Mathematical Abstraction: Constructing Concept of Parallel Coordinates
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.
Concept of Triangle: Examples of Mathematical Abstraction in Two Different Contexts
Directory of Open Access Journals (Sweden)
Farida Nurhasanah
2017-02-01
Full Text Available In attempt to explain how students learning geometry in concept of triangle, this study explore the learning process of students and the process of solving geometry problems in the topic of triangle. As known as one of the domain in school of mathematics, geometry has abstract notions to be learnt so that all those notions cannot be just transferred into students’ mind like a bunch of information that should be memorized. Students need to construct those concepts during their learning process. This process of knowledge construction can be considered as an abstraction process. This study aimed to qualitatively compare students’ abstraction process who learn topic of triangle in conventional method of teaching and in van Hiele model of teaching aided by Geometers’ sketchpad. Subjects of this study were junir high school students in grade 7. Based on the aims of this study, this is a qualitative study with grounded theory design. Data were collected through classroom observation, test, and task-based interview. Results of the study show that theoretical abstraction processes tend to dominate classrom with conventional method of teaching while classroom with van Hiele model of teaching aided by Geometers’ sketchpad accommodated empirical abstraction process of the students
Jost, Jürgen
2015-01-01
The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: · simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detaile...
Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.
2018-05-01
As one of the non-conventional mathematics concepts, Parallel Coordinates is potential to be learned by pre-service mathematics teachers in order to give them experiences in constructing richer schemes and doing abstraction process. Unfortunately, the study related to this issue is still limited. This study wants to answer a research question “to what extent the abstraction process of pre-service mathematics teachers in learning concept of Parallel Coordinates could indicate their performance in learning Analytic Geometry”. This is a case study that part of a larger study in examining mathematical abstraction of pre-service mathematics teachers in learning non-conventional mathematics concept. Descriptive statistics method is used in this study to analyze the scores from three different tests: Cartesian Coordinate, Parallel Coordinates, and Analytic Geometry. The participants in this study consist of 45 pre-service mathematics teachers. The result shows that there is a linear association between the score on Cartesian Coordinate and Parallel Coordinates. There also found that the higher levels of the abstraction process in learning Parallel Coordinates are linearly associated with higher student achievement in Analytic Geometry. The result of this study shows that the concept of Parallel Coordinates has a significant role for pre-service mathematics teachers in learning Analytic Geometry.
Mathematical games, abstract games
Neto, Joao Pedro
2013-01-01
User-friendly, visually appealing collection offers both new and classic strategic board games. Includes abstract games for two and three players and mathematical games such as Nim and games on graphs.
Abstracting Concepts and Methods.
Borko, Harold; Bernier, Charles L.
This text provides a complete discussion of abstracts--their history, production, organization, publication--and of indexing. Instructions for abstracting are outlined, and standards and criteria for abstracting are stated. Management, automation, and personnel are discussed in terms of possible economies that can be derived from the introduction…
Concepts of modern mathematics
Stewart, Ian
1995-01-01
Some years ago, ""new math"" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of ""new math"" have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor an
Abstract concepts in grounded cognition
Lakens, D.
2010-01-01
When people think about highly abstract concepts, they draw upon concrete experiences to structure their thoughts. For example, black knights in fairytales are evil, and knights in shining armor are good. The sensory experiences black and white are used to represent the abstract concepts of good and
Fundamental concepts of mathematics
Goodstein, R L
Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people
Handedness shapes children's abstract concepts.
Casasanto, Daniel; Henetz, Tania
2012-03-01
Can children's handedness influence how they represent abstract concepts like kindness and intelligence? Here we show that from an early age, right-handers associate rightward space more strongly with positive ideas and leftward space with negative ideas, but the opposite is true for left-handers. In one experiment, children indicated where on a diagram a preferred toy and a dispreferred toy should go. Right-handers tended to assign the preferred toy to a box on the right and the dispreferred toy to a box on the left. Left-handers showed the opposite pattern. In a second experiment, children judged which of two cartoon animals looked smarter (or dumber) or nicer (or meaner). Right-handers attributed more positive qualities to animals on the right, but left-handers to animals on the left. These contrasting associations between space and valence cannot be explained by exposure to language or cultural conventions, which consistently link right with good. Rather, right- and left-handers implicitly associated positive valence more strongly with the side of space on which they can act more fluently with their dominant hands. Results support the body-specificity hypothesis (Casasanto, 2009), showing that children with different kinds of bodies think differently in corresponding ways. Copyright © 2011 Cognitive Science Society, Inc.
Grounding abstractness: Abstract concepts and the activation of the mouth
Directory of Open Access Journals (Sweden)
Anna M Borghi
2016-10-01
Full Text Available One key issue for theories of cognition is how abstract concepts, such as freedom, are represented. According to the WAT (Words As social Tools proposal, abstract concepts activate both sensorimotor and linguistic/social information, and their acquisition modality involves the linguistic experience more than the acquisition of concrete concepts. We report an experiment in which participants were presented with abstract and concrete definitions followed by concrete and abstract target-words. When the definition and the word matched, participants were required to press a key, either with the hand or with the mouth. Response times and accuracy were recorded. As predicted, we found that abstract definitions and abstract words yielded slower responses and more errors compared to concrete definitions and concrete words. More crucially, there was an interaction between the target-words and the effector used to respond (hand, mouth. While responses with the mouth were overall slower, the advantage of the hand over the mouth responses was more marked with concrete than with abstract concepts. The results are in keeping with grounded and embodied theories of cognition and support the WAT proposal, according to which abstract concepts evoke linguistic-social information, hence activate the mouth. The mechanisms underlying the mouth activation with abstract concepts (re-enactment of acquisition experience, or re-explanation of the word meaning, possibly through inner talk are discussed. To our knowledge this is the first behavioral study demonstrating with real words that the advantage of the hand over the mouth is more marked with concrete than with abstract concepts, likely because of the activation of linguistic information with abstract concepts.
Arche papers on the mathematics of abstraction
Cook, Roy T
2007-01-01
This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Gottlob Frege's original logicist project was, in effect, refuted by Russell's paradox. Crispin Wright has recently revived Frege's enterprise, however, providing a philosophical and technical framework within which a reconstruction of arithmetic is possible. While the Neo-Fregean project has recieved extensive attention and discussion, the present volume is unique in pre
Concepts of mathematical modeling
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
Embodied cognition, abstract concepts, and body manipulation
Directory of Open Access Journals (Sweden)
Katinka eDijkstra
2014-08-01
Full Text Available Current approaches on cognition hold that concrete concepts are grounded in concrete experiences. There is no consensus, however, as to whether this is equally true for abstract concepts. In this review we discuss how the body might be involved in understanding abstract concepts through metaphor activation. Substantial research has been conducted on the activation of common orientational metaphors with bodily manipulations, such as ‘power is up’ and ‘more is up’ representations. We will focus on the political metaphor that has a more complex association between the concept and the concrete domain. However, the outcomes of studies on this political metaphor have not always been consistent, possibly because the experimental manipulation was not implicit enough. The inclusion of new technological devices in this area of research, such as the Wii Balance Board, seems promising in order to assess the groundedness of abstract conceptual spatial metaphors in an implicit manner. This may aid further research to effectively demonstrate the interrelatedness between the body and more abstract representations.
Grounded understanding of abstract concepts: The case of STEM learning.
Hayes, Justin C; Kraemer, David J M
2017-01-01
Characterizing the neural implementation of abstract conceptual representations has long been a contentious topic in cognitive science. At the heart of the debate is whether the "sensorimotor" machinery of the brain plays a central role in representing concepts, or whether the involvement of these perceptual and motor regions is merely peripheral or epiphenomenal. The domain of science, technology, engineering, and mathematics (STEM) learning provides an important proving ground for sensorimotor (or grounded) theories of cognition, as concepts in science and engineering courses are often taught through laboratory-based and other hands-on methodologies. In this review of the literature, we examine evidence suggesting that sensorimotor processes strengthen learning associated with the abstract concepts central to STEM pedagogy. After considering how contemporary theories have defined abstraction in the context of semantic knowledge, we propose our own explanation for how body-centered information, as computed in sensorimotor brain regions and visuomotor association cortex, can form a useful foundation upon which to build an understanding of abstract scientific concepts, such as mechanical force. Drawing from theories in cognitive neuroscience, we then explore models elucidating the neural mechanisms involved in grounding intangible concepts, including Hebbian learning, predictive coding, and neuronal recycling. Empirical data on STEM learning through hands-on instruction are considered in light of these neural models. We conclude the review by proposing three distinct ways in which the field of cognitive neuroscience can contribute to STEM learning by bolstering our understanding of how the brain instantiates abstract concepts in an embodied fashion.
Mathematical concepts of optical superresolution
International Nuclear Information System (INIS)
Lindberg, Jari
2012-01-01
Optical imaging beyond the diffraction limit, i.e., optical superresolution, has been studied extensively in various contexts. This paper presents an overview of some mathematical concepts relevant to superresolution in linear optical systems. Properties of bandlimited functions are surveyed and are related to both instrumental and computational aspects of superresolution. The phenomenon of superoscillation and its relation to superresolution are discussed. (review article)
Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course
Cook, John Paul
2015-01-01
This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…
Introduction to proof in abstract mathematics
Wohlgemuth, Andrew
2011-01-01
The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixe
Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Discovering Mathematics with Magma Reducing the Abstract to the Concrete
Bosma, Wieb
2006-01-01
With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning theoretical results.
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
Wasserman, Nicholas H.
2016-01-01
This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
Teachers' Conceptions of Mathematical Modeling
Gould, Heather
2013-01-01
The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…
Learning mathematics concepts in a traditional socio-culture ...
African Journals Online (AJOL)
Abstract. This paper argues that each culture has its unique applications of mathematical concepts. It presents this argument by showing how the Great Zimbabwe Monument that was built between the 12th and 14th century applied some geometrical concepts that some secondary school students in Zimbabwe find difficult ...
Directory of Open Access Journals (Sweden)
Aurel Pera
2015-10-01
Full Text Available This study is part of a broader research which will be found in future work, Psychology and epistemology of mathematical creation, complementary work of experimental research psychology mathematics, whose investigative approach, promoting the combination type cross section paradigms and quantitative methods and qualitative and comparative method and the analytic-synthetic, based on the following idea: to make learning as efficient, contents and methods must be appropriate to the individual particularities of the pupils, a measure of the balance between converging and diverging dosing tasks as a promising opening to the transition from education proficiency in math performance. At this juncture, mathematical existence as ontological approach against the background of a history of "abstraction" mathematical and theoretical observations on the abstraction, realization and other mathematical thought processes, explanatory approach fulfills the context in which s mathematics constituted an important factor in psychological and methodological perspective, in a context of maximizing the educational effectiveness that depends on the quality of the methods used in teaching, focused on knowledge of the general principles of psycho-didactics not only mathematical and mental organization individual student or knowledge of the factors that make possible psycho-educational learning process.
Mathematical concepts for mechanical engineering design
Asli, Kaveh Hariri; Aliyev, Soltan Ali Ogli
2013-01-01
PrefaceIntroductionHeat Flow: From Theory to PracticeDispersed Fluid and Ideal Fluid MechanicsModeling for Pressure Wave into Water PipelineHeat Transfer and Vapor BubbleMathematical Concepts and Computational Approaches on Hydrodynamics InstabilityMathematical Concepts and Dynamic ModelingModeling for Predictions of Air Entrance into Water PipelineIndex
Teaching Abstract Concepts: Keys to the World of Ideas.
Flatley, Joannis K.; Gittinger, Dennis J.
1990-01-01
Specific teaching strategies to help hearing-impaired secondary students comprehend abstract concepts include (1) pinpointing facts and fallacies, (2) organizing information visually, (3) categorizing ideas, and (4) reinforcing new vocabulary and concepts. Figures provide examples of strategy applications. (DB)
Proofs and fundamentals a first course in abstract mathematics
Bloch, Ethan D
2003-01-01
In an effort to make advanced mathematics accessible to a wide variety of students, and to give even the most mathematically inclined students a solid basis upon which to build their continuing study of mathematics, there has been a tendency in recent years to introduce students to the for mulation and writing of rigorous mathematical proofs, and to teach topics such as sets, functions, relations and countability, in a "transition" course, rather than in traditional courses such as linear algebra. A transition course functions as a bridge between computational courses such as Calculus, and more theoretical courses such as linear algebra and abstract algebra. This text contains core topics that I believe any transition course should cover, as well as some optional material intended to give the instructor some flexibility in designing a course. The presentation is straightforward and focuses on the essentials, without being too elementary, too exces sively pedagogical, and too full to distractions. Some of ...
Construction and reconstruction concept in mathematics instruction
Mumu, Jeinne; Charitas Indra Prahmana, Rully; Tanujaya, Benidiktus
2017-12-01
The purpose of this paper is to describe two learning activities undertaken by lecturers, so that students can understand a mathematical concept. The mathematical concept studied in this research is the Vector Space in Linear Algebra instruction. Classroom Action Research used as a research method with pre-service mathematics teacher at University of Papua as the research subject. Student participants are divided into two parallel classes, 24 students in regular class, and remedial class consist of 18 students. Both approaches, construct and reconstruction concept, are implemented on both classes. The result shows that concept construction can only be done in regular class while in remedial class, learning with concept construction approach is not able to increase students' understanding on the concept taught. Understanding the concept of a student in a remedial class can only be carried out using the concept reconstruction approach.
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
Abstract concepts, language and sociality: from acquisition to inner speech.
Borghi, Anna M; Barca, Laura; Binkofski, Ferdinand; Tummolini, Luca
2018-08-05
The problem of representation of abstract concepts, such as 'freedom' and 'justice', has become particularly crucial in recent years, owing to the increased success of embodied and grounded views of cognition. We will present a novel view on abstract concepts and abstract words. Since abstract concepts do not have single objects as referents, children and adults might rely more on input from others to learn them; we, therefore, suggest that linguistic and social experience play an important role for abstract concepts. We will discuss evidence obtained in our and other laboratories showing that processing of abstract concepts evokes linguistic interaction and social experiences, leading to the activation of the mouth motor system. We will discuss the possible mechanisms that underlie this activation. Mouth motor system activation can be due to re-enactment of the experience of conceptual acquisition, which occurred through the mediation of language. Alternatively, it could be due to the re-explanation of the word meaning, possibly through inner speech. Finally, it can be due to a metacognitive process revealing low confidence in the meaning of our concepts. This process induces in us the need to rely on others to ask/negotiate conceptual meaning. We conclude that with abstract concepts language works as a social tool: it extends our thinking abilities and pushes us to rely on others to integrate our knowledge.This article is part of the theme issue 'Varieties of abstract concepts: development, use, and representation in the brain'. © 2018 The Author(s).
Pacifier Overuse and Conceptual Relations of Abstract and Emotional Concepts.
Barca, Laura; Mazzuca, Claudia; Borghi, Anna M
2017-01-01
This study explores the impact of the extensive use of an oral device since infancy (pacifier) on the acquisition of concrete, abstract, and emotional concepts. While recent evidence showed a negative relation between pacifier use and children's emotional competence (Niedenthal et al., 2012), the possible interaction between use of pacifier and processing of emotional and abstract language has not been investigated. According to recent theories, while all concepts are grounded in sensorimotor experience, abstract concepts activate linguistic and social information more than concrete ones. Specifically, the Words As Social Tools (WAT) proposal predicts that the simulation of their meaning leads to an activation of the mouth (Borghi and Binkofski, 2014; Borghi and Zarcone, 2016). Since the pacifier affects facial mimicry forcing mouth muscles into a static position, we hypothesize its possible interference on acquisition/consolidation of abstract emotional and abstract not-emotional concepts, which are mainly conveyed during social and linguistic interactions, than of concrete concepts. Fifty-nine first grade children, with a history of different frequency of pacifier use, provided oral definitions of the meaning of abstract not-emotional, abstract emotional, and concrete words. Main effect of concept type emerged, with higher accuracy in defining concrete and abstract emotional concepts with respect to abstract not-emotional concepts, independently from pacifier use. Accuracy in definitions was not influenced by the use of pacifier, but correspondence and hierarchical clustering analyses suggest that the use of pacifier differently modulates the conceptual relations elicited by abstract emotional and abstract not-emotional. While the majority of the children produced a similar pattern of conceptual relations, analyses on the few (6) children who overused the pacifier (for more than 3 years) showed that they tend to distinguish less clearly between concrete and
Pacifier Overuse and Conceptual Relations of Abstract and Emotional Concepts
Directory of Open Access Journals (Sweden)
Laura Barca
2017-12-01
Full Text Available This study explores the impact of the extensive use of an oral device since infancy (pacifier on the acquisition of concrete, abstract, and emotional concepts. While recent evidence showed a negative relation between pacifier use and children's emotional competence (Niedenthal et al., 2012, the possible interaction between use of pacifier and processing of emotional and abstract language has not been investigated. According to recent theories, while all concepts are grounded in sensorimotor experience, abstract concepts activate linguistic and social information more than concrete ones. Specifically, the Words As Social Tools (WAT proposal predicts that the simulation of their meaning leads to an activation of the mouth (Borghi and Binkofski, 2014; Borghi and Zarcone, 2016. Since the pacifier affects facial mimicry forcing mouth muscles into a static position, we hypothesize its possible interference on acquisition/consolidation of abstract emotional and abstract not-emotional concepts, which are mainly conveyed during social and linguistic interactions, than of concrete concepts. Fifty-nine first grade children, with a history of different frequency of pacifier use, provided oral definitions of the meaning of abstract not-emotional, abstract emotional, and concrete words. Main effect of concept type emerged, with higher accuracy in defining concrete and abstract emotional concepts with respect to abstract not-emotional concepts, independently from pacifier use. Accuracy in definitions was not influenced by the use of pacifier, but correspondence and hierarchical clustering analyses suggest that the use of pacifier differently modulates the conceptual relations elicited by abstract emotional and abstract not-emotional. While the majority of the children produced a similar pattern of conceptual relations, analyses on the few (6 children who overused the pacifier (for more than 3 years showed that they tend to distinguish less clearly between
Crafting by concepts fiber arts and mathematics
Belcastro, Sarah-Marie
2016-01-01
From the editors of the popular Making Mathematics with Needlework, this book presents projects that highlight the relationship between types of needlework and mathematics. Chapters start with accessible overviews presenting the interplay between mathematical concepts and craft expressions. Following sections explain the mathematics in more detail, and provide suggestions for classroom activities. Each chapter ends with specific crafting instructions. Types of needlework included are knitting, crochet, needlepoint, cross-stitch, quilting, temari balls, beading, tatting, and string art. Instructions are written as ordinary patterns, so the formatting and language will be familiar to crafters.
Development of abstract mathematical reasoning: the case of algebra.
Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja
2014-01-01
Algebra typically represents the students' first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students' ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16-17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15-16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students' transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition.
Abstract spatial concept priming dynamically influences real-world actions
Directory of Open Access Journals (Sweden)
Sarah M Tower-Richardi
2012-09-01
Full Text Available Experienced regularities in our perceptions and actions play important roles in grounding abstract concepts such as social status, time, and emotion. Might we similarly ground abstract spatial concepts in more experienced-based domains? The present experiment explores this possibility by implicitly priming abstract spatial terms (north, south, east, west and then measuring participants’ hand movement trajectories while they respond to a body-referenced spatial target (up, down, left, right in a verbal (Exp. 1 or spatial (Exp. 2 format. Results from two experiments demonstrate temporally-dynamic and prime-biased movement trajectories when the primes are incongruent with the targets (e.g., north – left, west – up. That is, priming abstract coordinate directions influences subsequent actions in response to concrete target directions. These findings provide the first evidence that abstract concepts of world-centered coordinate axes are implicitly understood in the context of concrete body-referenced axes; critically, this abstract-concrete relationship manifests in motor movements, and may have implications for spatial memory organization.
Key Concept Mathematics and Management Science Models
Macbeth, Thomas G.; Dery, George C.
1973-01-01
The presentation of topics in calculus and matrix algebra to second semester freshmen along with a treatment of exponential and power functions would permit them to cope with a significant portion of the mathematical concepts that comprise the essence of several disciplines in a business school curriculum. (Author)
Non-Determinism: An Abstract Concept in Computer Science Studies
Armoni, Michal; Gal-Ezer, Judith
2007-01-01
Non-determinism is one of the most important, yet abstract, recurring concepts of Computer Science. It plays an important role in Computer Science areas such as formal language theory, computability theory, distributed computing, and operating systems. We conducted a series of studies on the perception of non-determinism. In the current research,…
'Who Thinks Abstractly?': Quantum Theory and the Architecture of Physical Concepts
International Nuclear Information System (INIS)
Plotnitsky, Arkady
2011-01-01
Beginning with its introduction by W. Heisenberg, quantum mechanics was often seen as an overly abstract theory, mathematically and physically, vis-a-vis classical physics or relativity. This perception was amplified by the fact that, while the quantum-mechanical formalism provided effective predictive algorithms for the probabilistic predictions concerning quantum experiments, it appeared unable to describe, even by way idealization, quantum processes themselves in space and time, in the way classical mechanics or relativity did. The aim of the present paper is to reconsider the nature of mathematical and physical abstraction in modern physics by offering an analysis of the concept of ''physical fact'' and of the concept of 'physical concept', in part by following G. W. F. Hegel's and G. Deleuze's arguments concerning the nature of conceptual thinking. In classical physics, relativity, and quantum physics alike, I argue, physical concepts are defined by the following main features - 1) their multi-component multiplicity; 2) their essential relations to problems; 3) and the interactions between physical, mathematical, and philosophical components within each concept. It is the particular character of these interactions in quantum mechanics, as defined by its essentially predictive (rather than descriptive) nature, that distinguishes it from classical physics and relativity.
Hong, Jee Yun; Kim, Min Kyeong
2016-01-01
Ill-structured problems can be regarded as one of the measures that meet recent social needs emphasizing students' abilities to solve real-life problems. This study aimed to analyze the mathematical abstraction process in solving such problems, and to identify the mathematical abstraction level ([I] Recognition of mathematical structure through…
Institute of Scientific and Technical Information of China (English)
2011-01-01
The Western Theories of War Ethics and Contemporary Controversies Li Xiaodong U Ruijing （4） [ Abstract] In the field of international relations, war ethics is a concept with distinct westem ideological color. Due to factors of history and reality, the in
Learning Abstract Physical Concepts from Experience: Design and Use of an RC Circuit
Parra, Alfredo; Ordenes, Jorge; de la Fuente, Milton
2018-05-01
Science learning for undergraduate students requires grasping a great number of theoretical concepts in a rather short time. In our experience, this is especially difficult when students are required to simultaneously use abstract concepts, mathematical reasoning, and graphical analysis, such as occurs when learning about RC circuits. We present a simple experimental model in this work that allows students to easily design, build, and analyze RC circuits, thus providing an opportunity to test personal ideas, build graphical descriptions, and explore the meaning of the respective mathematical models, ultimately gaining a better grasp of the concepts involved. The result suggests that the simple setup indeed helps untrained students to visualize the essential points of this kind of circuit.
Moral concepts set decision strategies to abstract values.
Directory of Open Access Journals (Sweden)
Svenja Caspers
Full Text Available Persons have different value preferences. Neuroimaging studies where value-based decisions in actual conflict situations were investigated suggest an important role of prefrontal and cingulate brain regions. General preferences, however, reflect a superordinate moral concept independent of actual situations as proposed in psychological and socioeconomic research. Here, the specific brain response would be influenced by abstract value systems and moral concepts. The neurobiological mechanisms underlying such responses are largely unknown. Using functional magnetic resonance imaging (fMRI with a forced-choice paradigm on word pairs representing abstract values, we show that the brain handles such decisions depending on the person's superordinate moral concept. Persons with a predominant collectivistic (altruistic value system applied a "balancing and weighing" strategy, recruiting brain regions of rostral inferior and intraparietal, and midcingulate and frontal cortex. Conversely, subjects with mainly individualistic (egocentric value preferences applied a "fight-and-flight" strategy by recruiting the left amygdala. Finally, if subjects experience a value conflict when rejecting an alternative congruent to their own predominant value preference, comparable brain regions are activated as found in actual moral dilemma situations, i.e., midcingulate and dorsolateral prefrontal cortex. Our results demonstrate that superordinate moral concepts influence the strategy and the neural mechanisms in decision processes, independent of actual situations, showing that decisions are based on general neural principles. These findings provide a novel perspective to future sociological and economic research as well as to the analysis of social relations by focusing on abstract value systems as triggers of specific brain responses.
Moral Concepts Set Decision Strategies to Abstract Values
Caspers, Svenja; Heim, Stefan; Lucas, Marc G.; Stephan, Egon; Fischer, Lorenz; Amunts, Katrin; Zilles, Karl
2011-01-01
Persons have different value preferences. Neuroimaging studies where value-based decisions in actual conflict situations were investigated suggest an important role of prefrontal and cingulate brain regions. General preferences, however, reflect a superordinate moral concept independent of actual situations as proposed in psychological and socioeconomic research. Here, the specific brain response would be influenced by abstract value systems and moral concepts. The neurobiological mechanisms underlying such responses are largely unknown. Using functional magnetic resonance imaging (fMRI) with a forced-choice paradigm on word pairs representing abstract values, we show that the brain handles such decisions depending on the person's superordinate moral concept. Persons with a predominant collectivistic (altruistic) value system applied a “balancing and weighing” strategy, recruiting brain regions of rostral inferior and intraparietal, and midcingulate and frontal cortex. Conversely, subjects with mainly individualistic (egocentric) value preferences applied a “fight-and-flight” strategy by recruiting the left amygdala. Finally, if subjects experience a value conflict when rejecting an alternative congruent to their own predominant value preference, comparable brain regions are activated as found in actual moral dilemma situations, i.e., midcingulate and dorsolateral prefrontal cortex. Our results demonstrate that superordinate moral concepts influence the strategy and the neural mechanisms in decision processes, independent of actual situations, showing that decisions are based on general neural principles. These findings provide a novel perspective to future sociological and economic research as well as to the analysis of social relations by focusing on abstract value systems as triggers of specific brain responses. PMID:21483767
Exploring international gender differences in mathematics self-concept
Goldman, Amy D.; Penner, Andrew M.
2013-01-01
This study provides an international perspective on mathematics by examnnng mathematics self-concept, achievement, and the desire to enter a career involving mathematics among eighth graders in 49 countries. Using data from the Trends in International Mathematics and Science Study, this study shows that self-concept in mathematics is more closely related to the desire to enter a career using mathematics than achievement is. Further, while gender differences in mathematics self-concept are smaller in more egalitarian countries, both girls and boys have lower mathematics self-concepts and less interest in mathematics careers in these countries. These findings reveal a policy paradox: policies aimed at training the next generation of STEM professionals often highlight the need to close the gender gap, but countries with smaller gender gaps have fewer boys and girls interested in mathematics-intensive careers. We conclude by highlighting the importance of disentangling instrumental and expressive aspects of gender inequality in STEM fields. PMID:27840545
The concept of stability in numerical mathematics
Hackbusch, Wolfgang
2014-01-01
In this book, the author compares the meaning of stability in different subfields of numerical mathematics. Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations. In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.
