this research is to examine the mathematical creative and critical thinking ability of students who get rigorous mathematical thinking (RMT) approach and students who get expository approach. This research was quasi experiment with control group pretest-posttest design. The population were all of students grade 11th in one of the senior high school in Bandung. The result showed that: the achievement of mathematical creative and critical thinking abilities of student who obtain RMT is better than students who obtain expository approach. The use of Psychological tools and mediation with criteria of intentionality, reciprocity, and mediated of meaning on RMT helps students in developing condition in critical and creative processes. This achievement contributes to the development of integrated learning design on students’ critical and creative thinking processes.

Unpacking the Male Superiority Myth and Masculinization of Mathematics at the Intersections: A Review of Research on Gender in Mathematics Education

Science.gov (United States)

Leyva, Luis A.

2017-01-01

Gender research in mathematics education has experienced methodological and theoretical shifts over the past 45 years. Although achievement studies have used assessment tools to explore and subsequently challenge the assumption of male superiority on mathematics assessments, research on participation has unpacked these studies' sex-based…

Immanence or Transcendence? A Mathematical View

Directory of Open Access Journals (Sweden)

H Chris Ransford

2016-03-01

Full Text Available This paper uses the tools of mathematical analysis to try and shed light on the age-old question of whether a monotheist God would be simultaneously present everywhere in the wider Universe, or whether It would rather usually keep to privileged locations within space-time. On the narrow basis of where the mathematics leads, it reaches an unexpected but definite conclusion.

Computer mathematics for programmers

CERN Document Server

Abney, Darrell H; Sibrel, Donald W

1985-01-01

Computer Mathematics for Programmers presents the Mathematics that is essential to the computer programmer.The book is comprised of 10 chapters. The first chapter introduces several computer number systems. Chapter 2 shows how to perform arithmetic operations using the number systems introduced in Chapter 1. The third chapter covers the way numbers are stored in computers, how the computer performs arithmetic on real numbers and integers, and how round-off errors are generated in computer programs. Chapter 4 details the use of algorithms and flowcharting as problem-solving tools for computer p

Talking about teaching and learning mathematics in indigenous schools

Directory of Open Access Journals (Sweden)

Lucélida de Fátima Maia da Costa

2012-09-01

Full Text Available To teach and to learn mathematics are not always conjugated concomitantly, particularly in the context of formal indigenous schools. This article puts in discussion some facts about the role of schools in indigenous communities, often mistakenly called Indian schools, as well as questions about the meaning of teaching mathematics in those contexts. Based on the concepts of ethnomathematics, it shows that a dialogue is possible between the traditional mathematical knowledge of various ethnic groups of the Amazon and the knowledge disseminated by formal school teaching practice.

Heuristic Biases in Mathematical Reasoning

Science.gov (United States)

Inglis, Matthew; Simpson, Adrian

2005-01-01

In this paper we briefly describe the dual process account of reasoning, and explain the role of heuristic biases in human thought. Concentrating on the so-called matching bias effect, we describe a piece of research that indicates a correlation between success at advanced level mathematics and an ability to override innate and misleading…

'Whys' and 'Hows' of using philosophy in mathematics education

DEFF Research Database (Denmark)

Jankvist, Uffe Thomas; Iversen, Steffen Møllegaard

2014-01-01

The article elaborates and exemplifies a potential categorization of the reasons for using philosophy, in particular the philosophy of mathematics, in mathematics education and approaches to doing so—the so-called ‘whys’ and ‘hows’. More precisely, the ‘whys’ are divided into the two categories...... of ‘philosophy as a tool’ for teaching and learning mathematics, and ‘philosophy as a goal’, referring to a stance of considering it a purpose in itself to teach students certain aspects regarding the philosophy of mathematics. A division of the ‘hows’ into three different categories is offered: illumination...... approaches; modules approaches; and philosophy-based approaches. A major part of the article is spent on providing illustrative exemplifications of each of these approaches by referring to already implemented uses of philosophy of mathematics in mathematics education as well as by suggesting new ones....

Mathematics++ selected topics beyond the basic courses

CERN Document Server

Kantor, Ida; Šámal, Robert

2015-01-01

Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is comp

The challenge of computer mathematics.

Science.gov (United States)

Barendregt, Henk; Wiedijk, Freek

2005-10-15

Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.

Minimization of Surface Roughness and Tool Vibration in CNC Milling Operation

Directory of Open Access Journals (Sweden)

Sukhdev S. Bhogal

2015-01-01

Full Text Available Tool vibration and surface roughness are two important parameters which affect the quality of the component and tool life which indirectly affect the component cost. In this paper, the effect of cutting parameters on tool vibration, and surface roughness has been investigated during end milling of EN-31 tool steel. Response surface methodology (RSM has been used to develop mathematical model for predicting surface finish, tool vibration and tool wear with different combinations of cutting parameters. The experimental results show that feed rate is the most dominating parameter affecting surface finish, whereas cutting speed is the major factor effecting tool vibration. The results of mathematical model are in agreement with experimental investigations done to validate the mathematical model.

History, applications, and philosophy in mathematics education

DEFF Research Database (Denmark)

Jankvist, Uffe Thomas

2013-01-01

on the observation that a use of history, applications, and philosophy as a 'goal' is best realized through a modules approach, the article goes on to discuss how to actually design such teaching modules. It is argued that a use of primary original sources through a so-called guided reading along with a use......The article first investigates the basis for designing teaching activities dealing with aspects of history, applications, and philosophy of mathematics in unison by discussing and analyzing the different 'whys' and 'hows' of including these three dimensions in mathematics education. Based...... of student essay assignments, which are suitable for bringing out relevant meta-issues of mathematics, is a sensible way of realizing a design encompassing the three dimensions. Two concrete teaching modules on aspects of the history, applications, and philosophy of mathematics-HAPh-modules-are outlined...

Student talk and opportunities for mathematical learning in small group interactions

OpenAIRE

Wood, M.; Kalinec, C.

2012-01-01

Small group interactions are an important tool for mathematical learning and yet researchers have neither examined small group talk across entire lessons nor have they focused on moments of mathematical learning in small groups. We examined such talk and identified kinds of interactions and connections between interactions and mathematical learning. We differentiated talk based upon its focus: mathematical objects (mathematizing), people (subjectifying), or more specifically, people’s attribu...

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…

Electronics around the accelerators- mathematical recalls

International Nuclear Information System (INIS)

Le Meur, G.

1992-02-01

The author presents the main mathematical tools used in electronics and in particular in accelerator electronics: complex functions, distributions, Fourier series, Laplace transformation, Fourier transformation and probabilities

Combinatorial Speculations and the Combinatorial Conjecture for Mathematics

OpenAIRE

Mao, Linfan

2006-01-01

Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to find combinatorial behavior for objectives. Recently, such research works appeared on journals for mathematics and theoretical physics on cosmos. The main purpose of this paper is to survey these thinking and ideas for mathematics and cosmological physics, s...

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.

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

Focus on the use of language in the multicultural mathematics classroom

DEFF Research Database (Denmark)

Johansen, Lene Østergaard

. understanding the meaning of the words "in front of") when they enter first grade in primary school (Nyborg and Nyborg, 1990). Students who lack these abilities either with regard to mathematics or language are from the beginning of schooling limited in their mathematical performance and in a "risk zone......" of developing learning difficulties in mathematics. Teaching the teachers a consciousness for the use of language in mathematics teaching as well as educating them to have a special focus on developing the vocabulary of the students can render the mathematics teaching more inclusive. Furthermore, it may help......Learning mathematics can be seen as learning a foreign language or learning a particular mathematical discourse.  Nolte (2004) calls mathematics the students' first second language. The use of language in mathematics teaching, hence the way we talk and the way we write, differ from the way the same...

Understanding the Problems of Learning Mathematics.

Science.gov (United States)

Semilla-Dube, Lilia

1983-01-01

A model is being developed to categorize problems in teaching and learning mathematics. Categories include problems due to language difficulties, lack of prerequisite knowledge, and those related to the affective domain. This paper calls on individuals to share teaching and learning episodes; those submitted will then be compiled and categorized.…

Mathematics Literacy on Problem Based Learning with Indonesian Realistic Mathematics Education Approach Assisted E-Learning Edmodo

Science.gov (United States)

Wardono; Waluya, S. B.; Mariani, Scolastika; Candra D, S.

2016-02-01

This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.

Glogs as Non-Routine Problem Solving Tools in Mathematics

Science.gov (United States)

Devine, Matthew T.

2013-01-01

In mathematical problem solving, American students are falling behind their global peers because of a lack of foundational and reasoning skills. A specific area of difficulty with problem solving is working non-routine, heuristic-based problems. Many students are not provided with effective instruction and often grow frustrated and dislike math.…

Students with ‘Special Rights' for mathematics education

DEFF Research Database (Denmark)

Lindenskov, Lena; Gervasoni, Ann

2011-01-01

The issues of equity and quality have been central to international debates on mathematics in research, policy, curriculum and teaching. This book covers a wide variety of topics in the research and practice of mathematics education, demonstrating how equity and quality are inherently political...... equity and quality within various educational contexts and with a variety of marginalized populations. Written by teachers, researchers and academics from all over the world, this book represents a powerful response to the international call for quality education of all students in mathematics around...... terms whose political bedrock is obscured by them being taken for granted. Mapping Equity and Quality in Mathematics Education is broken into four parts. Section 1 addresses the constructs of equity and quality from a variety of theoretical perspectives and outlines new directions to approach...

Dialogue in mathematics classrooms: Beyond question-and- answer methods

Directory of Open Access Journals (Sweden)

Karin Brodie

2007-10-01

Full Text Available This paper explores different kinds of interaction observed in South African mathematics classrooms in order to unpack the notion of participation in mathematics learning. It argues that conventional question-and-answer methods do not promote the kind of interaction that the new South African curriculum calls for. It presents more appropriate kinds of interactions, where teachers maintain high task demands, respond to genuine learner questions and support conversations among learners. The paper argues that combinations of different kinds of interaction are  most likely to support learner participation and mathematical thinking in classrooms.

Addressing Mathematization Obstacles with Unformalized Problems in Physics Education

DEFF Research Database (Denmark)

Niss, Martin

2018-01-01

Abstract: Solving a physics problem requires that the problem solver either implicitly or explicitly structure the problem situation in such a way that she can set up the mathematical equations based on the relevant physics. This part of the mathematization process has been shown to cause obstacles...... for students (Niss, 2016). In the paper, we show how the students’ ability to perform this mathematization process can be trained by using so-called unformalized physics problems. Some examples of how this training can be done are provided from a course on problem solving in physics taught at Roskilde...

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)

Basic mathematical cognition.

Science.gov (United States)

Gaber, David; Schlimm, Dirk

2015-01-01

Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. © 2015 John Wiley & Sons, Ltd.

Mathematical Practices and Arts Integration in an Activity-Based Projective Geometry Course

Science.gov (United States)

Ernest, Jessica Brooke

It is a general assumption that the mathematical activity of students in school should, at least to some degree, parallel the practices of professional mathematicians (Brown, Collins, Duguid, 1989; Moschkovich, 2013). This assumption is reflected in the Common Core State Standards (CCSSI, 2010) and National Council of Teachers of Mathematics (NCTM, 2000) standards documents. However, the practices included in these standards documents, while developed to reflect the practices of professional mathematicians, may be idealized versions of what mathematicians actually do (Moschkovich, 2013). This might lead us to question then: "What is it that mathematicians do, and what practices are not being represented in the standards documents?" In general, the creative work of mathematicians is absent from the standards and, in turn, from school mathematics curricula, much to the dismay of some mathematicians and researchers (Lockhart, 2009; Rogers, 1999). As a result, creativity is not typically being fostered in mathematics students. As a response to this lack of focus on fostering creativity (in each of the science, technology, engineering, and mathematics disciplines--the STEM disciplines), a movement to integrate the arts emerged. This movement, called the STEAM movement--introducing the letter A into the acronym STEM to signify incorporating the arts--has been gaining momentum, yet limited research has been carried out on the efficacy of integrating the arts into mathematics courses. My experiences as the co-instructor for an activity-based course focused on projective geometry led me to consider the course as a setting for investigating both mathematical practices and arts integration. In this work, I explored the mathematical practices in which students engaged while working to develop an understanding of projective geometry through group activities. Furthermore, I explored the way in which students' learning experiences were enriched through artistic engagement in the

African Journal of Educational Studies in Mathematics and Sciences ...

African Journals Online (AJOL)

African Journal of Educational Studies in Mathematics and Sciences. ... The level of detail varies; some disciplines produce manuscripts that comprise discrete .... Duplicate publication, sometimes called self-plagiarism, occurs when an author ...

Gestures as Semiotic Resources in the Mathematics Classroom

Science.gov (United States)

Arzarello, Ferdinando; Paola, Domingo; Robutti, Ornella; Sabena, Cristina

2009-01-01

In this paper, we consider gestures as part of the resources activated in the mathematics classroom: speech, inscriptions, artifacts, etc. As such, gestures are seen as one of the semiotic tools used by students and teacher in mathematics teaching-learning. To analyze them, we introduce a suitable model, the "semiotic bundle." It allows focusing…

Enhancing Undergraduate Mathematics Curriculum via Coding Theory and Cryptography

Science.gov (United States)

Aydin, Nuh

2009-01-01

The theory of error-correcting codes and cryptography are two relatively recent applications of mathematics to information and communication systems. The mathematical tools used in these fields generally come from algebra, elementary number theory, and combinatorics, including concepts from computational complexity. It is possible to introduce the…

School mathematical discourse in a learning landscape

DEFF Research Database (Denmark)

Valero, Paola; Meaney, Tamsin; Alrø, Helle

By bringing our research work together, we are able to discuss the potential of combining the notions of the learning landscape and school mathematical discourse. We do so in a search for concepts and methodological tools to challenge the simplification of issues in regard to mathematics learning...... in multicultural settings, when adopting restricted perspectives on issues of bilingualism. In the paper we discuss the relationship between the learning landscape and school mathematical discourse. We then use these notions to analyse two case studies in Danish and New Zealand schools. Our conclusion raises...... possibilities about how these notions can be used when researching mathematics education in multicultural settings....

Connecting Mathematics and Literature: An Analysis of Pre-Service Elementary School Teachers' Changing Beliefs and Knowledge

Science.gov (United States)

Wilburne, Jane M.; Napoli, Mary

2008-01-01

The National Council of Teachers of Mathematics calls for students to see relationships and connections with mathematics (2000). This study examined the influences on eight pre-service elementary school teachers' beliefs and knowledge of teaching mathematics through literature. The semester long project involved both the language arts and…

Call Forecasting for Inbound Call Center

Directory of Open Access Journals (Sweden)

Peter Vinje

2009-01-01

Full Text Available In a scenario of inbound call center customer service, the ability to forecast calls is a key element and advantage. By forecasting the correct number of calls a company can predict staffing needs, meet service level requirements, improve customer satisfaction, and benefit from many other optimizations. This project will show how elementary statistics can be used to predict calls for a specific company, forecast the rate at which calls are increasing/decreasing, and determine if the calls may stop at some point.

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...

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.

TUTOR SUPPORT OF TEACHING MATHEMATICS WITH INFORMATION AND COMMUNICATION TECHNOLOGIES

Directory of Open Access Journals (Sweden)

Kateryna P. Osadcha

2017-10-01

Full Text Available The paper describes the tutor activity in the process of mathematics teaching support on the basis of the use of information and communication technologies (ICT. The author has analysed the available Internet resources and mobile applications in mathematics, which are classified according to their functional purposes into groups: systems of mass open courses, platforms for adaptive learning, video channels, mathematical online simulators, online tasks, mathematical games, mathematical portals, online platforms, mathematical sites, mathematical online platforms, mathematical services, mobile applications in mathematics (simulators, games, generators of example, assistant programs, training complexes, calculators. In accordance with the student age categories mathematical information and communication technologies are divided into three groups: for elementary school students, secondary school students and high school students. The basic ICT tools for teaching mathematics are outlined. The algorithm for constructing tutorial classes with their application is presented.

Implementing a 'European' appoach to mathematics education in Indonesia through teacher education

NARCIS (Netherlands)

Zulkardi, Z.; Nieveen, N.M.; van den Akker, Jan; de Lange, Jan

2002-01-01

This paper reports on the results of a four-year study called CASCADE-IMEI that is a learning environment (LE) in the form of a face-to-face course and a web site (www.clix.to/zulkardi ) which aims to introduce Realistic Mathematics Education (RME), Dutch approach to mathematics education, as an

The roles of Mesopotamian bronze age mathematics tool for state formation and administration

DEFF Research Database (Denmark)

Høyrup, Jens

2007-01-01

The article describes the social and cultural roles of Mesopotamian mathematics and the interplay of these roles with such patterns of mathematical thought as can be traced through the sources; it covers the period from the first formation of a genuine state, shortly after the mid-fourth millenni...