Guide to mathematical concepts of quantum theory
International Nuclear Information System (INIS)
Heinosaari, T.; Ziman, M.
2008-01-01
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory (Authors)
Guide to mathematical concepts of quantum theory
International Nuclear Information System (INIS)
Heinosaari, T.; Ziman, M.
2008-01-01
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory. (author)
Formal Methods for Abstract Specifications – A Comparison of Concepts
DEFF Research Database (Denmark)
Instenberg, Martin; Schneider, Axel; Schnetter, Sabine
2006-01-01
In industry formal methods are becoming increasingly important for the verification of hardware and software designs. However current practice for specification of system and protocol functionality on high level of abstraction is textual description. For verification of the system behavior manual...... inspections and tests are usual means. To facilitate the introduction of formal methods in the development process of complex systems and protocols, two different tools evolved from research activities – UPPAAL and SpecEdit – have been investigated and compared regarding their concepts and functionality...
Akkus, Oylum
2008-01-01
The purpose of this study was to investigate preservice elementary mathematics teachers' ability of relating mathematical concepts and daily life context. Two research questions were set; what is the preservice elementary mathematics teachers' level of relating mathematical concepts and daily life context regarding to their education year and…
Yang, Kai-Lin
2014-01-01
This study used phenomenography, a qualitative method, to investigate Taiwanese mathematics teachers' conceptions of school mathematics, school statistics, and their differences. To collect data, we interviewed five mathematics teachers by open questions. They also responded to statements drawn on mathematical/statistical conceptions and…
Mathematical models in marketing a collection of abstracts
Funke, Ursula H
1976-01-01
Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...
Nardi, Elena
2000-01-01
Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical…
Auracher, Jan
2017-01-01
The concept of sound iconicity implies that phonemes are intrinsically associated with non-acoustic phenomena, such as emotional expression, object size or shape, or other perceptual features. In this respect, sound iconicity is related to other forms of cross-modal associations in which stimuli from different sensory modalities are associated with each other due to the implicitly perceived correspondence of their primal features. One prominent example is the association between vowels, categorized according to their place of articulation, and size, with back vowels being associated with bigness and front vowels with smallness. However, to date the relative influence of perceptual and conceptual cognitive processing on this association is not clear. To bridge this gap, three experiments were conducted in which associations between nonsense words and pictures of animals or emotional body postures were tested. In these experiments participants had to infer the relation between visual stimuli and the notion of size from the content of the pictures, while directly perceivable features did not support-or even contradicted-the predicted association. Results show that implicit associations between articulatory-acoustic characteristics of phonemes and pictures are mainly influenced by semantic features, i.e., the content of a picture, whereas the influence of perceivable features, i.e., size or shape, is overridden. This suggests that abstract semantic concepts can function as an interface between different sensory modalities, facilitating cross-modal associations.
The Vector Space as a Unifying Concept in School Mathematics.
Riggle, Timothy Andrew
The purpose of this study was to show how the concept of vector space can serve as a unifying thread for mathematics programs--elementary school to pre-calculus college level mathematics. Indicated are a number of opportunities to demonstrate how emphasis upon the vector space structure can enhance the organization of the mathematics curriculum.…
Concept mapping learning strategy to enhance students' mathematical connection ability
Hafiz, M.; Kadir, Fatra, Maifalinda
2017-05-01
The concept mapping learning strategy in teaching and learning mathematics has been investigated by numerous researchers. However, there are still less researchers who have scrutinized about the roles of map concept which is connected to the mathematical connection ability. Being well understood on map concept, it may help students to have ability to correlate one concept to other concept in order that the student can solve mathematical problems faced. The objective of this research was to describe the student's mathematical connection ability and to analyze the effect of using concept mapping learning strategy to the students' mathematical connection ability. This research was conducted at senior high school in Jakarta. The method used a quasi-experimental with randomized control group design with the total number was 72 students as the sample. Data obtained through using test in the post-test after giving the treatment. The results of the research are: 1) Students' mathematical connection ability has reached the good enough level category; 2) Students' mathematical connection ability who had taught with concept mapping learning strategy is higher than who had taught with conventional learning strategy. Based on the results above, it can be concluded that concept mapping learning strategycould enhance the students' mathematical connection ability, especially in trigonometry.
Construction of the mathematical concept of pseudo thinking students
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.
Introduction to mathematical physics methods and concepts
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...
Misu, La; Ketut Budayasa, I.; Lukito, Agung
2018-03-01
This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.
Directory of Open Access Journals (Sweden)
Louise M. Saija
2012-09-01
Full Text Available Salah satu standar yang diberikan oleh National Council of Teachers of Mathematics (NCTM adalah disposisi matematik. Disposisi bukan sekedar merujuk pada sikap tetapi suatu kecenderungan untuk berpikir dan bersikap dalam cara yang positif. Penelitian ini bertujuan untuk menganalisa disposisi matematik dan hubungannya dengan hasil belajar matematika siswa-siswa sekolah menengah atas (SMA. Sampel pada penelitian ini adalah 149 siswa SMA di Bandung. Analisa statistik didasarkan pada korelasi peringkat Spearman dan uji-t. Ditemukan bahwa secara rata-rata, disposisi matematik dari siswa-siswa SMA dikategorikan rendah. Selanjutnya, terdapat korelasi positif dan signifikan antara disposisi matematik dan hasil belajar matematika siswa-siswa SMA, walaupun nilai koefisien korelasinya tidak tinggi. Suatu observasi juga dilakukan untuk menganalisa hubungan ini, dan didapati bahwa walaupun beberapa siswa memiliki disposisi matematik yang baik, kadang kala mereka tidak dapat menyelesaikan ujian dengan baik, karena padatnya kurikulum, dan juga aktifitas sosial mereka, yang membuat hasil belajar matematika mereka lebih rendah. Temuan lainnya adalah bahwa siswa-siswa SMA memerlukan guru-guru matematika dengan lebih banyak strategi mengajar agar mereka dapat memiliki disposisi matematik yang lebih baik. Kata Kunci: Disposisi Matematik, Hasil Belajar Matematika One of the evaluation standards given by the National Council of Teachers of Mathematics (NCTM was mathematical disposition. Disposition refers not simply to attitudes but to a tendency to think and to act in positive ways. This study aimed to analyze the mathematical disposition and its correlation with mathematics achievement of senior high school (SMA students. A total of 149 SMA students in Bandung were procured as samples. Statistical analysis was based on the Spearman rank correlation and on the t-test. The findings showed that at average, the mathematical disposition of the SMA
African Journals Online (AJOL)
PROF. OLIVER OSUAGWA
Many mathematical models of stochastic dynamical systems were based on the assumption that the drift ... stochastic process with state space S is a ..... The algorithm was implemented through a MatLab script and the result of the simulation is.
Foundations and fundamental concepts of mathematics
Eves, Howard
1997-01-01
Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.
Dijkstra, K.; Eerland, A.; Zijlmans, J.; Post, L.S.
2014-01-01
Current approaches on cognition hold that concrete concepts are grounded in concrete experiences. There is no consensus, however, as to whether this is equally true for abstract concepts. In this review we discuss how the body might be involved in understanding abstract concepts through metaphor
K. Dijkstra (Katinka); A. Eerland (Anita); J. Zijlmans (Josjan); L.S. Post (Lysanne)
2014-01-01
textabstractCurrent approaches on cognition hold that concrete concepts are grounded in concrete experiences. There is no consensus, however, as to whether this is equally true for abstract concepts. In this review we discuss how the body might be involved in understanding abstract concepts through
Games in the mathematics curriculum: Some conceptions and ...
African Journals Online (AJOL)
Games in the mathematics curriculum: Some conceptions and experiences of teachers in the Upper West Region of Ghana. ... The study investigated primary school teachers' experiences with games as ... AJOL African Journals Online.
Mathematical concepts of quantum mechanics. 2. ed.
International Nuclear Information System (INIS)
Gustafson, Stephen J.; Sigal, Israel Michael
2011-01-01
The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory. (orig.)
Abstract concepts: sensory-motor grounding, metaphors, and beyond
Pecher, D.; Boot, I.; van Dantzig, S.
2011-01-01
In the last decade many researchers have obtained evidence for the idea that cognition shares processing mechanisms with perception and action. Most of the evidence supporting the grounded cognition framework focused on representations of concrete concepts, which leaves open the question how
Improving students’ understanding of mathematical concept using maple
Ningsih, Y. L.; Paradesa, R.
2018-01-01
This study aimed to improve students’ understanding of mathematical concept ability through implementation of using Maple in learning and expository learning. This study used a quasi-experimental research with pretest-posttest control group design. The sample on this study was 61 students in the second semester of Mathematics Education of Universitas PGRI Palembang, South Sumatera in academic year 2016/2017. The sample was divided into two classes, one class as the experiment class who using Maple in learning and the other class as a control class who received expository learning. Data were collective through the test of mathematical initial ability and mathematical concept understanding ability. Data were analyzed by t-test and two ways ANOVA. The results of this study showed (1) the improvement of students’ mathematical concept understanding ability who using Maple in learning is better than those who using expository learning; (2) there is no interaction between learning model and students’ mathematical initial ability toward the improvement of students’ understanding of mathematical concept ability.
Prospective Mathematics Teachers' Understanding of the Base Concept
Horzum, Tugba; Ertekin, Erhan
2018-01-01
The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers (PMTs) have about the base concept (BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn…
Students' Conceptions of Function Transformation in a Dynamic Mathematical Environment
Daher, Wajeeh; Anabousy, Ahlam
2015-01-01
The study of function transformations helps students understand the function concept which is a basic and main concept in mathematics, but this study is problematic to school students as well as college students, especially when transformations are performed on non-basic functions. The current research tried to facilitate grade 9 students'…
Zhang, Xiaohong; Han, Zaizhu; Bi, Yanchao
2013-01-01
Using the blocked-translation paradigm with healthy participants, we examined Crutch and Warrington's hypothesis that concrete and abstract concepts are organized by distinct principles: concrete concepts by semantic similarities and abstract ones by associations. In three experiments we constructed two types of experimental blocking (similar…
Designing an image retrieval interface for abstract concepts within the domain of journalism
R. Besseling (Ron)
2011-01-01
htmlabstractResearch has shown that users have difficulties finding images which illustrate abstract concepts. We carried out a user study that confirms the finding that the selection of search terms is perceived difficult and that users find the subjectivity of abstract concepts problematic. In
Institute of Scientific and Technical Information of China (English)
2017-01-01
Supplementary Short Board: Orderly Cultivate Housing Leasing Market WANG Guangtao (Former Minister of Ministry of Construction) Abstract: In December 2016, Central Economic Work Conference proposed that to promote the steady and healthy development of the real estate market, it should adhere to the “house is used to live, not used to speculate” position. At present, the development of housing leasing market in China is lagging behind. It is urgent to improve the housing conditions of large cities and promote the urbanization of small and medium-sized cities. Therefore, it is imperative to innovate and supplement the short board to accelerate the development of housing leasing market.
Institute of Scientific and Technical Information of China (English)
2012-01-01
Strategic Realism： An Option for China＇ s Grand Strategy Song Dexing （4） [ Abstract] As a non-Western emerging power, China should positively adapt its grand strategy to the strategic psychological traits in the 21st century, maintain a realist tone consistent with the national conditions of China, and avoid adventurist policies while awaring both strategic strength and weakness. In the 21st century, China＇ s grand strategy should be based on such core values as security, development, peace and justice, especially focusing on development in particular, which we named ＂strategic realism＂. Given the profound changes in China and the world, strategic realism encourages active foreign policy to safe- guard the long-term national interests of China. Following the self-help logic and the fun- damental values of security and prosperity, strategic realism concerns national interests as its top-priority. It advocates smart use of power, and aims to achieve its objectives by optimizing both domestic and international conditions. From the perspective of diplomatic phi- losophy, strategic realism is not a summarization of concrete policies but a description of China＇ s grand strategy orientations in the new century. [ Key Words] China, grand strategy, strategic realism [ Author]Song Dexing, Professor, Ph.D. Supervisor, and Director of the Center for International Strategic Studies, University of International Studies of PLA.
Mathematical knowledge in teaching of fraction concepts using diagrammatical approach
Veloo, Palanisamy Kathir; Puteh, Marzita
2017-05-01
Teachers need various types of knowledge in order to deliver various fraction concepts at elementary level. In this paper, Balls' framework (2008) or, Mathematical Knowledge for Teaching (MKT) is used as benchmark guideline. This paper investigates and explores component of MKT knowledge among eight experienced teachers of the primary school. Data was collected using paper pencil test, interview and video recording. This paper, narrowed to teacher's knowledge and their practices while teaching of various fractions concepts using diagrammatical approach in present of MKT. The data gathered from teachers were analyzed using thematic analysis techniques. The results indicated that teachers lack various components of MKT knowledge as a proposal by various researchers and assumed that teaching as procedural more than enough due to lack of deep understanding of mathematics and the various types of MKT is not required due to the present of practices in the mathematics classroom.
Undergraduate Mathematics Students' Understanding of the Concept of Function
Bardini, Caroline; Pierce, Robyn; Vincent, Jill; King, Deborah
2014-01-01
Concern has been expressed that many commencing undergraduate mathematics students have mastered skills without conceptual understanding. A pilot study carried out at a leading Australian university indicates that a significant number of students, with high tertiary entrance ranks, have very limited understanding of the concept of function,…
Yusepa, B. G. P.; Kusumah, Y. S.; Kartasasmita, B. G.
2018-01-01
The aim of this study is to get an in-depth understanding of students’ abstract-thinking ability in mathematics learning. This study was an experimental research with pre-test and post-test control group design. The subject of this study was eighth-grade students from two junior high schools in Bandung. In each schools, two parallel groups were selected and assigned into control and experimental groups. The experimental group was exposed to Cognitive Apprenticeship Instruction (CAI) treatment, whereas the control group was exposed to conventional learning. The results showed that abstract-thinking ability of students in experimental group was better than that of those in control group in which it could be observed from the overall and school level. It could be concluded that CAI could be a good alternative learning model to enhance students’ abstract-thinking ability.
Naming a Lego world. The role of language in the acquisition of abstract concepts.
Granito, Carmen; Scorolli, Claudia; Borghi, Anna Maria
2015-01-01
While embodied approaches of cognition have proved to be successful in explaining concrete concepts and words, they have more difficulties in accounting for abstract concepts and words, and several proposals have been put forward. This work aims to test the Words As Tools proposal, according to which both abstract and concrete concepts are grounded in perception, action and emotional systems, but linguistic information is more important for abstract than for concrete concept representation, due to the different ways they are acquired: while for the acquisition of the latter linguistic information might play a role, for the acquisition of the former it is instead crucial. We investigated the acquisition of concrete and abstract concepts and words, and verified its impact on conceptual representation. In Experiment 1, participants explored and categorized novel concrete and abstract entities, and were taught a novel label for each category. Later they performed a categorical recognition task and an image-word matching task to verify a) whether and how the introduction of language changed the previously formed categories, b) whether language had a major weight for abstract than for concrete words representation, and c) whether this difference had consequences on bodily responses. The results confirm that, even though both concrete and abstract concepts are grounded, language facilitates the acquisition of the latter and plays a major role in their representation, resulting in faster responses with the mouth, typically associated with language production. Experiment 2 was a rating test aiming to verify whether the findings of Experiment 1 were simply due to heterogeneity, i.e. to the fact that the members of abstract categories were more heterogeneous than those of concrete categories. The results confirmed the effectiveness of our operationalization, showing that abstract concepts are more associated with the mouth and concrete ones with the hand, independently from
Naming a Lego world. The role of language in the acquisition of abstract concepts.
Directory of Open Access Journals (Sweden)
Carmen Granito
Full Text Available While embodied approaches of cognition have proved to be successful in explaining concrete concepts and words, they have more difficulties in accounting for abstract concepts and words, and several proposals have been put forward. This work aims to test the Words As Tools proposal, according to which both abstract and concrete concepts are grounded in perception, action and emotional systems, but linguistic information is more important for abstract than for concrete concept representation, due to the different ways they are acquired: while for the acquisition of the latter linguistic information might play a role, for the acquisition of the former it is instead crucial. We investigated the acquisition of concrete and abstract concepts and words, and verified its impact on conceptual representation. In Experiment 1, participants explored and categorized novel concrete and abstract entities, and were taught a novel label for each category. Later they performed a categorical recognition task and an image-word matching task to verify a whether and how the introduction of language changed the previously formed categories, b whether language had a major weight for abstract than for concrete words representation, and c whether this difference had consequences on bodily responses. The results confirm that, even though both concrete and abstract concepts are grounded, language facilitates the acquisition of the latter and plays a major role in their representation, resulting in faster responses with the mouth, typically associated with language production. Experiment 2 was a rating test aiming to verify whether the findings of Experiment 1 were simply due to heterogeneity, i.e. to the fact that the members of abstract categories were more heterogeneous than those of concrete categories. The results confirmed the effectiveness of our operationalization, showing that abstract concepts are more associated with the mouth and concrete ones with the hand
Wang, Yimeng; Bargh, John A
2016-01-01
Consistent with neural reuse theory, empirical tests of the related "scaffolding" principle of abstract concept development show that higher-level concepts "reuse" and are built upon fundamental motives such as survival, safety, and consumption. This produces mutual influence between the two levels, with far-ranging impacts from consumer behavior to political attitudes.
Babb, Jeff
2005-01-01
This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323-1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite series. The historical importance and pedagogical value of his work will be considered in the context of an undergraduate course on…
Viewing Formal Mathematics from Yoruba Conception of the Sky
Segla, Aimé
2016-01-01
Yoruba Cosmology resembles a generative system at the foundation of concepts. The traditional thought, which derives from the reality of the identical pair incorporated from cosmology into real life, exemplifies all kind of existing knowledge, culture and practices. Previous studies by the author show in some detail the scientific interests in Yoruba cosmology. The present paper aims to view formal mathematics through the interpretation of Yoruba sky knowledge. It attempts to demonstrate tha...
Nanna, Robert J.
2016-01-01
Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…
THE EFFECT OF SELF-CONCEPT ON THE MATHEMATICS LEARNING ACHIEVEMENT
Directory of Open Access Journals (Sweden)
Rosliana Siregar
2018-05-01
Full Text Available Abstract. This study aims to determine the effect of self-concepts on mathematics learning achievement of students of class X at State Senior High School 14 Medan. The population in this study is all students of class X State Senior High School 14 Medan which amounted to 304 students. Technique of sampling using technique of Proportionate Stratified Random Sampling counted 40 student for research sample. Data collection using questionnaire method and documentation method. Data analysis technique used is regression analysis, correlation analysis and t test with significance level of 5%. Testing data in this study using the help of SPSS 15 for Windows program for each test result. The results showed that there is a significant influence between self-concept and mathematics learning achievement obtained from the t count (3,572> t table (1.68, with a probability significance of 0.01 <0.05. The magnitude of the determination coefficient of 25.1%
Hayes, Brett K.; Conway, Robert N.
2000-01-01
A study investigated effects of variations in the number of instances comprising a category on concept acquisition by 31 children (ages 9-14) with mild intellectual disability and 19 controls. Intellectual disability had little effect on ability to abstract a category prototype but did reduce use of exemplar-specific information for recognition.…
Dijkstra, Katinka; Eerland, Anita; Zijlmans, Josjan; Post, Lysanne S.
2014-01-01
Current approaches on cognition hold that concrete concepts are grounded in concrete experiences. There is no consensus, however, as to whether this is equally true for abstract concepts. In this review we discuss how the body might be involved in understanding abstract concepts through metaphor activation. Substantial research has been conducted on the activation of common orientational metaphors with bodily manipulations, such as “power is up” and “more is up” representations. We will focus on the political metaphor that has a more complex association between the concept and the concrete domain. However, the outcomes of studies on this political metaphor have not always been consistent, possibly because the experimental manipulation was not implicit enough. The inclusion of new technological devices in this area of research, such as the Wii Balance Board, seems promising in order to assess the groundedness of abstract conceptual spatial metaphors in an implicit manner. This may aid further research to effectively demonstrate the interrelatedness between the body and more abstract representations. PMID:25191282
Perrenet, J.C.; Kaasenbrood, E.J.S.
2006-01-01
In a former, mainly quantitative, study we defined four levels of abstraction in Computer Science students' thinking about the concept of algorithm. We constructed a list of questions about algorithms to measure the answering level as an indication for the thinking level. The answering level
Abstraction of complex concepts with a refined partial-area taxonomy of SNOMED
Wang, Yue; Halper, Michael; Wei, Duo; Perl, Yehoshua; Geller, James
2012-01-01
An algorithmically-derived abstraction network, called the partial-area taxonomy, for a SNOMED hierarchy has led to the identification of concepts considered complex. The designation “complex” is arrived at automatically on the basis of structural analyses of overlap among the constituent concept groups of the partial-area taxonomy. Such complex concepts, called overlapping concepts, constitute a tangled portion of a hierarchy and can be obstacles to users trying to gain an understanding of the hierarchy’s content. A new methodology for partitioning the entire collection of overlapping concepts into singly-rooted groups, that are more manageable to work with and comprehend, is presented. Different kinds of overlapping concepts with varying degrees of complexity are identified. This leads to an abstract model of the overlapping concepts called the disjoint partial-area taxonomy, which serves as a vehicle for enhanced, high-level display. The methodology is demonstrated with an application to SNOMED’s Specimen hierarchy. Overall, the resulting disjoint partial-area taxonomy offers a refined view of the hierarchy’s structural organization and conceptual content that can aid users, such as maintenance personnel, working with SNOMED. The utility of the disjoint partial-area taxonomy as the basis for a SNOMED auditing regimen is presented in a companion paper. PMID:21878396
Deonarain Brijlall; Sarah Bansilal; Deborah Moore-Russo
2012-01-01
This article reports on an exploration of teachers’ views on the meaning of mathematical representations in a democratic South Africa. We explored teachers’ conceptions of ‘mathematical representations’ as a means to promote dialogue and negotiation. These conceptions helped us to gauge how these teachers viewed representations in mathematics. Semi-structured questionnaires were administered to 76 high school mathematics teachers who were registered for an upgrading mathematics education...
Bowman, Caitlin R; Zeithamova, Dagmar
2018-02-07
Memory function involves both the ability to remember details of individual experiences and the ability to link information across events to create new knowledge. Prior research has identified the ventromedial prefrontal cortex (VMPFC) and the hippocampus as important for integrating across events in service of generalization in episodic memory. The degree to which these memory integration mechanisms contribute to other forms of generalization, such as concept learning, is unclear. The present study used a concept-learning task in humans (both sexes) coupled with model-based fMRI to test whether VMPFC and hippocampus contribute to concept generalization, and whether they do so by maintaining specific category exemplars or abstract category representations. Two formal categorization models were fit to individual subject data: a prototype model that posits abstract category representations and an exemplar model that posits category representations based on individual category members. Latent variables from each of these models were entered into neuroimaging analyses to determine whether VMPFC and the hippocampus track prototype or exemplar information during concept generalization. Behavioral model fits indicated that almost three quarters of the subjects relied on prototype information when making judgments about new category members. Paralleling prototype dominance in behavior, correlates of the prototype model were identified in VMPFC and the anterior hippocampus with no significant exemplar correlates. These results indicate that the VMPFC and portions of the hippocampus play a broad role in memory generalization and that they do so by representing abstract information integrated from multiple events. SIGNIFICANCE STATEMENT Whether people represent concepts as a set of individual category members or by deriving generalized concept representations abstracted across exemplars has been debated. In episodic memory, generalized memory representations have been shown
Examining of Perceptions of Gifted Students toward Mathematics Concept
Directory of Open Access Journals (Sweden)
Mesut ÖZTÜRK
2014-12-01
Full Text Available The purpose of this study bring out owned intellectual image interested in mathematics concept of gifted students. Participant of twenty-eight gifted students that they selected via WISC-R intelligent test. A phenomenology design that one of qualitative research methods was adopted and data collection focus group interview. Data analysis consisted of content analysis. Students who participant made up different sixteen metaphor. The most widely used of them kainite. When examined justifications lie behind of metaphor gifted students have different three perception such as affected with people of math, influence toward math of the nature, the nature of math. The result of examine of math perception according to grade level when grade level increased, gifted students more interested the nature of math whereas depended on needed of people more interested math concept.
Auditing complex concepts of SNOMED using a refined hierarchical abstraction network.
Wang, Yue; Halper, Michael; Wei, Duo; Gu, Huanying; Perl, Yehoshua; Xu, Junchuan; Elhanan, Gai; Chen, Yan; Spackman, Kent A; Case, James T; Hripcsak, George
2012-02-01
Auditors of a large terminology, such as SNOMED CT, face a daunting challenge. To aid them in their efforts, it is essential to devise techniques that can automatically identify concepts warranting special attention. "Complex" concepts, which by their very nature are more difficult to model, fall neatly into this category. A special kind of grouping, called a partial-area, is utilized in the characterization of complex concepts. In particular, the complex concepts that are the focus of this work are those appearing in intersections of multiple partial-areas and are thus referred to as overlapping concepts. In a companion paper, an automatic methodology for identifying and partitioning the entire collection of overlapping concepts into disjoint, singly-rooted groups, that are more manageable to work with and comprehend, has been presented. The partitioning methodology formed the foundation for the development of an abstraction network for the overlapping concepts called a disjoint partial-area taxonomy. This new disjoint partial-area taxonomy offers a collection of semantically uniform partial-areas and is exploited herein as the basis for a novel auditing methodology. The review of the overlapping concepts is done in a top-down order within semantically uniform groups. These groups are themselves reviewed in a top-down order, which proceeds from the less complex to the more complex overlapping concepts. The results of applying the methodology to SNOMED's Specimen hierarchy are presented. Hypotheses regarding error ratios for overlapping concepts and between different kinds of overlapping concepts are formulated. Two phases of auditing the Specimen hierarchy for two releases of SNOMED are reported on. With the use of the double bootstrap and Fisher's exact test (two-tailed), the auditing of concepts and especially roots of overlapping partial-areas is shown to yield a statistically significant higher proportion of errors. Copyright © 2011 Elsevier Inc. All rights
Auditing Complex Concepts of SNOMED using a Refined Hierarchical Abstraction Network
Wang, Yue; Halper, Michael; Wei, Duo; Gu, Huanying; Perl, Yehoshua; Xu, Junchuan; Elhanan, Gai; Chen, Yan; Spackman, Kent A.; Case, James T.; Hripcsak, George
2012-01-01
Auditors of a large terminology, such as SNOMED CT, face a daunting challenge. To aid them in their efforts, it is essential to devise techniques that can automatically identify concepts warranting special attention. “Complex” concepts, which by their very nature are more difficult to model, fall neatly into this category. A special kind of grouping, called a partial-area, is utilized in the characterization of complex concepts. In particular, the complex concepts that are the focus of this work are those appearing in intersections of multiple partial-areas and are thus referred to as overlapping concepts. In a companion paper, an automatic methodology for identifying and partitioning the entire collection of overlapping concepts into disjoint, singly-rooted groups, that are more manageable to work with and comprehend, has been presented. The partitioning methodology formed the foundation for the development of an abstraction network for the overlapping concepts called a disjoint partial-area taxonomy. This new disjoint partial-area taxonomy offers a collection of semantically uniform partial-areas and is exploited herein as the basis for a novel auditing methodology. The review of the overlapping concepts is done in a top-down order within semantically uniform groups. These groups are themselves reviewed in a top-down order, which proceeds from the less complex to the more complex overlapping concepts. The results of applying the methodology to SNOMED’s Specimen hierarchy are presented. Hypotheses regarding error ratios for overlapping concepts and between different kinds of overlapping concepts are formulated. Two phases of auditing the Specimen hierarchy for two releases of SNOMED are reported on. With the use of the double bootstrap and Fisher’s exact test (two-tailed), the auditing of concepts and especially roots of overlapping partial-areas is shown to yield a statistically significant higher proportion of errors. PMID:21907827
Learning and Processing Abstract Words and Concepts: Insights From Typical and Atypical Development.
Vigliocco, Gabriella; Ponari, Marta; Norbury, Courtenay
2018-05-21
The paper describes two plausible hypotheses concerning the learning of abstract words and concepts. According to a first hypothesis, children would learn abstract words by extracting co-occurrences among words in linguistic input, using, for example, mechanisms as described by models of Distributional Semantics. According to a second hypothesis, children would exploit the fact that abstract words tend to have more emotional associations than concrete words to infer that they refer to internal/mental states. Each hypothesis makes specific predictions with regards to when and which abstract words are more likely to be learned; also they make different predictions concerning the impact of developmental disorders. We start by providing a review of work characterizing how abstract words and concepts are learned in development, especially between the ages of 6 and 12. Second, we review some work from our group that tests the two hypotheses above. This work investigates typically developing (TD) children and children with atypical development (developmental language disorders [DLD] and autism spectrum disorder [ASD] with and without language deficits). We conclude that the use of strategies based on emotional information, or on co-occurrences in language, may play a role at different developmental stages. © 2018 Cognitive Science Society Inc.
Arslan, Cigdem; Erbay, Hatice Nur; Guner, Pinar
2017-01-01
In the present study we try to highlight prospective mathematics teachers' ability to identify mistakes of sixth grade students related to angle concept. And also we examined prospective mathematics teachers' knowledge of angle concept. Study was carried out with 30 sixth-grade students and 38 prospective mathematics teachers. Sixth grade students…
Young Children's Self-Concepts Include Representations of Abstract Traits and the Global Self.
Cimpian, Andrei; Hammond, Matthew D; Mazza, Giulia; Corry, Grace
2017-11-01
There is debate about the abstractness of young children's self-concepts-specifically, whether they include representations of (a) general traits and abilities and (b) the global self. Four studies (N = 176 children aged 4-7) suggested these representations are indeed part of early self-concepts. Studies 1 and 2 reexamined prior evidence that young children cannot represent traits and abilities. The results suggested that children's seemingly immature judgments in previous studies were due to peculiarities of the task context not the inadequacy of children's self-concepts. Similarly, Studies 3 and 4 revealed that, contrary to claims of immaturity in reasoning about the global self, young children update their global self-evaluations in flexible, context-sensitive ways. This evidence suggests continuity in the structure of self-concepts across childhood. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.
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Nurullah YAZICI
2017-05-01
Full Text Available This research was conducted in order to examine the subject matter of Mathematics teachers in the context of "Mathematical Knowledge For Teaching" (MKT model of "Basic Concepts in Sets" which is the first topic of the 9th class "Sets". The study group, which is one of the qualitative research methods, used the case study design, constitutes 5 mathematics teachers who work in different education levels (primary and secondary education in the academic year of 2015-2016. Open-ended questions and semi-structured interview form developed by the researcher were used for data collection. A descriptive analysis technique was used to analyze the data obtained through interviews. While analyzing the data, teacher and student textbooks, which were prepared by the Ministry of National Education for the purpose of teaching in 2015-2016 academic year, were taken as a reference. According to the research findings, it was determined that the teachers had deficiencies in the subject field of "Basic Concepts in the Sets" and had superficial knowledge rather than in depth knowledge.
Temporal Dynamics of Task Switching and Abstract-Concept Learning in Pigeons
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Thomas Alexander Daniel
2015-09-01
Full Text Available The current study examined whether pigeons could learn to use abstract concepts as the basis for conditionally switching behavior as a function of time. Using a mid-session reversal task, experienced pigeons were trained to switch from matching-to-sample (MTS to non-matching-to-sample (NMTS conditional discriminations within a session. One group had prior training with MTS, while the other had prior training with NMTS. Over training, stimulus set size was progressively doubled from 3 to 6 to 12 stimuli to promote abstract concept development. Prior experience had an effect on the initial learning at each of the set sizes but by the end of training there were no group differences, as both groups showed similar within-session linear matching functions. After acquiring the 12-item set, abstract-concept learning was tested by placing novel stimuli at the beginning and end of a test session. Prior matching and non-matching experience affected transfer behavior. The matching experienced group transferred to novel stimuli in both the matching and non-matching portion of the sessions using a matching rule. The non-matching experienced group transferred to novel stimuli in both portions of the session using a non-matching rule. The representations used as the basis for mid-session reversal of the conditional discrimination behaviors and subsequent transfer behavior appears to have different temporal sources. The implications for the flexibility and organization of complex behaviors are considered.
Semantic Size of Abstract Concepts: It Gets Emotional When You Can’t See It
Yao, Bo; Vasiljevic, Milica; Weick, Mario; Sereno, Margaret E.; O’Donnell, Patrick J.; Sereno, Sara C.
2013-01-01
Size is an important visuo-spatial characteristic of the physical world. In language processing, previous research has demonstrated a processing advantage for words denoting semantically “big” (e.g., jungle) versus “small” (e.g., needle) concrete objects. We investigated whether semantic size plays a role in the recognition of words expressing abstract concepts (e.g., truth). Semantically “big” and “small” concrete and abstract words were presented in a lexical decision task. Responses to “big” words, regardless of their concreteness, were faster than those to “small” words. Critically, we explored the relationship between semantic size and affective characteristics of words as well as their influence on lexical access. Although a word’s semantic size was correlated with its emotional arousal, the temporal locus of arousal effects may depend on the level of concreteness. That is, arousal seemed to have an earlier (lexical) effect on abstract words, but a later (post-lexical) effect on concrete words. Our findings provide novel insights into the semantic representations of size in abstract concepts and highlight that affective attributes of words may not always index lexical access. PMID:24086421
Semantic size of abstract concepts: it gets emotional when you can't see it.
Yao, Bo; Vasiljevic, Milica; Weick, Mario; Sereno, Margaret E; O'Donnell, Patrick J; Sereno, Sara C
2013-01-01
Size is an important visuo-spatial characteristic of the physical world. In language processing, previous research has demonstrated a processing advantage for words denoting semantically "big" (e.g., jungle) versus "small" (e.g., needle) concrete objects. We investigated whether semantic size plays a role in the recognition of words expressing abstract concepts (e.g., truth). Semantically "big" and "small" concrete and abstract words were presented in a lexical decision task. Responses to "big" words, regardless of their concreteness, were faster than those to "small" words. Critically, we explored the relationship between semantic size and affective characteristics of words as well as their influence on lexical access. Although a word's semantic size was correlated with its emotional arousal, the temporal locus of arousal effects may depend on the level of concreteness. That is, arousal seemed to have an earlier (lexical) effect on abstract words, but a later (post-lexical) effect on concrete words. Our findings provide novel insights into the semantic representations of size in abstract concepts and highlight that affective attributes of words may not always index lexical access.
Prospective mathematics teachers' understanding of the base concept
Horzum, Tuğba; Ertekin, Erhan
2018-02-01
The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers(PMTs) have about the base concept(BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn by PMTs. As a result, it was determined that PMTs dealt with the BC in a broad range of seven different images. It was also determined that the base perception of PMTs was limited mostly to their usage in daily life and in this context, they have position-dependent and word-dependent images. It was also determined that PMTs named the base to explain the BC or paid attention to the naming of three-dimensional geometric figures through the statement: 'objects are named according to their bases'. At the same time, it was also determined that PMTs had more than one concept imageswhich were contradicting with each other. According to these findings, potential explanations and advices were given.
Hamideh Jafari Koshkouei; Ahmad Shahvarani; Mohammad Hassan Behzadi; Mohsen Rostamy-Malkhalifeh
2016-01-01
The present study was carried out to investigate the influence of mathematics self-concept (MSC), motivation to learn mathematics (SMOT) and self-regulation learning (SRL) on students' mathematics academic achievement. This study is of a descriptive survey type. 300 female students at the first grade of high school (the second period) in City Qods, were selected by multiple step cluster sampling method and completed MSC, SMOT and SRL questionnaires. Mathematics academic achievement was measur...
Explorations in Mathematical Physics The Concepts Behind an Elegant Language
Koks, Don
2006-01-01
Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You'll see how the accelerated frames of special relativity tell us about gravity. On the journey, you'll discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis buil...
Il Concetto di Infinito nell'Intuizione Matematica (Concept of Infinity in Mathematical Intuition).
Ferrari, E.; And Others
1995-01-01
Investigated the acquisition and maturation of the infinity concept in mathematics of students ages 13-15. Found the infinity concept is learned by students only when provided with appropriate guidance. (Author/MKR)
Secondary School Mathematics in Perspective: Conceptions of its Nature and Relevance.
Frid, Sandra; White, Loren
This study investigated the nature of secondary school students' and teachers' conceptions of what mathematics is, the purposes of school mathematics, and the outcomes of school mathematics. Interviews were conducted with a sample of grades 10, 11, and 12 students (n=40), teachers (n=19), counselors (n=2), and administrators (n=2) from a large…
Self-concept mediates the relation between achievement and emotions in mathematics.
Van der Beek, Jojanneke P J; Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Leseman, Paul P M
2017-09-01
Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. The aims were (1) to investigate the mediating role of mathematical self-concept in the relation between mathematics achievement and the achievement emotions of enjoyment and anxiety in a comprehensive model, and (2) to test possible differences in this mediating role between low-, average-, and high-achieving students. Participants were ninth-grade students (n = 1,014) from eight secondary schools in the Netherlands. Through an online survey including mathematical problems, students were asked to indicate their levels of mathematics enjoyment, anxiety, and self-concept. Structural equation modelling was used to test the mediating role of self-concept in the relation between mathematics achievement and emotions. Multigroup analyses were performed to compare these relations across the three achievement groups. Results confirmed full mediation of the relation between mathematics achievement and emotions by mathematical self-concept. Furthermore, we found higher self-concepts, more enjoyment and less math anxiety in high-achieving students compared to their average and low-achieving peers. No differences across these achievement groups were found in the relations in the mediational model. Mathematical self-concept plays a pivotal role in students' appraisal of mathematics. Mathematics achievement is only one factor explaining students' self-concept. Likely also classroom instruction and teachers' feedback strategies help to shape students' self-concept. © 2017 The British Psychological Society.
Priatna, N.; Martadiputra, B. A. P.; Wibisono, Y.
2018-05-01
The development of science and technology requires reform in the utilization of various resources for mathematics teaching and learning process. One of the efforts that can be made is the implementation of GeoGebra-assisted Reciprocal Teaching strategy in mathematics instruction as an effective strategy in improving students’ cognitive, affective, and psychomotor abilities. This research is intended to implement GeoGebra-assisted Reciprocal Teaching strategy in improving abstraction ability, lateral thinking, and mathematical persistence of junior high school students. It employed quasi-experimental method with non-random pre-test and post-test control design. More specifically, it used the 2x3 factorial design, namely the learning factors that included GeoGebra-assisted Reciprocal Teaching and conventional teaching learning, and levels of early mathematical ability (high, middle, and low). The subjects in this research were the eighth grade students of junior high school, taken with purposive sampling. The results of this research show: Abstraction and lateral abilities of students who were taught with GeoGebra-assisted Reciprocal Teaching strategy were significantly higher than those of students who received conventional learning. Mathematical persistence of students taught with GeoGebra-assisted Reciprocal Teaching strategy was also significantly higher than of those taught with conventional learning.
Teaching Mathematics for Social Justice: Examining Preservice Teachers' Conceptions
Jong, Cindy; Jackson, Christa
2016-01-01
Teaching for social justice is a critical pedagogy used to empower students to be social agents in the world they live. This critical pedagogy has extended to mathematics education. Over the last decade, mathematics education researchers have conceptualized what it means to teach mathematics for social justice, but little is known about preservice…
Using the Tower of Hanoi Puzzle to Infuse Your Mathematics Classroom with Computer Science Concepts
Marzocchi, Alison S.
2016-01-01
This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…
Incorporating Learning Motivation and Self-Concept in Mathematical Communicative Ability
Rajagukguk, Waminton
2016-01-01
This research is trying to determine of the mathematical concepts, instead by integrating the learning motivation (X[subscript 1]) and self-concept (X[subscript 2]) can contribute to the mathematical communicative ability (Y). The test instruments showed the following results: (1) simple regressive equation Y on X[subscript 1] was Y = 32.891 +…
Isbell, Linda M; Rovenpor, Daniel R; Lair, Elicia C
2016-10-01
Research suggests that anger promotes global, abstract processing whereas sadness and fear promote local, concrete processing (see Schwarz & Clore, 2007 for a review). Contrary to a large and influential body of work suggesting that specific affective experiences are tethered to specific cognitive outcomes, the affect-as-cognitive-feedback account maintains that affective experiences confer positive or negative value on currently dominant processing styles, and thus can lead to either global or local processing (Huntsinger, Isbell, & Clore, 2014). The current work extends this theoretical perspective by investigating the impact of discrete negative emotions on the self-concept. By experimentally manipulating information processing styles and discrete negative emotions that vary in appraisals of certainty, we demonstrate that the impact of discrete negative emotions on the spontaneous self-concept depends on accessible processing styles. When global processing was accessible, individuals in angry (negative, high certainty) states generated more abstract statements about themselves than individuals in either sad (Experiment 1) or fearful (Experiment 2; negative, low certainty) states. When local processing was made accessible, however, the opposite pattern emerged, whereby individuals in angry states generated fewer abstract statements than individuals in sad or fearful states. Together these studies provide new insights into the mechanisms through which discrete emotions influence cognition. In contrast to theories assuming a dedicated link between emotions and processing styles, these results suggest that discrete emotions provide feedback about accessible ways of thinking, and are consistent with recent evidence suggesting that the impact of affect on cognition is highly context-dependent. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
On problems in defining abstract and metaphysical concepts--emergence of a new model.
Nahod, Bruno; Nahod, Perina Vukša
2014-12-01
Basic anthropological terminology is the first project covering terms from the domain of the social sciences under the Croatian Special Field Terminology program (Struna). Problems that have been sporadically noticed or whose existence could have been presumed during the processing of terms mainly from technical fields and sciences have finally emerged in "anthropology". The principles of the General Theory of Terminology (GTT), which are followed in Struna, were put to a truly exacting test, and sometimes stretched beyond their limits when applied to concepts that do not necessarily have references in the physical world; namely, abstract and metaphysical concepts. We are currently developing a new terminographical model based on Idealized Cognitive Models (ICM), which will hopefully ensure a better cross-filed implementation of various types of concepts and their relations. The goal of this paper is to introduce the theoretical bases of our model. Additionally, we will present a pilot study of the series of experiments in which we are trying to investigate the nature of conceptual categorization in special languages and its proposed difference form categorization in general language.
Kjeldsen, Tinne Hoff; Lützen, Jesper
2015-07-01
In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.
Directory of Open Access Journals (Sweden)
Deonarain Brijlall
2012-12-01
Full Text Available This article reports on an exploration of teachers’ views on the meaning of mathematical representations in a democratic South Africa. We explored teachers’ conceptions of ‘mathematical representations’ as a means to promote dialogue and negotiation. These conceptions helped us to gauge how these teachers viewed representations in mathematics. Semi-structured questionnaires were administered to 76 high school mathematics teachers who were registered for an upgrading mathematics education qualification at a South African university. Common themes in teacher conceptions of representations were investigated as part of an inductive analysis of the written responses, which were considered in terms of practices that support dialogue and negotiation. Findings suggest that these conceptions are in line with progressive notions of classroom interactions such as the inquiry cooperation model. Furthermore, the findings suggest that teachers can support the development of classroom environments that promote democratic values.
Directory of Open Access Journals (Sweden)
Jennifer EDELMAN
2017-06-01
Full Text Available This descriptive study examines the elements of mathematical knowledge for teaching (MKT that elementary teacher candidates exhibit as they plan, teach, and reflect on a mathematics lesson that integrates children’s literature. Data for this study were gathered from observations and written work of preservice elementary teacher candidates enrolled in a methods of teaching mathematics course. The data were analyzed using three criteria: that of knowledge of content and students, knowledge of content and teaching, and knowledge of content and curriculum. The findings suggest a need for further development of teacher candidates’ ability to identify and locate mathematical concepts in children’s literature, as well as the need for supporting teacher candidates’ critical analysis of curricular materials and mathematical representations in children’s literature.
Directory of Open Access Journals (Sweden)
Jennifer Edelman
2017-06-01
Full Text Available This descriptive study examines the elements of mathematical knowledge for teaching (MKT that elementary teacher candidates exhibit as they plan, teach, and reflect on a mathematics lesson that integrates children’s literature. Data for this study were gathered from observations and written work of preservice elementary teacher candidates enrolled in a methods of teaching mathematics course. The data were analyzed using three criteria: that of knowledge of content and students, knowledge of content and teaching, and knowledge of content and curriculum. The findings suggest a need for further development of teacher candidates’ ability to identify and locate mathematical concepts in children’s literature, as well as the need for supporting teacher candidates’ critical analysis of curricular materials and mathematical representations in children’s literature.
Practice and Conceptions: Communicating Mathematics in the Workplace
Wood, Leigh N.
2012-01-01
The study examined the experience of communication in the workplace for mathematics graduates with a view to enriching university curriculum. I broaden the work of Burton and Morgan (2000), who investigated the discourse practices of academic mathematicians to examine the discourse used by new mathematics graduates in industry and their…
Learning abstract visual concepts via probabilistic program induction in a Language of Thought.
Overlan, Matthew C; Jacobs, Robert A; Piantadosi, Steven T
2017-11-01
The ability to learn abstract concepts is a powerful component of human cognition. It has been argued that variable binding is the key element enabling this ability, but the computational aspects of variable binding remain poorly understood. Here, we address this shortcoming by formalizing the Hierarchical Language of Thought (HLOT) model of rule learning. Given a set of data items, the model uses Bayesian inference to infer a probability distribution over stochastic programs that implement variable binding. Because the model makes use of symbolic variables as well as Bayesian inference and programs with stochastic primitives, it combines many of the advantages of both symbolic and statistical approaches to cognitive modeling. To evaluate the model, we conducted an experiment in which human subjects viewed training items and then judged which test items belong to the same concept as the training items. We found that the HLOT model provides a close match to human generalization patterns, significantly outperforming two variants of the Generalized Context Model, one variant based on string similarity and the other based on visual similarity using features from a deep convolutional neural network. Additional results suggest that variable binding happens automatically, implying that binding operations do not add complexity to peoples' hypothesized rules. Overall, this work demonstrates that a cognitive model combining symbolic variables with Bayesian inference and stochastic program primitives provides a new perspective for understanding people's patterns of generalization. Copyright © 2017 Elsevier B.V. All rights reserved.
Currents in industrial mathematics from concepts to research to education
Prätzel-Wolters, Dieter
2015-01-01
Mathematics has many branches: there are the pure, the applied, and the applicable; the theoretical and the practical. There is mathematics for school, for college, and for industry. All these belong to the same family and are bound together by a "mathematical way of thinking." Some mathematicians devote themselves entirely to the well being of this family by preserving it, developing it, and teaching it to the next generation. Others use the familial attributes to help outsiders by taking up their problems and transforming them into mathematical questions in order to solve them. The work of these mathematicians is thus problem driven, based on mathematical models, and oriented on the goal of offering practicable solutions. This second group is sizeable; its members include almost all college graduates working in industry, in the private sector, or in the Fraunhofer Institutes, for example. This group is hardly visible, however, and one seldom hears its voices either. This book remedies this situation by rela...
Pietsch, James; Walker, Richard; Chapman, Elaine
2003-01-01
Examines the relationship among self-concept, self-efficacy, and performance in mathematics among 416 high school students. Confirmatory factor analyses supported the existence of two self-concept components--a competency component and an affective component. Self-efficacy items and the competency items of self-concept also loaded on a single…
Energy Technology Data Exchange (ETDEWEB)
NONE
1997-12-31
The conference focused on computational and modeling issues in the geosciences. Of the geosciences, problems associated with phenomena occurring in the earth`s subsurface were best represented. Topics in this area included petroleum recovery, ground water contamination and remediation, seismic imaging, parameter estimation, upscaling, geostatistical heterogeneity, reservoir and aquifer characterization, optimal well placement and pumping strategies, and geochemistry. Additional sessions were devoted to the atmosphere, surface water and oceans. The central mathematical themes included computational algorithms and numerical analysis, parallel computing, mathematical analysis of partial differential equations, statistical and stochastic methods, optimization, inversion, homogenization and renormalization. The problem areas discussed at this conference are of considerable national importance, with the increasing importance of environmental issues, global change, remediation of waste sites, declining domestic energy sources and an increasing reliance on producing the most out of established oil reservoirs.
A mathematical model for the third-body concept
Czech Academy of Sciences Publication Activity Database
Krejčí, Pavel; Petrov, A.
2018-01-01
Roč. 23, č. 3 (2018), s. 420-432 ISSN 1081-2865 R&D Projects: GA ČR(CZ) GA15-12227S Institutional support: RVO:67985840 Keywords : third-body * hysteresis operators * variational inequality Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 2.953, year: 2016 http://journals.sagepub.com/doi/abs/10.1177/1081286517732827
Jacobson, Erik; Simpson, Amber
2018-04-01
Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser's (Educational Studies in Mathematics 75:241-251, 2010) study of prospective elementary teachers' conceptions of multidigit number and examined the main claim that most elementary pre-service teachers think about digits incorrectly at least some of the time. Results indicated no statistically significant difference in the distribution of conceptions between the original and replication samples and, moreover, no statistically significant differences in the distribution of sub-conceptions among prospective teachers with the most common conception. These results suggest confidence is warranted both in the generality of the main claim and in the utility of the conceptions framework for describing prospective elementary teachers' conceptions of multidigit number. The report further contributes a framework for replication of mathematics education research adapted from the field of psychology.
杉野, 裕子
2014-01-01
I have been studying to show the importance of adopting a programming in the mathematical education and developed the LOGO teaching materials which is made good use of in the field of Euclidean geometry, in order to improve understanding and learning figure concepts. The present article offers a theoretical framework with consistency about my study and also new programming materials in which I embody my theory. I consider logically the system of mathematical expression with computers and espe...
Justification of the concept of mathematical methods and models in making decisions on taxation
KORKUNA NATALIA MIKHAYLOVNA
2017-01-01
The paper presents the concept of the application of mathematical methods and models in making decisions on taxation in Ukraine as a phased process. Its performance result is the selection of an effective decision based on regression and optimization models.
Logical thinking in the pyramidal schema of concepts the logical and mathematical elements
Geldsetzer, Lutz
2014-01-01
This book proposes a new way of formalizing in logic and mathematics - a "pyramidal graph system," devised by the author and based on Porphyrian trees and modern concepts of classification, in both of which pyramids act as the organizing schema.
Self-concept mediates the relation between achievement and emotions in mathematics
Van der Beek, Jojanneke P J; Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Leseman, Paul P M
BACKGROUND: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions.
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…
Patel, Rita Manubhai
2013-01-01
This dissertation examined understanding of slope and derivative concepts and mathematical dispositions of first-semester college calculus students, who are recent high school graduates, transitioning to university mathematics. The present investigation extends existing research in the following ways. First, based on this investigation, the…
Self-concept mediates the relation between achievement and emotions in mathematics
Beek, J.P.J. van der; Ven, S.H.G. van der; Kroesbergen, E.H.; Leseman, P.P.M.
2017-01-01
Background: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions.
An Investigation of K-8 Preservice Teachers' Concept Images and Mathematical Definitions of Polygons
Ward, Robin A.
2004-01-01
In this paper, the author presents a study which explored K-8 preservice teachers' concept images and mathematical definitions of polygons. This study was carried out in which K-8 teacher candidates enrolled in an elementary mathematics content course were asked to sort, identify, and provide definitions of such shapes including triangles,…
Self-Concept Mediates the Relation between Achievement and Emotions in Mathematics
Van der Beek, Jojanneke P. J.; Van der Ven, Sanne H. G.; Kroesbergen, Evelyn H.; Leseman, Paul P. M.
2017-01-01
Background: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. Aims: The aims were (1) to investigate the…
Yang, Kai-Lin
2016-01-01
This study aims at analyzing how Pythagoras' theorem is handled in three versions of Taiwanese textbooks using a conceptual framework of a constructive-empirical perspective on abstraction, which comprises three key attributes: the generality of the object, the connectivity of the subject and the functionality of diagrams as the focused semiotic…
Kjeldsen, Tinne Hoff; Lützen, Jesper
2015-01-01
In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…
Ibrahim Rajab Abbas Ibrahim
2017-01-01
The purpose of this study was to identify the effectiveness of cooperative learning in improving mathematical concepts among students with mild intellectual disability (SMID). The sample of the study consisted of 8 SMID at Najran in the Kingdom of Saudi Arabia. The sample of the study was divided randomly into two equal groups control and experimental. The students in the experimental group have studied the mathematical concepts by using cooperative learning; however the students in the contr...
USSR and Eastern Europe Scientific Abstracts, Physics and Mathematics, Number 34
1977-04-27
USSR UDC 621.315.592 ANOMALOUS PHOTOCONDUCTIVITY AND DARK CONDUCTIVITY OF SEMI-INSULATING CADMIUM TELLURIDE Leningrad FIZIKA I TEKHNIKA...conductivity activation energy of CdTe. The temperature characteristic of the dark conductivity, measured within the ohmic range of the current...A. V., Joint Institute for Nuclear Research [Abstract] The purpose of this theoretical paper is to show that the quark -parton modification offers
Angraini, L. M.; Kusumah, Y. S.; Dahlan, J. A.