Frogs Call at a Higher Pitch in Traffic Noise

Directory of Open Access Journals (Sweden)

Kirsten M. Parris

2009-06-01

Full Text Available Male frogs call to attract females for mating and to defend territories from rival males. Female frogs of some species prefer lower-pitched calls, which indicate larger, more experienced males. Acoustic interference occurs when background noise reduces the active distance or the distance over which an acoustic signal can be detected. Birds are known to call at a higher pitch or frequency in urban noise, decreasing acoustic interference from low-frequency noise. Using Bayesian linear regression, we investigated the effect of traffic noise on the pitch of advertisement calls in two species of frogs, the southern brown tree frog (Litoria ewingii and the common eastern froglet (Crinia signifera. We found evidence that L. ewingii calls at a higher pitch in traffic noise, with an average increase in dominant frequency of 4.1 Hz/dB of traffic noise, and a total effect size of 123 Hz. This frequency shift is smaller than that observed in birds, but is still large enough to be detected by conspecific frogs and confer a significant benefit to the caller. Mathematical modelling predicted a 24% increase in the active distance of a L. ewingii call in traffic noise with a frequency shift of this size. Crinia signifera may also call at a higher pitch in traffic noise, but more data are required to be confident of this effect. Because frog calls are innate rather than learned, the frequency shift demonstrated by L. ewingii may represent an evolutionary adaptation to noisy conditions. The phenomenon of frogs calling at a higher pitch in traffic noise could therefore constitute an intriguing trade-off between audibility and attractiveness to potential mates.

On Mathematical Naturalism and the Powers of Symbolisms

Directory of Open Access Journals (Sweden)

Murray Code

2005-08-01

Full Text Available Advances in modern mathematics indicate that progress in this field of knowledge depends mainly on culturally inflected imaginative intuitions, or intuitive imaginings—which mysteriously result in the growth of systems of symbolism that are often efficacious, although fallible and very likely evolutionary. Thus the idea that a trouble-free epistemology can be constructed out of an intuition-free mathematical naturalism would seem to be question begging of a very high order. I illustrate the point by examining Philip Kitcher’s attempt to frame an empiricist philosophy of mathematics, which he calls “mathematical naturalism,” wherein he proposes to explain novelty in mathematics by means of the notion of ‘rational interpractice transitions,’ only to end with an appeal to science to supply a meaning for rationality. A more promising naturalistic approach is adumbrated by Noam Chomsky who begins with a straightforward acceptance of mind and language as ‘natural’ or concrete facts which bespeak the need for a linguistic faculty. This indicates in turn that there may also be a mathematical faculty capable of generating and exploiting the powers of mathematical symbolisms in a manner analogous to the linguistic faculty.

Using an evaluative tool to develop effective mathscasts

Science.gov (United States)

Galligan, Linda; Hobohm, Carola; Peake, Katherine

2017-09-01

This study is situated in a course designed for both on-campus and online pre-service and in-service teachers, where student-created mathscasts provide a way for university lecturers to assess students' quality of teaching, and understanding of mathematics. Teachers and pre-service teachers, in a university course with 90% online enrolment, were asked to create mathscasts to explain mathematics concepts at middle school level. This paper describes the process of developing and refining a tool for the creation and evaluation of quality student-produced mathscasts. The study then investigates the usefulness of the tool within the context of pedagogy and mathematical understanding. Despite an abundance of mathscasts already available on the web, there is merit in creating mathscasts, not only as a tool for teaching, but also as a means of learning by doing. The premise for creating student-produced mathscasts was to capture the creators' mathematical understanding and pedagogical approach to teaching a mathematical concept, which were then peer-assessed and graded. The analysis included surveys, practice mathscasts with peer- and self-reviews, and students' final assessed mathscasts. The results indicate that the use of the evaluative tool resulted in an improvement in quality of student-created mathscasts and critiques thereof. The paper concludes with a discussion on future directions of student-produced mathscasts.

SOME ASPECTS OF USING MATHEMATICS IN MEDICAL SCIENCES

Directory of Open Access Journals (Sweden)

Ivana Ilic

2008-01-01

Full Text Available The aim of the paper was to present some new possibilities of using mathematicsin medical sciences and medical practice. The so-called mathematical way of thinkingis presented, which is, basically, the starting point of usual way of thinking, and alsothe essence of scientific and technological literacy, necessary for the development oftheoretical and practical modern medicine. The aim of the paper was to show that it isreasonable to choose certain mathematical points of view, present them to thestudents of medicine, and thus, help them to use that knowledge in their futurestudies in order to be more successful in their professions. Modern mathematical andstatistical methods are important in professional and scientific work in clinical andlaboratory environment.

Salient Beliefs of Secondary School Mathematics Teachers Using Dynamic Geometry Software

Science.gov (United States)

Chan, Kan Kan

2015-01-01

Even though dynamic geometry software (DGS) is becoming an emergent instructional tool for mathematics teachers, many teachers are still in the process of consideration about whether to use it. In order to encourage teachers to use DGS, this study seeks to discover mathematics teachers' salient beliefs about the use of DGS in mathematics class.…

Mathematical models in biology bringing mathematics to life

CERN Document Server

Ferraro, Maria; Guarracino, Mario

2015-01-01

This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy.  The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...

Mathematical Tools for Geomagnetic Data Monitoring and the Intermagnet Russian Segment

Directory of Open Access Journals (Sweden)

Anatoly Soloviev

2013-02-01

Full Text Available In this paper, a new approach to the detection of anomalies in geophysical records is connected with a fuzzy mathematics application. The theory of discrete mathematical analysis and collection of algorithms for time series processing constructed on its basis represents the results of this research direction. These algorithms are the consequence of fuzzy modeling of the logic of an interpreter who visually recognizes anomalies in records. They allow analyzing large data sets that are not subjected to manual processing. The efficiency of these algorithms is demonstrated in several important geophysical applications. Plans for an extension of the Russian INTERMAGNET segment are presented.

Mathematics and Microeconomics

Directory of Open Access Journals (Sweden)

Catalin Angelo Ioan

2014-04-01

Full Text Available The article deals a number of issues regarding the use of mathematics in economics. The end of construction entails a different approach. Good organization of its with bright windows on each floor, gives confidence and calls the frightened yesterday, to come and admire both crystal mirrors (outstanding results facing each other, which increases in a continuous recurring building details. On each floor, the visitor is coming from one of the windows and enjoys the scenery as you climb, always different, more comprehensive and fascinating.

The mathematics of soap films

CERN Document Server

Oprea, John

2000-01-01

Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the Maple® applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautif...

Mathematical paradigms of climate science

CERN Document Server

Cannarsa, Piermarco; Jones, Christopher; Portaluri, Alessandro

2016-01-01

This book, featuring a truly interdisciplinary approach, provides an overview of cutting-edge mathematical theories and techniques that promise to play a central role in climate science. It brings together some of the most interesting overview lectures given by the invited speakers at an important workshop held in Rome in 2013 as a part of MPE2013 (“Mathematics of Planet Earth 2013”). The aim of the workshop was to foster the interaction between climate scientists and mathematicians active in various fields linked to climate sciences, such as dynamical systems, partial differential equations, control theory, stochastic systems, and numerical analysis. Mathematics and statistics already play a central role in this area. Likewise, computer science must have a say in the efforts to simulate the Earth’s environment on the unprecedented scale of petabytes. In the context of such complexity, new mathematical tools are needed to organize and simplify the approach. The growing importance of data assimilation te...

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...

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…

The Measurement of Students' Achievement in Teaching Primary School Fifth Year Mathematics Classes

Science.gov (United States)

Doganay, Ahmet; Bal, Ayten Pinar

2010-01-01

The aim of this study was to investigate students' and teachers' point of views about preparing measurement tools used in mathematics classes, the level of learning that these tools are intended to measure, how often they are used and how they are scored in terms of assessing 5th grade primary school mathematic courses. The population of the study…

Advances in mathematical economics

CERN Document Server

Yamazaki, Akira

2005-01-01

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. The editorial board of this series comprises the following prominent economists and mathematicians: Managing Editors: S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.). Editors: R. Anderson (U.C. Berkeley), C. Castaing (Univ. Montpellier), F.H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeley), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J.-M. Grandmont...

Mathematics and electromagnetism; Matematicas y electromagnetismo

Energy Technology Data Exchange (ETDEWEB)

Rodriguez Danta, M.

2000-07-01

Symbiosis between mathematics and electromagnetism is analyzed in a simple and concise manner by taking a historical perspective. The universal tool character of mathematical models allowed the transfer of models from several branches of physics into the realm of electromagnetism by drawing analogies. The mutual interdependence between covariant formulation and tensor calculus is marked. The paper focuses on the guiding idea of field theory and Maxwell's equations. Likewise, geometrization of interactions in connection with gauge fields is also noted. (Author)

Mathematical methods for physicists and engineers

CERN Document Server

Collins, Royal Eugene

2011-01-01

This practical, highly readable text provides physics and engineering students with the essential mathematical tools for thorough comprehension of their disciplines. Featuring all the necessary topics in applied mathematics in the form of programmed instruction, the text can be understood by advanced undergraduates and beginning graduate students without any assistance from the instructor. Topics include elementary vector calculus, matrix algebra, and linear vector operations; the many and varied methods of solving linear boundary value problems, including the more common special functions o

MATHEMATICAL AND CHEMOMETRICAL MODELS – TOOLS TO EVALUATE HEAVY METALS CONTAMINATION

Directory of Open Access Journals (Sweden)

Despina Maria Bordean

2017-11-01

Full Text Available The aim of the this study is to present a combined view of bio – geo - chemistry, soil – plant interactions, mathematic models and statistic analysis, based on the correlation between the levels of soil contamination, and the remanence of polluting substances in soil and respectively in harvested fruits and vegetables. Most of the mathematical models which describe plant - soil interactions are integrated in plant growth models or climate change models. The models presented by this paper are Soil – Plant Interaction Models, Pollution Indices, The Indices for Evaluating the Adaptative Strategies of Plants and Chemo-metrical Methods, and they have the role to synthesize and evaluate the information regarding heavy metals contamination.

Robotic Toys as a Catalyst for Mathematical Problem Solving

Science.gov (United States)

Highfield, Kate

2010-01-01

Robotic toys present unique opportunities for teachers of young children to integrate mathematics learning with engaging problem-solving tasks. This article describes a series of tasks using Bee-bots and Pro-bots, developed as part a larger project examining young children's use of robotic toys as tools in developing mathematical and metacognitive…

Didactic Transposition in Mathematics Textbooks.

Science.gov (United States)

Kang, Wan; Kilpatrick, Jeremy

1992-01-01

Didactic transposition theory asserts that bodies of knowledge are designed not to be taught but to be used. Discusses didactic transposition, the transposition of knowledge regarded as a tool to be used to knowledge as something to be learned in mathematics textbooks. (14 references) (MDH)

Web 2.0 in the Mathematics Classroom

Science.gov (United States)

McCoy, Leah P.

2014-01-01

A key characteristic of successful mathematics teachers is that they are able to provide varied activities that promote student learning and assessment. Web 2.0 applications can provide an assortment of tools to help produce creative activities. A Web 2.0 tool enables the student to enter data and create multimedia products using text, graphics,…

Developing a model of pedagogical content knowledge for secondary and post-secondary mathematics instruction

Directory of Open Access Journals (Sweden)

Shandy Hauk

2014-07-01

Full Text Available The accepted framing of mathematics pedagogical content knowledge (PCK as part of mathematical knowledge for teaching has centered on the question: What mathematical reasoning, insight, understanding, and skills are required for a person to teach elementary mathematics? Many have worked to address this question in K-8 teaching. Yet, there remains a call for examples and theory in the context of teachers with greater mathematical preparation and older students with varied and complex experiences in learning mathematics. In this theory development report we offer background and examples for an extended model of PCK – as the interplay among conceptually-rich mathematical understandings, experience in and of teaching, and multiple culturally-mediated classroom interactions.

E-Learning and Affective Student’s Profile in Mathematics

Directory of Open Access Journals (Sweden)

Giovannina Albano

2008-12-01

Full Text Available This paper is concerned with the personalisation of teaching/learning paths in mathematics education. Such personalisation would exploit the research results on the connection between the affective experience of the student learning mathematics and his/her success or failure in mathematics, which produces the learner’s attitude towards mathematics. We present a model for the learner’s affective profile in mathematics, which would extend the current user profile in an e-learning platform taking into account the learner’s attitude, to be used in order to offer and manage a Unit of Learning in mathematics better tailored on the global student’ needs. Tools for the implementation of the model in an e-learning platform have been devised. Activities templates suitable to various attitudes towards mathematics have been designed and their experimentation is in progress.

Effects of "Handep" Cooperative Learning Based on Indigenous Knowledge on Mathematical Problem Solving Skill

Science.gov (United States)

Demitra; Sarjoko

2018-01-01

Indigenous people of Dayak tribe in Kalimantan, Indonesia have traditionally relied on a system of mutual cooperation called "handep." The cultural context has an influence on students mathematics learning. The "handep" system might be suitable for modern learning situations to develop mathematical problem-solving skill. The…

Strategy Feedback in an E-learning Tool for Mathematical Exercises

NARCIS (Netherlands)

Jeuring, J.T.; Pasman, W.

2007-01-01

Exercises in mathematics are often solved using a standard procedure, such as for example solving a system of linear equations by subtracting equations from top to bottom, and then substituting variables from bottom to top. Students have to practice such procedural skills: they have to learn how

Integrating Touch-Enabled and Mobile Devices into Contemporary Mathematics Education

Science.gov (United States)

Meletiou-Mavrotheris, Maria, Ed.; Mavrou, Katerina, Ed.; Paparistodemou, Efi, Ed.

2015-01-01

Despite increased interest in mobile devices as learning tools, the amount of available primary research studies on their integration into mathematics teaching and learning is still relatively small due to the novelty of these technologies. "Integrating Touch-Enabled and Mobile Devices into Contemporary Mathematics Education" presents…

Teaching Mathematics for Spatial Justice: An Investigation of the Lottery

Science.gov (United States)

Rubel, Laurie H.; Lim, Vivian Y.; Hall-Wieckert, Maren; Sullivan, Mathew

2016-01-01

This article explores integrating place-based education with critical mathematics toward teaching mathematics for spatial justice. "Local Lotto," a curricular module with associated digital tools, was designed to investigate the lottery as a critical spatial phenomenon and piloted in urban high schools. This article describes findings…

Influence of Math Club Activities on Primary Students’ Mathematics Achievement

Directory of Open Access Journals (Sweden)

Alenka Lipovec

2014-12-01

Full Text Available An intervention program called Didactic pentagon is described. Participants are teachers, students, parents, pre-service teachers and teacher educators. The programme is shaped as a math club activity. Empirical results focus on comparing mathematics achievements of students included in the programme and mathematically promising students taking part in TIMSS 2003. Experimental group has surpassed control group in overall results. Statistically significant differences in favour of experimental group can be found at intermediate international benchmark of mathematics achievements and at problem solving cognitive domain. The results can be assigned to pentagon activities guided by pre-service teachers. Cooperation between university and schools has evidently overcome the lack of pre-service teachers’ experience and helped in raising mathematical knowledge of school youth.

Analyzing Similarity in Mathematical Content To Enhance the Detection of Academic Plagiarism

OpenAIRE

Isele, Maurice-Roman

2018-01-01

Despite the effort put into the detection of academic plagiarism, it continues to be a ubiquitous problem spanning all disciplines. Various tools have been developed to assist human inspectors by automatically identifying suspicious documents. However, to our knowledge currently none of these tools use mathematical content for their analysis. This is problematic, because mathematical content potentially represents a significant amount of the scientific contribution in academic documents. Henc...

VIPER: a web application for rapid expert review of variant calls.

Science.gov (United States)

Wöste, Marius; Dugas, Martin

2018-01-15

With the rapid development in next-generation sequencing, cost and time requirements for genomic sequencing are decreasing, enabling applications in many areas such as cancer research. Many tools have been developed to analyze genomic variation ranging from single nucleotide variants to whole chromosomal aberrations. As sequencing throughput increases, the number of variants called by such tools also grows. Often employed manual inspection of such calls is thus becoming a time-consuming procedure. We developed the Variant InsPector and Expert Rating tool (VIPER) to speed up this process by integrating the Integrative Genomics Viewer into a web application. Analysts can then quickly iterate through variants, apply filters and make decisions based on the generated images and variant metadata. VIPER was successfully employed in analyses with manual inspection of more than 10,000 calls. VIPER is implemented in Java and Javascript and is freely available at https://github.com/MarWoes/viper. Marius.Woeste@uni-muenster.de. Supplementary data are available at Bioinformatics online. © The Author (2018). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com

Mathematical modelling of a continuous biomass torrefaction reactor: TORSPYDTM column

International Nuclear Information System (INIS)

Ratte, J.; Fardet, E.; Mateos, D.; Hery, J.-S.

2011-01-01

Torrefaction is a soft thermal process usually applied to cocoa or coffee beans to obtain the Maillard reaction to produce aromatics and enhance the flavour. In the case of biomass the main interest of torrefaction it is to break the fibers. To do so, Thermya company has developed and patented a biomass torrefaction/depolymerisation process called TORSPYD TM . It is a homogeneous 'soft' thermal process that takes place in an inert atmosphere. The process progressively eliminates the biomass water content transforms a portion of the biomass organic matter and breaks the biomass structure by depolymerisation of the fibers. This produces a high performance solid fuel, called Biocoal, which offers a range of benefits over and above that of normal biomass fuel. To develop such a process, this company has developed two main tools: - a continuous torrefaction laboratory pilot with a capacity to produce 3 - 8 kg/h of torrefied biomass; - a mathematical model dedicated to the design and optimisation of the TORSPYD reactor. The mathematical model is able to describe the chemical and physical processes that take place in the torrefaction column at two different scales, namely: the particle, and the surrounding gas. The model enables the gas temperature profiles inside the column to be predicted, and the results of the model are then validated through experiment in the laboratory pilot. The model also allows us to estimate the thermal power necessary to torrefy any type of biomass for a given moisture content. -- Highlights: → We model a patented torrefaction/depolymerisation biomass process: TORPSPYD. → We compare simulated results to experimental data obtained from our torrefaction pilot plant. → We describe phenomenon that occurs in our torrefaction reactor and discuss about the influence of moisture of the input biomass.