2018-05-01
This study aims to see the enhancement of mathematical analogical reasoning ability of the university students through concept attainment model learning based on overall and Prior Mathematical Knowledge (PMK) and interaction of both. Quasi experiments with the design of this experimental-controlled equivalent group involved 54 of second semester students at the one of State Islamic University. The instrument used is pretest-postest. Kolmogorov-Smirnov test, Levene test, t test, two-way ANOVA test were used to analyse the data. The result of this study includes: (1) The enhancement of the mathematical analogical reasoning ability of the students who gets the learning of concept attainment model is better than the enhancement of the mathematical analogical reasoning ability of the students who gets the conventional learning as a whole and based on PMK; (2) There is no interaction between the learning that is used and PMK on enhancing mathematical analogical reasoning ability.
Sociocultural context as a facilitator of student learning of function concepts in mathematics
Directory of Open Access Journals (Sweden)
Evangelina Díaz Obando
2016-03-01
Full Text Available In Costa Rica, many secondary students have serious difficulties to establish relationships between mathematics and real-life contexts. They question the utilitarian role of the school mathematics. This fact motivated the research object of this report which evidences the need to overcome methodologies unrelated to students’ reality, toward new didactical options that help students to value mathematics, reasoning and its applications, connecting it with their socio-cultural context. The research used a case study as a qualitative methodology and the social constructivism as an educational paradigm in which the knowledge is built by the student; as a product of his social interactions. A collection of learning situations was designed, validated, and implemented. It allowed establishing relationships between mathematical concepts and the socio-cultural context of participants. It analyzed the impact of students’socio-cultural context in their mathematics learning of basic concepts of real variable functions, consistent with the Ministry of Education (MEP Official Program. Among the results, it was found that using students’sociocultural context improved their motivational processes, mathematics sense making, and promoted cooperative social interactions. It was evidenced that contextualized learning situations favored concepts comprehension that allow students to see mathematics as a discipline closely related with their every-day life.
Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc
2016-01-01
Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…
McCarthy, Mary M.
2014-01-01
Games and simulations are increasingly used in courses on international politics. This study explores the hypothesis that games are better than simulations (as well as only reading and lectures) in introducing students to abstract concepts integral to an understanding of world politics. The study compares a two-level Prisoner's Dilemma game…
Mathematical rationalization for the renal tubular transport: revised concepts.
Mioni, Roberto; Marega, Alessandra; Romano, Giulio; Montanaro, Domenico
2017-09-01
The current emphasis on kinetics and in situ control of molecular exchanges, across the tubular membrane, has not been paralleled by corresponding improvements in our understanding of tubular behaviour at the macroscopic level of classical physiology. In this paper, we propose a mathematical rationalization of macroscopic tubular transport by means of a principal transport equation, originating from the law of mass action between substrate and carrier. The other equations, derived from the main one, demonstrate the possibility of distinguishing between transporters with low affinity and high capacity and transporters with high affinity and low capacity. Moreover, our model formalizes both tubular reabsorption and tubular secretion. Regarding the renal calcium handling, our model confirms the two-compartment system proposed by Mioni in 1971, with some important variants, which are in agreement with the fractional reabsorptions of this cation along the tubule, as verified by micro-puncture technique. To obtain the frequency distribution of saturated tubules, we have utilized the infinitesimal analysis method, starting from the equations proposed by Smith in 1943, concluding that all titration curves result from the combined effect of enzymatic approach and anatomical heterogeneity of the nephrons. The theoretical equations included in our manuscript reflect substantial and palpable physiological mechanisms able to suggest diagnosis and therapy of some electrolyte and hormonal disorders. At the end of this paper, we highlight advantages and disadvantages detectable by comparing our mathematical approach with Marshall's and Bijvoet's methods, proposed, respectively, in 1976 and 1984.
Mathematical modelling in engineering: A proposal to introduce linear algebra concepts
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Andrea Dorila Cárcamo
2016-03-01
Full Text Available The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts: span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.
Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis
2013-01-01
Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology. © 2013 by The International Union of Biochemistry and Molecular Biology.
PRE-SERVICE MATHEMATICS TEACHERS’ CONCEPTION OF HIGHER-ORDER THINKING LEVEL IN BLOOM'S TAXONOMY
Damianus D Samo
2017-01-01
The purpose of this study is to explore pre-service mathematics teachers' conception of higher-order thinking in Bloom's Taxonomy, to explore pre-service mathematics teachers' ability in categorizing six cognitive levels of Bloom's Taxonomy as lower-order thinking and higher-order thinking, and pre-service mathematics teachers' ability in identifying some questionable items as lower-order and higher-order thinking. The higher-order thinking is the type of non-algorithm thinking which include ...
An Abstract Interaction Concept for Designing Interaction Behaviour of Service Compositions
Dirgahayu, T.; Quartel, Dick; van Sinderen, Marten J.; Mertins, Kai; Ruggaber, Rainer; Popplewell, Keith; Xu, Xiaofei
2008-01-01
In a service composition, interaction behaviour specifies an information exchange protocol that must be complied with in order to guarantee interoperability between services. Interaction behaviour can be designed using a top-down design approach utilising high abstraction levels to control its
The Representation of Concrete and Abstract Concepts: Categorical versus Associative Relationships
Geng, Jingyi; Schnur, Tatiana T.
2015-01-01
In 4 word-translation experiments, we examined the different representational frameworks theory (Crutch & Warrington, 2005; 2010) that concrete words are represented primarily by category, whereas abstract words are represented by association. In our experiments, Chinese-English bilingual speakers were presented with an auditory Chinese word…
The Risky Path to a Followership Identity: From Abstract Concept to Situated Reality
DEFF Research Database (Denmark)
Larsson, Magnus; Nielsen, Mie Femø
2017-01-01
. The findings reveal the risks of misidentifying the task at hand, of being too authoritative, and of claiming too much knowledge. Also, our analyses highlight that leader and follower roles remain abstract in workplace interactions and, instead, people focus more on negotiated, task-oriented, practical...
Using Technology To Bring Abstract Concepts into Focus: A Programming Case Study.
Crews, Thad; Butterfield, Jeff
2002-01-01
Discusses the three-step implementation of an instructional technology tool and associated pedagogy to support teaching and learning computer programming concepts. The Flowchart Interpreter (FLINT) was proven through experiments to support novice programmers better than the traditional textbook approach. (EV)
Minásbate Equivalents of Mathematical Concepts: Their Socio-Cultural Undertones
Balbuena, Sherwin E.; Cantoria, Uranus E.; Cantoria, Amancio L., Jr.; Ferriol, Eny B.
2015-01-01
This paper presents the collection and analysis of Minásbate equivalents of some concepts used in the study of arithmetic, counting, and geometry as provided by the elderly residents of the province of Masbate. The glossary of mathematical terms derived from interviews would serve as an authoritative reference for mother tongue teachers in the…
Sumpter, Lovisa
2016-01-01
This study examines Swedish upper secondary school teachers' gendered conceptions about students' mathematical reasoning: whether reasoning was considered gendered and, if so, which type of reasoning was attributed to girls and boys. The sample consisted of 62 teachers from six different schools from four different locations in Sweden. The results…
The Power of Colombian Mathematics Teachers' Conceptions of Social/Institutional Factors of Teaching
Agudelo-Valderrama, Cecilia
2008-01-01
In this paper I shall discuss data from a study on Colombian mathematics teachers' conceptions of their own teaching practices of beginning algebra, which led to the development of a theoretical model of teachers' thought structures designed as a thinking tool at the initial stage of the study. With a focus on the perspectives of teachers, the…
The Vital Role of Basic Mathematics in Teaching and Learning the Mole Concept
Mehrotra, Alka; Koul, Anjni
2016-01-01
This article focuses on the importance of activity-based teaching in understanding the mole concept and the vital role of basic mathematical operations. It describes needs-based training for teachers in a professional development programme in India. Analysis of test results before and after the training indicates that teachers improved their…
The Impact of the Flipped Classroom on Mathematics Concept Learning in High School
Bhagat, Kaushal Kumar; Chang, Cheng-Nan; Chang, Chun-Yen
2016-01-01
The present study aimed to examine the effectiveness of the flipped classroom learning environment on learner's learning achievement and motivation, as well as to investigate the effects of flipped classrooms on learners with different achievement levels in learning mathematics concepts. The learning achievement and motivation were measured by the…
Lin, Chi-Hui
2002-01-01
Describes a study that determined the implications of computer graphics types and epistemological beliefs with regard to the design of computer-based mathematical concept learning with elementary school students in Taiwan. Discusses the factor structure of the epistemological belief questionnaire, student performance, and students' attitudes…
Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi
2017-06-01
This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.
The concept of competence and its relevance for science, technology, and mathematics education
DEFF Research Database (Denmark)
Ropohl, Mathias; Nielsen, Jan Alexis; Olley, Christopher
2018-01-01
. In contrast to earlier ed-ucational goals that focused more on basic skills and knowledge expectations, competences are more functionally oriented. They involve the ability to solve complex problems in a particular context, e.g. in vocational or everyday situations. In science, technology, and mathematics...... education, the concept of competence is closely linked to the concept of literacy. Apart from these rather cognitive and af-fective perspectives influenced by the need to assess students’ achievement of de-sired learning goals in relation to their interest and motivation, the perspectives of the concept...
McGee, Daniel; Moore-Russo, Deborah
2015-01-01
A test project at the University of Puerto Rico in Mayagüez used GeoGebra applets to promote the concept of multirepresentational fluency among high school mathematics preservice teachers. For this study, this fluency was defined as simultaneous awareness of all representations associated with a mathematical concept, as measured by the ability to…
A Teacher's Conception of Definition and Use of Examples When Doing and Teaching Mathematics
Johnson, Heather Lynn; Blume, Glendon W.; Shimizu, Jeanne K.; Graysay, Duane; Konnova, Svetlana
2014-01-01
To contribute to an understanding of the nature of teachers' mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher's conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical…
Kamoru, Usman; Ramon, Olosunde Gbolagade
2017-01-01
This study examined the relationship between self-concept, attitude of the students towards mathematics, and math achievement. Also, this study investigated the influence of study habits on achievement; study habits on attitude of students to mathematics. The influence of gender and self-concept and study habit group on achievement and attitude…
Developing self-concept instrument for pre-service mathematics teachers
Afgani, M. W.; Suryadi, D.; Dahlan, J. A.
2018-01-01
This study aimed to develop self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia. Type of this study was development research of non-test instrument in questionnaire form. A Validity test of the instrument was performed with construct validity test by using Pearson product moment and factor analysis, while reliability test used Cronbach’s alpha. The instrument was tested by 65 undergraduate students of mathematics education in one of the universities at Palembang, Indonesia. The instrument consisted of 43 items with 7 aspects of self-concept, that were the individual concern, social identity, individual personality, view of the future, the influence of others who become role models, the influence of the environment inside or outside the classroom, and view of the mathematics. The result of validity test showed there was one invalid item because the value of Pearson’s r was 0.107 less than the critical value (0.244; α = 0.05). The item was included in social identity aspect. After the invalid item was removed, Construct validity test with factor analysis generated only one factor. The Kaiser-Meyer-Olkin (KMO) coefficient was 0.846 and reliability coefficient was 0.91. From that result, we concluded that the self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia was valid and reliable with 42 items.
Exploiting abstract possibilities: a critique of the concept and practice of product patenting.
Radder, Hans
2004-01-01
Developments in biotechnology and genomics have moved the issue of patenting scientific and technological inventions toward the center of interest. In particular, the patentability of genes of plants, animals, or humans and of genetically modified (parts of) living organisms has been discussed, and questioned, from various normative perspectives. This paper aims to contribute to this debate. For this purpose, it first explains a number of relevant aspects of the theory and practice of patenting. The focus is on a special and increasingly significant type of patents, namely product patents. The paper provides three general arguments against the concept and practice of product patenting. The first argument briefly considers the claim that patents are legitimate because they promote socially useful innovation. Against this claim, it is argued that product patents may hamper rather than promote such innovation. The second and main argument concludes that product patents are not adequately based on actual technological inventions, as they should be according to the usual criteria of patentability. The principal moral issue is that product patents tend to reward patentees for inventions they have not really made available. The final argument proposes a method for patenting the heat of the sun. Assuming that granting this patent will be generally considered absurd, the argument exposes a further, fundamental problem of the concept and practice of product patenting.
From grasp to language: embodied concepts and the challenge of abstraction.
Arbib, Michael A
2008-01-01
The discovery of mirror neurons in the macaque monkey and the discovery of a homologous "mirror system for grasping" in Broca's area in the human brain has revived the gestural origins theory of the evolution of the human capability for language, enriching it with the suggestion that mirror neurons provide the neurological core for this evolution. However, this notion of "mirror neuron support for the transition from grasp to language" has been worked out in very different ways in the Mirror System Hypothesis model [Arbib, M.A., 2005a. From monkey-like action recognition to human language: an evolutionary framework for neurolinguistics (with commentaries and author's response). Behavioral and Brain Sciences 28, 105-167; Rizzolatti, G., Arbib, M.A., 1998. Language within our grasp. Trends in Neuroscience 21(5), 188-194] and the Embodied Concept model [Gallese, V., Lakoff, G., 2005. The brain's concepts: the role of the sensory-motor system in reason and language. Cognitive Neuropsychology 22, 455-479]. The present paper provides a critique of the latter to enrich analysis of the former, developing the role of schema theory [Arbib, M.A., 1981. Perceptual structures and distributed motor control. In: Brooks, V.B. (Ed.), Handbook of Physiology--The Nervous System II. Motor Control. American Physiological Society, pp. 1449-1480].
Pepin, B.; Hudson, B.; Buchberger, F.; Kansanen, P.
1999-01-01
This paper firstly explores the issues raised in the literature concerning epistemologies, beliefs and conceptions of mathematics and its teaching and learning. Secondly, it analyses the ways in which mathematics teachers’ classroom practices in England, France and Germany reflect teachers’ beliefs
Kristian, P. L. Y.; Cari, C.; Sunarno, W.
2018-04-01
This study purposes to describe and analyse the students' concept understanding of dynamic fluid. The subjects of this research are 10 students of senior high school. The data collected finished the essay test that consists of 5 questions have been adapted to the indicators of learning. The data of this research is analysed using descriptive-qualitative approach by referring of the student's argumentations about their answer from the questions that given. The results showed that students still have incorrect understanding the concept of dynamic fluids, especially on the Bernoulli’s principle and its application. Based on the results of this research, the teachers should emphasize the concept understanding of the students therefore the students don not only understand the physics concept in mathematical form.
Using Group Explorer in Teaching Abstract Algebra
Schubert, Claus; Gfeller, Mary; Donohue, Christopher
2013-01-01
This study explores the use of Group Explorer in an undergraduate mathematics course in abstract algebra. The visual nature of Group Explorer in representing concepts in group theory is an attractive incentive to use this software in the classroom. However, little is known about students' perceptions on this technology in learning concepts in…
Directory of Open Access Journals (Sweden)
Maher Abu-Hilal
2012-11-01
Full Text Available This study examined the structural relationships among cognitive constructs (intelligence and achievement and affective constructs (perceived parental help, effort and self-concept. It was proposed that the relationships are not invariant across gender. The sample consisted of 219 boys and 133 girls from elementary and preparatory public schools in Al Ain in the United Arab Emirates. Intelligence (IQ was measured by the Test of Non-verbal Intelligence (TONI and parental help was measured by 4-Likert-type items. Effort was measured by 4-Likert-type items. Self-concept (SC was measured by 8-Likert-type items taken from the SDQ I (Abu-Hilal, 2000. Mathematic Achievement was the scores of students in mathematics from school records. The structural model assumed that IQ would have an effect on parental help, effort, SC and achievement. Parental help would have an effect on effort, SC and achievement. Also, effort would have an effect on SC and achievement. Finally, SC would have an effect on achievement. The structural model was tested for invariance across gender. The measurement model proved to be invariant across gender and so was the structural model. The non-constrained model indicated that the structural relationships among the variables do vary according to gender. For example, boys benefited from parental help by exerting more effort while girls did not. Boys with high IQ exerted more effort than boys with low IQ; but girls with high IQ exerted the same amount of effort as girls with low IQ. The model explained 45% and 39% of the variance in math scores for boys and girls, respectively.
Walker, Caren M; Bridgers, Sophie; Gopnik, Alison
2016-11-01
We explore the developmental trajectory and underlying mechanisms of abstract relational reasoning. We describe a surprising developmental pattern: Younger learners are better than older ones at inferring abstract causal relations. Walker and Gopnik (2014) demonstrated that toddlers are able to infer that an effect was caused by a relation between two objects (whether they are the same or different), rather than by individual kinds of objects. While these findings are consistent with evidence that infants recognize same-different relations, they contrast with a large literature suggesting that older children tend to have difficulty inferring these relations. Why might this be? In Experiment 1a, we demonstrate that while younger children (18-30-month-olds) have no difficulty learning these relational concepts, older children (36-48-month-olds) fail to draw this abstract inference. Experiment 1b replicates the finding with 18-30-month-olds using a more demanding intervention task. Experiment 2 tests whether this difference in performance might be because older children have developed the general hypothesis that individual kinds of objects are causal - the high initial probability of this alternative hypothesis might override the data that favors the relational hypothesis. Providing additional information falsifying the alternative hypothesis improves older children's performance. Finally, Experiment 3 demonstrates that prompting for explanations during learning also improves performance, even without any additional information. These findings are discussed in light of recent computational and algorithmic theories of learning. Copyright © 2016 Elsevier B.V. All rights reserved.
Pre-service mathematics student teachers’ conceptions of nominal and effective interest rates
Directory of Open Access Journals (Sweden)
Judah P. Makonye
2017-04-01
Full Text Available The general public consumes financial products such as loans that are administered in the realm of nominal and effective interest rates. It is debatable if most consumers really understand how these rates function. This article explores the conceptions that student teachers have about nominal and effective interest rates. The APOS theory illuminates analysis of students’ levels of conception. Seventy second-year mathematics students’ responses to Grade 12 tasks on effective and nominal interest rates were analysed, after which 12 students were interviewed about their mathematical thinking in solving the tasks. The findings varied. While some students could not do the tasks due to erratic use of formulae (algebra, I ascertained that some students obtained correct answers through scrupulous adherence to the external prompt of formulae. Most of those students remained stuck at the action and process stages and could not view their processes as mathematical objects. A few students had reached the object and schema stages, showing mature understanding of the relationship between nominal and effective interest rates. As most students remained at the operational stages rather than the structural, the findings accentuate that when teaching this topic, teachers ought to take their time to build learners’ schema for these notions. They need to guide their learners through the necessary action-process-object loop and refrain from introducing students to formulae too soon as this stalls their advancement to the object and schema stages which are useful in making them smart consumers of financial products.
Joutsenlahti, Jorma; Kulju, Pirjo
2017-01-01
The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21) understand the concept of division. The data was collected over six…
Maričić, Sanja; Ćalić, Maja
2015-01-01
Starting from the fact that in early education the process of learning should be understood in its totality, as a system of activities in which the subject fields are interwoven and woven into every segment of a child's life together with other children and adults in preschool, the authors of the work point out the integration of the development of mathematical concepts and music education. Music education is viewed as a context which can contribute to the acquisition of mathematical concepts...
Benko, Matúš; Gfrerer, Helmut
2018-01-01
In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of [Formula: see text]-stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-called [Formula: see text]-stationarity. We show how the property of [Formula: see text]-stationarity (and thus also of M-stationarity) can be efficiently verified for the considered problem class by computing [Formula: see text]-stationary solutions of a certain quadratic program. We consider further the situation that the point which is to be tested for [Formula: see text]-stationarity, is not known exactly, but is approximated by some convergent sequence, as it is usually the case when applying some numerical method.
The learning evaluations of the concept function in the mathematical subject I
Directory of Open Access Journals (Sweden)
Wilmer Valle Castañeda
2018-03-01
Full Text Available The evaluation must be one of the most complex tasks that teachers face today, both for the process itself and for having to issue an assessment about the achievements and deficiencies of the students. It is for them that techniques and instruments were developed, which allow the evaluation of the function concept in the Mathematics I subject´s. Methods of the theoretical level, of the empirical level such as the historical-logical analysis, the surveys, were used in the research carried out. The documentary analyses, as well as procedures such as the analysis - synthesis that made it possible to investigate the theoretical and practical fundament´s learning evaluation´s. The evaluation instruments presented allowed for the evaluation of the students in Mathematics I, less than one of the most important functions of the evaluation: the formative or educational function. These constituted a reference for the continuous improvement of student learning.
Soro, S.; Maarif, S.; Kurniawan, Y.; Raditya, A.
2018-01-01
The aim of this study is to find out the effect of Dienes AEM (Algebra Experience Materials) on the ability of understanding concept of algebra on the senior high school student in Indonesia. This research is an experimental research with subject of all high school students in Indonesia. The samples taken were high school students in three provinces namely DKI Jakarta Province, West Java Province and Banten Province. From each province was taken senior high school namely SMA N 9 Bekasi West Java, SMA N 94 Jakarta and SMA N 5 Tangerang, Banten. The number of samples in this study was 114 high school students of tenth grade as experimental class and 115 high school students of tenth grade as control class. Learning algebra concept is needed in learning mathematics, besides it is needed especially to educate students to be able to think logically, systematically, critically, analytically, creatively, and cooperation. Therefore in this research will be developed an effective algebra learning by using Dienes AEM. The result of this research is that there is a significant influence on the students’ concept comprehension ability taught by using Dienes AEM learning as an alternative to instill the concept of algebra compared to the students taught by conventional learning. Besides, the students’ learning motivation increases because students can construct the concept of algebra with props.
PRELIMINARY ASSESSMENT OF FAMILIARITY WITH CONCEPTS MATHEMATICAL GEOGRAPHY OF COURSE UNDERGRADUATE
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Luis Alberto Martins Palhares de Melo
2015-12-01
Full Text Available The objective of the work described in this paper was to conduct a preliminary assessment about the familiarity with basic mathematical concepts by undergraduate students of Geography. This work assumed that the domain of basic concepts of mathematics is important for the students for the real understanding of quantification techniques applied to geography, used for better understanding about geographical space. Therefore, it was applied a questionnaire with six questions related to some basic mathematical concepts. 384 questionnaires were applied in undergraduate courses in geography, in six public institutions of higher education and a private college, located in the Federal District, Goias, Tocantins, Mato Grosso do Sul, Paraná and Rio Grande do Sul in May / 2013 June / 2013 August / 2013 and April / 2014. The results showed that the 384 respondents answered correctly on average 2,3 questions of an amount of six questions. This may mean that a priori there is little familiarity of undergraduate Geography students with basic concepts of mathematics. O objetivo do trabalho descrito neste artigo foi realizar uma avaliação preliminar a respeito da familiaridade com conceitos matemáticos em nível de Educação Básica por parte de graduandos de cursos de Geografia. Essa investigação partiu do princípio de que o domínio de conceitos básicos de Matemática é importante para a capacitação em técnicas de quantificação em Geografia, que por sua vez auxiliam o geógrafo, bacharel ou licenciado, a entender melhor o espaço geográfico. Para tanto foi utilizado o instrumento questionário com seis questões versando sobre alguns conceitos matemáticos básicos em nível de Educação Básica. Foram aplicados 384 questionários em cursos de graduação em Geografia, em seis instituições públicas de ensino superior e uma faculdade particular, localizadas no Distrito Federal, Goiás, Tocantins, Mato Grosso do Sul, Paraná e Rio Grande do
Fields, Chris
2013-08-01
The theory of computation and category theory both employ arrow-based notations that suggest that the basic metaphor "state changes are like motions" plays a fundamental role in all mathematical reasoning involving formal manipulations. If this is correct, structure-mapping inferences implemented by the pre-motor action planning system can be expected to be involved in solving any mathematics problems not solvable by table lookups and number line manipulations alone. Available functional imaging studies of multi-digit arithmetic, algebra, geometry and calculus problem solving are consistent with this expectation.
Vivaldi, Franco
2014-01-01
This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition. Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...
Peltier, Corey; Vannest, Kimberly J.
2018-01-01
Mr. Buxton is a perplexed elementary mathematics teacher. He co-teaches a second-grade classroom, with Ms. Snyder. In their classroom they have 25 students; five are identified as academically at risk, and three receive special education services. In the past Mr. Buxton successfully used an instructional approach consisting of (a) modeling, (b)…
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Sofan Tri Prasetiyo
2017-08-01
Full Text Available The purpose of this research was to know the effectiveness of MURDER cooperative model towards students’ mathematics reasoning ability and self concept of ten grade. Population of this research were students of MIA ten grade Senior High School 1 Kebumen in the academic year 2016/1017. Sampling technique using simple random sampling technique. The data collected by the method of documentation, test methods, observation methods, and questionnaire methods. The analyzed of data are used completeness test and average different test. The results showed that: (1 mathematics reasoning ability of students that following MURDER cooperative model have completed individual and classical study completeness; (2 mathematics reasoning ability of students that following MURDER cooperative model better than mathematics reasoning ability of students that following ekspository learning; (3 self concept of students that following MURDER cooperative model better than self concept of students that following ekspository learning.
Motivated Forgetting in Early Mathematics: A Proof-of-Concept Study
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Gerardo Ramirez
2017-12-01
Full Text Available Educators assume that students are motivated to retain what they are taught. Yet, students commonly report that they forget most of what they learn, especially in mathematics. In the current study I ask whether students may be motivated to forget mathematics because of academic experiences threaten the self-perceptions they are committed to maintaining. Using a large dataset of 1st and 2nd grade children (N = 812, I hypothesize that math anxiety creates negative experiences in the classroom that threaten children’s positive math self-perceptions, which in turn spurs a motivation to forget mathematics. I argue that this motivation to forget is activated during the winter break, which in turn reduces the extent to which children grow in achievement across the school year. Children were assessed for math self-perceptions, math anxiety and math achievement in the fall before going into winter break. During the spring, children’s math achievement was measured once again. A math achievement growth score was devised from a regression model of fall math achievement predicting spring achievement. Results show that children with higher math self-perceptions showed reduced growth in math achievement across the school year as a function of math anxiety. Children with lower math interest self-perceptions did not show this relationship. Results serve as a proof-of-concept for a scientific account of motivated forgetting within the context of education.
Kontorovich, Igor'
2018-01-01
This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…
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.
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А. Лопатьєв
2017-09-01
Full Text Available The objective is to systematize and adapt the basic definitions and concepts of the systems approach, mathematical modeling and information technologies to sports science. Materials and methods. The research has studied the availability of appropriate terms in shooting sports, which would meet the requirements of modern sports science. It has examined the compliance of the shooting sports training program for children and youth sports schools, the Olympic reserve specialized children and youth schools, schools of higher sports skills, and sports educational institutions with the modern requirements and principles. Research results. The paper suggests the basic definitions adapted to the requirements of technical sports and sports science. The research has thoroughly analyzed the shooting sports training program for children and youth sports schools, the Olympic reserve specialized children and youth schools, schools of higher sports skills, and sports educational institutions. The paper offers options to improve the training program in accordance with the modern tendencies of training athletes. Conclusions. The research suggests to systematize and adapt the basic definitions and concepts of the systems approach, mathematical modeling and information technologies using the example of technical sports.