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.

Mathematical Rigor in Introductory Physics

Science.gov (United States)

Vandyke, Michael; Bassichis, William

2011-10-01

Calculus-based introductory physics courses intended for future engineers and physicists are often designed and taught in the same fashion as those intended for students of other disciplines. A more mathematically rigorous curriculum should be more appropriate and, ultimately, more beneficial for the student in his or her future coursework. This work investigates the effects of mathematical rigor on student understanding of introductory mechanics. Using a series of diagnostic tools in conjunction with individual student course performance, a statistical analysis will be performed to examine student learning of introductory mechanics and its relation to student understanding of the underlying calculus.

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

Application of a functional mathematical index for antibacterial and anticarcinogenic effects of tea catechins.

Science.gov (United States)

Finotti, Enrico; Bersani, Enrico; Friedman, Mendel

2011-02-09

Tea leaves produce secondary metabolites that are involved in the defense of the plants against invading pathogens. In the case of green teas, these metabolites are polyphenolic compounds called catechins. Previous studies developed a mathematical formula called functional mathematical index (FMI) that was used to describe the quality of different olive oils and potatoes in terms of compositional parameters and antioxidative properties of individual components. This study extends the development of the FMI concept to define an "optimum tea" based on reported relationships between the content of structurally different catechins of a large number of teas and their dual beneficial effects: antimicrobial activities against a foodborne pathogen and inhibition of human cancer cell lines. The described mathematical approach may be useful for predicting relative beneficial effects of new teas based on their catechin content.

A Multifaceted Mathematical Approach for Complex Systems

Energy Technology Data Exchange (ETDEWEB)

Alexander, F.; Anitescu, M.; Bell, J.; Brown, D.; Ferris, M.; Luskin, M.; Mehrotra, S.; Moser, B.; Pinar, A.; Tartakovsky, A.; Willcox, K.; Wright, S.; Zavala, V.

2012-03-07

Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significant impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.

Bridging different perspectives of the physiological and mathematical disciplines.

Science.gov (United States)

Batzel, Jerry Joseph; Hinghofer-Szalkay, Helmut; Kappel, Franz; Schneditz, Daniel; Kenner, Thomas; Goswami, Nandu

2012-12-01

The goal of this report is to discuss educational approaches for bridging the different perspectives of the physiological and mathematical disciplines. These approaches can enhance the learning experience for physiology, medical, and mathematics students and simultaneously act to stimulate mathematical/physiological/clinical interdisciplinary research. While physiology education incorporates mathematics, via equations and formulas, it does not typically provide a foundation for interdisciplinary research linking mathematics and physiology. Here, we provide insights and ideas derived from interdisciplinary seminars involving mathematicians and physiologists that have been conducted over the last decade. The approaches described here can be used as templates for giving physiology and medical students insights into how sophisticated tools from mathematics can be applied and how the disciplines of mathematics and physiology can be integrated in research, thereby fostering a foundation for interdisciplinary collaboration. These templates are equally applicable to linking mathematical methods with other life and health sciences in the educational process.

Valuation of European Call Option via Inverse Fourier Transform

Directory of Open Access Journals (Sweden)

Rubenis Oskars

2017-12-01

Full Text Available Very few models allow expressing European call option price in closed form. Out of them, the famous Black- Scholes approach sets strong constraints - innovations should be normally distributed and independent. Availability of a corresponding characteristic function of log returns of underlying asset in analytical form allows pricing European call option by application of inverse Fourier transform. Characteristic function corresponds to Normal Inverse Gaussian (NIG probability density function. NIG distribution is obtained based on assumption that time series of log returns follows APARCH process. Thus, volatility clustering and leptokurtic nature of log returns are taken into account. The Fast Fourier transform based on trapezoidal quadrature is numerically unstable if a standard cumulative probability function is used. To solve the problem, a dampened cumulative probability is introduced. As a computation tool Matlab framework is chosen because it contains many effective vectorization tools that greatly enhance code readability and maintenance. The characteristic function of Normal Inverse Gaussian distribution is taken and exercised with the chosen set of parameters. Finally, the call price dependence on strike price is obtained and rendered in XY plot. Valuation of European call option with analytical form of characteristic function allows further developing models with higher accuracy, as well as developing models for some exotic options.

Mathematical models of hysteresis

International Nuclear Information System (INIS)

1998-01-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above

Mathematical models of hysteresis

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-08-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students’ mathematical performance

Directory of Open Access Journals (Sweden)

Bashirah Ibrahim

2017-10-01

Full Text Available We examine students’ mathematical performance on quantitative “synthesis problems” with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students’ mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students’ simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students’ formulation and combination of equations. Several reasons may explain this difference, including the students’ different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

Introduction to Mathematical Systems Theory: A Behavioral Approach

NARCIS (Netherlands)

Polderman, Jan W.; Willems, J.C.

1998-01-01

This is a book about modelling, analysis, and control of linear time-invariant systems. The book uses what is called the behavioral approach towards mathematical modelling. Thus a system is viewed as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems

Problem Solving in the Digital Age: New Ideas for Secondary Mathematics Teacher Education

Science.gov (United States)

Abramovich, Sergei; Connell, Michael

2017-01-01

The paper reflects on an earlier research on the use of technology in secondary mathematics teacher education through the lenses of newer digital tools (Wolfram Alpha, Maple), most recent standards for teaching mathematics, and recommendations for the preparation of schoolteachers. New ideas of technology integration into mathematics education…

Opportunity to Learn First Year Mathematics in Teacher Training ...

African Journals Online (AJOL)

kofimereku

first year teacher training mathematics syllabus were not taught by the end of the year and which ones .... training college in Kommenda, Central Region as a pilot study. The responses ..... calls for efforts to give more attention to these groups.

Mathematical modelling of metabolism

DEFF Research Database (Denmark)

Gombert, Andreas Karoly; Nielsen, Jens

2000-01-01

Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...

Application of computer mathematical modeling in nuclear well-logging industry

International Nuclear Information System (INIS)

Cai Shaohui

1994-01-01

Nuclear well logging techniques have made rapid progress since the first well log calibration facility (the API pits) was dedicated in 1959. Then came the first computer mathematical model in the late 70's. Mathematical modeling can now minimize design and experiment time, as well as provide new information and idea on tool design, environmental effects and result interpretation. The author gives a brief review on the achievements of mathematical modeling on nuclear logging problems

Sharing programming resources between Bio* projects through remote procedure call and native call stack strategies.

Science.gov (United States)

Prins, Pjotr; Goto, Naohisa; Yates, Andrew; Gautier, Laurent; Willis, Scooter; Fields, Christopher; Katayama, Toshiaki

2012-01-01

Open-source software (OSS) encourages computer programmers to reuse software components written by others. In evolutionary bioinformatics, OSS comes in a broad range of programming languages, including C/C++, Perl, Python, Ruby, Java, and R. To avoid writing the same functionality multiple times for different languages, it is possible to share components by bridging computer languages and Bio* projects, such as BioPerl, Biopython, BioRuby, BioJava, and R/Bioconductor. In this chapter, we compare the two principal approaches for sharing software between different programming languages: either by remote procedure call (RPC) or by sharing a local call stack. RPC provides a language-independent protocol over a network interface; examples are RSOAP and Rserve. The local call stack provides a between-language mapping not over the network interface, but directly in computer memory; examples are R bindings, RPy, and languages sharing the Java Virtual Machine stack. This functionality provides strategies for sharing of software between Bio* projects, which can be exploited more often. Here, we present cross-language examples for sequence translation, and measure throughput of the different options. We compare calling into R through native R, RSOAP, Rserve, and RPy interfaces, with the performance of native BioPerl, Biopython, BioJava, and BioRuby implementations, and with call stack bindings to BioJava and the European Molecular Biology Open Software Suite. In general, call stack approaches outperform native Bio* implementations and these, in turn, outperform RPC-based approaches. To test and compare strategies, we provide a downloadable BioNode image with all examples, tools, and libraries included. The BioNode image can be run on VirtualBox-supported operating systems, including Windows, OSX, and Linux.

Information systems performance evaluation, introducing a two-level technique: Case study call centers

Directory of Open Access Journals (Sweden)

Hesham A. Baraka

2015-03-01

The objective of this paper was to introduce a new technique that can support decision makers in the call centers industry to evaluate, and analyze the performance of call centers. The technique presented is derived from the research done on measuring the success or failure of information systems. Two models are mainly adopted namely: the Delone and Mclean model first introduced in 1992 and the Design Reality Gap model introduced by Heeks in 2002. Two indices are defined to calculate the performance of the call center; the success index and the Gap Index. An evaluation tool has been developed to allow call centers managers to evaluate the performance of their call centers in a systematic analytical approach; the tool was applied on 4 call centers from different areas, simple applications such as food ordering, marketing, and sales, technical support systems, to more real time services such as the example of emergency control systems. Results showed the importance of using information systems models to evaluate complex systems as call centers. The models used allow identifying the dimensions for the call centers that are facing challenges, together with an identification of the individual indicators in these dimensions that are causing the poor performance of the call center.

The Prevalent Rate of Problem-Solving Approach in Teaching Mathematics in Ghanaian Basic Schools

Science.gov (United States)

Nyala, Joseph; Assuah, Charles; Ayebo, Abraham; Tse, Newel

2016-01-01

Stakeholders of mathematics education decry the rate at which students' performance are falling below expectation; they call for a shift to practical methods of teaching the subject in Ghanaian basic schools. The study explores the extent to which Ghanaian basic school mathematics teachers use problem-solving approach in their lessons. The…

The Academic Procrastination in Junior High School Students' Mathematics Learning: A Qualitative Study

Science.gov (United States)

Asri, Dahlia Novarianing; Setyosari, Punaji; Hitipeuw, Imanuel; Chusniyah, Tutut

2017-01-01

Among the main causes of low learning achievement in mathematics learning is a delayed behavior to do tasks, commonly called academic procrastination. The objectives of this research are to describe and to explain the causal factors and consequences of academic procrastination in learning mathematics for junior high school students. This research…

Mathematical modelling and numerical simulation of forces in milling process

Science.gov (United States)

Turai, Bhanu Murthy; Satish, Cherukuvada; Prakash Marimuthu, K.

2018-04-01

Machining of the material by milling induces forces, which act on the work piece material, tool and which in turn act on the machining tool. The forces involved in milling process can be quantified, mathematical models help to predict these forces. A lot of research has been carried out in this area in the past few decades. The current research aims at developing a mathematical model to predict forces at different levels which arise machining of Aluminium6061 alloy. Finite element analysis was used to develop a FE model to predict the cutting forces. Simulation was done for varying cutting conditions. Different experiments was designed using Taguchi method. A L9 orthogonal array was designed and the output was measure for the different experiments. The same was used to develop the mathematical model.

On the interplay between mathematics and biology: hallmarks toward a new systems biology.

Science.gov (United States)

Bellomo, Nicola; Elaiw, Ahmed; Althiabi, Abdullah M; Alghamdi, Mohammed Ali

2015-03-01

This paper proposes a critical analysis of the existing literature on mathematical tools developed toward systems biology approaches and, out of this overview, develops a new approach whose main features can be briefly summarized as follows: derivation of mathematical structures suitable to capture the complexity of biological, hence living, systems, modeling, by appropriate mathematical tools, Darwinian type dynamics, namely mutations followed by selection and evolution. Moreover, multiscale methods to move from genes to cells, and from cells to tissue are analyzed in view of a new systems biology approach. Copyright © 2014 Elsevier B.V. All rights reserved.

Secondary School Mathematics Teachers’ and Students’ Views on Computer Assisted Mathematics Instruction in Turkey: Mathematica Example

Directory of Open Access Journals (Sweden)

Mehmet Alper Ardıç

2017-01-01

Full Text Available This study aimed at determining the secondary school mathematics teachers’ and students’ views on computer-assisted mathematics instruction (CAMI conducted via Mathematica. Accordingly, three mathematics teachers in Adıyaman and nine 10th-grade students participated in the research. Firstly, the researchers trained the mathematics teachers in the Mathematica program, a computer algebra system (CAS and CAMI. Then, they provided a suitable environment for teachers to practice CAMI with their students to teach quadratic functions (parabola. Case study, a qualitative research design, was utilized in the study. Semi-structured interview forms were used as data collection tools. The interview data were analyzed using descriptive and content analysis, and the codes and themes related to the topic were obtained. The findings revealed that all the teachers found CAMI implementations interesting as supported by students’ views. While all mathematics teachers wanted to benefit from CAMI in mathematics and geometry courses, most of the students asked that CAMI be used in different courses. It was found that students did not have any problems with the Mathematica used with CAMI activities. However, it was also revealed by one student and one teacher that involving CAMI constantly in the courses would hinder preparations for the university entrance exam.

Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.

Science.gov (United States)

Clément, Frédérique

2016-07-01

Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of

Mathematical model in economic environmental problems

Energy Technology Data Exchange (ETDEWEB)

Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)

1996-12-31

The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.

CoVaCS: a consensus variant calling system.

Science.gov (United States)

Chiara, Matteo; Gioiosa, Silvia; Chillemi, Giovanni; D'Antonio, Mattia; Flati, Tiziano; Picardi, Ernesto; Zambelli, Federico; Horner, David Stephen; Pesole, Graziano; Castrignanò, Tiziana

2018-02-05

The advent and ongoing development of next generation sequencing technologies (NGS) has led to a rapid increase in the rate of human genome re-sequencing data, paving the way for personalized genomics and precision medicine. The body of genome resequencing data is progressively increasing underlining the need for accurate and time-effective bioinformatics systems for genotyping - a crucial prerequisite for identification of candidate causal mutations in diagnostic screens. Here we present CoVaCS, a fully automated, highly accurate system with a web based graphical interface for genotyping and variant annotation. Extensive tests on a gold standard benchmark data-set -the NA12878 Illumina platinum genome- confirm that call-sets based on our consensus strategy are completely in line with those attained by similar command line based approaches, and far more accurate than call-sets from any individual tool. Importantly our system exhibits better sensitivity and higher specificity than equivalent commercial software. CoVaCS offers optimized pipelines integrating state of the art tools for variant calling and annotation for whole genome sequencing (WGS), whole-exome sequencing (WES) and target-gene sequencing (TGS) data. The system is currently hosted at Cineca, and offers the speed of a HPC computing facility, a crucial consideration when large numbers of samples must be analysed. Importantly, all the analyses are performed automatically allowing high reproducibility of the results. As such, we believe that CoVaCS can be a valuable tool for the analysis of human genome resequencing studies. CoVaCS is available at: https://bioinformatics.cineca.it/covacs .

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

Science.gov (United States)

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…

Variational principles are a powerful tool also for formulating field theories

OpenAIRE

Dell'Isola , Francesco; Placidi , Luca

2012-01-01

Variational principles and calculus of variations have always been an important tool for formulating mathematical models for physical phenomena. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest for scientists and engineers and are the main tool for the axiomatization of physical theories

Mathematical modeling of optical glazing performance

NARCIS (Netherlands)

Nijnatten, van P.A.; Wittwer, V.; Granqvist, C.G.; Lampert, C.M.

1994-01-01

Mathematical modelling can be a powerful tool in the design and optimalization of glazing. By calculation, the specifications of a glazing design and the optimal design parameters can be predicted without building costly prototypes first. Furthermore, properties which are difficult to measure, like

Bat calls while preying: A method for reconstructing the signal emitted by a directional sound source

DEFF Research Database (Denmark)

Guarato, Francesco; Hallam, John

2010-01-01

Understanding and modeling bat biosonar behavior should take into account what the bat actually emitted while exploring the surrounding environment. Recording of the bat calls could be performed by means of a telemetry system small enough to sit on the bat head, though filtering due to bat...... directivity affects recordings and not all bat species are able to carry such a device. Instead, remote microphone recordings of the bat calls could be processed by means of a mathematical method that estimates bat head orientation as a first step before calculating the amplitudes of each call for each...... and discussed. A further improvement of the method is necessary as its performance for call reconstruction strongly depends on correct choice of the sample at which the recorded call is thought to start in each microphone data set....