The big-fish-little-pond effect on mathematics self-concept: Evidence from the United Arab Emirates.
Areepattamannil, Shaljan; Khine, Myint Swe; Al Nuaimi, Samira
2017-08-01
This study examined the big-fish-little-pond effect (BFLPE; Marsh, 1987) on mathematics self-concept of 7404 adolescents (female = 3767 [51%], male = 3637 [49%]; M age = 15.85 years, SD = 0.28) from 456 schools in the United Arab Emirates, one of the Arab states of the Persian Gulf. The results of multilevel regression analyses indicated good support for the BFLPE's theoretical predictions: the effect of individual student mathematics achievement on individual student mathematics self-concept was positive and statistically significant, whereas the effect of school-average mathematics achievement on individual student mathematics self-concept was negative and statistically significant. Moreover, the interaction between school-average mathematics achievement and individual student mathematics achievement was small and non-significant. Implications of the findings for policy and practice are briefly discussed. Copyright © 2017 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.
Kudri, F.; Rahmi, R.; Haryono, Y.
2018-04-01
This research is motivated by the lack of understanding of mathematical concepts students and teachers have not familiarize students discussed in groups. This researchaims to determine whether an understanding of mathematical concepts junior class VIII SMPN 2 in Ranah Batahan Kabupaten Pasaman Barat by applying active learning strategy group to group types with LKS better than conventional learning. The type of research is experimental the design of randomized trials on the subject. The population in the study were all students VIII SMPN 2 Ranah Batahan Kabupaten Pasaman Barat in year 2012/2013 which consists of our class room experiment to determine the grade and control class with do nerandomly, so that classes VIII1 elected as a experiment class and class VIII4 as a control class. The instruments used in the test empirically understanding mathematical concepts are shaped by the essay with rt=0,82 greater than rt=0,468 means reliable tests used. The data analysis technique used is the test with the help of MINITAB. Based on the results of the data analisis known that both of the sample are normal and homogenity in real rate α = 0,05, so the hypothesis of this research is received. So, it can be concluded students’ understanding mathematical concept applied the active Group to Group learning strategy with LKS is better than the students’ understanding mathematical concept with Conventional Learning.
An original approach to the mathematical concept of graph from braid crafts
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Albanese Veronica
2016-01-01
Full Text Available In previous researches we found that a community of Argentinean artisans models its own practices of braiding using graphs. Inspired by these findings, we designed an educational activity to introduce the concept of graphs. The study of graphs helps students to develop combinatorial and systematic thinking as well as skills to model reality and abstract and generalize patterns from particular situations. The tasks proposed aim to construct the concept of graphs, then identify characteristics that allow some graphs to be models of braids and finally use them to invent more graphs for new braids. The activity performed in a secondary school teachers’ educational course, had quite satisfactory results due to the number of braids invented and the small amount of mistakes made by the participants.
Senyefia Bosson-Amedenu
2017-01-01
Further Mathematics is frequently perceived as a subject set aside for some exceptional individuals. It often induces feelings of worry; nervousness and panic among students. This study employed the survey research design aimed at investigating difficult concepts in senior secondary school further mathematics curriculum as perceived by students in Archbishop Porter Girls’ Senior High School in Ghana. The study was guided by two research questions and the sample for the study was 100, all of w...
Starobin, Soko S.; Laanan, Frankie Santos
Female and minority students have historically been underrepresented in the field of science, mathematics, and engineering at colleges and universities. Although a plethora of research has focused on students enrolled in 4-year colleges or universities, limited research addresses the factors that influence gender differences in community college students in science, mathematics, and engineering. Using a target population of 1,599 aspirants in science, mathematics, and engineering majors in public community colleges, this study investigates the determinants of self-concept by examining a hypothetical structural model. The findings suggest that background characteristics, high school academic performance, and attitude toward science have unique contributions to the development of self-concept among female community college students. The results add to the literature by providing new theoretical constructs and the variables that predict students' self-concept.
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Jorma Joutsenlahti
2017-01-01
Full Text Available The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21 understand the concept of division. The data was collected over six hours of teaching sessions, during which the pupils expressed their mathematical thinking mainly by writing and drawing. Their productions, as well as questionnaire after the process, were analyzed qualitatively. The results show that, in expressing the mathematical problem in verbal form, most of the students saw it as a division into parts. It was evident from the pupils’ texts and drawings that the mathematical expression of subtraction could be interpreted in three different ways. It was found that the pupils enjoyed using writing in the solution of word problems, and it is suggested that the use of different modes in expressing mathematical thinking may both strengthen the learning of mathematical concepts and support the evaluation of learning.
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Examination of Pre-Service Mathematics Teachers' Knowledge of Teaching Function Concept
Tasdan, Berna Tataroglu; Koyunkaya, Melike Yigit
2017-01-01
Teaching of mathematics could be improved with teachers who have a strong mathematical knowledge and have an ability to reflect this knowledge on their teaching. Therefore, it is important to develop mathematics teachers' theoretical and pedagogical knowledge. This study was designed to examine pre-service secondary mathematics teachers' (PSMT)…
Raychaudhuri, Debasree
2014-01-01
Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of reducing abstraction maps the abstract nature of mathematics to the nature of knowledge construction by offering three interpretations of how students reduce abstraction while learning mathematical concepts. We apply this framework to explain students' cognition processes as they construct the concept of solution to differential equations and related concepts during a semester long study. Additionally, we refine and extend the framework to elucidate various nuances of the interplay between mathematical structures and human thoughts.
Integrated learning of mathematics, science and technology concepts through LEGO/Logo projects
Wu, Lina
This dissertation examined integrated learning in the domains of mathematics, science and technology based on Piaget's constructivism, Papert's constructionism, and project-based approach to education. Ten fifth grade students were involved in a two-month long after school program where they designed and built their own computer-controlled LEGO/Logo projects that required the use of gears, ratios and motion concepts. The design of this study centered on three notions of integrated learning: (1) integration in terms of what educational materials/settings provide, (2) integration in terms of students' use of those materials, and (3) integration in the psychological sense. In terms of the first notion, the results generally showed that the LEGO/Logo environment supported the integrated learning of math, science and technology concepts. Regarding the second notion, the students all completed impressive projects of their own design. They successfully combined gears, motors, and LEGO parts together to create motion and writing control commands to manipulate the motion. But contrary to my initial expectations, their successful designs did not require numerical reasoning about ratios in designing effective gear systems. When they did reason about gear relationships, they worked with "qualitative" ratios, e.g., "a larger driver gear with a smaller driven gear increases the speed." In terms of the third notion of integrated learning, there was evidence in all four case study students of the psychological processes involved in linking mathematical, scientific, and/or technological concepts together to achieve new conceptual units. The students not only made connections between ideas and experiences, but also recognized decisive patterns and relationships in their project work. The students with stronger overall project performances showed more evidence of synthesis than the students with relatively weaker performances did. The findings support the conclusion that all three
Visual arts and the teaching of the mathematical concepts of shape and space in Grade R classrooms
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Dianne Wilmot
2015-09-01
Full Text Available This article addresses the need for research in the areas of Grade R curriculum and pedagogy, Grade R teacher professional development, and early years mathematics teaching. More specifically, it responds to the need for teacher professional development in Grade R mathematics teaching of the geometric concepts of space and shape. The article describes a study about teachers’ understanding of how visual arts can be used as pedagogical modality. The study was prompted by the findings of a ‘Maths and Science through Arts and Culture Curriculum’ intervention undertaken with Grade R teachers enrolled for a Bachelor of Education (Foundation Phase degree at a South African university. Post-intervention, teachers’ classroom practices did not change, and they were not using visual arts to teach mathematical concepts. The lessons learned from the research intervention may contribute to the wider debate about Grade R teaching and children’s learning.
Gultepe, Nejla; Yalcin Celik, Ayse; Kilic, Ziya
2013-01-01
The purpose of the study was to examine the effects of students' conceptual understanding of chemical concepts and mathematical processing skills on algorithmic problem-solving skills. The sample (N = 554) included grades 9, 10, and 11 students in Turkey. Data were collected using the instrument "MPC Test" and with interviews. The MPC…
Qudah, Ahmad Hassan
2016-01-01
This study aimed at identify the effect of using a proposed teaching strategy based on the selective thinking in acquire mathematical concepts by Classroom Teacher Students at Al- al- Bayt University, The sample of the study consisted of (74) students, equally distributed into a control group and an experimental group. The selective thinking…
Kombe, Dennis; Che, S. Megan; Carter, Traci L.; Bridges, William
2016-01-01
In this article, we present findings from a study that investigated the relationship between all-girls classes, all-boys classes, and coeducational classes on student mathematics self-concept and student perception of classroom environment. Further, we compared responses of girls in all-girls classes to girls in coeducational classes and responses…
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
Discourses of power in mathematics education research: Concepts and possibilities for action
DEFF Research Database (Denmark)
Valero, Paola
2008-01-01
Mathematics education is powerful. This is an assertion that appears often in mathematics education research papers. However, the meaning of the assertion is far from being clear. An analysis of different ways of talking about power in relation to mathematics education, in research literature, is...
Jackson, Christa; Jong, Cindy
2017-01-01
Teaching mathematics for equity is critical because it provides opportunities for all students, especially those who have been traditionally marginalised, to learn mathematics that is rigorous and relevant to their lives. This article reports on our work, as mathematics teacher educators, on exposing and engaging 60 elementary preservice teachers…
Qudah, Ahmad Hassan
2016-01-01
The study aimed to detect the effect of using an educational site on the Internet in the collection of bachelor's students in the course of basic concepts in mathematics at Al al-Bayt University, and the study sample consisted of all students in the course basic concepts in mathematics in the first semester of the academic year 2014/2015 and the…
International Nuclear Information System (INIS)
Demazure, M.
1988-01-01
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
Concept of Gender and Mathematics Education Conceito de Gênero e Educação Matemática
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Maria Celeste Reis Fernandes de Souza
2009-04-01
Full Text Available The text presents the emergence of the concept of gender in education, showing its different nuances, and proposes its incorporation as a category of analysis in the field of Mathematics Education, in which the discussions on gender are rarely detected, especially when we analyze the Brazilian production. Taking as references the female scholars in the field of gender studies, we have reflected on the need of incorporating such concept into the investigation about the processes of teaching and learning Mathematics, the subjects in the pedagogical relations, and the cultural mode of conceiving, using and evaluating mathematical knowledge. Such incorporation would imply, however, the disruption in the ways in which we have thought concepts related to female, male and mathematics. Keywords: Gender. Mathematics Education. Research.O texto expõe a emergência do conceito de gênero no campo da educação, mostrando suas diferentes nuances, e propõe sua incorporação como uma categoria de análise no campo da Educação Matemática, no qual as discussões sobre gênero aparecem muito raramente, especialmente quando se analisa a produção brasileira. Tomando como referência estudiosas do campo dos estudos de gênero, refletimos sobre a necessidade da incorporação de tal conceito às investigações sobre os processos de ensino e aprendizagem da Matemática, sobre os sujeitos das relações pedagógicas e sobre os modos culturais de se conceber, utilizar e avaliar conhecimentos matemáticos. Tal incorporação implicaria, porém, deslocamentos nos modos como temos pensado femininos, masculinos e matemática. Palavras-chave: Gênero. Educação Matemática. Pesquisa.
Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts
Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep
2016-01-01
The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…
Applying Mathematical Concepts with Hands-On, Food-Based Science Curriculum
Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Geist, Eugene; Duffrin, Melani W.
2015-01-01
This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the…
Parker, Frieda; Bartell, Tonya Gau; Novak, Jodie D.
2017-01-01
Research advances in teaching, learning, curriculum, and assessment have not changed the continued underperformance of marginalized students in mathematics education. Culturally responsive teaching is a means of addressing the needs of these students. It is sometimes challenging, however, to convince secondary mathematics teachers about the…
Bernhard Riemann 1826-1866 Turning Points in the Conception of Mathematics
Laugwitz, Detlef
2008-01-01
The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemann’s work. Einstein’s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemann’s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics. This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hi...
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Morten Andersen
Full Text Available The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.
From Abstract Art to Abstracted Artists
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Romi Mikulinsky
2016-11-01
Full Text Available What lineage connects early abstract films and machine-generated YouTube videos? Hans Richter’s famous piece Rhythmus 21 is considered to be the first abstract film in the experimental tradition. The Webdriver Torso YouTube channel is composed of hundreds of thousands of machine-generated test patterns designed to check frequency signals on YouTube. This article discusses geometric abstraction vis-à-vis new vision, conceptual art and algorithmic art. It argues that the Webdriver Torso is an artistic marvel indicative of a form we call mathematical abstraction, which is art performed by computers and, quite possibly, for computers.
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Hanne Møller Andersen
2010-04-01
Full Text Available Previous studies have found core teaching conceptions (CTCs to influence teachers’ actions, i.e. how they engage with new teaching practices (e.g. Lotter, Harwood, & Bonner, 2007. This study explores typical CTCs and their subject specific nature in a sample of teachers from physics, biology, and mathematics in Danish upper secondary school. Teachers’ CTCs were investigated through their essay responses to a set of open core questions, administered through a web-platform. Results demonstrate that teachers’ CTCs come in subject specific flavours, encompassing their purpose for teaching the subject, their conceptions of teaching and learning, and their conceptions of interdisciplinary teaching. It is argued that such differences shape teachers’ engagement with new cross-curricular innovations in the Danish context. Assessing and addressing typical and personal CTCs are found to be crucial to a successful implementation of current reform-initiatives, for teacher training, and for self-regulated professional development among teachers.
Discrete mathematics using a computer
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...
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Михаил Владимирович Боровиков
2012-12-01
Full Text Available Architectural concept of multifunctional information and educational center and its implementation is given in the author's project. Advanced information technology and mathematical models used in the development of the author project.
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Clélia Maria Ignatius Nogueira
2008-10-01
Full Text Available Piaget assumes that reflexive (réfléchissante abstraction is the process by which mathematical knowledge is produced. The aim of this article is to confirm to identify the presence of the reflexive abstraction or its components (réfléchissement and reflection in mathematicians description of the way they produce mathematical new knowledge as well as to discuss possible pedagogical implications of this process in Mathematics classrooms. Keywords: Mathematical education. Reflexive abstraction. Mathematical knowledge.Piaget afirma que a abstração reflexionante é o processo por excelência de produção do conhecimento matemático. Este trabalho teve por objetivo identificar a presença da abstração reflexionante ou de seus componentes (reflexionamento e reflexão na descrição que matemáticos fazem da forma como produzem novos conhecimentos e discutir possíveis implicações pedagógicas deste processo nas aulas de Matemática. Palavras-chave: Educação Matemática. Abstração reflexionante. Conhecimento matemático.
The deleuzian abstract machines
DEFF Research Database (Denmark)
Werner Petersen, Erik
2005-01-01
To most people the concept of abstract machines is connected to the name of Alan Turing and the development of the modern computer. The Turing machine is universal, axiomatic and symbolic (E.g. operating on symbols). Inspired by Foucault, Deleuze and Guattari extended the concept of abstract...
Böhm, Arno; Koizumi, Hiroyasu; Niu, Qian; Zwanziger, Joseph
2003-01-01
Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics) The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them
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.
Sierpinska, Anna
1994-01-01
The concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students'' understanding of the mathematics being taught.
Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A.; Bell, Ellis
2013-01-01
Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry,…
Influence of TANDUR Learning to Students's Mathematical Representation and Student Self-Concept
Directory of Open Access Journals (Sweden)
Dimas Fajar Maulana
2017-11-01
study is all students of class X which amounted to 350 students in one of the SMA Negeri in Cirebon city. From the population is taken the sample using simple random sampling technique as many as 60 students are divided into two groups namely groups who get TANDUR learning and groups that get conventional learning. The results showed that the TANDUR learning model had an effect of 66.9% on the selfconcept of the students, while the students' mathematical representation ability was 75.5%. Meanwhile, the correlation between selfconcept and student's mathematical representation is 74,3%.
International Nuclear Information System (INIS)
Whitaker, A
2004-01-01
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. To commence with general discussion of the new book, the authors recognise that the graduate student of today almost certainly has substantial experience of wave mechanics, and is probably familiar with the Dirac formalism. The new edition has been almost entirely rewritten; even at the level of basic text, it is difficult to trace sentences or paragraphs that have moved unscathed from one edition to the next. As well as the new topics, many of the old ones are discussed in much greater depth, and the general organisation is entirely different. As compared with the steady rise in level of the 1966 edition, the level of this book is fairly consistent throughout, and from the perspective of a beginning graduate student, I would estimate, a little tough. To sum up, Gottfried and Yan's book contains a vast amount of knowledge and understanding. The
Archambeault, Betty
1993-01-01
Holistic math focuses on problem solving with numbers and concepts. Whole math activities for adults include shopping for groceries, eating in restaurants, buying gas, taking medicine, measuring a room, estimating servings, and compiling a family cookbook. (SK)
Fundamental concepts of abstract algebra
Ehrlich, Gertrude
2012-01-01
This undergraduate text presents extensive coverage of set theory, groups, rings, modules, vector spaces, and fields. It offers numerous examples, definitions, theorems, proofs, and practice exercises. 1991 edition.
THE CONCEPT OF THE EDUCATIONAL COMPUTER MATHEMATICS SYSTEM AND EXAMPLES OF ITS IMPLEMENTATION
Directory of Open Access Journals (Sweden)
M. Lvov
2014-11-01
Full Text Available The article deals with the educational computer mathematics system, based in Kherson State University and resulted in more than 8 software tools to orders of the Ministry of Education, Science, Youth and Sports of Ukraine. The exact and natural sciences are notable among all disciplines both in secondary schools and universities. They form the fundamental scientific knowledge, based on precise mathematical models and methods. The educational process for these courses should include not only lectures and seminars, but active forms of studying as well: practical classes, laboratory work, practical training, etc. The enumerated peculiarities determine specific intellectual and architectural properties of information technologies, developed to be used in the educational process of these disciplines. Whereas, in terms of technologies used in the implementation of the functionality of software, they are actually the educational computer algebra system. Thus the algebraic programming system APS developed in the Institute of Cybernetics of the National Academy of Sciences of Ukraine led by Academician O.A. Letychevskyi in the 80 years of the twentieth century is especially important for their development.
The Critical Concepts. Final Version: English Language Arts, Mathematics, and Science
Simms, Julia A.
2016-01-01
Research indicates that most standards documents articulate far more content than can be taught in the time available to K-12 teachers. In response, analysts at Marzano Research sought to identify, as objectively as possible, a focused set of critical concepts for each K-12 grade level in the content areas of English language arts (ELA),…
KONTRIBUSI SELF CONCEPT MATEMATIS DAN MATHEMATICS ANXIETY TERHADAP HASIL BELAJAR MAHASISWA
Directory of Open Access Journals (Sweden)
Aan Subhan Pamungkas
2015-05-01
Full Text Available Penelitian ini mengkaji hubungan antara self concept dan kecemasan matematika dengan hasil belajar mahasiswa tingkat awal. Penelitian ini didasari oleh sebagian besar mahasiswa awal program studi pendidikan matematika masih merasa cemas ketika berhadapan dengan persoalan matematika dalam mata kuliah kalkulus I, selain itu dilihat dari performa mahasiswa ketika menyelesaikan persoalan matematika timbulnya rasa tidak pecaya diri atas kemampuan yang dimilikinya. Sehingga ketika akan menyelesaikan persoalan mahasiswa selalu bergantung kepada temannya, dengan tujuan memperoleh keyakinan atas jawabannya. Metode penelitian yang digunakan dalam penelitian ini adalah metode korelasional, metode ini digunakan untuk melihat seberapa kuat dan seberapa besar pengaruh self concept dan kecemasan matematika dengan hasil belajar mahasiswa. Populasi dalam penelitian ini adalah seluruh mahasiswa program studi pendidikan matematika tahun akademik 2013/2014, sampel penelitian diambil dengan teknik purposive sampling sebanyak 88 mahasiswa yang mengontrak mata kuliah Kalkulus I. Instrument yang digunakan dalam penelitian ini adalah skala self concept matematis dan skala kecemasan matematika. Hasil penelitian menunjukkan bahwa terdapat hubungan yang positif antara self concept dan kecemasan terhadap matematika dengan hasil belajar mahasiswa.DOI: http://dx.doi.org/10.22342/jpm.9.1.2191.01 - 10
Infinity as a Multi-Faceted Concept in History and in the Mathematics Classroom
Arzarello, Ferdinando; Bussi, Maria G., Bartolini; Robutti, Ornella
2004-01-01
This paper presents the conceptualisation of infinity as a multi-faceted concept, discussing two examples. The first is from history and illustrates the work of Euler, when using infinity in an algebraic context. The second sketches an activity in a school context, namely students who approach the definite integral with symbolic-graphic…
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…
TEACHERS WHO TEACH MATHEMATICS IN ADULT EDUCATION: CONCEPTS AND TEACHING PRACTICES
Directory of Open Access Journals (Sweden)
Andréa Thees
2012-12-01
Full Text Available This work represents a subset of a Masters’ research, which investigated how the pedagogical and non-pedagogical professional practices of mathematics teachers who teach in adult education are developed. In this paper we present the curricular management practices, tasks and materials, communication and evaluation. Through a case study of the daily activities of three math teachers who teach young people and adults, a qualitative research was developed, whose investigative tools were field observations, semi-structured interviews and questionnaires. Our study indicated that curriculum management practices are determined by a straightforward exposition teaching style, based on problem solving. Regarding the proposed tasks, teachers do not resort to learning materials other than blackboard and chalk, and rarely use the textbook. Communication in the classroom is univocal, sometimes supplemented by inadequate metaphors, especially in the teaching of algebra. The practices of student evaluation are predominantly focused on the summative function.
Gorter, Gerrit F.; Amsing, Hilda T. A.; Dekker, Jeroen J. H.
2016-01-01
Essential Economics, the influential economics education textbook written by Arnold Heertje for use in Dutch secondary schools in the 1970s, was characterized by a previously unknown and internationally exceptional degree of abstraction. Its users justified this degree of abstraction by arguing that it fulfilled the needs of mental schooling (in…
Energy Technology Data Exchange (ETDEWEB)
Kuebler, Knut
2013-01-15
The German federal government has laid down 30 quantitative goals in its energy concept and in doing so has determined the road to Germany's future energy supply system. One target which will be decisive for the success or failure of the energy turnaround, little discussed though it may be, is for Germany to lower its use of primary energy by 50% in the time from 2008 to 2050. In order to achieve this and other goals the federal government is pursuing a policy for a ''state-programmed energy supply''. The implications of this policy can easily be derived by performing some basic as well as more intricate calculations on the figures given in the energy concept. On doing so one finds that the energy concept has decided on the fate of every single energy carrier. It also becomes clear that rising energy prices will not only be a consequence but in fact a prerequisite for the success of the energy turnaround. This article advocates an energy policy that will permit changes of course if new facts and figures should so demand without departing from its overarching goals.
Directory of Open Access Journals (Sweden)
Ирина Викторовна Кузнецова
2012-12-01
Full Text Available The paper proposes the concept of learning activities in online communities for teaching algebraic structures of the future teachers of mathematics, including a set of theoretical and methodological positions, laws, principles, factors, and pedagogical conditions of its implementation. Work is executed with support of the Russian fund of basic researches under the initiative project № 11-07-00733 «The Hypertext information retrieval thesaurus» a science Meta language» (structure; mathematical, linguistic and program maintenance; sections linguistics, mathematics, economy».
DEFF Research Database (Denmark)
Andersen, Morten; Sajid, Zamra; Pedersen, Rasmus K.
2017-01-01
The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs.......The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks...... or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal...
Nurhayati, Dian Mita; Hartono
2017-05-01
This study aims to determine whether there is a difference in the ability of understanding the concept of mathematics between students who use cooperative learning model Student Teams Achievement Division type with Realistic Mathematic Education approach and students who use regular learning in seventh grade SMPN 35 Pekanbaru. This study was quasi experiments with Posttest-only Control Design. The populations in this research were all the seventh grade students in one of state junior high school in Pekanbaru. The samples were a class that is used as the experimental class and one other as the control class. The process of sampling is using purposive sampling technique. Retrieval of data in this study using the documentation, observation sheets, and test. The test use t-test formula to determine whether there is a difference in student's understanding of mathematical concepts. Before the t-test, should be used to test the homogeneity and normality. Based in the analysis of these data with t0 = 2.9 there is a difference in student's understanding of mathematical concepts between experimental and control class. Percentage of students experimental class with score more than 65 was 76.9% and 56.4% of students control class. Thus be concluded, the ability of understanding mathematical concepts students who use the cooperative learning model type STAD with RME approach better than students using the regular learning. So that cooperative learning model type STAD with RME approach is well used in learning process.
Mathematics and art a cultural history
Gamwell, Lynn
2016-01-01
This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell’s comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians’ search for the foundations of their science, such as David Hilbert’s conception of mathematics as an arrangement of meaning-free signs, as well as artists’ search for the essence of their craft, such as Aleksandr Rodchenko’s monochrome paintings. She shows t...
Andreescu, Titu; Tetiva, Marian
2017-01-01
Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...
Stout, Jane G; Dasgupta, Nilanjana; Hunsinger, Matthew; McManus, Melissa A
2011-02-01
Three studies tested a stereotype inoculation model, which proposed that contact with same-sex experts (advanced peers, professionals, professors) in academic environments involving science, technology, engineering, and mathematics (STEM) enhances women's self-concept in STEM, attitudes toward STEM, and motivation to pursue STEM careers. Two cross-sectional controlled experiments and 1 longitudinal naturalistic study in a calculus class revealed that exposure to female STEM experts promoted positive implicit attitudes and stronger implicit identification with STEM (Studies 1-3), greater self-efficacy in STEM (Study 3), and more effort on STEM tests (Study 1). Studies 2 and 3 suggested that the benefit of seeing same-sex experts is driven by greater subjective identification and connectedness with these individuals, which in turn predicts enhanced self-efficacy, domain identification, and commitment to pursue STEM careers. Importantly, women's own self-concept benefited from contact with female experts even though negative stereotypes about their gender and STEM remained active. (PsycINFO Database Record (c) 2010 APA, all rights reserved).
An introduction to abstract algebra
Robinson, Derek JS
2003-01-01
This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader''s skill and progress. The book should be suitable for students ...