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

MATHEMATICS TEACHER: MOVING KNOWLEDGE UNDER FORMATION

Directory of Open Access Journals (Sweden)

Roselaine Machado Albernaz

2010-07-01

Full Text Available This essay approaches the Mathematics teacher forming process from his/her experiences in the school system and the set of knowledge that hashistorical, philosophical and politically constituted him/her. This set of knowledge not only comprises academic knowledge, but also involves the subjective effects of knowledge it incorporates. Starting from a tale, the character, called ‘researcher-teacher’, conducts the text throughout questions about the forming processes of teachers of such a particular subject as Mathematics. The character seems to have an “interrogative something” which is peculiar to us, teachers, concerned about our disciplinary field. Having the objective of problematize the formation and knowledge of our character, her ways of being, thinking and perceiving, we intend to question, with and through her, the new requirements that have been demanded towards Mathematics teachers and the set of knowledge that constitute her, the way she is, her way of acting and taking  position in the school universe. The proposed essay seeks for an articulation between the fields of Art, Philosophy, Science and Education. It speaks about the intriguing school world, but not least, the ways we think to treat the forming process of Mathematics teachers from a set of logical, subjective and sensitive knowledge.  Key words: Forming process of teachers; mathematics; aesthetic experience; philosophy of difference.

Using Assessment for Learning Mathematics with Mobile Tablet Based Solutions

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Ghislain Maurice Norbert Isabwe

2014-03-01

Full Text Available This article discusses assessment for learning in mathematics subjects. Teachers of large classes face the challenge of regularly assessing studentsཿ ongoing mathematical learning achievements. Taking the complexity of assessment and feedback for learning as a background, we have developed a new approach to the assessment for learning mathematics at university level. We devised mobile tablet technology supported assessment processes, and we carried out user studies in both Rwanda and Norway. Results of our study indicated that students found it fruitful to be involved in assessing other studentsཿ mathematics work, i.e. assessing fellow studentsཿ answers to mathematical tasks. By being involved in the assessment process, the students expected mathematical learning gains. Their providing and obtaining of feedback to/from their fellow students using technology supported tools were highly appreciated as regards their own mathematical learning process.

Mathematical Modeling of Neuro-Vascular Coupling in Rat Cerebellum

DEFF Research Database (Denmark)

Rasmussen, Tina

Activity in the neurons called climbing fibers causes blood flow changes. But the physiological mechanisms which mediate the coupling are not well understood. This PhD thesis investigates the mechanisms of neuro-vascular coupling by means of mathematical methods. In experiments, the extracellularly...... measured field potential is used as an indicator of neuronal activity, and the cortical blood flow is measured by means of laser-Doppler flowmetry. Using system identification methods, these measurements have been used to construct and validate parametric mathematical models of the neuro-vascular system...

Construction of the mathematical concept of pseudo thinking students

Science.gov (United States)

Anggraini, D.; Kusmayadi, T. A.; Pramudya, I.

2018-05-01

Thinking process is a process that begins with the acceptance of information, information processing and information calling in memory with structural changes that include concepts or knowledges. The concept or knowledge is individually constructed by each individual. While, students construct a mathematical concept, students may experience pseudo thinking. Pseudo thinking is a thinking process that results in an answer to a problem or construction to a concept “that is not true”. Pseudo thinking can be classified into two forms there are true pseudo and false pseudo. The construction of mathematical concepts in students of pseudo thinking should be immediately known because the error will have an impact on the next construction of mathematical concepts and to correct the errors it requires knowledge of the source of the error. Therefore, in this article will be discussed thinking process in constructing of mathematical concepts in students who experience pseudo thinking.

My Entirely Plausible Fantasy: Early Mathematics Education in the Age of the Touchscreen Computer

Science.gov (United States)

Ginsburg, Herbert P.

2014-01-01

This paper offers an account of what early mathematics education could look like in an age of young digital natives. Each "Tubby," as the tablets are called, presents Nicole (our generic little child) with stimulating mathematics microworlds, from which, beginning at age 3, she can learn basic math concepts, as well as methods of…

The State of Proof in Finnish and Swedish Mathematics Textbooks--Capturing Differences in Approaches to Upper-Secondary Integral Calculus

Science.gov (United States)

Bergwall, Andreas; Hemmi, Kirsti

2017-01-01

Students' difficulties with proof, scholars' calls for proof to be a consistent part of K-12 mathematics, and the extensive use of textbooks in mathematics classrooms motivate investigations on how proof-related items are addressed in mathematics textbooks. We contribute to textbook research by focusing on opportunities to learn proof-related…

Mathematical theory of compressible viscous fluids analysis and numerics

CERN Document Server

Feireisl, Eduard; Pokorný, Milan

2016-01-01

This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematic...

Student Talk and Opportunities for Mathematical Learning in Small Group Interactions

Science.gov (United States)

Wood, Marcy B.; Kalinec, Crystal A.

2012-01-01

Small group interactions are an important tool for mathematical learning and yet researchers have neither examined small group talk across entire lessons nor have they focused on moments of mathematical learning in small groups. We examined such talk and identified kinds of interactions and connections between interactions and mathematical…

Case Study of an Epistemic Mathematics Computer Game

Science.gov (United States)

Buteau, Chantal; Muller, Eric

2018-01-01

E-Brock Bugs is a serious educational game (SEG) about probability which was created based on Devlin's design principles for games whose players adopt identities of mathematically able persons. This kind of games in which "players think and act like real world professionals" has been called epistemic. This article presents an empirical…

Place Matters: Mathematics Education Reform in Urban Schools

Science.gov (United States)

Rousseau Anderson, Celia

2014-01-01

While mathematics education research has often focused at the level of the classroom (Rousseau Anderson & Tate, 2008), there are emerging calls for attention to shift from individual classrooms to consider the process of reform at the school or district level. Investigating the role of the institution and conditions of the organization becomes…

Marketing, Management and Performance: Multilingualism as Commodity in a Tourism Call Centre

Science.gov (United States)

Duchene, Alexandre

2009-01-01

This paper focuses on the ways an institution of the new economy--a tourism call centre in Switzerland--markets, manages and performs multilingual services. In particular, it explores the ways multilingualism operates as a strategic and managerial tool within tourism call centres and how the institutional regulation of language practices…

The perfection of the construction of a combined cutting tool on the basis of the results of mathematical modelling of working cutting processes in RecurDyn

Directory of Open Access Journals (Sweden)

Poddubny Vladimir

2017-01-01

Full Text Available As the title implies the article describes how to optimize the construction of a combined cutting tool on the example of developed design of the face milling cutter with regulable rigidity of damping elements in order to improve the vibration resistance of the cutting process. RecurDyn is proposed, which is widely used for creating models of different mechanical systems, their analysis and optimization of construction, uses the ideology of visual object-oriented programming and computer research of volume solid-state models. Much attention is given to the description of the mechanical and mathematical model of the face milling cutter in RecurDyn and the results of mathematical modeling of the face milling cutter with damping elements, consisting of individual elements, with the possibility of program controlling its operation in the process of cutting. The applying of RecurDyn made it possible to carry out a complex assessment of influence of separate elements of a design of the combined cutting tool on quantitative and qualitative parameters of milling process and to define optimal values of the input and output parameters of technological process of machining for various damping elements.

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

ECONOMIC AND MATHEMATICAL MODELING INNOVATION SYSTEMS

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D.V. Makarov

2014-06-01

Full Text Available The paper presents one of the mathematical tools for modeling innovation processes. With the help of Kondratieff long waves can define innovation cycles. However, complexity of the innovation system implies a qualitative description. The article describes the problems of this area of research.

Spatial mathematics theory and practice through mapping

CERN Document Server

Arlinghaus, Sandra Lach

2013-01-01

In terms of statistics, GIS offers many connections. With GIS, data are gathered, displayed, summarized, examined, and interpreted to discover patterns. Spatial Mathematics: Theory and Practice through Mapping uses GIS as a platform to teach mathematical concepts and skills through visualization of numbers. It examines theory and practice from disparate academic disciplines such as geography, mathematics, physics, and general social science. This approach allows students to grapple with biodiversity, crime, natural hazards, climate, energy, water, and other relevant real-world issues of the twenty-first century. Includes QR Codes Linked to Animated Maps, a Mapping Activity Site, or to an Interactive Webpage, Creating an Interactive Resource That Stays Relevant The book integrates competing philosophical views of the world: synthesis and analysis. These two approaches yield different results and employ different tools. This book considers both approaches to looking at real-world issues that have mathematics as...

Mathematical statistics essays on history and methodology

CERN Document Server

Pfanzagl, Johann

2017-01-01

This book presents a detailed description of the development of statistical theory. In the mid twentieth century, the development of mathematical statistics underwent an enduring change, due to the advent of more refined mathematical tools. New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance. Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, because a meaningful concept of optimality (based on the regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson’s Theorem) was not yet available. The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions. In four engaging essays, this book presents a detailed description of how the use of mathematical methods stimulated...

Learning fraction comparison by using a dynamic mathematics software - GeoGebra

Science.gov (United States)

Poon, Kin Keung

2018-04-01

GeoGebra is a mathematics software system that can serve as a tool for inquiry-based learning. This paper deals with the application of a fraction comparison software, which is constructed by GeoGebra, for use in a dynamic mathematics environment. The corresponding teaching and learning issues have also been discussed.

Mathematical Making in Teacher Preparation: What Knowledge Is Brought to Bear?

Science.gov (United States)

Greenstein, Steven; Seventko, Justin

2017-01-01

In this paper, we describe an experience within mathematics teacher preparation that engages preservice teachers (PSTs) in Making and design practices that we hypothesized would inform their conceptual and pedagogical thinking. With a focus on the design of new tools to support mathematics teaching and learning, this Learning by Design experience…

Learning Fraction Comparison by Using a Dynamic Mathematics Software--GeoGebra

Science.gov (United States)

Poon, Kin Keung

2018-01-01

GeoGebra is a mathematics software system that can serve as a tool for inquiry-based learning. This paper deals with the application of a fraction comparison software, which is constructed by GeoGebra, for use in a dynamic mathematics environment. The corresponding teaching and learning issues have also been discussed.

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.

A review of mathematical models for the formation of vascular networks

KAUST Repository

Scianna, M.; Bell, C.G.; Preziosi, L.

2013-01-01

process generally called lymphangiogenesis. A number of mathematical approaches have been used to analyze these phenomena. In this paper, we review the different types of models, with special emphasis on their ability to reproduce different biological

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.

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…

Concept Map as an Assessment Tool in Secondary School Mathematics: An Analysis of Teachers' Perspectives

Science.gov (United States)

Mutodi, Paul; Chigonga, Benard

2016-01-01

This paper reports on teachers' views on concept mapping: its applicability; reliability; advantages and; difficulties. A close-ended questionnaire was administered to 50 purposefully selected secondary school mathematics teachers from Sekhukhune District, Limpopo, South Africa. The findings indicate that mathematics teachers generally perceive…

Young Children Use Graphs to Build Mathematical Reasoning

Science.gov (United States)

Larson, Mark J.; Whitin, David J.

2010-01-01

Mathematical, scientific, and technological knowledge is critical for people in a 21st Century world that is dependent upon a global interconnectedness and a knowledge-based economy. This is the kind of knowledge that will power innovations and drive decision making in the years ahead. Schools are therefore being called upon to devise a…

Prevalence of Mixed Methods Research in Mathematics Education

Science.gov (United States)

Ross, Amanda A.; Onwuegbuzie, Anthony J.

2012-01-01

In wake of federal legislation such as the No Child Left Behind Act of 2001 that have called for "scientifically based research in education," this study examined the possible trends in mixed methods research articles published in 2 peer-reviewed mathematics education journals (n = 87) from 2002 to 2006. The study also illustrates how…

Developing Mathematical Literacy through project work: A teacher/teaching perspective

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Renuka Vithal

2006-10-01

Full Text Available The implementation of the new Mathematical Literacy curriculum in South Africa is assuming several different conceptions of mathematics and therefore also being realised through a range of different pedagogies. In this paper I begin from a particular privileging of a critical perspective in mathematics education, which I argue is one (among others of the forces shaping the new South African curriculum reforms, particularly the Mathematical Literacy curriculum. If so, then the case for a specific pedagogy, that of project work, can be shown to support the development of a mathematical literacy from a critical perspective. In this paper a particular set of conceptual tools, principles and practices associated with project work, as developed in the Scandanavian context but researched in South Africa, are elaborated from the perspective of teachers/teaching of mathematical literacy.

Learner Perceptions of the Introduction of Computer-Assisted Learning in Mathematics at a Peri-Urban School in South Africa

Science.gov (United States)

Hartley, M. Shaheed; Treagust, David F.

2014-01-01

This study responded to a national call to improve the outcomes in mathematics in the Grade 12 matriculation examination in South Africa by reporting learners' perceptions of the introduction of computer-assisted learning in their mathematics classrooms. Three Grade 12 mathematics classes in a peri-urban school in South Africa were visited over a…

Mathematical methods linear algebra normed spaces distributions integration

CERN Document Server

Korevaar, Jacob

1968-01-01

Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions.The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector

Lectures on the mathematics of quantum mechanics I

CERN Document Server

Dell'Antonio, Gianfausto

2015-01-01

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving th...

Which Techno-mathematical Literacies Are Essential for Future Engineers?

NARCIS (Netherlands)

van der Wal, Nathalie J.; Bakker, Arthur; Drijvers, Paul

Due to increased use of technology, the workplace practices of engineers have changed. So-called techno-mathematical literacies (TmL) are necessary for engineers of the 21st century. Because it is still unknown which TmL engineers actually use in their professional practices, the purpose of this

Mathematical manipulative models: in defense of "beanbag biology".

Science.gov (United States)

Jungck, John R; Gaff, Holly; Weisstein, Anton E

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

Mathematical disposition of junior high school students viewed from learning styles

Science.gov (United States)

Putra, Arief Karunia; Budiyono, Slamet, Isnandar

2017-08-01

The relevance of this study is the growth of character values for students in Indonesia. Mathematics is a subject that builds the character values for students. It can be seen from the students' confidence in answering mathematics problems, their persistent and resilience in mathematics task. In addition, students have a curiosity in mathematics and appreciate the usefulness of mathematics. In mathematics, it is called a mathematical disposition. One of the factors that can affect students' mathematical disposition is learning style. Each student has a dominant learning style. Three of the most popular ones are visual, auditory, and kinesthetic. The most important uses of learning styles is that it makes it easy for teachers to incorporate them into their teaching. The purpose of this study was to determine which one that gives better mathematical dispositions among students with learning styles of visual, auditory, or kinesthetic. The subjects were 150 students in Sleman regency. Data obtained through questionnaires. Based on data analysis that has been done with benchmark assessment method, it can be concluded that students with visual learning style has a mathematical disposition better than students with auditory and kinesthetic learning styles, while students with kinesthetic learning style has a mathematical disposition better than students with auditory learning style. These results can be used as a reference for students with individual learning styles to improve the mathematical positive disposition in the learning process of mathematics.

Line integral on engineering mathematics

Science.gov (United States)

Wiryanto, L. H.

2018-01-01

Definite integral is a basic material in studying mathematics. At the level of calculus, calculating of definite integral is based on fundamental theorem of calculus, related to anti-derivative, as the inverse operation of derivative. At the higher level such as engineering mathematics, the definite integral is used as one of the calculating tools of line integral. the purpose of this is to identify if there is a question related to line integral, we can use definite integral as one of the calculating experience. The conclusion of this research says that the teaching experience in introducing the relation between both integrals through the engineer way of thinking can motivate and improve students in understanding the material.

Framing the structural role of mathematics in physics lectures: A case study on electromagnetism

Directory of Open Access Journals (Sweden)

Ricardo Karam

2014-05-01

Full Text Available Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations. Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction. Starting from an overall distinction between a technical approach, which involves an instrumental (tool-like use of mathematics, and a structural one, focused on reasoning about the physical world mathematically, the goal of this study is to characterize the development of the latter in didactic contexts. For this purpose, a case study was conducted on the electromagnetism course given by a distinguished physics professor. The analysis of selected teaching episodes with the software Videograph led to the identification of a set of categories that describe different strategies used by the professor to emphasize the structural role of mathematics in his lectures. As a consequence of this research, an analytic tool to enable future comparative studies between didactic approaches regarding the way mathematics is treated in physics teaching is provided.

Applying mathematical finance tools to the competitive Nordic electricity market

OpenAIRE

Vehviläinen, Iivo

2004-01-01

This thesis models competitive electricity markets using the methods of mathematical finance. Fundamental problems of finance are market price modelling, derivative pricing, and optimal portfolio selection. The same questions arise in competitive electricity markets. The thesis presents an electricity spot price model based on the fundamental stochastic factors that affect electricity prices. The resulting price model has sound economic foundations, is able to explain spot market price mo...

A Mathematical Formalization Proposal for Business Growth

Directory of Open Access Journals (Sweden)

Gheorghe BAILESTEANU

2013-01-01

Full Text Available Economic sciences have known a spectacular evolution in the last century; beginning to use axiomatic methods, applying mathematical instruments as a decision-making tool. The quest to formalization needs to be addressed from various different angles, reducing entry and operating formal costs, increasing the incentives for firms to operate formally, reducing obstacles to their growth, and searching for inexpensive approaches through which to enforce compliancy with government regulations. This paper proposes a formalized approach to business growth, based on mathematics and logics, taking into consideration the particularities of the economic sector.

Technology-Supported Mathematics Environments: Telecollaboration in a Secondary Statistics Classroom

Science.gov (United States)

Staley, John; Moyer-Packenham, Patricia; Lynch, Monique C.

2005-01-01

The Internet, an exciting and radically different medium infiltrating pop culture, business, and education, is also a powerful educational tool with teaching and learning potential for mathematics. Web-based instructional tools allow students and teachers to actively and interactively participate in the learning process (Lynch, Moyer, Frye & Suh,…

Using poison center exposure calls to predict methadone poisoning deaths.

Directory of Open Access Journals (Sweden)

Nabarun Dasgupta

Full Text Available PURPOSE: There are more drug overdose deaths in the Untied States than motor vehicle fatalities. Yet the US vital statistics reporting system is of limited value because the data are delayed by four years. Poison centers report data within an hour of the event, but previous studies suggested a small proportion of poisoning deaths are reported to poison centers (PC. In an era of improved electronic surveillance capabilities, exposure calls to PCs may be an alternate indicator of trends in overdose mortality. METHODS: We used PC call counts for methadone that were reported to the Researched Abuse, Diversion and Addiction-Related Surveillance (RADARS® System in 2006 and 2007. US death certificate data were used to identify deaths due to methadone. Linear regression was used to quantify the relationship of deaths and poison center calls. RESULTS: Compared to decedents, poison center callers tended to be younger, more often female, at home and less likely to require medical attention. A strong association was found with PC calls and methadone mortality (b=0.88, se=0.42, t=9.5, df=1, p<0.0001, R(2 =0.77. These findings were robust to large changes in a sensitivity analysis assessing the impact of underreporting of methadone overdose deaths. CONCLUSIONS: Our results suggest that calls to poison centers for methadone are correlated with poisoning mortality as identified on death certificates. Calls received by poison centers may be used for timely surveillance of mortality due to methadone. In the midst of the prescription opioid overdose epidemic, electronic surveillance tools that report in real-time are powerful public health tools.

Physics to Mathematics: from Lintearia to Lemniscate - I

Indian Academy of Sciences (India)

Physics to Mathematics: from Lintearia to Lemniscate - I. R Sridharan. The elastic curve, also called elastica, is the name given to the shape assumed by a uniform elastic rod when bent into a plane curve under a stress of a certain kind. This curve, defined by James Bernoulli in the lSth century has been an interesting object ...

An Early Mathematical Patterning Assessment: identifying young Australian Indigenous children's patterning skills

Science.gov (United States)

Papic, Marina

2015-12-01

This paper presents an Early Mathematical Patterning Assessment (EMPA) tool that provides early childhood educators with a valuable opportunity to identify young children's mathematical thinking and patterning skills through a series of hands-on and drawing tasks. EMPA was administered through one-to-one assessment interviews to children aged 4 to 5 years in the year prior to formal school. Two hundred and seventeen assessments indicated that the young low socioeconomic and predominantly Australian Indigenous children in the study group had varied patterning and counting skills. Three percent of the study group was able to consistently copy and draw an ABABAB pattern made with coloured blocks. Fifty percent could count to six by ones and count out six items with 4 % of the total group able to identify six items presented in regular formations without counting. The integration of patterning into early mathematics learning is critical to the abstraction of mathematical ideas and relationships and to the development of mathematical reasoning in young children. By using the insights into the children's thinking that the EMPA tool provides, early childhood educators can better inform mathematics teaching and learning and so help close the persistent gap in numeracy between Indigenous and non-Indigenous children.

Theological Metaphors in Mathematics

Directory of Open Access Journals (Sweden)

Krajewski Stanisław

2016-03-01

Full Text Available Examples of possible theological influences upon the development of mathematics are indicated. The best known connection can be found in the realm of infinite sets treated by us as known or graspable, which constitutes a divine-like approach. Also the move to treat infinite processes as if they were one finished object that can be identified with its limits is routine in mathematicians, but refers to seemingly super-human power. For centuries this was seen as wrong and even today some philosophers, for example Brian Rotman, talk critically about “theological mathematics”. Theological metaphors, like “God’s view”, are used even by contemporary mathematicians. While rarely appearing in official texts they are rather easily invoked in “the kitchen of mathematics”. There exist theories developing without the assumption of actual infinity the tools of classical mathematics needed for applications (For instance, Mycielski’s approach. Conclusion: mathematics could have developed in another way. Finally, several specific examples of historical situations are mentioned where, according to some authors, direct theological input into mathematics appeared: the possibility of the ritual genesis of arithmetic and geometry, the importance of the Indian religious background for the emergence of zero, the genesis of the theories of Cantor and Brouwer, the role of Name-worshipping for the research of the Moscow school of topology. Neither these examples nor the previous illustrations of theological metaphors provide a certain proof that religion or theology was directly influencing the development of mathematical ideas. They do suggest, however, common points and connections that merit further exploration.

The Systems Biology Research Tool: evolvable open-source software

Directory of Open Access Journals (Sweden)

Wright Jeremiah

2008-06-01

Full Text Available Abstract Background Research in the field of systems biology requires software for a variety of purposes. Software must be used to store, retrieve, analyze, and sometimes even to collect the data obtained from system-level (often high-throughput experiments. Software must also be used to implement mathematical models and algorithms required for simulation and theoretical predictions on the system-level. Results We introduce a free, easy-to-use, open-source, integrated software platform called the Systems Biology Research Tool (SBRT to facilitate the computational aspects of systems biology. The SBRT currently performs 35 methods for analyzing stoichiometric networks and 16 methods from fields such as graph theory, geometry, algebra, and combinatorics. New computational techniques can be added to the SBRT via process plug-ins, providing a high degree of evolvability and a unifying framework for software development in systems biology. Conclusion The Systems Biology Research Tool represents a technological advance for systems biology. This software can be used to make sophisticated computational techniques accessible to everyone (including those with no programming ability, to facilitate cooperation among researchers, and to expedite progress in the field of systems biology.

An Environment for Analyzing Space Optimizations in Call-by-Need Functional Languages

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Nils Dallmeyer

2017-01-01

Full Text Available We present an implementation of an interpreter LRPi for the call-by-need calculus LRP, based on a variant of Sestoft's abstract machine Mark 1, extended with an eager garbage collector. It is used as a tool for exact space usage analyses as a support for our investigations into space improvements of call-by-need calculi.

Developing a Mathematics Education Quality Scale

Science.gov (United States)

Ciftci, S. Koza; Karadag, Engin

2016-01-01

The aim of this study was to evaluate students' perceptions of the quality of mathematics education and to develop a reliable and valid measurement tool. The research was conducted with 638 (first study) and 407 (second study) secondary school students in Eskisehir, Turkey. Item discrimination, structural validity (exploratory factor analysis and…

Teacher's Ability to Develop Learning Materials Potentially Mathematical Discourse

Directory of Open Access Journals (Sweden)

Hamdani Hamdani

2017-10-01

Full Text Available In the process of learning in the field, the teacher still dominates the conversation while the students as a passive listener. As a result, not only the communication skills of students who are less developed, the understanding of student material is also lacking. Therefore it is necessary to research the ability of teachers in developing learning tools potentially mathematical discourse to improve students' mathematical communication skills. The research method used is descriptive. Research activities include: identification of problems through questionnaires, observation, and interviews; teacher training; teachers develop learning tools; validation; and enhancement of the device by the teacher. The subject of this research is the junior high school mathematics teacher from several districts in the border area of Sambas-Sarawak Regency. The results show that in every learning mathematics there is always a conversation between teachers and students, but rarely use the question "why" and "how". Most teacher-made lesson plans contain scenarios of conversations between teachers and students, but just plain questioning, have not led to a debate between each other so that understanding becomes deeper. Student worksheet made by the teacher in the form of a matter of the ordinary story, rarely load non-routine problem let alone open-ended.

Your move: The effect of chess on mathematics test scores.

Science.gov (United States)

Rosholm, Michael; Mikkelsen, Mai Bjørnskov; Gumede, Kamilla

2017-01-01

We analyse the effect of substituting a weekly mathematics lesson in primary school grades 1-3 with a lesson in mathematics based on chess instruction. We use data from the City of Aarhus in Denmark, combining test score data with a comprehensive data set obtained from administrative registers. We use two different methodological approaches to identify and estimate treatment effects and we tend to find positive effects, indicating that knowledge acquired through chess play can be transferred to the domain of mathematics. We also find larger impacts for unhappy children and children who are bored in school, perhaps because chess instruction facilitates learning by providing an alternative approach to mathematics for these children. The results are encouraging and suggest that chess may be an important and effective tool for improving mathematical capacity in young students.

Diffusion tensor and diffusion weighted imaging. Pictorial mathematics

Energy Technology Data Exchange (ETDEWEB)

Nakada, Tsutomu [California Univ., Davis, CA (United States)

1995-06-01

A new imaging algorithm for the treatment of a second order apparent diffusion tensor, D{sub app}{sup {xi}} is described. The method calls for only mathematics of images (pictorial mathematics) without necessity of eigenvalues/eigenvectors estimation. Nevertheless, it is capable of extracting properties of D{sub app}{sup {xi}} invariant to observation axes. While trace image is an example of images weighted by invariance of the tensor matrix, three dimensional anisotropy (3DAC) contrast represents the imaging method making use to anisotropic direction of tensor ellipsoid producing color coded contrast of exceptionally high anatomic resolution. Contrary to intuition, the processes require only a simple algorithm directly applicable to clinical magnetic resonance imaging (MRI). As a contrast method which precisely represents physical characteristics of a target tissue, invariant D{sub app}{sup {xi}} images produced by pictorial mathematics possess significant potential for a number of biological and clinical applications. (author).

The Influence of Mathematics Professional Development, School-Level, and Teacher-Level Variables on Primary Students' Mathematics Achievement

Science.gov (United States)

Polly, Drew; Wang, Chuang; Martin, Christie; Lambert, Richard; Pugalee, David; Middleton, Catherina

2018-01-01

This study examined the influence of a professional development project about an internet-based mathematics formative assessment tool and related pedagogies on primary teachers' instruction and student achievement. Teachers participated in 72 h of professional development during the year. Descriptive statistics and multivariate analyses of…

Adaptation of abbreviated mathematics anxiety rating scale for engineering students

Science.gov (United States)

Nordin, Sayed Kushairi Sayed; Samat, Khairul Fadzli; Sultan, Al Amin Mohamed; Halim, Bushra Abdul; Ismail, Siti Fatimah; Mafazi, Nurul Wirdah

2015-05-01

Mathematics is an essential and fundamental tool used by engineers to analyse and solve problems in their field. Due to this, most engineering education programs involve a concentration of study in mathematics courses whereby engineering students have to take mathematics courses such as numerical methods, differential equations and calculus in the first two years and continue to do so until the completion of the sequence. However, the students struggled and had difficulties in learning courses that require mathematical abilities. Hence, this study presents the factors that caused mathematics anxiety among engineering students using Abbreviated Mathematics Anxiety Rating Scale (AMARS) through 95 students of Universiti Teknikal Malaysia Melaka (UTeM). From 25 items in AMARS, principal component analysis (PCA) suggested that there are four mathematics anxiety factors, namely experiences of learning mathematics, cognitive skills, mathematics evaluation anxiety and students' perception on mathematics. Minitab 16 software was used to analyse the nonparametric statistics. Kruskal-Wallis Test indicated that there is a significant difference in the experience of learning mathematics and mathematics evaluation anxiety among races. The Chi-Square Test of Independence revealed that the experience of learning mathematics, cognitive skills and mathematics evaluation anxiety depend on the results of their SPM additional mathematics. Based on this study, it is recommended to address the anxiety problems among engineering students at the early stage of studying in the university. Thus, lecturers should play their part by ensuring a positive classroom environment which encourages students to study mathematics without fear.

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching

OpenAIRE

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...

Scattering theory in quantum mechanics. Physical principles and mathematical methods

International Nuclear Information System (INIS)

Amrein, W.O.; Jauch, J.M.; Sinha, K.B.

1977-01-01

A contemporary approach is given to the classical topics of physics. The purpose is to explain the basic physical concepts of quantum scattering theory, to develop the necessary mathematical tools for their description, to display the interrelation between the three methods (the Schroedinger equation solutions, stationary scattering theory, and time dependence) to derive the properties of various quantities of physical interest with mathematically rigorous methods

REVIEW OF MATHEMATICAL METHODS AND ALGORITHMS OF MEDICAL IMAGE PROCESSING ON THE EXAMPLE OF TECHNOLOGY OF MEDICAL IMAGE PROCESSING FROM WOLFRAM MATHEMATICS

Directory of Open Access Journals (Sweden)

O. Ye. Prokopchenko

2015-10-01

Full Text Available The article analyzes the basic methods and algorithms of mathematical processing of medical images as objects of computer mathematics. The presented methods and computer algorithms of mathematics relevant and may find application in the field of medical imaging - automated processing of images; as a tool for measurement and determination the optical parameters; identification and formation of medical images database. Methods and computer algorithms presented in the article and based on Wolfram Mathematica are also relevant to the problem of modern medical education. As an example of Wolfram Mathematics may be considered appropriate demonstration, such as recognition of special radiographs and morphological imaging. These methods are used to improve  the diagnostic significance and value of medical (clinical research and can serve as an educational interactive demonstration. Implementation submitted individual methods and algorithms of computer Wolfram Mathematics contributes, in general, the optimization process of practical processing and presentation of medical images.

Mathematical analysis I

CERN Document Server

Canuto, Claudio

2015-01-01

The purpose of the volume is to provide a support for a first course in Mathematics. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques. Proofs to the main results befit the intermediate level, together with several remarks and complementary notes enhancing the treatise. The last, and farthest-reaching, level requires the additional study of ...

Mathematics Teachers' Representations of Authority

Science.gov (United States)

Wagner, David; Herbel-Eisenmann, Beth

2014-01-01

Issues of authority abound in education and schooling but have not been interrogated sufficiently. We describe a tool that we have developed to initiate dialogue with teachers about authority in their classrooms--using a diagram to represent authority in their classrooms. Our analysis of the diagrams mathematics teachers created and discussed in…

Integrated Sensing and Processing (ISP). A Mathematical Methodology for Managing and Integrating Sensors and Processors in Distributed Systems for Radar and Communication

National Research Council Canada - National Science Library

Spooner, Chad M

2005-01-01

.... The approach is to consider systems of targets and sensors in as general a general mathematical formulation as possible, to develop mathematical tools to study such systems, and to apply the tools...

Biomimetic agent based modelling using male Frog calling behaviour as a case study

DEFF Research Database (Denmark)

Jørgensen, Søren V.; Demazeau, Yves; Christensen-Dalsgaard, Jakob

2014-01-01

by individuals to generate their observed population behaviour. A number of existing agent-modelling frameworks are considered, but none have the ability to handle large numbers of time-dependent event-generating agents; hence the construction of a new tool, RANA. The calling behaviour of the Puerto Rican Tree...... Frog, E. coqui, is implemented as a case study for the presentation and discussion of the tool, and results from this model are presented. RANA, in its present stage of development, is shown to be able to handle the problem of modelling calling frogs, and several fruitful extensions are proposed...

Computer-aided tool for the teaching of relational algebra in data base courses

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Johnny Villalobos Murillo

2016-03-01

Full Text Available This article describes the design and implementation of computer-aided tool called Relational Algebra Translator (RAT in data base courses, for the teaching of relational algebra. There was a problem when introducing the relational algebra topic in the course EIF 211 Design and Implementation of Databases, which belongs to the career of Engineering in Information Systems of the National University of Costa Rica, because students attending this course were lacking profound mathematical knowledge, which led to a learning problem, being this an important subject to understand what the data bases search and request do RAT comes along to enhance the teaching-learning process. It introduces the architectural and design principles required for its implementation, such as: the language symbol table, the gramatical rules and the basic algorithms that RAT uses to translate from relational algebra to SQL language. This tool has been used for one periods and has demonstrated to be effective in the learning-teaching process.  This urged investigators to publish it in the web site: www.slinfo.una.ac.cr in order for this tool to be used in other university courses.

17th European Conference on Mathematics for Industry

CERN Document Server

Günther, Michael; Marheineke, Nicole

2014-01-01

This book contains the proceedings of the 17th European Conference on Mathematics for Industry, ECMI2012, held in Lund, Sweden, July 2012, at which ECMI celebrated its 25th anniversary. It covers mathematics in a wide range of applications and methods, from circuit and electromagnetic devices, environment, fibers, flow, medicine, robotics and automotive industry, further applications to methods and education. The book includes contributions from leading figures in business, science and academia who promote the application of mathematics to industry and emphasize industrial sectors that offer the most exciting opportunities. The contributions reinforce the role of mathematics as being a catalyst for innovation as well as an overarching resource for industry and business. The book features an accessible presentation of real-world problems in industry and finance, provides insight and tools for engineers and scientists which will help them to solve similar problems, and offers modeling and simulation techniques ...

CALDoseX: a software tool for absorbed dose calculations in diagnostic radiology

International Nuclear Information System (INIS)

Kramer, R.; Khourya, H.J.; Vieira, J.W.