M3 version 3.0: Concepts, methods, and mathematical formulation
Energy Technology Data Exchange (ETDEWEB)
Gomez, Javier B. [Univ. of Zaragoza (Spain). Dept. of Earth Sciences; Laaksoharju, Marcus [Geopoint AB, Sollentuna (Sweden); Skaarman, Erik [Abscondo, Bromma (Sweden); Gurban, Ioana [3D-Terra, Montreal, PQ (Canada)
2006-07-15
Hydrochemical evaluation is a complex type of work, carried out by specialists. The outcome of this work is generally presented as qualitative models and process descriptions of a site. To support and help quantify the processes in an objective way, a multivariate mathematical tool named M (Multivariate Mixing and Mass balance calculations) has been constructed. The computer code can be used to trace the origin of the groundwater and calculate the mixing portions and mass balances even from ambiguous groundwater data. The groundwater composition used traditionally to describe the reactions taking place in the bedrock can now be used to trace the present and past groundwater flow with increased accuracy. The M code is a groundwater response model, which means that the changes in the groundwater chemistry in terms of sources and sinks are traced in relation to an ideal mixing model. The complexity of the measured groundwater data determines the configuration of the ideal mixing model. Deviations or similarities with the ideal mixing model are interpreted as being due to mixing or reactions. Assumptions concerning important mineral phases altering the groundwater or uncertainties associated with thermodynamic constants do not affect the modelling because the calculations are solely based on the measured groundwater composition. M uses the opposite approach to that of many standard hydrochemical models. In M mixing is evaluated and calculated first. The constituents that cannot be described by mixing are described by reactions. The M model consists of three steps: the first is a standard principal component analysis, followed by mixing and finally mass balance calculations. The measured groundwater composition can be described in terms of mixing portions in % and the sink/sources of an element associated with reactions are reported in mg/l.
M3 version 3.0: Concepts, methods, and mathematical formulation
International Nuclear Information System (INIS)
Gomez, Javier B.; Skaarman, Erik; Gurban, Ioana
2006-07-01
Hydrochemical evaluation is a complex type of work, carried out by specialists. The outcome of this work is generally presented as qualitative models and process descriptions of a site. To support and help quantify the processes in an objective way, a multivariate mathematical tool named M (Multivariate Mixing and Mass balance calculations) has been constructed. The computer code can be used to trace the origin of the groundwater and calculate the mixing portions and mass balances even from ambiguous groundwater data. The groundwater composition used traditionally to describe the reactions taking place in the bedrock can now be used to trace the present and past groundwater flow with increased accuracy. The M code is a groundwater response model, which means that the changes in the groundwater chemistry in terms of sources and sinks are traced in relation to an ideal mixing model. The complexity of the measured groundwater data determines the configuration of the ideal mixing model. Deviations or similarities with the ideal mixing model are interpreted as being due to mixing or reactions. Assumptions concerning important mineral phases altering the groundwater or uncertainties associated with thermodynamic constants do not affect the modelling because the calculations are solely based on the measured groundwater composition. M uses the opposite approach to that of many standard hydrochemical models. In M mixing is evaluated and calculated first. The constituents that cannot be described by mixing are described by reactions. The M model consists of three steps: the first is a standard principal component analysis, followed by mixing and finally mass balance calculations. The measured groundwater composition can be described in terms of mixing portions in % and the sink/sources of an element associated with reactions are reported in mg/l
Belkić, Dževad; Belkić, Karen
2015-06-01
Magnetic resonance (MR)-based modalities aid breast cancer detection without exposure to ionizing radiation. Magnetic resonance imaging is very sensitive but costly and insufficiently specific. Molecular imaging through magnetic resonance spectroscopy (MRS) can provide information about key metabolites. Here, the measured/encoded time signals cannot be interpreted directly, necessitating mathematics for mapping to the more manageable frequency domain. Conventional applications of MRS are hampered by data analysis via the fast Fourier transform (FFT) and postprocessing by fitting techniques. Most in vivo MRS studies on breast cancer rely upon estimations of total choline (tCHO). These have yielded only incremental improvements in diagnostic accuracy. In vitro studies reveal richer metabolic information for identifying breast cancer, particularly in closely overlapping components of tCHO. Among these are phosphocholine (PC), a marker of malignant transformation of the breast. The FFT cannot assess these congested spectral components. This can be done by the fast Padé transform (FPT), a high-resolution, quantification-equipped method, which we presently apply to noisy MRS time signals consistent with those encoded in breast cancer. The FPT unequivocally and robustly extracted the concentrations of all physical metabolites, including PC. In sharp contrast, the FFT produced a rough envelope spectrum with a few distorted peaks and key metabolites absent altogether. As such, the FFT has poor resolution for these typical MRS time signals from breast cancer. Hence, based on Fourier-estimated envelope spectra, tCHO estimates are unreliable. Using even truncated time signals, the FPT clearly distinguishes noise from true metabolites whose concentrations are accurately extracted. The high resolution of the FPT translates directly into shortened examination time of the patient. These capabilities strongly suggest that by applying the FPT to time signals encoded in vivo from
International Nuclear Information System (INIS)
Morell, Morell; Todorovik, Olivija; Dimitrov, Dobri
2004-01-01
BALWOIS 2004 is supported by the European Commission, Ministry of Education and Science of Republic of Macedonia, French Embassy in Macedonia and the International Association of Hydrological Sciences. BALWOIS Conference is prepared by l'Institut de Recherche pour le Developpement (IRD - Montpellier - France) and the Meteorological Association of the Republic of Macedonia (METEO MAK) with the kind support of the Hydro meteorological Services of Macedonia, Hydro biological Institute of Ohrid, National Hydro meteorological Institutes of Albania and Bulgaria, and the Municipality of Ohrid as well. Its international shared waters (rivers, lakes and groundwater tables) make this area an earth of challenges to apply the well known concept of Integrated Water Resources Management in a context of regional climate changes and anthropogenic pressures on environment. The role of a water observation and information system for decision support is to enhance the links between research institutions and operational centres, to help the decision makers and all water actors as well as to disseminate to large public useful information on related water issues. The main objectives of BALWOIS are to encourage scientific exchanges between researchers coming from Balkan institutions and to offer them opportunities to improve their networking at European and global level. Ohrid is one of the most welcoming towns of Republic of Macedonia with a very significant cultural heritage. Nobody would contest that Ohrid Lake - 358 km 2 , several millions years old and surrounded by splendid Macedonian and Albanian mountains - is among the most beautiful lakes of Europe. Together Ohrid and Prespa lakes and their environments offer a large biodiversity with endemic species. The location of the conference on the shore of Ohrid lake is particularly well chosen to work on topics linked with climate change which already affects the balance of the lakes, protection of the biodiversity against increasing
Directory of Open Access Journals (Sweden)
Tatag Bagus Argikas
2016-10-01
Full Text Available This research aims to: (1 describe the implementation of learning mathematics with Reciprocal Teaching methods that is for improving the concept of learning understanding mathematic in class VIIA SMP Negeri 2 Depok. (2 Knowing the increased understanding of student learning in class VIIA SMP Negeri 2 Depok use Reciprocal Teaching methods. This research constitutes an action in class that is according along the teacher. The data of research was collated by sheet observations and each evaluation of cycles. That is done in two cycles. The first was retrieved the average value of student learning achievement of 70.96%. The second was retrieved achievement of 90.32%. Thus this learning model can increase student learning understanding. Key word: The understanding of Mathematical Concept, Reciprocal Teaching Method.
Garza, Jennifer M.
2017-01-01
The purpose of this study is to inform and further the discussion of academic (i.e., teachers and school counselors) and non-academic (i.e., parents, family, friends, etc.) validating agents on Latina students' mathematics and science self-concepts. This study found a relationship between Latina students' interactions with academic and…
Moseley, Rachel L; Pulvermüller, Friedemann
2018-03-01
Within the neurocognitive literature there is much debate about the role of the motor system in language, social communication and conceptual processing. We suggest, here, that autism spectrum conditions (ASC) may afford an excellent test case for investigating and evaluating contemporary neurocognitive models, most notably a neurobiological theory of action perception integration where widely-distributed cell assemblies linking neurons in action and perceptual brain regions act as the building blocks of many higher cognitive functions. We review a literature of functional motor abnormalities in ASC, following this with discussion of their neural correlates and aberrancies in language development, explaining how these might arise with reference to the typical formation of cell assemblies linking action and perceptual brain regions. This model gives rise to clear hypotheses regarding language comprehension, and we highlight a recent set of studies reporting differences in brain activation and behaviour in the processing of action-related and abstract-emotional concepts in individuals with ASC. At the neuroanatomical level, we discuss structural differences in long-distance frontotemporal and frontoparietal connections in ASC, such as would compromise information transfer between sensory and motor regions. This neurobiological model of action perception integration may shed light on the cognitive and social-interactive symptoms of ASC, building on and extending earlier proposals linking autistic symptomatology to motor disorder and dysfunction in action perception integration. Further investigating the contribution of motor dysfunction to higher cognitive and social impairment, we suggest, is timely and promising as it may advance both neurocognitive theory and the development of new clinical interventions for this population and others characterised by early and pervasive motor disruption. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights
Saidi, Trust; Sigauke, Esther
2017-10-01
Nanotechnology is an emerging technology, and it is regarded as the basis for the next industrial revolution. In developing countries, nanotechnology promises to solve everyday challenges, such as the provision of potable water, reliable energy sources and effective medication. However, there are several challenges in the exploitation of nanotechnology. One of the notable challenges is the lack of adequate knowledge about how materials behave at the nanoscale. As nanotechnology is relatively new, the current generation of scientists have not had the opportunity to learn the fundamentals of the technology at an early stage. Young students who are at the primary school level may follow the same trajectory if they are not exposed to the technology. There is a need to lay a strong foundation by introducing nanoscience and nanotechnology to students at the primary school level. It is during the early stages of child development that students master basic concepts for life long learning. Nevertheless, many primary school children, particularly those in developing countries are missing the chance of learning about nanoscience and nanotechnology because it is regarded as being abstract and complex. In this paper, we argue that despite the complexity of nanoscience and nanotechnology, science centres can be used as one of the platforms for exposing young students to the discipline. We use a case study of a museum-based science centre as an example to illustrate that young students can be exposed to nanoscience and nanotechnology using tactile and hands-on experience. The early engagement of primary school children with nanoscience and nanotechnology is important in raising the next generation of scientists who are firmly grounded in the discipline.
Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.
2015-01-01
Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…
Garrett, Paul B
2007-01-01
Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal
On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics
Kalanov, Temur Z.
2016-03-01
Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.
Artificial Intelligence, Computational Thinking, and Mathematics Education
Gadanidis, George
2017-01-01
Purpose: The purpose of this paper is to examine the intersection of artificial intelligence (AI), computational thinking (CT), and mathematics education (ME) for young students (K-8). Specifically, it focuses on three key elements that are common to AI, CT and ME: agency, modeling of phenomena and abstracting concepts beyond specific instances.…
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
African Journals Online (AJOL)
Abstract. Simple learning tools to improve clinical laboratory practical skills training. B Taye, BSc, MPH. Addis Ababa University, College of Health Sciences, Addis Ababa, ... concerns about the competence of medical laboratory science graduates. ... standardised practical learning guides and assessment checklists would.
Owre, Sam; Shankar, Natarajan
1997-01-01
PVS (Prototype Verification System) is a general-purpose environment for developing specifications and proofs. This document deals primarily with the abstract datatype mechanism in PVS which generates theories containing axioms and definitions for a class of recursive datatypes. The concepts underlying the abstract datatype mechanism are illustrated using ordered binary trees as an example. Binary trees are described by a PVS abstract datatype that is parametric in its value type. The type of ordered binary trees is then presented as a subtype of binary trees where the ordering relation is also taken as a parameter. We define the operations of inserting an element into, and searching for an element in an ordered binary tree; the bulk of the report is devoted to PVS proofs of some useful properties of these operations. These proofs illustrate various approaches to proving properties of abstract datatype operations. They also describe the built-in capabilities of the PVS proof checker for simplifying abstract datatype expressions.
The origin of the logic of symbolic mathematics Edmund Husserl and Jacob Klein
Hopkins, Burt C
2011-01-01
Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts-especially mathematical concepts and the process of mathematical abstraction that generates them-have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.
Jothi, A Lenin
2009-01-01
Financial services, particularly banking and insurance services is the prominent sector for the development of a nation. After the liberalisation of financial sector in India, the scope of getting career opportunities has been widened. It is heartening to note that various universities in India have introduced professional courses on banking and insurance. A new field of applied mathematics has come into prominence under the name of Financial Mathematics. Financial mathematics has attained much importance in the recent years because of the role played by mathematical concepts in decision - m
Abstract algebra for physicists
International Nuclear Information System (INIS)
Zeman, J.
1975-06-01
Certain recent models of composite hadrons involve concepts and theorems from abstract algebra which are unfamiliar to most theoretical physicists. The algebraic apparatus needed for an understanding of these models is summarized here. Particular emphasis is given to algebraic structures which are not assumed to be associative. (2 figures) (auth)
Sumpter, Lovisa
2016-01-01
Previous results show that Swedish upper secondary school teachers attribute gender to cases describing different types of mathematical reasoning. The purpose of this study was to investigate how these teachers gender stereotype aspects of students' mathematical reasoning by studying the symbols that were attributed to boys and girls,…
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…
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...
International Nuclear Information System (INIS)
Leigh, C.
2000-01-01
The purpose of the inventory abstraction as directed by the development plan (CRWMS M and O 1999b) is to: (1) Interpret the results of a series of relative dose calculations (CRWMS M and O 1999c, 1999d). (2) Recommend, including a basis thereof, a set of radionuclides that should be modeled in the Total System Performance Assessment in Support of the Site Recommendation (TSPA-SR) and the Total System Performance Assessment in Support of the Final Environmental Impact Statement (TSPA-FEIS). (3) Provide initial radionuclide inventories for the TSPA-SR and TSPA-FEIS models. (4) Answer the U.S. Nuclear Regulatory Commission (NRC)'s Issue Resolution Status Report ''Key Technical Issue: Container Life and Source Term'' (CLST IRSR) (NRC 1999) key technical issue (KTI): ''The rate at which radionuclides in SNF [Spent Nuclear Fuel] are released from the EBS [Engineered Barrier System] through the oxidation and dissolution of spent fuel'' (Subissue 3). The scope of the radionuclide screening analysis encompasses the period from 100 years to 10,000 years after the potential repository at Yucca Mountain is sealed for scenarios involving the breach of a waste package and subsequent degradation of the waste form as required for the TSPA-SR calculations. By extending the time period considered to one million years after repository closure, recommendations are made for the TSPA-FEIS. The waste forms included in the inventory abstraction are Commercial Spent Nuclear Fuel (CSNF), DOE Spent Nuclear Fuel (DSNF), High-Level Waste (HLW), naval Spent Nuclear Fuel (SNF), and U.S. Department of Energy (DOE) plutonium waste. The intended use of this analysis is in TSPA-SR and TSPA-FEIS. Based on the recommendations made here, models for release, transport, and possibly exposure will be developed for the isotopes that would be the highest contributors to the dose given a release to the accessible environment. The inventory abstraction is important in assessing system performance because
International Nuclear Information System (INIS)
Ragan, G.
2001-01-01
The purpose of the inventory abstraction, which has been prepared in accordance with a technical work plan (CRWMS M andO 2000e for/ICN--02 of the present analysis, and BSC 2001e for ICN 03 of the present analysis), is to: (1) Interpret the results of a series of relative dose calculations (CRWMS M andO 2000c, 2000f). (2) Recommend, including a basis thereof, a set of radionuclides that should be modeled in the Total System Performance Assessment in Support of the Site Recommendation (TSPA-SR) and the Total System Performance Assessment in Support of the Final Environmental Impact Statement (TSPA-FEIS). (3) Provide initial radionuclide inventories for the TSPA-SR and TSPA-FEIS models. (4) Answer the U.S. Nuclear Regulatory Commission (NRC)'s Issue Resolution Status Report ''Key Technical Issue: Container Life and Source Term'' (CLST IRSR) key technical issue (KTI): ''The rate at which radionuclides in SNF [spent nuclear fuel] are released from the EBS [engineered barrier system] through the oxidation and dissolution of spent fuel'' (NRC 1999, Subissue 3). The scope of the radionuclide screening analysis encompasses the period from 100 years to 10,000 years after the potential repository at Yucca Mountain is sealed for scenarios involving the breach of a waste package and subsequent degradation of the waste form as required for the TSPA-SR calculations. By extending the time period considered to one million years after repository closure, recommendations are made for the TSPA-FEIS. The waste forms included in the inventory abstraction are Commercial Spent Nuclear Fuel (CSNF), DOE Spent Nuclear Fuel (DSNF), High-Level Waste (HLW), naval Spent Nuclear Fuel (SNF), and U.S. Department of Energy (DOE) plutonium waste. The intended use of this analysis is in TSPA-SR and TSPA-FEIS. Based on the recommendations made here, models for release, transport, and possibly exposure will be developed for the isotopes that would be the highest contributors to the dose given a release
Fujita, Shinsaku
2015-01-01
Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. A new stereoisogram approach, developed by the author, is introduced in this book, providing a theoretical framework for mathematical aspects of modern stereochemistry. The discussion covers point-groups and permutation symmetry and exemplifies the concepts using organic molecules and inorganic complexes.
Teaching abstraction in introductory courses
Koppelman, Herman; van Dijk, Betsy
Abstraction is viewed as a key concept in computer science. It is not only an important concept but also one that is difficult to master. This paper focuses on the problems that novices experience when they first encounter this concept. Three assignments from introductory courses are analyzed, to
What is the problem in problem-based learning in higher education mathematics
Dahl, Bettina
2018-01-01
Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.
Metaphor: Bridging embodiment to abstraction.
Jamrozik, Anja; McQuire, Marguerite; Cardillo, Eileen R; Chatterjee, Anjan
2016-08-01
Embodied cognition accounts posit that concepts are grounded in our sensory and motor systems. An important challenge for these accounts is explaining how abstract concepts, which do not directly call upon sensory or motor information, can be informed by experience. We propose that metaphor is one important vehicle guiding the development and use of abstract concepts. Metaphors allow us to draw on concrete, familiar domains to acquire and reason about abstract concepts. Additionally, repeated metaphoric use drawing on particular aspects of concrete experience can result in the development of new abstract representations. These abstractions, which are derived from embodied experience but lack much of the sensorimotor information associated with it, can then be flexibly applied to understand new situations.
Virtual Manipulatives: Tools for Teaching Mathematics to Students with Learning Disabilities
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)…
Seaton, Marjorie; Parker, Philip; Marsh, Herbert W.; Craven, Rhonda G.; Yeung, Alexander Seeshing
2014-01-01
Research suggests that motivated students and those with high academic self-concepts perform better academically. Although substantial evidence supports a reciprocal relation between academic self-concept and achievement, there is less evidence supporting a similar relation between achievement goal orientations and achievement. There is also a…
A mathematics course for political and social research
Moore, Will H
2013-01-01
Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a ""math camp"" or a semester-long or yearlong course to acquire the necessary skills. Available textbooks are written for mathematics or economics majors, and fail to convey to students of political science and sociology the reasons for learning often-abstract mathematical concepts. A Mathematics Course for Political and Social Research fills this gap, providing both a primer for math novices in the social s
International Nuclear Information System (INIS)
Entsua-Mensah, C.
2004-01-01
This issue of the Ghana Science Abstracts combines in one publication all the country's bibliographic output in science and technology. The objective is to provide a quick reference source to facilitate the work of information professionals, research scientists, lecturers and policy makers. It is meant to give users an idea of the depth and scope and results of the studies and projects carried out. The scope and coverage comprise research outputs, conference proceedings and periodical articles published in Ghana. It does not capture those that were published outside Ghana. Abstracts reported have been grouped under the following subject areas: Agriculture, Biochemistry, Biodiversity conservation, biological sciences, biotechnology, chemistry, dentistry, engineering, environmental management, forestry, information management, mathematics, medicine, physics, nuclear science, pharmacy, renewable energy and science education
Abstracting Sequences: Reasoning That Is a Key to Academic Achievement.
Pasnak, Robert; Kidd, Julie K; Gadzichowski, K Marinka; Gallington, Debbie A; Schmerold, Katrina Lea; West, Heather
2015-01-01
The ability to understand sequences of items may be an important cognitive ability. To test this proposition, 8 first-grade children from each of 36 classes were randomly assigned to four conditions. Some were taught sequences that represented increasing or decreasing values, or were symmetrical, or were rotations of an object through 6 or 8 positions. Control children received equal numbers of sessions on mathematics, reading, or social studies. Instruction was conducted three times weekly in 15-min sessions for seven months. In May, the children taught sequences applied their understanding to novel sequences, and scored as well or better on three standardized reading tests as the control children. They outscored all children on tests of mathematics concepts, and scored better than control children on some mathematics scales. These findings indicate that developing an understanding of sequences is a form of abstraction, probably involving fluid reasoning, that provides a foundation for academic achievement in early education.
Medical physics 2013. Abstracts
International Nuclear Information System (INIS)
Treuer, Harald
2013-01-01
The proceedings of the medical physics conference 2013 include abstract of lectures and poster sessions concerning the following issues: Tele-therapy - application systems, nuclear medicine and molecular imaging, neuromodulation, hearing and technical support, basic dosimetry, NMR imaging -CEST (chemical exchange saturation transfer), medical robotics, magnetic particle imaging, audiology, radiation protection, phase contrast - innovative concepts, particle therapy, brachytherapy, computerized tomography, quantity assurance, hybrid imaging techniques, diffusion and lung NMR imaging, image processing - visualization, cardiac and abdominal NMR imaging.
An abstract approach to music.
Energy Technology Data Exchange (ETDEWEB)
Kaper, H. G.; Tipei, S.
1999-04-19
In this article we have outlined a formal framework for an abstract approach to music and music composition. The model is formulated in terms of objects that have attributes, obey relationships, and are subject to certain well-defined operations. The motivation for this approach uses traditional terms and concepts of music theory, but the approach itself is formal and uses the language of mathematics. The universal object is an audio wave; partials, sounds, and compositions are special objects, which are placed in a hierarchical order based on time scales. The objects have both static and dynamic attributes. When we realize a composition, we assign values to each of its attributes: a (scalar) value to a static attribute, an envelope and a size to a dynamic attribute. A composition is then a trajectory in the space of aural events, and the complex audio wave is its formal representation. Sounds are fibers in the space of aural events, from which the composer weaves the trajectory of a composition. Each sound object in turn is made up of partials, which are the elementary building blocks of any music composition. The partials evolve on the fastest time scale in the hierarchy of partials, sounds, and compositions. The ideas outlined in this article are being implemented in a digital instrument for additive sound synthesis and in software for music composition. A demonstration of some preliminary results has been submitted by the authors for presentation at the conference.
Mathematics for the nonmathematician
Kline, Morris
1967-01-01
Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.
Statistical Content in Middle Grades Mathematics Textbooks
Pickle, Maria Consuelo Capiral
2012-01-01
This study analyzed the treatment and scope of statistical concepts in four, widely-used, contemporary, middle grades mathematics textbook series: "Glencoe Math Connects," "Prentice Hall Mathematics," "Connected Mathematics Project," and "University of Chicago School Mathematics Project." There were three…
Implementing CRA with Secondary Students with Learning Disabilities in Mathematics
Witzel, Bradley S.; Riccomini, Paul J.; Schneider, Elke
2008-01-01
Students with learning disabilities struggle to acquire essential mathematical concepts and skills, especially at the secondary level. One effective approach to improving secondary math performance supported by research is the concrete-to-representational-to-abstract (CRA) sequence of instruction. Although CRA is an evidenced-based instructional…
Garza, Jennifer M.
The purpose of this study is to inform and further the discussion of academic (i.e. teachers and school counselors) and non-academic (i.e. parents, family, friends, etc.) validating agents on Latina students' mathematics and science self-concepts. This study found a relationship between Latina students' interactions with academic and non-academic validating agents and their math and science self-concept at the K-12 level. Through the review of the literature the researcher addresses identifiable factors and strategies that inform the field of education in the areas of validation theory, family characteristics, and access to STEM fields for Latina students. The researcher used an established instrument designed, administered, and validated through the National Center for Education Statistics (NCES). For purposes of this study, a categorical subset of participants who self-identified as being a Latina student was used. As a result, the total subset number in this study was N=1,882. To determine if academic and non-academic validating agents had an observable statistically significant relationship with Latina students' math and science self-concept, a series of one-way ANOVAs were calculated to compare differences in students' math and science self-concept based on academic and non-academic validating agents for the weighted sample of Latinas for the HLS:09 survey. A path analysis was also employed to assess the factors involved in Latina students' math and science self-concepts. The findings are consistent with previous research involving the influence that academic and non-academic validating agents have on the math and science self-concept of Latina students. The results indicated that students who had teachers that believed in the students, regardless of family background, social economic status or home environment influences had higher math and science self concepts than those who did not. Similarly, it was found that students who had counselors that set high
Misu, L.; Budayasa, I. K.; Lukito, A.
2018-01-01
This research is to describe metacognition profile of female and male mathematics’ pre-service teachers in understanding the concept of integral calculus. The subjects of this study are one female and 1 male mathematics’ pre-service teachers who have studied integral calculus. This research type is an explorative study with the qualitative approach. The main data collection of this research was obtained by using Interview technique. In addition, there are supporting data which is the result of the written work of research subjects (SP) in understanding the question of integral calculus. The results of this study are as follows: There is a difference in metacognition profiles between male and female mathematics’ pre-service teachers in the understanding concept of integral calculus in the interpreting category, especially the definite integral concept. While in the category of exemplifying, there is no difference in metacognition profile between male and female mathematics’ pre-service teachers either the definite integral concept and the indefinite integral concept.
Yakubova, Gulnoza; Hughes, Elizabeth M.; Shinaberry, Megan
2016-01-01
The purpose of this study was to determine the effectiveness of a video modeling intervention with concrete-representational-abstract instructional sequence in teaching mathematics concepts to students with autism spectrum disorder (ASD). A multiple baseline across skills design of single-case experimental methodology was used to determine the…
DEFF Research Database (Denmark)
Tamborg, Andreas Lindenskov
2018-01-01
Currently, digital learning platforms are being implemented in Danish elementary schools. These platforms are developed with a dual aim of both supporting teachers’ planning and classroom teaching. This paper investigates and discusses the opportunities of using the documentational approach to st...... to study Danish mathematics teachers’ use of these platforms for classroom teaching and preliminary findings here of in the context of an ongoing PhD project.......Currently, digital learning platforms are being implemented in Danish elementary schools. These platforms are developed with a dual aim of both supporting teachers’ planning and classroom teaching. This paper investigates and discusses the opportunities of using the documentational approach...
Wadsworth, A R
2017-01-01
This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.
Rust, Amanda L.
This study attempted to determine which teaching method, mainly manipulatives or the standard curriculum, best allowed the students to learn first grade math concepts. The manipulatives consisted of objects such as unifix cubes, personal chalkboards, work mats, and various other articles, which allowed the students to see the math that they were…
Logman, P.S.W.M.; Kaper, W.H.; Ellermeijer, A.L.; Taşar, M.F.