2008-01-01

Conversion coefficients (CCs) between absorbed dose to organs and tissues at risk and measurable quantities commonly used in X-ray diagnosis have been calculated for the last 30 years mostly with mathematical MIRD5-type phantoms, in which organs are represented by simple geometrical bodies, like ellipsoids, tori, truncated cylinders, etc. In contrast, voxel-based phantoms are true to nature representations of human bodies. The purpose of this study is therefore to calculate CCs for common examinations in X-ray diagnosis with the recently developed MAX06 (Male Adult voXel) and FAX06 (Female Adult voXel) phantoms for various projections and different X-ray spectra and to make these CCs available to the public through a software tool, called CALDose X (CALculation of Dose for X-ray diagnosis). (author)

Un estudio exploratorio de los esquemas que emplean los alumnos de bachillerato para validar resultados matemáticos/ An exploratory study of schemes used by senior high school students to validate mathematic results

Directory of Open Access Journals (Sweden)

Víctor Larios Osorio

2018-04-01

Full Text Available Mathematics, as a body of scientific knowledge, includes not only a set of concepts and theories described in books and scientific journals but a procedural knowledge used for solving problems and proving the resulting solution. There is a tool for proving solutions, the so-called mathematical proof, which is worth to be included in the educational process. To complete the study herein described a random stratified sample was selected and given a test demanding to explain the answers given. However, high school students (15-18 years old do not rely on the use of the known proof scheme. For that reason, a diagnostic study was carried out at the Autonomous University of Querétaro (UAQ in order to identify the strategies the students are currently following and finding ways to teach such mathematical proof scheme. The findings are a description of individual students’ argumentative practices and the identification and grouping of the most frequently used proof scheme.

Spatial Harmonic Decomposition as a tool for unsteady flow phenomena analysis

International Nuclear Information System (INIS)

Duparchy, A; Guillozet, J; De Colombel, T; Bornard, L

2014-01-01

Hydropower is already the largest single renewable electricity source today but its further development will face new deployment constraints such as large-scale projects in emerging economies and the growth of intermittent renewable energy technologies. The potential role of hydropower as a grid stabilizer leads to operating hydro power plants in ''off-design'' zones. As a result, new methods of analyzing associated unsteady phenomena are needed to improve the design of hydraulic turbines. The key idea of the development is to compute a spatial description of a phenomenon by using a combination from several sensor signals. The spatial harmonic decomposition (SHD) extends the concept of so-called synchronous and asynchronous pulsations by projecting sensor signals on a linearly independent set of a modal scheme. This mathematical approach is very generic as it can be applied on any linear distribution of a scalar quantity defined on a closed curve. After a mathematical description of SHD, this paper will discuss the impact of instrumentation and provide tools to understand SHD signals. Then, as an example of a practical application, SHD is applied on a model test measurement in order to capture and describe dynamic pressure fields. Particularly, the spatial description of the phenomena provides new tools to separate the part of pressure fluctuations that contribute to output power instability or mechanical stresses. The study of the machine stability in partial load operating range in turbine mode or the comparison between the gap pressure field and radial thrust behavior during turbine brake operation are both relevant illustrations of SHD contribution

Lakatos and Hersh on Mathematical Proof

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Hossein Bayat

2015-12-01

Full Text Available The concept of Mathematical Proof has been controversial for the past few decades. Different philosophers have offered different theories about the nature of Mathematical Proof, among which theories presented by Lakatos and Hersh have had significant similarities and differences with each other. It seems that a comparison and critical review of these two theories will lead to a better understanding of the concept of mathematical proof and will be a big step towards solving many related problems. Lakatos and Hersh argue that, firstly, “mathematical proof” has two different meanings, formal and informal; and, secondly, informal proofs are affected by human factors, such as individual decisions and collective agreements. I call these two thesis, respectively, “proof dualism” and “humanism”. But on the other hand, their theories have significant dissimilarities and are by no means equivalent. Lakatos is committed to linear proof dualism and methodological humanism, while Hersh’s theory involves some sort of parallel proof dualism and sociological humanism. According to linear proof dualism, the two main types of proofs are provided in order to achieve a common goal: incarnation of mathematical concepts and methods and truth. However, according to the parallel proof dualism, two main types of proofs are provided in order to achieve two different types of purposes: production of a valid sequence of signs (the goal of the formal proof and persuasion of the audience (the goal of the informal proof. Hersh’s humanism is informative and indicates pluralism; whereas, Lakatos’ version of humanism is normative and monistic.

A Guided Tour of Mathematical Methods - 2nd Edition

Science.gov (United States)

Snieder, Roel

2004-09-01

Mathematical methods are essential tools for all physical scientists. This second edition provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are well integrated. The mathematical insights that the student acquires are therefore driven by their physical insight. Topics that are covered include vector calculus, linear algebra, Fourier analysis, scale analysis, complex integration, Green's functions, normal modes, tensor calculus, and perturbation theory. The second edition contains new chapters on dimensional analysis, variational calculus, and the asymptotic evaluation of integrals. This book can be used by undergraduates, and lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks. All the material is presented in the form of problems Mathematical insights are gained by getting the reader to develop answers themselves Many applications of the mathematics are given

Stochastic tools in turbulence

CERN Document Server

Lumey, John L

2012-01-01

Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the

Your move: The effect of chess on mathematics test scores

DEFF Research Database (Denmark)

Rosholm, Michael; Mikkelsen, Mai Bjørnskov; Gumede, Kamilla Trille

2017-01-01

We analyse the effect of substituting a weekly mathematics lesson in primary school grades 1–3 with a lesson in mathematics based on chess instruction. We use data from the City of Aarhus in Denmark, combining test score data with a comprehensive data set obtained from administrative registers. We...... use two different methodological approaches to identify and estimate treatment effects and we tend to find positive effects, indicating that knowledge acquired through chess play can be transferred to the domain of mathematics. We also find larger impacts for unhappy children and children who...... are bored in school, perhaps because chess instruction facilitates learning by providing an alternative approach to mathematics for these children. The results are encouraging and suggest that chess may be an important and effective tool for improving mathematical capacity in young students....

Your move: The effect of chess on mathematics test scores.

Directory of Open Access Journals (Sweden)

Michael Rosholm

Full Text Available We analyse the effect of substituting a weekly mathematics lesson in primary school grades 1-3 with a lesson in mathematics based on chess instruction. We use data from the City of Aarhus in Denmark, combining test score data with a comprehensive data set obtained from administrative registers. We use two different methodological approaches to identify and estimate treatment effects and we tend to find positive effects, indicating that knowledge acquired through chess play can be transferred to the domain of mathematics. We also find larger impacts for unhappy children and children who are bored in school, perhaps because chess instruction facilitates learning by providing an alternative approach to mathematics for these children. The results are encouraging and suggest that chess may be an important and effective tool for improving mathematical capacity in young students.

On the Edge: Intelligent CALL in the 1990s.

Science.gov (United States)

Underwood, John

1989-01-01

Examines the possibilities of developing computer-assisted language learning (CALL) based on the best of modern technology, arguing that artificial intelligence (AI) strategies will radically improve the kinds of exercises that can be performed. Recommends combining AI technology with other tools for delivering instruction, such as simulation and…

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

Science.gov (United States)

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

Science.gov (United States)

Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

2013-01-01

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

Mathematical analysis and numerical methods for science and technology

CERN Document Server

Dautray, Robert

These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which ...

A quest towards a mathematical theory of living systems

CERN Document Server

Bellomo, Nicola; Gibelli, Livio; Outada, Nisrine

2017-01-01

This monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory. The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation, mean field models, and Monte Carlo methods are also briefly covered. Chapter Three...

Mathematical determination of image quality

Energy Technology Data Exchange (ETDEWEB)

Barrett, H H

1982-01-01

The subjective term ''image quality'' is generally not easy to define and to measure. If, however, we limit ourselves, to determine certain anomalies in blurred images, then the task can be done more easily. The efficiency can in fact be measured and the results can be presented as ROC-characteristics (receiver operating characteristics). One can determine a relation between the characteristic and the noise distance of the imaging system, and this way the efficiency of an hypothetical ideal observer can be predicted. Furthermore one can compute noise distance and other statistical parameters of X-ray images distorted by quantum interference by special techniques that are founded on the so-called ''blur core''. The technique proved to be very successful in nuclear medicine, but is also valid in computerized tomography and X-ray diagnostics. The technique is explained without mathematical details. The question will be answered concerning the role mathematical analysis will play in the determination and optimization of the quality of diagnostic exposures.

Stochastic Distribution of Wear of Carbide Tools during Machining ...

African Journals Online (AJOL)

Journal of the Nigerian Association of Mathematical Physics ... The stochastic point model was used to determine the rate of wear distribution of the carbide tool ... Keywords: cutting speed, feed rate, machining time, tool life, reliability, wear.

Lesson play in mathematics education a tool for research and professional development

CERN Document Server

Zazkis, Rina; Liljedahl, Peter

2015-01-01

This book applies years of experience in the use of lesson play to a variety of situations involving mathematics thinking and learning. Covers lesson play in pre-service teacher education, and discusses its potential for both researchers and teacher educators.

The Teaching of Mathematics in Secondary Schools as a Tool for Self-Reliance and Re-Branding Process in Nigeria

Science.gov (United States)

Jonah, Tali D.; Caleb, Mbwas .L.; Stephen, Abe A.

2012-01-01

Mathematics teaching is an interaction between the teacher and the learners that leads to acquisition of desirable mathematical knowledge, ideas and skills necessary for applicability in our everyday life. This paper therefore looks at the concept of self-reliance, the concept of mathematics teaching, problems and prospects of mathematics teaching…

Investigating Language Learning Activity Using a CALL Task in the Self-access Centre

Directory of Open Access Journals (Sweden)

Carlos Montoro

2011-09-01

Full Text Available This article describes a small study of the language learning activity of individual learners using a CALL task in a self-access environment. The research focuses on the nature of the language learning activity, the most salient elements that make up its structure and major disturbances observed between and within some of those elements. It is set in the context of computer-assisted language learning (CALL and activity theory. A CALL task designed by the authors was made available online to be used as a research and learning tool. Empirical data was collected from two participants using ethnographic tools, such as participant observation and stimulated recall sessions. The analysis focuses on disturbances mainly involving the subject (i.e., the learner, mediating artefacts (e.g., the CALL task, the community (e.g., management and other self-access centre users and the object of the activity (i.e., learning English. It is recommended that future studies should look deeper into contradictions in the learning activity from a cultural-historical perspective.

A Primer on Mathematical Modeling in the Study of Organisms and Their Parts.

Science.gov (United States)

Montévil, Maël

2018-01-01

Mathematical modeling is a very powerful tool for understanding natural phenomena. Such a tool carries its own assumptions and should always be used critically. In this chapter, we highlight the key ingredients and steps of modeling and focus on their biological interpretation. In particular, we discuss the role of theoretical principles in writing models. We also highlight the meaning and interpretation of equations. The main aim of this chapter is to facilitate the interaction between biologists and mathematical modelers. We focus on the case of cell proliferation and motility in the context of multicellular organisms.

Tool-Supported User-Centred Prototyping of Mobile Applications

DEFF Research Database (Denmark)

Leichtenstern, Karin; André, Elisabeth; Rehm, Matthias

2011-01-01

the process both cost-effective and time-effective. In this paper we cover that problem and provide insights in so-called user-centered prototyping (UCP) tools which support the production of prototypes as well as their evaluation with end-users. In particular, we introduce our UCP tool called Mo...

Development of a personalized dosimetric tool for radiation protection in case of internal contamination and targeted radiotherapy in nuclear medicine

International Nuclear Information System (INIS)

Chiavassa, S.

2005-12-01

Current internal dosimetric estimations are based on the M.I.R.D. formalism and used standard mathematical models. These standard models are often far from a given patient morphology and do not allow to perform patient-specific dosimetry. The aim of this study was to develop a personalized dosimetric tool, which takes into account real patient morphology, composition and densities. This tool, called O.E.D.I.P.E., a French acronym of Tool for the Evaluation of Personalized Internal Dose, is a user-friendly graphical interface. O.E.D.I.P.E. allows to create voxel-based patient-specific geometries and associates them with the M.C.N.P.X. Monte Carlo code. Radionuclide distribution and absorbed dose calculation can be performed at the organ and voxel scale. O.E.D.I.P.E. can be used in nuclear medicine for targeted radiotherapy and in radiation protection in case of internal contamination. (author)

Storming a Citadel: Mathematical Theory and Experimental Practice

Science.gov (United States)

Sichau, Christian

2006-09-01

Based upon a comparison of the viscosity experiments of James Clerk Maxwell (1831 1879) and Oskar Emil Meyer (1834 1909) in the 1860s, I argue that mathematical theory plays a significant role in both aspects of experimental practice, the design and construction of an experimental apparatus and the transformation of the observed experimental data into the value of a physical quantity. I argue further that Maxwell’s and Meyer’s evaluation of each other’s theoretical and experimental work depended significantly on the mathematical tools they employed in their theories.

Gear cutting tools fundamentals of design and computation

CERN Document Server

Radzevich, Stephen P

2010-01-01

Presents the DG/K-based method of surface generation, a novel and practical mathematical method for designing gear cutting tools with optimal parameters. This book proposes a scientific classification for the various kinds of the gear machining meshes, discussing optimal designs of gear cutting tools.

Recent developments of mathematical fluid mechanics

CERN Document Server

Giga, Yoshikazu; Kozono, Hideo; Okamoto, Hisashi; Yamazaki, Masao

2016-01-01

The book addresses recent developments of the mathematical research on the Navier-Stokes and Euler equations as well as on related problems. In particular, there are covered:   1) existence, uniqueness, and the regularity of weak solutions; 2) stability of the motion in rest and the asymptotic behavior of solutions; 3) singularity and blow-up of weak and strong solutions; 4) vorticity and energy conservation; 5) motions of rotating fluids, or of fluids surrounding a rotating body; 6) free boundary problems; 7) maximal regularity theory and other abstract results for mathematical fluid mechanics.   For this quarter century, these topics have been playing a central role in both pure and applied mathematics and having a great influence to the developm ent of the functional analysis, harmonic analysis and numerical analysis whose tools make a a substantial contribution to the investigation of nonlinear partial differential equations, particularly the Navier-Stokes and the Euler equations.      There are 24...

CAN INFOGRAPHICS FACILITATE THE LEARNING OF INDIVIDUALS WITH MATHEMATICAL LEARNING DIFFICULTIES?

Directory of Open Access Journals (Sweden)

Basak Baglama

2017-12-01

Full Text Available Visualization of data has recently gained great importance in education and use of infographics is regarded as an important tool in teaching mathematics since it presents information in a clear and abstract way. Therefore, use of infographics for helping individuals with mathematical learning difficulties has become an important research question. This study aims to provide an overview on the use of infographics in teaching mathematics to individuals with mathematical learning difficulties. This is a qualitative study in which document analysis was used the collect the data. Results provided information about the definition of infographics, effectiveness of using infographics in education and facilitative role of infographics in enhancing learning of individuals with mathematical learning difficulties, namely dyscalculia. Results were discussed with relevant literature and recommendations for further research and practices were also presented.

Mathematics related anxiety: Mathematics bogeyman or not?

Directory of Open Access Journals (Sweden)

Videnović Marina

2011-01-01

Full Text Available Data of the PISA 2003 survey indicate high levels of mathematics anxiety of students in Serbia. More than half of our students worry whether they will have difficulties in mathematics class or whether they will earn poor marks. Aims of this study therefore are: examining relationship between math anxiety and achievement at mathematics literacy scale; establishing possible predictors of math anxiety and identification of students' groups in relations to their relationship towards mathematics as a subject. Mathematics anxiety is statistically negatively correlated with school achievement and achievement at mathematics literacy scale. Socio-demographic factors, motivational and cognitive aspects related to learning mathematics, perception of school and classroom climate explain 40% variance of mathematics anxiety. Based on students' relationship towards mathematics they cam be divided into three groups; while dimensions that apart them are uninterested-interested in mathematics and presence-absence of anxiety. The group displaying anxiety scores lowest among the three. Applying qualitative analysis students' and teachers' attitudes on specific issues related to teaching and learning mathematics was examined.

Toxicity Estimation Software Tool (TEST)

Science.gov (United States)

The Toxicity Estimation Software Tool (TEST) was developed to allow users to easily estimate the toxicity of chemicals using Quantitative Structure Activity Relationships (QSARs) methodologies. QSARs are mathematical models used to predict measures of toxicity from the physical c...

Achilles and the tortoise: Some caveats to mathematical modeling in biology.

Science.gov (United States)

Gilbert, Scott F

2018-01-31

Mathematical modeling has recently become a much-lauded enterprise, and many funding agencies seek to prioritize this endeavor. However, there are certain dangers associated with mathematical modeling, and knowledge of these pitfalls should also be part of a biologist's training in this set of techniques. (1) Mathematical models are limited by known science; (2) Mathematical models can tell what can happen, but not what did happen; (3) A model does not have to conform to reality, even if it is logically consistent; (4) Models abstract from reality, and sometimes what they eliminate is critically important; (5) Mathematics can present a Platonic ideal to which biologically organized matter strives, rather than a trial-and-error bumbling through evolutionary processes. This "Unity of Science" approach, which sees biology as the lowest physical science and mathematics as the highest science, is part of a Western belief system, often called the Great Chain of Being (or Scala Natura), that sees knowledge emerge as one passes from biology to chemistry to physics to mathematics, in an ascending progression of reason being purification from matter. This is also an informal model for the emergence of new life. There are now other informal models for integrating development and evolution, but each has its limitations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Teachers' Mathematics as Mathematics-at-Work

Science.gov (United States)

Bednarz, Nadine; Proulx, Jérôme

2017-01-01

Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…

Pre-Service Mathematics Teachers’ Problem Solving Processes with Geometer’s Sketchpad: Mirror Problem

OpenAIRE

ÖÇAL, Mehmet Fatih; ŞİMŞEK, Mertkan

2016-01-01

Problem solving skill is the core of mathematics education and its importance cannot be denied. This study specifically examined 56 freshmen pre-service mathematics teachers’ problem solving processes on a specific problem with the help of Geometer’s Sketchpad (GSP). They were grouped into two-person teams to solve a problem called "the mirror problem". They were expected to solve it by means of GSP. According to their works on GSP and related reflections, there appeared two differe...

Renewing U.S. mathematics: A plan for the 1990s

Energy Technology Data Exchange (ETDEWEB)

NONE

1990-12-31

In 1981 a committee of the National Research Council was formed to investigate the health of the mathematical sciences in the US. Its 1984 report, Renewing US Mathematics: Critical Resource for the future found that although the field was thriving intellectually, government support had deteriorated to a dangerously low level. Moreover, the number of young people entering the mathematical sciences had decreased to a level inadequate to replenish the field. The 1984 Report recommended a plan for renewal, the National Plan for Graduate and Postdoctoral Education in the Mathematical Sciences. That plan`s essential feature was a call for funding to bring support for the mathematical sciences into balance with support for the physical sciences and engineering. The interdisciplinary committee that wrote the 1984 Report quickly realized that the low level of research support for US mathematical sciences was so severe that it threatened the vitality of the entire scientific enterprise. As requested by the National Science Foundation (NSF) and the Interagency Committee for Extramural Mathematics Programs (ICEMAP), this report updates the 1984 Report. Specifically, the charge directed the committee to (1) update that report, describing the infrastructure and support for US mathematical sciences research; (2) assess trends and progress over the intervening five years against the recommendations of the 1984 Report; (3) briefly assess the field scientifically and identify significant opportunities for research, including cross-disciplinary collaboration; and (4) make appropriate recommendations designed to ensure that US mathematical sciences research will meet national needs in coming years.

Taking the Danish Speech Trainer from CALL to ICALL

DEFF Research Database (Denmark)

Juel Henrichsen, Peter

2015-01-01

Talebob (Speech Bob) is a newly developed interactive CALL-tool for training Danish speech with special regard to the pronunciation of highly idiomatic phrases. Talebob is currently being tested in primary schools in Nuuk, Hafnarfjörður and Tórshavn (where Danish is taught as a L2). The purpose...

Multi-objective optimization problems concepts and self-adaptive parameters with mathematical and engineering applications

CERN Document Server

Lobato, Fran Sérgio

2017-01-01

This book is aimed at undergraduate and graduate students in applied mathematics or computer science, as a tool for solving real-world design problems. The present work covers fundamentals in multi-objective optimization and applications in mathematical and engineering system design using a new optimization strategy, namely the Self-Adaptive Multi-objective Optimization Differential Evolution (SA-MODE) algorithm. This strategy is proposed in order to reduce the number of evaluations of the objective function through dynamic update of canonical Differential Evolution parameters (population size, crossover probability and perturbation rate). The methodology is applied to solve mathematical functions considering test cases from the literature and various engineering systems design, such as cantilevered beam design, biochemical reactor, crystallization process, machine tool spindle design, rotary dryer design, among others.

Modeling interdisciplinary activities involving Mathematics

DEFF Research Database (Denmark)

Iversen, Steffen Møllegaard

2006-01-01

In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...

Mathematical modelling in solid mechanics

CERN Document Server

Sofonea, Mircea; Steigmann, David

2017-01-01

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...

vFitness: a web-based computing tool for improving estimation of in vitro HIV-1 fitness experiments

Directory of Open Access Journals (Sweden)

Demeter Lisa

2010-05-01

Full Text Available Abstract Background The replication rate (or fitness between viral variants has been investigated in vivo and in vitro for human immunodeficiency virus (HIV. HIV fitness plays an important role in the development and persistence of drug resistance. The accurate estimation of viral fitness relies on complicated computations based on statistical methods. This calls for tools that are easy to access and intuitive to use for various experiments of viral fitness. Results Based on a mathematical model and several statistical methods (least-squares approach and measurement error models, a Web-based computing tool has been developed for improving estimation of virus fitness in growth competition assays of human immunodeficiency virus type 1 (HIV-1. Conclusions Unlike the two-point calculation used in previous studies, the estimation here uses linear regression methods with all observed data in the competition experiment to more accurately estimate relative viral fitness parameters. The dilution factor is introduced for making the computational tool more flexible to accommodate various experimental conditions. This Web-based tool is implemented in C# language with Microsoft ASP.NET, and is publicly available on the Web at http://bis.urmc.rochester.edu/vFitness/.

Capturing Student Mathematical Engagement through Differently Enacted Classroom Practices: Applying a Modification of Watson's Analytical Tool

Science.gov (United States)

Patahuddin, Sitti Maesuri; Puteri, Indira; Lowrie, Tom; Logan, Tracy; Rika, Baiq

2018-01-01

This study examined student mathematical engagement through the intended and enacted lessons taught by two teachers in two different middle schools in Indonesia. The intended lesson was developed using the ELPSA learning design to promote mathematical engagement. Based on the premise that students will react to the mathematical tasks in the forms…

Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

Science.gov (United States)

Hebert, Michael A.; Powell, Sarah R.

2016-01-01

Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…

Electrorheological fluids modeling and mathematical theory

CERN Document Server

Růžička, Michael

2000-01-01

This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.

Student transition into university mathematics education: transformation of people, tools and practices

NARCIS (Netherlands)

Pepin, B.; Rezat, S.; Hattermann, M.; Peter-Koop, A.

2014-01-01

In this article the concept of Feedback and Self-Regulated Learning has been used to investigate student ‘transition’ from upper secondary to university mathematics education. The findings are anchored in data from the TransMaths project (at the University of Manchester), more particularly the case

Personalizing oncology treatments by predicting drug efficacy, side-effects, and improved therapy: mathematics, statistics, and their integration.

Science.gov (United States)

Agur, Zvia; Elishmereni, Moran; Kheifetz, Yuri

2014-01-01

Despite its great promise, personalized oncology still faces many hurdles, and it is increasingly clear that targeted drugs and molecular biomarkers alone yield only modest clinical benefit. One reason is the complex relationships between biomarkers and the patient's response to drugs, obscuring the true weight of the biomarkers in the overall patient's response. This complexity can be disentangled by computational models that integrate the effects of personal biomarkers into a simulator of drug-patient dynamic interactions, for predicting the clinical outcomes. Several computational tools have been developed for personalized oncology, notably evidence-based tools for simulating pharmacokinetics, Bayesian-estimated tools for predicting survival, etc. We describe representative statistical and mathematical tools, and discuss their merits, shortcomings and preliminary clinical validation attesting to their potential. Yet, the individualization power of mathematical models alone, or statistical models alone, is limited. More accurate and versatile personalization tools can be constructed by a new application of the statistical/mathematical nonlinear mixed effects modeling (NLMEM) approach, which until recently has been used only in drug development. Using these advanced tools, clinical data from patient populations can be integrated with mechanistic models of disease and physiology, for generating personal mathematical models. Upon a more substantial validation in the clinic, this approach will hopefully be applied in personalized clinical trials, P-trials, hence aiding the establishment of personalized medicine within the main stream of clinical oncology. © 2014 Wiley Periodicals, Inc.

Longitudinal Effects of Technology Integration and Teacher Professional Development on Students' Mathematics Achievement

Science.gov (United States)

Bicer, Ali; Capraro, Robert M.

2017-01-01

MathForward is a program that provides teacher professional development and integrates the use of technology as a tool in the classroom. The present study examined students' mathematics growth from 2012 to 2013 and observed how students' mathematics scores changed after their school implemented the MathForward program. The sample consisted of two…

Isabelle/PIDE as Platform for Educational Tools

Directory of Open Access Journals (Sweden)

Makarius Wenzel

2012-02-01

Full Text Available The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface. Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE" is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.

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 Praxeological Study of Proportionality in Mathematics Lower Secondary Textbooks

DEFF Research Database (Denmark)

Wijayanti, Dyana

Research on the uses and contents of mathematics textbooks has expanded over the past decades, due to the central role textbooks occupy in mathematics teaching worldwide. However, the methodology of analysing the texts themselves often appears underdeveloped or even naïve, especially when it comes...... to specific mathematical content. The central idea of this thesis is to deploy the anthropological theory of the didactic, and especially the notion of praxeology, to analyse how textbooks treat three specific and related areas (or more precisely, sectors) of mathematical contents for lower secondary school......, namely "proportion and ratio" (in Arithmetic), "similar plane figures" (in Geometry), and "linear functions" (in Algebra). This leads to a new and very precise methodological tool for analysing the practices (types of tasks, techniques) supported by the textbooks through examples, explanations...

Teaching Mathematical Modeling in Mathematics Education

Science.gov (United States)

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

The graphics calculator in mathematics education: A critical review of recent research

Science.gov (United States)

Penglase, Marina; Arnold, Stephen

1996-04-01

The graphics calculator, sometimes referred to as the "super calculator," has sparked great interest among mathematics educators. Considered by many to be a tool which has the potential to revolutionise mathematics education, a significant amount of research has been conducted into its effectiveness as a tool for instruction and learning within precalculus and calculus courses, specifically in the study of functions, graphing and modelling. Some results suggest that these devices (a) can facilitate the learning of functions and graphing concepts and the development of spatial visualisation skills; (b) promote mathematical investigation and exploration; and (c) encourage a shift in emphasis from algebraic manipulation and proof to graphical investigation and examination of the relationship between graphical, algebraic and geometric representations. Other studies, however, indicate that there is still a need for manipulative techniques in the learning of function and graphing concepts, that the use of graphics calculators may not facilitate the learning of particular precalculus topics, and that some "de-skilling" may occur, especially among males. It is the contention of this paper, however, that much of the research in this new and important field fails to provide clear guidance or even to inform debate in adequate ways regarding the role of graphics calculators in mathematics teaching and learning. By failing to distinguish the role of the tool from that of the instructional process, many studies reviewed could be more appropriately classified as "program evaluations" rather than as research on the graphics calculator per se. Further, claims regarding the effectiveness of the graphics calculator as a tool for learning frequently fail to recognise that judgments of effectiveness result directly from existing assumptions regarding both assessment practice and student "achievement."

Properties of mathematical objects (Goedel on classes, properties and concepts)

International Nuclear Information System (INIS)

Materna, Pavel

2007-01-01

In terms of a sufficiently fine-grained theory we should distinguish between classes, properties and concepts. Since properties are best modeled as a kind of non-trivial intensions while mathematical objects are never non-trivial intensions we should not speak about properties of mathematical objects. When we do use the term property in mathematics (as Goedel did) we either mean classes, or the more fine-grained entities to be called concepts. In the latter case concepts have to be defined so that various distinct concepts could identify one and the same object. The notion of construction in transparent intensional logic makes it possible to construe concepts as abstract procedures. At the same time we have to distinguish between this notion and the notion of construction in constructivist systems: the former - unlike the latter - are objective and, therefore, acceptable for a realist

Marriages of mathematics and physics: A challenge for biology.

Science.gov (United States)

Islami, Arezoo; Longo, Giuseppe

2017-12-01

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of "geometric judgments" from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) "space" should be revisited for the purposes of life sciences. Copyright © 2017. Published by Elsevier Ltd.

Mathematical Modeling and Pure Mathematics

Science.gov (United States)

Usiskin, Zalman

2015-01-01

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

What Do Monkey Calls Mean?

Science.gov (United States)

Schlenker, Philippe; Chemla, Emmanuel; Zuberbühler, Klaus

2016-12-01

A field of primate linguistics is gradually emerging. It combines general questions and tools from theoretical linguistics with rich data gathered in experimental primatology. Analyses of several monkey systems have uncovered very simple morphological and syntactic rules and have led to the development of a primate semantics that asks new questions about the division of semantic labor between the literal meaning of monkey calls, additional mechanisms of pragmatic enrichment, and the environmental context. We show that comparative studies across species may validate this program and may in some cases help in reconstructing the evolution of monkey communication over millions of years. Copyright © 2016. Published by Elsevier Ltd.

Uncertainty and Complexity in Mathematical Modeling

Science.gov (United States)

Cannon, Susan O.; Sanders, Mark

2017-01-01

Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…

Math tools 500+ applications in science and arts

CERN Document Server

Glaeser, Georg

2017-01-01

In this book, topics such as algebra, trigonometry, calculus and statistics are brought to life through over 500 applications ranging from biology, physics and chemistry to astronomy, geography and music. With over 600 illustrations emphasizing the beauty of mathematics, Math Tools complements more theoretical textbooks on the market, bringing the subject closer to the reader and providing a useful reference to students. By highlighting the ubiquity of mathematics in practical fields, the book will appeal not only to students and teachers, but to anyone with a keen interest in mathematics and its applications.

DigitalHuman (DH): An Integrative Mathematical Model ofHuman Physiology

Science.gov (United States)

Hester, Robert L.; Summers, Richard L.; lIescu, Radu; Esters, Joyee; Coleman, Thomas G.

2010-01-01

Mathematical models and simulation are important tools in discovering the key causal relationships governing physiological processes and improving medical intervention when physiological complexity is a central issue. We have developed a model of integrative human physiology called DigitalHuman (DH) consisting of -5000 variables modeling human physiology describing cardiovascular, renal, respiratory, endocrine, neural and metabolic physiology. Users can view time-dependent solutions and interactively introduce perturbations by altering numerical parameters to investigate new hypotheses. The variables, parameters and quantitative relationships as well as all other model details are described in XML text files. All aspects of the model, including the mathematical equations describing the physiological processes are written in XML open source, text-readable files. Model structure is based upon empirical data of physiological responses documented within the peer-reviewed literature. The model can be used to understand proposed physiological mechanisms and physiological interactions that may not be otherwise intUitively evident. Some of the current uses of this model include the analyses of renal control of blood pressure, the central role of the liver in creating and maintaining insulin resistance, and the mechanisms causing orthostatic hypotension in astronauts. Additionally the open source aspect of the modeling environment allows any investigator to add detailed descriptions of human physiology to test new concepts. The model accurately predicts both qualitative and more importantly quantitative changes in clinically and experimentally observed responses. DigitalHuman provides scientists a modeling environment to understand the complex interactions of integrative physiology. This research was supported by.NIH HL 51971, NSF EPSCoR, and NASA

Mathematical and numerical foundations of turbulence models and applications

CERN Document Server

Chacón Rebollo, Tomás

2014-01-01

With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering, and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation, and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics,...

Mathematical principles of signal processing Fourier and wavelet analysis

CERN Document Server

Brémaud, Pierre

2002-01-01

Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...

Learners' Performance in Mathematics: A Case Study of Public High Schools, South Africa

Science.gov (United States)

Mapaire, Lawrence

2016-01-01

Mathematics is fundamental to national prosperity in providing tools for understanding science, technology, engineering and economics. It is essential in public decision-making and for participation in the knowledge economy. Mathematics equips pupils with uniquely powerful ways to describe, analyse and change the world. It can stimulate moments of…

Using dynamic software in mathematics: the case of reflection symmetry

Science.gov (United States)

Tatar, Enver; Akkaya, Adnan; Berrin Kağizmanli, Türkan

2014-10-01

This study was carried out to examine the effects of computer-assisted instruction (CAI) using dynamic software on the achievement of students in mathematics in the topic of reflection symmetry. The study also aimed to ascertain the pre-service mathematics teachers' opinions on the use of CAI in mathematics lessons. In the study, a mixed research method was used. The study group of this research consists of 30 pre-service mathematics teachers. The data collection tools used include a reflection knowledge test, a survey and observations. Based on the analysis of the data obtained from the study, the use of CAI had a positive effect on achievement in the topic of reflection symmetry of the pre-service mathematics teachers. The pre-service mathematics teachers were found to largely consider that a mathematics education which is carried out utilizing CAI will be more beneficial in terms of 'visualization', 'saving of time' and 'increasing interest/attention in the lesson'. In addition, it was found that the vast majority of them considered using computers in their teaching on the condition that the learning environment in which they would be operating has the appropriate technological equipment.

Linking Preservice Teachers' Mathematics Self-Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

Science.gov (United States)

Bates, Alan B.; Latham, Nancy; Kim, Jin-ah

2011-01-01

This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…

Should mathematics be a creative subject? How is this realized in practice in Denmark?

DEFF Research Database (Denmark)

Ejersbo, Lisser Rye

as a creative subject. How do they understand creativity and how do they realize it in practice? And what makes mathematics a creative subject? Is it the task, the way it is performed or the relationship between teacher and students? The crucial difference between different classrooms seems to be the ways......The ministerial objectives for mathematics education in the Danish Folkeskole (grades K-ten) state that students will learn that mathematics is both a tool for problem-solving and a creative subject. In this article, I explore how teachers in Denmark meet the challenge of teaching mathematics....... The discussion will focus on how to make mathematics a creative subject....