2014-01-01
Guiding sixteen-year-old students to rediscover the concept of energy conservation may be done in three distinct learning steps. First, we have chosen for the students to reinvent what we call partial laws of energy conservation (e.g. Σm∙g∙h = k1). Secondly, the students are asked to combine these
Leaper, Campbell
2010-01-01
The study investigated Latina and European American adolescent girls’ (N = 345, M = 15.2 years, range = 13 to 18) experiences with academic sexism in mathematics and science (M/S) and their M/S perceived competence and M/S value (liking and importance). M/S academic sexism was based on girls’ reported experiences hearing sexist comments about girls’ abilities in math and science. Older European American adolescents, and both younger and older Latina adolescents, who experienced several instances of academic sexism felt less competent in M/S than girls who experienced less sexism (controlling for M/S grades). In addition, among older girls (regardless of ethnicity), those who experienced several instances of academic sexism valued M/S less than girls who experienced less sexism. PMID:21212810
Brown, Christia Spears; Leaper, Campbell
2010-12-01
The study investigated Latina and European American adolescent girls' (N = 345, M = 15.2 years, range = 13 to 18) experiences with academic sexism in mathematics and science (M/S) and their M/S perceived competence and M/S value (liking and importance). M/S academic sexism was based on girls' reported experiences hearing sexist comments about girls' abilities in math and science. Older European American adolescents, and both younger and older Latina adolescents, who experienced several instances of academic sexism felt less competent in M/S than girls who experienced less sexism (controlling for M/S grades). In addition, among older girls (regardless of ethnicity), those who experienced several instances of academic sexism valued M/S less than girls who experienced less sexism.
Uffmann, Kai; Gruetter, Rolf
2007-11-15
A novel approach for the mathematical modeling of (13)C label incorporation into amino acids via the TCA cycle that eliminates the explicit calculation of the labeling of the TCA cycle intermediates is described, resulting in one differential equation per measurable time course of labeled amino acid. The equations demonstrate that both glutamate C4 and C3 labeling depend in a predictable manner on both transmitochondrial exchange rate, V(X), and TCA cycle rate, V(TCA). For example, glutamate C4 labeling alone does not provide any information on either V(X) or V(TCA) but rather a composite "flux". Interestingly, glutamate C3 simultaneously receives label not only from pyruvate C3 but also from glutamate C4, described by composite precursor functions that depend in a probabilistic way on the ratio of V(X) to V(TCA): An initial rate of labeling of glutamate C3 (or C2) being close to zero is indicative of a high V(X)/V(TCA). The derived analytical solution of these equations shows that, when the labeling of the precursor pool pyruvate reaches steady state quickly compared with the turnover rate of the measured amino acids, instantaneous labeling can be assumed for pyruvate. The derived analytical solution has acceptable errors compared with experimental uncertainty, thus obviating precise knowledge on the labeling kinetics of the precursor. In conclusion, a substantial reformulation of the modeling of label flow via the TCA cycle turnover into the amino acids is presented in the current study. This approach allows one to determine metabolic rates by fitting explicit mathematical functions to measured time courses.
Finite mathematics models and applications
Morris, Carla C
2015-01-01
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.
EBS Radionuclide Transport Abstraction
International Nuclear Information System (INIS)
J. Prouty
2006-01-01
The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment (TSPA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport model considers advective transport and diffusive transport
EBS Radionuclide Transport Abstraction
Energy Technology Data Exchange (ETDEWEB)
J. Prouty
2006-07-14
The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment (TSPA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport model considers advective transport and diffusive transport
Learning abstract algebra with ISETL
Dubinsky, Ed
1994-01-01
Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics...
Pugh, Charles C
2015-01-01
Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis. New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the un...
Mathematics Curriculum, the Philosophy of Mathematics and its ...
African Journals Online (AJOL)
It is my observation that the current school mathematics curriculum in Ethiopia is not producing competent mathematics students. Many mathematicians in Ethiopia and other part of the world have often expressed grief that the majority of students do not understand mathematical concepts, or do not see why mathematical ...
Concepts of formal concept analysis
Žáček, Martin; Homola, Dan; Miarka, Rostislav
2017-07-01
The aim of this article is apply of Formal Concept Analysis on concept of world. Formal concept analysis (FCA) as a methodology of data analysis, information management and knowledge representation has potential to be applied to a verity of linguistic problems. FCA is mathematical theory for concepts and concept hierarchies that reflects an understanding of concept. Formal concept analysis explicitly formalizes extension and intension of a concept, their mutual relationships. A distinguishing feature of FCA is an inherent integration of three components of conceptual processing of data and knowledge, namely, the discovery and reasoning with concepts in data, discovery and reasoning with dependencies in data, and visualization of data, concepts, and dependencies with folding/unfolding capabilities.
Modal abstractions of concurrent behavior
DEFF Research Database (Denmark)
Nielson, Flemming; Nanz, Sebastian; Nielson, Hanne Riis
2011-01-01
We present an effective algorithm for the automatic construction of finite modal transition systems as abstractions of potentially infinite concurrent processes. Modal transition systems are recognized as valuable abstractions for model checking because they allow for the validation as well...... as refutation of safety and liveness properties. However, the algorithmic construction of finite abstractions from potentially infinite concurrent processes is a missing link that prevents their more widespread usage for model checking of concurrent systems. Our algorithm is a worklist algorithm using concepts...... from abstract interpretation and operating upon mappings from sets to intervals in order to express simultaneous over- and underapprox-imations of the multisets of process actions available in a particular state. We obtain a finite abstraction that is 3-valued in both states and transitions...
Identifying STEM Concepts Associated with Junior Livestock Projects
Wooten, Kate; Rayfield, John; Moore, Lori L.
2013-01-01
Science, technology, engineering, and mathematics (STEM) education is intended to provide students with a cross-subject, contextual learning experience. To more fully prepare our nation's students to enter the globally competitive workforce, STEM integration allows students to make connections between the abstract concepts learned in core subject…
Pre-Service Physics Teachers' Comprehension of Quantum Mechanical Concepts
Didis, Nilufer; Eryilmaz, Ali; Erkoc, Sakir
2010-01-01
When quantum theory caused a paradigm shift in physics, it introduced difficulties in both learning and teaching of physics. Because of its abstract, counter-intuitive and mathematical structure, students have difficulty in learning this theory, and instructors have difficulty in teaching the concepts of the theory. This case study investigates…
On the application of Discrete Time Optimal Control Concepts to ...
African Journals Online (AJOL)
On the application of Discrete Time Optimal Control Concepts to Economic Problems. ... Journal of the Nigerian Association of Mathematical Physics ... Abstract. An extension of the use of the maximum principle to solve Discrete-time Optimal Control Problems (DTOCP), in which the state equations are in the form of general ...
Dantzig, Tobias
2006-01-01
More than a history of mathematics, this lively book traces mathematical ideas and processes to their sources, stressing the methods used by the masters of the ancient world. Author Tobias Dantzig portrays the human story behind mathematics, showing how flashes of insight in the minds of certain gifted individuals helped mathematics take enormous forward strides. Dantzig demonstrates how the Greeks organized their precursors' melange of geometric maxims into an elegantly abstract deductive system. He also explains the ways in which some of the famous mathematical brainteasers of antiquity led
Internal process: what is abstraction and distortion process?
Fiantika, F. R.; Budayasa, I. K.; Lukito, A.
2018-03-01
Geometry is one of the branch of mathematics that plays a major role in the development of science and technology. Thus, knowing the geometry concept is needed for students from their early basic level of thinking. A preliminary study showed that the elementary students have difficulty in perceiving parallelogram shape in a 2-dimention of a cube drawing as a square shape. This difficulty makes the students can not solve geometrical problems correctly. This problem is related to the internal thinking process in geometry. We conducted the exploration of students’ internal thinking processes in geometry particularly in distinguishing the square and parallelogram shape. How the students process their internal thinking through distortion and abstraction is the main aim of this study. Analysis of the geometrical test and deep interview are used in this study to obtain the data. The result of this study is there are two types of distortion and abstraction respectively in which the student used in their internal thinking processes.
Abstract quantum computing machines and quantum computational logics
Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto
2016-06-01
Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.
Stellar Presentations (Abstract)
Young, D.
2015-12-01
(Abstract only) The AAVSO is in the process of expanding its education, outreach and speakers bureau program. powerpoint presentations prepared for specific target audiences such as AAVSO members, educators, students, the general public, and Science Olympiad teams, coaches, event supervisors, and state directors will be available online for members to use. The presentations range from specific and general content relating to stellar evolution and variable stars to specific activities for a workshop environment. A presentation—even with a general topic—that works for high school students will not work for educators, Science Olympiad teams, or the general public. Each audience is unique and requires a different approach. The current environment necessitates presentations that are captivating for a younger generation that is embedded in a highly visual and sound-bite world of social media, twitter and U-Tube, and mobile devices. For educators, presentations and workshops for themselves and their students must support the Next Generation Science Standards (NGSS), the Common Core Content Standards, and the Science Technology, Engineering and Mathematics (STEM) initiative. Current best practices for developing relevant and engaging powerpoint presentations to deliver information to a variety of targeted audiences will be presented along with several examples.
Raychaudhuri, Debasree
2014-01-01
Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…
EBS Radionuclide Transport Abstraction
Energy Technology Data Exchange (ETDEWEB)
J.D. Schreiber
2005-08-25
The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in ''Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration'' (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment for the license application (TSPA-LA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA-LA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport
EBS Radionuclide Transport Abstraction
International Nuclear Information System (INIS)
J.D. Schreiber
2005-01-01
The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in ''Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration'' (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment for the license application (TSPA-LA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA-LA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport model considers
International Nuclear Information System (INIS)
1975-01-01
Abstracts of 25 papers presented at the congress are given. The abstracts cover various topics including radiotherapy, radiopharmaceuticals, radioimmunoassay, health physics, radiation protection and nuclear medicine
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...
Elements of abstract harmonic analysis
Bachman, George
2013-01-01
Elements of Abstract Harmonic Analysis provides an introduction to the fundamental concepts and basic theorems of abstract harmonic analysis. In order to give a reasonably complete and self-contained introduction to the subject, most of the proofs have been presented in great detail thereby making the development understandable to a very wide audience. Exercises have been supplied at the end of each chapter. Some of these are meant to extend the theory slightly while others should serve to test the reader's understanding of the material presented. The first chapter and part of the second give
Basic concepts in modern mathematics
Hafstrom, John Edward
2013-01-01
In-depth overview, geared toward undergraduates of all backgrounds, covers natural numbers; sets, variables, and statement forms; mappings and operations; groups; relations and partitions; integers; and rational and real numbers. 1961 edition.
Mathematics, anxiety, and the brain.
Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer
2017-05-24
Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.
Abstract Cauchy problems three approaches
Melnikova, Irina V
2001-01-01
Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularization methods. Semigroup and distribution methods restore well-posedness, in a modern weak sense. Regularization methods provide approximate solutions to ill-posed problems. Although these approaches were extensively developed over the last decades by many researchers, nowhere could one find a comprehensive treatment of all three approaches.Abstract Cauchy Problems: Three Approaches provides an innovative, self-contained account of these methods and, furthermore, demonstrates and studies some of the profound connections between them. The authors discuss the application of different methods not only to the Cauchy problem that is not well-posed in the classical sense, b...
Berkeley's Philosophy of Mathematics
Jesseph, Douglas M
1993-01-01
In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph begins with Berkeley's r
2011-01-01
Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics.
Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving
Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio
2016-01-01
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),…
Mathematics and Engineering in Real Life through Mathematical Competitions
More, M.
2018-01-01
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…
Directory of Open Access Journals (Sweden)
Izaak Hendrik Wenno
2015-01-01
Full Text Available The purpose of the study is to determine the relation between interest at Physics and knowledge of Mathematics basic concepts with the ability to solve Physics problems. The populations are all students in the 7th grade at the junior high school in Ambon, Maluku, Indonesia. The used sample schools are Junior High Schools 8, 9, and 10 during 2013/2014 academic year with 44 students per school. Two independent variables and one dependent variable are studied. The independent variables are the interest at Physics (X1 and the knowledge of Mathematics basic concepts (X2, while the dependent variable is the ability to solve Physics problems (Y. Data collection technique for X1 is an interview with questionnaire instrument, while for the X2 and Y is using the test technique with test items instrument. The obtained data from the measurements were analyzed with descriptive analysis and inferential analysis. The results show that there is a positive relation between interest at Physics and knowledge of Mathematics basic concepts with students’ ability to solve Physics problems.
International Nuclear Information System (INIS)
1975-01-01
Abstracts of the papers given at the conference are presented. The abstracts are arranged under sessions entitled:Theoretical Physics; Nuclear Physics; Solid State Physics; Spectroscopy; Physics Education; SANCGASS; Astronomy; Plasma Physics; Physics in Industry; Applied and General Physics
Energy Technology Data Exchange (ETDEWEB)
1975-01-01
Abstracts of the papers given at the conference are presented. The abstracts are arranged under sessions entitled:Theoretical Physics; Nuclear Physics; Solid State Physics; Spectroscopy; Physics Education; SANCGASS; Astronomy; Plasma Physics; Physics in Industry; Applied and General Physics.
Introduction to abstract algebra
Nicholson, W Keith
2012-01-01
Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."-Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately be
Teaching Mathematics in Geography Degrees
Bennett, Robert
1978-01-01
Examines ways of developing college students' motivation for mathematical training; describes the type of mathematical knowledge required in the geography discipline; and explores an applied approach to mathematics teaching based on a systems concept. For journal availability, see SO 506 224. (Author/AV)
Teaching secondary mathematics
Rock, David
2013-01-01
Solidly grounded in up-to-date research, theory and technology,?Teaching Secondary Mathematics?is a practical, student-friendly, and popular text for secondary mathematics methods courses. It provides clear and useful approaches for mathematics teachers, and shows how concepts typically found in a secondary mathematics curriculum can be taught in a positive and encouraging way. The thoroughly revised fourth edition combines this pragmatic approach with truly innovative and integrated technology content throughout. Synthesized content between the book and comprehensive companion websi
Kuipers, L
1969-01-01
International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examp
Vukovic, Rose K; Lesaux, Nonie K
2013-06-01
This longitudinal study examined how language ability relates to mathematical development in a linguistically and ethnically diverse sample of children from 6 to 9 years of age. Study participants were 75 native English speakers and 92 language minority learners followed from first to fourth grades. Autoregression in a structural equation modeling (SEM) framework was used to evaluate the relation between children's language ability and gains in different domains of mathematical cognition (i.e., arithmetic, data analysis/probability, algebra, and geometry). The results showed that language ability predicts gains in data analysis/probability and geometry, but not in arithmetic or algebra, after controlling for visual-spatial working memory, reading ability, and sex. The effect of language on gains in mathematical cognition did not differ between language minority learners and native English speakers. These findings suggest that language influences how children make meaning of mathematics but is not involved in complex arithmetical procedures whether presented with Arabic symbols as in arithmetic or with abstract symbols as in algebraic reasoning. The findings further indicate that early language experiences are important for later mathematical development regardless of language background, denoting the need for intensive and targeted language opportunities for language minority and native English learners to develop mathematical concepts and representations. Copyright © 2013. Published by Elsevier Inc.
Abstracts of Research, July 1975-June 1976.
Ohio State Univ., Columbus. Computer and Information Science Research Center.
Abstracts of research papers in computer and information science are given for 62 papers in the areas of information storage and retrieval; computer facilities; information analysis; linguistics analysis; artificial intelligence; information processes in physical, biological, and social systems; mathematical technigues; systems programming;…
Waste management research abstracts No. 18
International Nuclear Information System (INIS)
1987-12-01
The eighteenth issue of this publication contains over 750 abstracts from 33 IAEA member countries comprehending various aspects of radioactive waste management. Radioactive waste disposal, processing and storage, geochemical and geological investigations related to waste management, mathematical models and environmental impacts are reviewed
2002 Conference Programme and Book of Abstracts
International Nuclear Information System (INIS)
2002-01-01
The 25th Annual (Silver Jubilee) Conference 2002 Conference Programme and Book of Abstracts gives a brief on the Nigerian Institute of Physics, the Sheda Science and Technology Complex. It carries the Conference programme and carries the abstracts of all the papers presented. The abstracts cover a wide range of subjects including topics in atmospheric physics, education, policy and planning, geophysics, instrumentation, mathematical sciences, theoretical physics, nuclear and health physics, solid state, electronic and health physics. We are grateful to the Nigerian Institute of Physics for this volume
2018 Congress Poster Abstracts
2018-02-21
Each abstract has been indexed according to the first author. Abstracts appear as they were submitted and have not undergone editing or the Oncology Nursing Forum’s review process. Only abstracts that will be presented appear here. Poster numbers are subject to change. For updated poster numbers, visit congress.ons.org or check the Congress guide. Data published in abstracts presented at the ONS 43rd Annual Congress are embargoed until the conclusion of the presentation. Coverage and/or distribution of an abstract, poster, or any of its supplemental material to or by the news media, any commercial entity, or individuals, including the authors of said abstract, is strictly prohibited until the embargo is lifted. Promotion of general topics and speakers is encouraged within these guidelines.
2018 Congress Podium Abstracts
2018-02-21
Each abstract has been indexed according to first author. Abstracts appear as they were submitted and have not undergone editing or the Oncology Nursing Forum’s review process. Only abstracts that will be presented appear here. For Congress scheduling information, visit congress.ons.org or check the Congress guide. Data published in abstracts presented at the ONS 43rd Annual Congress are embargoed until the conclusion of the presentation. Coverage and/or distribution of an abstract, poster, or any of its supplemental material to or by the news media, any commercial entity, or individuals, including the authors of said abstract, is strictly prohibited until the embargo is lifted. Promotion of general topics and speakers is encouraged within these guidelines.
Compilation of Theses Abstracts
National Research Council Canada - National Science Library
2005-01-01
This publication contains unclassified/unrestricted abstracts of classified or restricted theses submitted for the degrees of Doctor of Philosophy, Master of Business Administration, Master of Science...
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Reconstruction of abstract quantum theory
International Nuclear Information System (INIS)
Drieschner, M.; Goernitz, T.; von Weizsaecker, C.F.
1988-01-01
Understanding quantum theory as a general theory of prediction, we reconstruct abstract quantum theory. Abstract means the general frame of quantum theory, without reference to a three-dimensional position space, to concepts like particle or field, or to special laws of dynamics. Reconstruction is the attempt to do this by formulating simple and plausible postulates on prediction in order to derive the basic concepts of quantum theory from them. Thereby no law of classical physics is presupposed which would then have to be quantized. We briefly discuss the relationship of theory and interpretation in physics and the fundamental role of time as a basic concept for physics. Then a number of assertions are given, formulated as succinctly as possible in order to make them easily quotable and comparable. The assertations are arranged in four groups: heuristic principles, verbal definitions of some terms, three basic postulates, and consequences. The three postulates of separable alternatives, indeterminism, and kinematics are the central points of this work. These brief assertions are commented upon, and their relationship with the interpretation of quantum theory is discussed. Also given are an outlook on the further development into concrete quantum theory and some philosophical reflections
Nuclear medicine. Abstracts; Nuklearmedizin 2000. Abstracts
Energy Technology Data Exchange (ETDEWEB)
Anon.
2000-07-01
This issue of the journal contains the abstracts of the 183 conference papers as well as 266 posters presented at the conference. Subject fields covered are: Neurology, psychology, oncology, pediatrics, radiopharmacy, endocrinology, EDP, measuring equipment and methods, radiological protection, cardiology, and therapy. (orig./CB) [German] Die vorliegende Zeitschrift enthaelt die Kurzfassungen der 183 auf der Tagung gehaltenen Vortraege sowie der 226 praesentierten Poster, die sich mit den folgenden Themen befassten: Neurologie, Psychiatrie, Onkologie, Paediatrie, Radiopharmazie, Endokrinologie, EDV, Messtechnik, Strahlenschutz, Kardiologie sowie Therapie. (MG)
Directory of Open Access Journals (Sweden)
Miarka Roger
2010-01-01
Full Text Available Esta pesquisa busca trabalhar com diferentes concepções de mundo e de conhecimento, investigando a articulação entre o sentido que elas possuem para os professores de Matemática e suas concepções de ensino e de Educação. O estudo gira em torno de discussões que ocorreram em um curso de extensão para professores de Matemática. Esse curso tratou de concepções de mundo e de conhecimento, relacionando-as com diferentes regiões do saber, como Matemática, Física, Ecologia e Artes, focando a transição entre a concepção de mundo da Época Moderna para a concepção de mundo que vem se construindo na denominada Época Pós-moderna ou Contemporânea. A meta é compreender o sentido que aquelas concepções têm para os professores e destacar possíveis momentos de metacompreensão sobre a articulação entre essas concepções e sua prática docente. A metodologia utilizada é qualitativa, de uma perspectiva fenomenológica.This research aims to work with different world and knowledge conceptions, inquiring about articulations between the meanings that Mathematics teachers have and their learning and teaching conceptions. This study revolves around discussions that occurred in an extension course for Mathematics teachers. This course addressed different conceptions of world and of knowledge, and their association with different fields such as Mathematics, Physics, Ecology and Arts, focusing on the transition between the Modern Era world conception and the world conception that has been evolving in the so-called Post-Modern Era. The goal is to understand the meanings that teachers have about those conceptions, highlighting possible moments of meta-understanding regarding the articulation between these conceptions and their practice. A qualitative research methodology was employed for the study from a phenomenological perspective.
Novak, Gordon S., Jr.
GLISP is a high-level computer language (based on Lisp and including Lisp as a sublanguage) which is compiled into Lisp. GLISP programs are compiled relative to a knowledge base of object descriptions, a form of abstract datatypes. A primary goal of the use of abstract datatypes in GLISP is to allow program code to be written in terms of objects,…
DEFF Research Database (Denmark)
Brock-Nannestad, Taus; Schürmann, Carsten
2012-01-01
indefinitely, finding neither a proof nor a disproof of a given subgoal. In this paper we characterize a family of truth-preserving abstractions from intuitionistic first-order logic to the monadic fragment of classical first-order logic. Because they are truthful, these abstractions can be used to disprove...
International Nuclear Information System (INIS)
1976-01-01
Abstracts of the papers given at the conference are presented. The abstracts are arranged under sessions entitled: Theoretical Physics; Nuclear Physics; Solid State Physics; Spectroscopy; Plasma Physics; Solar-Terrestrial Physics; Astrophysics and Astronomy; Radioastronomy; General Physics; Applied Physics; Industrial Physics
Completeness of Lyapunov Abstraction
Directory of Open Access Journals (Sweden)
Rafael Wisniewski
2013-08-01
Full Text Available In this work, we continue our study on discrete abstractions of dynamical systems. To this end, we use a family of partitioning functions to generate an abstraction. The intersection of sub-level sets of the partitioning functions defines cells, which are regarded as discrete objects. The union of cells makes up the state space of the dynamical systems. Our construction gives rise to a combinatorial object - a timed automaton. We examine sound and complete abstractions. An abstraction is said to be sound when the flow of the time automata covers the flow lines of the dynamical systems. If the dynamics of the dynamical system and the time automaton are equivalent, the abstraction is complete. The commonly accepted paradigm for partitioning functions is that they ought to be transversal to the studied vector field. We show that there is no complete partitioning with transversal functions, even for particular dynamical systems whose critical sets are isolated critical points. Therefore, we allow the directional derivative along the vector field to be non-positive in this work. This considerably complicates the abstraction technique. For understanding dynamical systems, it is vital to study stable and unstable manifolds and their intersections. These objects appear naturally in this work. Indeed, we show that for an abstraction to be complete, the set of critical points of an abstraction function shall contain either the stable or unstable manifold of the dynamical system.
Alter, David; Grenache, David G; Bosler, David S; Karcher, Raymond E; Nichols, James; Rajadhyaksha, Aparna; Camelo-Piragua, Sandra; Rauch, Carol; Huddleston, Brent J; Frank, Elizabeth L; Sluss, Patrick M; Lewandrowski, Kent; Eichhorn, John H; Hall, Janet E; Rahman, Saud S; McPherson, Richard A; Kiechle, Frederick L; Hammett-Stabler, Catherine; Pierce, Kristin A; Kloehn, Erica A; Thomas, Patricia A; Walts, Ann E; Madan, Rashna; Schlesinger, Kathie; Nawgiri, Ranjana; Bhutani, Manoop; Kanber, Yonca; Abati, Andrea; Atkins, Kristen A; Farrar, Robert; Gopez, Evelyn Valencerina; Jhala, Darshana; Griffin, Sonya; Jhala, Khushboo; Jhala, Nirag; Bentz, Joel S; Emerson, Lyska; Chadwick, Barbara E; Barroeta, Julieta E; Baloch, Zubair W; Collins, Brian T; Middleton, Owen L; Davis, Gregory G; Haden-Pinneri, Kathryn; Chu, Albert Y; Keylock, Joren B; Ramoso, Robert; Thoene, Cynthia A; Stewart, Donna; Pierce, Arand; Barry, Michelle; Aljinovic, Nika; Gardner, David L; Barry, Michelle; Shields, Lisa B E; Arnold, Jack; Stewart, Donna; Martin, Erica L; Rakow, Rex J; Paddock, Christopher; Zaki, Sherif R; Prahlow, Joseph A; Stewart, Donna; Shields, Lisa B E; Rolf, Cristin M; Falzon, Andrew L; Hudacki, Rachel; Mazzella, Fermina M; Bethel, Melissa; Zarrin-Khameh, Neda; Gresik, M Vicky; Gill, Ryan; Karlon, William; Etzell, Joan; Deftos, Michael; Karlon, William J; Etzell, Joan E; Wang, Endi; Lu, Chuanyi M; Manion, Elizabeth; Rosenthal, Nancy; Wang, Endi; Lu, Chuanyi M; Tang, Patrick; Petric, Martin; Schade, Andrew E; Hall, Geraldine S; Oethinger, Margret; Hall, Geraldine; Picton, Avis R; Hoang, Linda; Imperial, Miguel Ranoa; Kibsey, Pamela; Waites, Ken; Duffy, Lynn; Hall, Geraldine S; Salangsang, Jo-Anne M; Bravo, Lulette Tricia C; Oethinger, Margaret D; Veras, Emanuela; Silva, Elvia; Vicens, Jimena; Silva, Elvio; Keylock, Joren; Hempel, James; Rushing, Elizabeth; Posligua, Lorena E; Deavers, Michael T; Nash, Jason W; Basturk, Olca; Perle, Mary Ann; Greco, Alba; Lee, Peng; Maru, Dipen; Weydert, Jamie Allen; Stevens, Todd M; Brownlee, Noel A; Kemper, April E; Williams, H James; Oliverio, Brock J; Al-Agha, Osama M; Eskue, Kyle L; Newlands, Shawn D; Eltorky, Mahmoud A; Puri, Puja K; Royer, Michael C; Rush, Walter L; Tavora, Fabio; Galvin, Jeffrey R; Franks, Teri J; Carter, James Elliot; Kahn, Andrea Graciela; Lozada Muñoz, Luis R; Houghton, Dan; Land, Kevin J; Nester, Theresa; Gildea, Jacob; Lefkowitz, Jerry; Lacount, Rachel A; Thompson, Hannis W; Refaai, Majed A; Quillen, Karen; Lopez, Ana Ortega; Goldfinger, Dennis; Muram, Talia; Thompson, Hannis
2009-02-01
The following abstracts are compiled from Check Sample exercises published in 2008. These peer-reviewed case studies assist laboratory professionals with continuing medical education and are developed in the areas of clinical chemistry, cytopathology, forensic pathology, hematology, microbiology, surgical pathology, and transfusion medicine. Abstracts for all exercises published in the program will appear annually in AJCP.