Occupational voice demands and their impact on the call-centre industry

Directory of Open Access Journals (Sweden)

Duffy OM

2009-04-01

Full Text Available Abstract Background Within the last decade there has been a growth in the call-centre industry in the UK, with a growing awareness of the voice as an important tool for successful communication. Occupational voice problems such as occupational dysphonia, in a business which relies on healthy, effective voice as the primary professional communication tool, may threaten working ability and occupational health and safety of workers. While previous studies of telephone call-agents have reported a range of voice symptoms and functional vocal health problems, there have been no studies investigating the use and impact of vocal performance in the communication industry within the UK. This study aims to address a significant gap in the evidence-base of occupational health and safety research. The objectives of the study are: 1. to investigate the work context and vocal communication demands for call-agents; 2. to evaluate call-agents' vocal health, awareness and performance; and 3. to identify key risks and training needs for employees and employers within call-centres. Methods and design This is an occupational epidemiological study, which plans to recruit call-centres throughout the UK and Ireland. Data collection will consist of three components: 1. interviews with managers from each participating call-centre to assess their communication and training needs; 2. an online biopsychosocial questionnaire will be administered to investigate the work environment and vocal demands of call-agents; and 3. voice acoustic measurements of a random sample of participants using the Multi-dimensional Voice Program (MDVP. Qualitative content analysis from the interviews will identify underlying themes and issues. A multivariate analysis approach will be adopted using Structural Equation Modelling (SEM, to develop voice measurement models in determining the construct validity of potential factors contributing to occupational dysphonia. Quantitative data will be

Lectures on the mathematics of quantum mechanics II selected topics

CERN Document Server

Dell'Antonio, Gianfausto

2016-01-01

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving th...

Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations

Science.gov (United States)

Darlington, Ellie

2014-01-01

This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…

Applying Mathematical Tools to Accelerate Vaccine Development: Modeling Shigella Immune Dynamics

Science.gov (United States)

Davis, Courtney L.; Wahid, Rezwanul; Toapanta, Franklin R.; Simon, Jakub K.

2013-01-01

We establish a mathematical framework for studying immune interactions with Shigella, a bacteria that kills over one million people worldwide every year. The long-term goal of this novel approach is to inform Shigella vaccine design by elucidating which immune components and bacterial targets are crucial for establishing Shigella immunity. Our delay differential equation model focuses on antibody and B cell responses directed against antigens like lipopolysaccharide in Shigella’s outer membrane. We find that antibody-based vaccines targeting only surface antigens cannot elicit sufficient immunity for protection. Additional boosting prior to infection would require a four-orders-of-magnitude increase in antibodies to sufficiently prevent epithelial invasion. However, boosting anti-LPS B memory can confer protection, which suggests these cells may correlate with immunity. We see that IgA antibodies are slightly more effective per molecule than IgG, but more total IgA is required due to spatial functionality. An extension of the model reveals that targeting both LPS and epithelial entry proteins is a promising avenue to advance vaccine development. This paper underscores the importance of multifaceted immune targeting in creating an effective Shigella vaccine. It introduces mathematical models to the Shigella vaccine development effort and lays a foundation for joint theoretical/experimental/clinical approaches to Shigella vaccine design. PMID:23589755

Applying mathematical finance tools to the competitive Nordic electricity market

International Nuclear Information System (INIS)

Vehvilaeinen, I.

2004-01-01

This thesis models competitive electricity markets using the methods of mathematical finance. Fundamental problems of finance are market price modelling, derivative pricing, and optimal portfolio selection. The same questions arise in competitive electricity markets. The thesis presents an electricity spot price model based on the fundamental stochastic factors that affect electricity prices. The resulting price model has sound economic foundations, is able to explain spot market price movements, and offers a computationally efficient way of simulating spot prices. The thesis shows that the connection between spot prices and electricity forward prices is nontrivial because electricity is a commodity that must be consumed immediately. Consequently, forward prices of different times are based on the supply-demand conditions at those times. This thesis introduces a statistical model that captures the main characteristics of observed forward price movements. The thesis presents the pricing problems relating to the common Nordic electricity derivatives, as well as the pricing relations between electricity derivatives. The special characteristics of electricity make spot electricity market incomplete. The thesis assumes the existence of a risk-neutral martingale measure so that formal pricing results can be obtained. Some concepts introduced in financial markets are directly usable in the electricity markets. The risk management application in this thesis uses a static optimal portfolio selection framework where Monte Carlo simulation provides quantitative results. The application of mathematical finance requires careful consideration of the special characteristics of the electricity markets. Economic theory and reasoning have to be taken into account when constructing financial models in competitive electricity markets. (orig.)

A review of mathematical functions for the analysis of growth in poultry

NARCIS (Netherlands)

Darmani Kuhi, H.; Porter, T.; Lopez, S.; Kebreab, E.; Strathe, A.B.; Dumas, A.; Dijkstra, J.; France, J.

2010-01-01

Poultry industries face various decisions in the production cycle that affect the profitability of an operation. Predictions of growth when the birds are ready for sale are important factors that contribute to the economy of poultry operations. Mathematical functions called ‘growth functions’ have

Performance Analysis of Parallel Mathematical Subroutine library PARCEL

International Nuclear Information System (INIS)

Yamada, Susumu; Shimizu, Futoshi; Kobayashi, Kenichi; Kaburaki, Hideo; Kishida, Norio

2000-01-01

The parallel mathematical subroutine library PARCEL (Parallel Computing Elements) has been developed by Japan Atomic Energy Research Institute for easy use of typical parallelized mathematical codes in any application problems on distributed parallel computers. The PARCEL includes routines for linear equations, eigenvalue problems, pseudo-random number generation, and fast Fourier transforms. It is shown that the results of performance for linear equations routines exhibit good parallelization efficiency on vector, as well as scalar, parallel computers. A comparison of the efficiency results with the PETSc (Portable Extensible Tool kit for Scientific Computations) library has been reported. (author)

Proposal of a pedagogical model for mathematics teacher education

Directory of Open Access Journals (Sweden)

Alfonso Jiménez Espinosa

2011-01-01

Full Text Available This research-based article reflects on mathematics teacher education, and proposes a pedagogical model for this purpose, called Gradual Research Pedagogical Model (MPGI. This model considers the central curricular elements of any academic education process: student, teacher and contents, with evaluation as transversal element for analysis and feedback. The training of future teachers is constituted by three moments, each with its specific emphasis: the first is “contextualization”, which aims at having the student understand his or her new academic role, and identify and overcome his or her academic weak points, the second is “knowledge foundation”, which offers basic education in the fields of mathematics and pedagogy, as well as sensibilization towards social issues, opening up the student’s possibilities as leader and agent of change, and lastly, “knowledge immersion”, which is centered on research and the identification and study of topics and problems of the mathematical discipline as well as the pedagogical field.

Introduction of the Thematic Issue on the Interplay of Physics and Mathematics

DEFF Research Database (Denmark)

Avelar Sotomaior Karam, Ricardo

2015-01-01

for the students. They have a hard time understanding where mathematical concepts come from and why physics has little to do with their experiential world. This problem demands a systematic research effort from experts in different fields, especially the ones who aim at informing educational practices......Since their beginnings Physics (natural philosophy) and mathematics have been deeply interrelated, and this mutual influence has played an essential role in both their developments. However, the image typically found in educational contexts is often quite different. In physics education......, it is usual to find mathematics being seen as a mere tool to describe and calculate, whereas in mathematics education, physics is commonly viewed as a possible context for the application of mathematical concepts that were previously defined abstractly. This dichotomy creates significant learning problems...

"Just Don't": The Suppression and Invitation of Dialogue in the Mathematics Classroom

Science.gov (United States)

Wagner, David; Herbel-Eisenmann, Beth

2008-01-01

Responding to concerns raised by grade 11 mathematics students, we examined a broad set of mathematics classroom transcripts from multiple teachers to examine how the word "just" was and could be used to suppress and invite dialogue. We used corpus linguistics tools to process and quantify the large body of text, not to describe the nature of the…

ACER Mathematics Profile Series: Number Test. (Test Booklet, Answer and Record Sheet, Score Key, and Teachers Handbook).

Science.gov (United States)

Cornish, Greg; Wines, Robin

The Number Test of the ACER Mathematics Profile Series, contains 30 items, for each of three suggested grade levels: 7-8, 8-9, and 9-10. Raw scores on all tests in the ACER Mathematics Profile Series (Number, Operations, Space and Measurement) are converted to a common scale called MAPS, a major feature of the Series. Based on the Rasch Model,…

Unlocking the black box: teaching mathematical modeling with popular culture.

Science.gov (United States)

Lofgren, Eric T

2016-10-01

Mathematical modeling is an important tool in biological research, allowing for the synthesis of results from many studies into an understanding of a system. Despite this, the need for extensive subject matter knowledge and complex mathematics often leaves modeling as an esoteric subspecialty. A 2-fold approach can be used to make modeling more approachable for students and those interested in obtaining a functional knowledge of modeling. The first is the use of a popular culture disease system-a zombie epidemic-to allow for exploration of the concepts of modeling using a flexible framework. The second is the use of available interactive and non-calculus-based tools to allow students to work with and implement models to cement their understanding. © FEMS 2016. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Mathematics of shape description a morphological approach to image processing and computer graphics

CERN Document Server

Ghosh, Pijush K

2009-01-01

Image processing problems are often not well defined because real images are contaminated with noise and other uncertain factors. In Mathematics of Shape Description, the authors take a mathematical approach to address these problems using the morphological and set-theoretic approach to image processing and computer graphics by presenting a simple shape model using two basic shape operators called Minkowski addition and decomposition. This book is ideal for professional researchers and engineers in Information Processing, Image Measurement, Shape Description, Shape Representation and Computer Graphics. Post-graduate and advanced undergraduate students in pure and applied mathematics, computer sciences, robotics and engineering will also benefit from this book.  Key FeaturesExplains the fundamental and advanced relationships between algebraic system and shape description through the set-theoretic approachPromotes interaction of image processing geochronology and mathematics in the field of algebraic geometryP...

Blended call center with idling times during the call service

NARCIS (Netherlands)

Legros, Benjamin; Jouini, Oualid; Koole, Ger

We consider a blended call center with calls arriving over time and an infinitely backlogged amount of outbound jobs. Inbound calls have a non-preemptive priority over outbound jobs. The inbound call service is characterized by three successive stages where the second one is a break; i.e., there is

Using Mathematics Literature with Prospective Secondary Mathematics Teachers

Science.gov (United States)

Jett, Christopher C.

2014-01-01

Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

Outlooks for mathematical modelling of the glass melting process

Energy Technology Data Exchange (ETDEWEB)

Waal, H. de [TNO Institute of Applied Physics, Delft (Netherlands)

1997-12-31

Mathematical modelling is nowadays a standard tool for major producers of float glass, T.V. glass and fiberglass. Also for container glass furnaces, glass tank modelling proves to be a valuable method to optimize process conditions. Mathematical modelling is no longer just a way to visualize the flow patterns and to provide data on heat transfer. It can also predict glass quality in relation to process parameters, because all chemical and physical phenomena are included in the latest generation of models, based on experimental and theoretical research on these phenomena.

Improved mathematical and computational tools for modeling photon propagation in tissue

Science.gov (United States)

Calabro, Katherine Weaver

Light interacts with biological tissue through two predominant mechanisms: scattering and absorption, which are sensitive to the size and density of cellular organelles, and to biochemical composition (ex. hemoglobin), respectively. During the progression of disease, tissues undergo a predictable set of changes in cell morphology and vascularization, which directly affect their scattering and absorption properties. Hence, quantification of these optical property differences can be used to identify the physiological biomarkers of disease with interest often focused on cancer. Diffuse reflectance spectroscopy is a diagnostic tool, wherein broadband visible light is transmitted through a fiber optic probe into a turbid medium, and after propagating through the sample, a fraction of the light is collected at the surface as reflectance. The measured reflectance spectrum can be analyzed with appropriate mathematical models to extract the optical properties of the tissue, and from these, a set of physiological properties. A number of models have been developed for this purpose using a variety of approaches -- from diffusion theory, to computational simulations, and empirical observations. However, these models are generally limited to narrow ranges of tissue and probe geometries. In this thesis, reflectance models were developed for a much wider range of measurement parameters, and influences such as the scattering phase function and probe design were investigated rigorously for the first time. The results provide a comprehensive understanding of the factors that influence reflectance, with novel insights that, in some cases, challenge current assumptions in the field. An improved Monte Carlo simulation program, designed to run on a graphics processing unit (GPU), was built to simulate the data used in the development of the reflectance models. Rigorous error analysis was performed to identify how inaccuracies in modeling assumptions can be expected to affect the accuracy

Teachers’ beliefs about the discipline of mathematics and the use of technology in the classroom

DEFF Research Database (Denmark)

Misfeldt, Morten; Thomas Jankvist, Uffe; Sánchez Arguilar, Mario

2016-01-01

In the article, three Danish secondary level mathematics teachers’ beliefs about the use of technological tools in the teaching of mathematics and their beliefs about mathematics as a scientific discipline are identified and classified - and the process also aspects of their beliefs about...... the teaching and learning of mathematics. The potential relationships between these sets of beliefs are also explored. Results show that the teachers not only manifest different beliefs about the use of technology and mathematics as a discipline, but that one set of beliefs can influence the other set...... of beliefs. The article concludes with a discussion of the research findings and their validity as well as their implications for both practice and research in mathematics education....

Mathematics and culture in Micronesia

Directory of Open Access Journals (Sweden)

A. J. (Sandy Dawson

2015-07-01

Full Text Available Wheatley and Frieze‟s book, Walk Out Walk On, provides the conceptual framework for an examination of Project MACIMISE, a National Science Foundation funded project that focused on the languages and cultural practices of nine Pacific islands and the state of Hawai„i. MACIMISE, pronounced as if spelled „maximize‟, is a 5-year Project. The Project‟s task is the development of elementary school mathematics curriculum units sensitive to local mathematical thought and experience. There were twenty-one participants (who call themselves the Macimisers in the Project. The participants were educated in ethnographic and anthropological research strategies to enable them to retrieve/uncover cultural practices extant in the communities where they lived. This academics work was accomplished partially via distance learning when the participants were registered in advanced degree programs at the University of Hawai„i—Mānoa. In this paper, the Project is analyzed in terms of the concepts (scaling across, start anywhere—follow it everywhere, intervention to friendship, the art of hosting and the use of circle advanced by Wheatley and Frieze.

International Conference on Recent Advances in Mathematical Biology, Analysis and Applications

CERN Document Server

Saleem, M; Srivastava, H; Khan, Mumtaz; Merajuddin, M

2016-01-01

The book contains recent developments and contemporary research in mathematical analysis and in its application to problems arising from the biological and physical sciences. The book is of interest to readers who wish to learn of new research in such topics as linear and nonlinear analysis, mathematical biology and ecology, dynamical systems, graph theory, variational analysis and inequalities, functional analysis, differential and difference equations, partial differential equations, approximation theory, and chaos. All papers were prepared by participants at the International Conference on Recent Advances in Mathematical Biology, Analysis and Applications (ICMBAA-2015) held during 4–6 June 2015 in Aligarh, India. A focal theme of the conference was the application of mathematics to the biological sciences and on current research in areas of theoretical mathematical analysis that can be used as sophisticated tools for the study of scientific problems. The conference provided researchers, academicians and ...

Geo mathematic tools for the design of a radioisotopes monitoring network in order to modelling the groundwater dynamics processes and hydrodynamic management

International Nuclear Information System (INIS)

Peralta, J.L.; Gil, R.; Leyva, D.; Molerio, L.F.; Pin, M.

2004-01-01

The present paper, shows the application of geo mathematic tools [Mangin,1981; Molerio,1997] for the design of a radioisotopes monitoring network in order to modelling the groundwater dynamics processes and hydrodynamic management of a Karstic Basin (Almendares-Vento watershed), which is very difficult to evaluate due to the physical-geographical, geologic and hydrogeological characteristics. The Almendares Vento watershed (AVW) is close to the Jaruco-Aguacate watershed, with a similar hydrogeologic and geologic structure, therefore similar result must be expected. In the AVW case is necessary to identify, with more precision, the water propagation limits of the stratified layers according to the waters transit times, recharges and dynamics aquifers, residence time, groundwater contamination and the groundwater-surface water interaction due to the dam placed on the basin. The paper allowed the identification of a monitoring points network, taking into account, between other statistical approaches, the good correlation, the high memory effect, etc. According to the analysis of the variances spectral, have been obtained and optimized the sampling frequency of the network points in the Basin. Besides, it have been identified the necessities to include the detailed evaluation of a specific point of the network in the hydrodynamic study (Vento watershed). In order to evaluate the optimization of the designed monitoring network, the geo mathematic study developed was compared with the results of the mathematical model AQUIMPE, the final result showed the validation of the obtained design. The results of the work allow the best monitoring of the parameters in order to determine the aquifer recharge, residence times, the vulnerability to the waters contamination and the groundwater-surface water interaction

Classroom Assessment in Malawi: Teachersâ Perceptions and Practices in Mathematics

OpenAIRE

Susuwele-Banda, William John

2005-01-01

This study investigated teachersâ perceptions of classroom assessment in mathematics and their current classroom assessments practices. Specifically, the study sought to gain an understanding of the extent to which teachers use different classroom assessment methods and tools to understand and to support both the learning and teaching processes. The following three questions guided the study: 1) How do primary school teachers perceive classroom assessment in mathematics? 2) What kinds of a...

Bridging the gap between actual and required mathematics background at undergraduate university level

DEFF Research Database (Denmark)