Using the virtual-abstract instructional sequence to teach addition of fractions.
Bouck, Emily C; Park, Jiyoon; Sprick, Jessica; Shurr, Jordan; Bassette, Laura; Whorley, Abbie
2017-11-01
Limited literature examines mathematics education for students with mild intellectual disability. This study investigated the effects of using the Virtual-Abstract instructional sequenceto teach middle school students, predominantly with mild intellectual disability, to add fractions of unlike denominators. Researchers used a multiple probe across participants design to determine if a functional relation existed between the Virtual-Abstract instructional sequence strategy and students' ability to add fractions with unlike denominators. The study of consisted of three-to-nine baseline sessions, 6-11 intervention sessions, and two maintenance sessions for each student. Data were collected on accuracy across five addition of fractions with unlike denominators problems. The VA instructional strategy was effective in thestudents to add fractions with unlike denominators; a functional relation existed between the VA instructional sequence and adding fractions with unlike denominators for three of the four students. The Virtual-Abstract instructional sequencemay be appropriate to support students with mild intellectual disability in learning mathematics, especially when drawing or representing the mathematical concepts may prove challenging. Copyright © 2017 Elsevier Ltd. All rights reserved.
Dennery, Philippe
1967-01-01
""A fine example of how to present 'classical' physical mathematics."" - American ScientistWritten for advanced undergraduate and graduate students, this volume provides a thorough background in the mathematics needed to understand today's more advanced topics in physics and engineering. Without sacrificing rigor, the authors develop the theoretical material at length, in a highly readable, and, wherever possible, in an intuitive manner. Each abstract idea is accompanied by a very simple, concrete example, showing the student that the abstraction is merely a generalization from easily understo
African Journals Online (AJOL)
MATHEMATICS CONNECTION aims at providing a forum topromote the development of Mathematics Education in Ghana. Articles that seekto enhance the teaching and/or learning of mathematics at all levels of theeducational system are welcome.
New Challenges in the Teaching of Mathematics.
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…
The complex road to mathematization in physics instruction
DEFF Research Database (Denmark)
Avelar Sotomaior Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche
2012-01-01
to the research in this field, we have analysed a set of lectures given by a distinguished physics professor. In this proposal we present the analysis of two lectures where the abstract concepts of charge density and electric flux are taught. The complexity of the mathematization of these concepts is evident both...... explicitly and made punctual metacognitive remarks. Taking into account the future perspectives of our research, the categorization of the didactical strategies used by this professor shall allows us to develop comparative studies with other lectures on the same topic. Moreover, the derivation promising......How to facilitate students’ understanding of science’s abstract concepts is definitely a major concern of every dedicated physics teacher. However, discussions about promising ways to be successful at this task are not always part of teacher training curricula. With the goal of contributing...
Operating System Abstraction Layer (OSAL)
Yanchik, Nicholas J.
2007-01-01
This viewgraph presentation reviews the concept of the Operating System Abstraction Layer (OSAL) and its benefits. The OSAL is A small layer of software that allows programs to run on many different operating systems and hardware platforms It runs independent of the underlying OS & hardware and it is self-contained. The benefits of OSAL are that it removes dependencies from any one operating system, promotes portable, reusable flight software. It allows for Core Flight software (FSW) to be built for multiple processors and operating systems. The presentation discusses the functionality, the various OSAL releases, and describes the specifications.
Completeness of Lyapunov Abstraction
DEFF Research Database (Denmark)
Wisniewski, Rafal; Sloth, Christoffer
2013-01-01
the vector field, which allows the generation of a complete abstraction. To compute the functions that define the subdivision of the state space in an algorithm, we formulate a sum of squares optimization problem. This optimization problem finds the best subdivisioning functions, with respect to the ability......This paper addresses the generation of complete abstractions of polynomial dynamical systems by timed automata. For the proposed abstraction, the state space is divided into cells by sublevel sets of functions. We identify a relation between these functions and their directional derivatives along...
Prince, Kyle
2016-01-01
With traditional teaching methods pervasive in the U.S., it is crucial that mathematics teacher educators and professional development leaders understand what methods result in authentic changes in classroom instruction. Lesson study presents a promising approach to developing reform-oriented instruction, as it is situated within the classroom,…
Wong, Sissy S.; Firestone, Jonah B.; Ronduen, Lionnel G.; Bang, EunJin
2016-01-01
Science, Technology, Engineering, and Mathematics (STEM) education has become one of the main priorities in the United States. Science education communities and researchers advocate for integration of STEM disciplines throughout the teaching curriculum. This requires teacher knowledge in STEM disciplines, as well as competence in scientific…
ABSTRACT IMPLEMENTATION OF A KIND TO MANAGE DATA SETS USING PROGRAMMING LANGUAGE C + +
Ruiz L., Edgar; Hinojosa L., Hilmar
2014-01-01
This article presents the implementation of a data abstract type to represent the Set Theory Mathematical Concept, The program has been written in C++ Program Language applying the Object Oriented Programming Paradigm through a Dev C++ v.4.1 Compiler, a GNU compiler with GPL licence. El artículo presenta la implementación de un tipo abstracto de datos para representar el concepto matemático de la teoría de conjuntos. El programa ha sido escrito en lenguaje de programación C++ aplicando el ...
International Nuclear Information System (INIS)
1999-01-01
The document is a collection of the scientific meeting abstracts in the fields of nuclear physics, medical sciences, chemistry, agriculture, environment, engineering, different aspects of energy and presents research done in 1999 in these fields
International Nuclear Information System (INIS)
2000-01-01
the document is a collection of the science meeting abstracts in the fields of nuclear physics, medical sciences, chemistry, agriculture, environment, engineering, material sciences different aspects of energy and presents research done in 2000 in these fields
Mathematics for electronic technology
Howson, D P
1975-01-01
Mathematics for Electronic Technology is a nine-chapter book that begins with the elucidation of the introductory concepts related to use of mathematics in electronic engineering, including differentiation, integration, partial differentiation, infinite series, vectors, vector algebra, and surface, volume and line integrals. Subsequent chapters explore the determinants, differential equations, matrix analysis, complex variable, topography, graph theory, and numerical analysis used in this field. The use of Fourier method for harmonic analysis and the Laplace transform is also described. The ma
Mathematical foundations of thermodynamics
Giles, R; Stark, M; Ulam, S
2013-01-01
Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodyn
Abstract Algebra to Secondary School Algebra: Building Bridges
Christy, Donna; Sparks, Rebecca
2015-01-01
The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…
Abstracts of contributed papers
Energy Technology Data Exchange (ETDEWEB)
1994-08-01
This volume contains 571 abstracts of contributed papers to be presented during the Twelfth US National Congress of Applied Mechanics. Abstracts are arranged in the order in which they fall in the program -- the main sessions are listed chronologically in the Table of Contents. The Author Index is in alphabetical order and lists each paper number (matching the schedule in the Final Program) with its corresponding page number in the book.
Quantum language and the migration of scientific concepts
Burwell, Jennifer
2018-01-01
How highly abstract quantum concepts were represented in language, and how these concepts were later taken up by philosophers, literary critics, and new-age gurus. The principles of quantum physics -- and the strange phenomena they describe -- are represented most precisely in highly abstract algebraic equations. Why, then, did these mathematically driven concepts compel founders of the field, particularly Erwin Schrödinger, Niels Bohr, and Werner Heisenberg, to spend so much time reflecting on ontological, epistemological, and linguistic concerns? What is it about quantum concepts that appeals to latter-day Eastern mystics, poststructuralist critics, and get-rich-quick schemers? How did their interpretations and misinterpretations of quantum phenomena reveal their own priorities? In this book, Jennifer Burwell examines these questions and considers what quantum phenomena -- in the context of the founders' debates over how to describe them -- reveal about the relationship between everyday experience, percep...
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....
Mathematical Footprints Discovering Mathematics Everywhere
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
The fundamentals of mathematical analysis
Fikhtengol'ts, G M
1965-01-01
The Fundamentals of Mathematical Analysis, Volume 1 is a textbook that provides a systematic and rigorous treatment of the fundamentals of mathematical analysis. Emphasis is placed on the concept of limit which plays a principal role in mathematical analysis. Examples of the application of mathematical analysis to geometry, mechanics, physics, and engineering are given. This volume is comprised of 14 chapters and begins with a discussion on real numbers, their properties and applications, and arithmetical operations over real numbers. The reader is then introduced to the concept of function, i
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.
The Princeton companion to mathematics
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
THE METHODICAL ASPECTS OF THE ALGEBRA AND THE MATHEMATICAL ANALYSIS STUDY USING THE SAGEMATH CLOUD
Directory of Open Access Journals (Sweden)
M. Popel
2014-06-01
Full Text Available The quality of mathematics education depends largely on the quality of education in general. The main idea may be summarized as follows: in order to educate the younger generation of people to be able to meet adequately the demands of the time, it is necessary to create conditions for the high-quality mathematics education. Improving the quality of mathematics education of pupils in secondary school is one of the most pressing problems. Contents of the school course of mathematics and its teaching method has always been the subject of undammed and sometimes stormy scientific debates. There are especially true methods of teaching algebra and the analisis in the high secondary school. Still in the study process the algebraic concepts and principles of analysis are given in such an abstract and generalized form that the student may has considerable difficulties to map these general abstract concepts to the certain concrete images, they are generalizations of. Improving education quality indicators can be achieved by using the appropriate computer technology. The article deals with the use of the cloud-oriented systems of computer mathematics (SCM. The prospects of development of the Web-SCM in terms of cloud-based learning environment are considered. The pedagogical features of the SageMath Cloud use as a tool for mathematics learning are revealed. The methodological aspects of algebra and elementary analysis teaching in a high profile school using the cloud-oriented the SCM SageMath Cloud are revealed.
Putting Foundations Into Mathematics
Hubbard, G. L.
1972-01-01
For meaningful learning of mathematics, a learning set is required which demands that all things accepted as true should be demonstrable in terms of a paradigm appropriate to the child's cognitive development: preparatory, concrete-particular, concrete-general, formal-abstract. Future teachers should experience all paradigms to become aware that…
Exploring Mathematical Definition Construction Processes
Ouvrier-Buffet, Cecile
2006-01-01
The definition of "definition" cannot be taken for granted. The problem has been treated from various angles in different journals. Among other questions raised on the subject we find: the notions of "concept definition" and "concept image", conceptions of mathematical definitions, redefinitions, and from a more axiomatic point of view, how to…
DEFF Research Database (Denmark)
Robering, Klaus
2014-01-01
Verbs do often take arguments of quite different types. In an orthodox type-theoretic framework this results in an extreme polysemy of many verbs. In this article, it is shown that this unwanted consequence can be avoided when a theory of "abstract objects" is adopted according to which these obj......Verbs do often take arguments of quite different types. In an orthodox type-theoretic framework this results in an extreme polysemy of many verbs. In this article, it is shown that this unwanted consequence can be avoided when a theory of "abstract objects" is adopted according to which...... these objects represent non-objectual entities in contexts from which they are excluded by type restrictions. Thus these objects are "abstract'' in a functional rather than in an ontological sense: they function as representatives of other entities but they are otherwise quite normal objects. Three examples...
Squeezed States and Uncertainty Relations. Abstracts
International Nuclear Information System (INIS)
Masahito, Hayashi; Reynaud, S.; Jaekel, M.Th.; Fiuraaek, J.; Garcia-Patron, R.; Cerf, N.J.; Hage, B.; Chelkowski, S.; Franzen, A.; Lastzka, N.; Vahlbruch, N.; Danzmann, K.; Schnabel, R.; Hassan, S.S.; Joshi, A.; Jakob, M.; Bergou, J.A.; Kozlovskii, A.V.; Prakash, H.; Kumar, R.
2005-01-01
The purpose of the conference was to bring together people working in the field of quantum optics, with special emphasis on non-classical light sources and related areas, quantum computing, statistical mechanics and mathematical physics. As a novelty, this edition will include the topics of quantum imaging, quantum phase noise and number theory in quantum mechanics. This document gives the program of the conference and gathers the abstracts
Waste management research abstracts no. 21
International Nuclear Information System (INIS)
1992-12-01
The 21th issue of this publication contains over 700 abstracts from 35 IAEA Member Countries comprehending various aspects of radioactive waste management. Radioactive waste disposal, processing and storage, geochemical and geological investigations related to waste management, mathematical models and environmental impacts are reviewed. Many programs involve cooperation among several countries and further international cooperation is expected to be promoted through availability of compiled information on research programs, institutions and scientists engaged in waste management
Waste management research abstracts. No. 20
International Nuclear Information System (INIS)
1990-10-01
The 20th issue of this publication contains over 700 abstracts from 32 IAEA Member Countries comprehending various aspects of radioactive waste management. Radioactive waste disposal, processing and storage, geochemical and geological investigations related to waste management, mathematical models and environmental impacts are reviewed. Many programs involve cooperation among several countries and further international cooperation is expected to be promoted through availability of compiled information on research programs, institutions and scientists engaged in waste management
Building Safe Concurrency Abstractions
DEFF Research Database (Denmark)
Madsen, Ole Lehrmann
2014-01-01
Concurrent object-oriented programming in Beta is based on semaphores and coroutines and the ability to define high-level concurrency abstractions like monitors, and rendezvous-based communication, and their associated schedulers. The coroutine mechanism of SIMULA has been generalized into the no......Concurrent object-oriented programming in Beta is based on semaphores and coroutines and the ability to define high-level concurrency abstractions like monitors, and rendezvous-based communication, and their associated schedulers. The coroutine mechanism of SIMULA has been generalized...
DEFF Research Database (Denmark)
2014-01-01
Verbs do often take arguments of quite different types. In an orthodox type-theoretic framework this results in an extreme polysemy of many verbs. In this article, it is shown that this unwanted consequence can be avoided when a theory of "abstract objects" is adopted according to which...... these objects represent non-objectual entities in contexts from which they are excluded by type restrictions. Thus these objects are "abstract'' in a functional rather than in an ontological sense: they function as representatives of other entities but they are otherwise quite normal objects. Three examples...
Abstract Algebra for Teachers: An Evaluative Case Study
Hoffman, Andrew Joseph
2017-01-01
This manuscript describes the study of an abstract algebra course for preservice secondary mathematics teachers (PSMTs). Often, courses in abstract algebra have not been viewed as productive, beneficial learning experiences for future teachers, both by researchers and PSMTs themselves. This despite calls for increased content knowledge for…
Abstracts of Research, July 1973 through June 1974.
Ohio State Univ., Columbus. Computer and Information Science Research Center.
Abstracts of research papers in the fields of computer and information science are given; 72 papers are abstracted in the areas of information storage and retrieval, information processing, linguistic analysis, artificial intelligence, mathematical techniques, systems programing, and computer networks. In addition, the Ohio State University…
Applied Mathematics Seminar 1982
International Nuclear Information System (INIS)
1983-01-01
This report contains the abstracts of the lectures delivered at 1982 Applied Mathematics Seminar of the DPD/LCC/CNPq and Colloquy on Applied Mathematics of LCC/CNPq. The Seminar comprised 36 conferences. Among these, 30 were presented by researchers associated to brazilian institutions, 9 of them to the LCC/CNPq, and the other 6 were given by visiting lecturers according to the following distribution: 4 from the USA, 1 from England and 1 from Venezuela. The 1981 Applied Mathematics Seminar was organized by Leon R. Sinay and Nelson do Valle Silva. The Colloquy on Applied Mathematics was held from october 1982 on, being organized by Ricardo S. Kubrusly and Leon R. Sinay. (Author) [pt
International Nuclear Information System (INIS)
Anon.
2000-01-01
This issue of the journal contains the abstracts of the 183 conference papers as well as 266 posters presented at the conference. Subject fields covered are: Neurology, psychology, oncology, pediatrics, radiopharmacy, endocrinology, EDP, measuring equipment and methods, radiological protection, cardiology, and therapy. (orig./CB) [de
Seismic Consequence Abstraction
International Nuclear Information System (INIS)
Gross, M.
2004-01-01
The primary purpose of this model report is to develop abstractions for the response of engineered barrier system (EBS) components to seismic hazards at a geologic repository at Yucca Mountain, Nevada, and to define the methodology for using these abstractions in a seismic scenario class for the Total System Performance Assessment - License Application (TSPA-LA). A secondary purpose of this model report is to provide information for criticality studies related to seismic hazards. The seismic hazards addressed herein are vibratory ground motion, fault displacement, and rockfall due to ground motion. The EBS components are the drip shield, the waste package, and the fuel cladding. The requirements for development of the abstractions and the associated algorithms for the seismic scenario class are defined in ''Technical Work Plan For: Regulatory Integration Modeling of Drift Degradation, Waste Package and Drip Shield Vibratory Motion and Seismic Consequences'' (BSC 2004 [DIRS 171520]). The development of these abstractions will provide a more complete representation of flow into and transport from the EBS under disruptive events. The results from this development will also address portions of integrated subissue ENG2, Mechanical Disruption of Engineered Barriers, including the acceptance criteria for this subissue defined in Section 2.2.1.3.2.3 of the ''Yucca Mountain Review Plan, Final Report'' (NRC 2003 [DIRS 163274])
Journal of Engineering Education, 1972
1972-01-01
Includes abstracts of papers presented at the 80th Annual Conference of the American Society for Engineering Education. The broad areas include aerospace, affiliate and associate member council, agricultural engineering, biomedical engineering, continuing engineering studies, chemical engineering, civil engineering, computers, cooperative…
International Nuclear Information System (INIS)
Cessac, B.; Bianchi, E.; Bellon, M.; Fried, H.; Krajewski, T.; Schubert, C.; Barre, J.; Hofmann, R.; Muller, B.; Raffaelli, B.
2014-01-01
The object of this Workshop is to consolidate and publicize new efforts in non perturbative-like Field Theories, relying in Functional Methods, Renormalization Group, and Dyson-Schwinger Equations. A presentation deals with effective vertices and photon-photon scattering in SU(2) Yang-Mills thermodynamics. This document gathers the abstracts of the presentations
Seismic Consequence Abstraction
Energy Technology Data Exchange (ETDEWEB)
M. Gross
2004-10-25
The primary purpose of this model report is to develop abstractions for the response of engineered barrier system (EBS) components to seismic hazards at a geologic repository at Yucca Mountain, Nevada, and to define the methodology for using these abstractions in a seismic scenario class for the Total System Performance Assessment - License Application (TSPA-LA). A secondary purpose of this model report is to provide information for criticality studies related to seismic hazards. The seismic hazards addressed herein are vibratory ground motion, fault displacement, and rockfall due to ground motion. The EBS components are the drip shield, the waste package, and the fuel cladding. The requirements for development of the abstractions and the associated algorithms for the seismic scenario class are defined in ''Technical Work Plan For: Regulatory Integration Modeling of Drift Degradation, Waste Package and Drip Shield Vibratory Motion and Seismic Consequences'' (BSC 2004 [DIRS 171520]). The development of these abstractions will provide a more complete representation of flow into and transport from the EBS under disruptive events. The results from this development will also address portions of integrated subissue ENG2, Mechanical Disruption of Engineered Barriers, including the acceptance criteria for this subissue defined in Section 2.2.1.3.2.3 of the ''Yucca Mountain Review Plan, Final Report'' (NRC 2003 [DIRS 163274]).
DEFF Research Database (Denmark)
Nygaard, Mikkel; Winskel, Glynn
2003-01-01
A fully abstract denotational semantics for the higher-order process language HOPLA is presented. It characterises contextual and logical equivalence, the latter linking up with simulation. The semantics is a clean, domain-theoretic description of processes as downwards-closed sets of computation...
Gortais, Bernard
2003-07-29
In a given social context, artistic creation comprises a set of processes, which relate to the activity of the artist and the activity of the spectator. Through these processes we see and understand that the world is vaster than it is said to be. Artistic processes are mediated experiences that open up the world. A successful work of art expresses a reality beyond actual reality: it suggests an unknown world using the means and the signs of the known world. Artistic practices incorporate the means of creation developed by science and technology and change forms as they change. Artists and the public follow different processes of abstraction at different levels, in the definition of the means of creation, of representation and of perception of a work of art. This paper examines how the processes of abstraction are used within the framework of the visual arts and abstract painting, which appeared during a period of growing importance for the processes of abstraction in science and technology, at the beginning of the twentieth century. The development of digital platforms and new man-machine interfaces allow multimedia creations. This is performed under the constraint of phases of multidisciplinary conceptualization using generic representation languages, which tend to abolish traditional frontiers between the arts: visual arts, drama, dance and music.
Composing Interfering Abstract Protocols
2016-04-01
Tecnologia , Universidade Nova de Lisboa, Caparica, Portugal. This document is a companion technical report of the paper, “Composing Interfering Abstract...a Ciência e Tecnologia (Portuguese Foundation for Science and Technology) through the Carnegie Mellon Portugal Program under grant SFRH / BD / 33765
Reasoning abstractly about resources
Clement, B.; Barrett, A.
2001-01-01
r describes a way to schedule high level activities before distributing them across multiple rovers in order to coordinate the resultant use of shared resources regardless of how each rover decides how to perform its activities. We present an algorithm for summarizing the metric resource requirements of an abstract activity based n the resource usages of its potential refinements.
International Nuclear Information System (INIS)
1987-01-01
The conference proceedings contain 152 abstracts of presented papers relating to various aspects of personnel dosimetry, the dosimetry of the working and living environment, various types of dosemeters and spectrometers, the use of radionuclides in various industrial fields, the migration of radionuclides on Czechoslovak territory after the Chernobyl accident, theoretical studies of some parameters of ionizing radiation detectors, and their calibration. (M.D.)
DEFF Research Database (Denmark)
Fortescue, Michael David
The main thesis of this book is that abstraction, far from being confined to higher formsof cognition, language and logical reasoning, has actually been a major driving forcethroughout the evolution of creatures with brains. It is manifest in emotive as well as rationalthought. Wending its way th...
Impredicative concurrent abstract predicates
DEFF Research Database (Denmark)
Svendsen, Kasper; Birkedal, Lars
2014-01-01
We present impredicative concurrent abstract predicates { iCAP { a program logic for modular reasoning about concurrent, higher- order, reentrant, imperative code. Building on earlier work, iCAP uses protocols to reason about shared mutable state. A key novel feature of iCAP is the ability to dene...
Le Grice, Malcolm
A theoretical and historical account of the main preoccupations of makers of abstract films is presented in this book. The book's scope includes discussion of nonrepresentational forms as well as examination of experiments in the manipulation of time in films. The ten chapters discuss the following topics: art and cinematography, the first…
International Nuclear Information System (INIS)
2015-01-01
The volume contains the abstracts of the SPR (society for pediatric radiology) 2015 meeting covering the following issues: fetal imaging, muscoskeletal imaging, cardiac imaging, chest imaging, oncologic imaging, tools for process improvement, child abuse, contrast enhanced ultrasound, image gently - update of radiation dose recording/reporting/monitoring - meaningful or useless meaning?, pediatric thoracic imaging, ALARA.
DEFF Research Database (Denmark)
Olesen, Henning Salling
2006-01-01
The anniversary of the International Journal of Lifelong Education takes place in the middle of a conceptual landslide from lifelong education to lifelong learning. Contemporary discourses of lifelong learning etc are however abstractions behind which new functions and agendas for adult education...
Proceedings of the ASIS Annual Meeting, 1994
1994-01-01
Includes abstracts of 18 special interest group (SIG) sessions. Highlights include natural language processing, information science and terminology science, classification, knowledge-intensive information systems, information value and ownership issues, economics and theories of information science, information retrieval interfaces, fuzzy thinking…
Circularity and Lambda Abstraction
DEFF Research Database (Denmark)
Danvy, Olivier; Thiemann, Peter; Zerny, Ian
2013-01-01
unknowns from what is done to them, which we lambda-abstract with functions. The circular unknowns then become dead variables, which we eliminate. The result is a strict circu- lar program a la Pettorossi. This transformation is reversible: given a strict circular program a la Pettorossi, we introduce...
Energy Technology Data Exchange (ETDEWEB)
NONE
2015-04-01
The volume contains the abstracts of the SPR (society for pediatric radiology) 2015 meeting covering the following issues: fetal imaging, muscoskeletal imaging, cardiac imaging, chest imaging, oncologic imaging, tools for process improvement, child abuse, contrast enhanced ultrasound, image gently - update of radiation dose recording/reporting/monitoring - meaningful or useless meaning?, pediatric thoracic imaging, ALARA.
Controlling groundwater over abstraction
Naber, Al Majd; Molle, Francois
2017-01-01
The control of groundwater over abstraction is a vexing problem worldwide. Jordan is one of the countries facing severe water scarcity which has implemented a wide range of measures and policies over the past 20 years. While the gap between formal legal and policy frameworks and local practices on
DEFF Research Database (Denmark)
Sergey, Ilya; Devriese, Dominique; Might, Matthew
2013-01-01
to instrument an analysis with high-level strategies for improving precision and performance, such as abstract garbage collection and widening. While the paper itself runs the development for continuationpassing style, our generic implementation replays it for direct-style lambda-calculus and Featherweight Java...
EBS Radionuclide Transport Abstraction
International Nuclear Information System (INIS)
Schreiner, R.
2001-01-01
The purpose of this work is to develop the Engineered Barrier System (EBS) radionuclide transport abstraction model, as directed by a written development plan (CRWMS M and O 1999a). This abstraction is the conceptual model that will be used to determine the rate of release of radionuclides from the EBS to the unsaturated zone (UZ) in the total system performance assessment-license application (TSPA-LA). In particular, this model will be used to quantify the time-dependent radionuclide releases from a failed waste package (WP) and their subsequent transport through the EBS to the emplacement drift wall/UZ interface. The development of this conceptual model will allow Performance Assessment Operations (PAO) and its Engineered Barrier Performance Department to provide a more detailed and complete EBS flow and transport abstraction. The results from this conceptual model will allow PA0 to address portions of the key technical issues (KTIs) presented in three NRC Issue Resolution Status Reports (IRSRs): (1) the Evolution of the Near-Field Environment (ENFE), Revision 2 (NRC 1999a), (2) the Container Life and Source Term (CLST), Revision 2 (NRC 1999b), and (3) the Thermal Effects on Flow (TEF), Revision 1 (NRC 1998). The conceptual model for flow and transport in the EBS will be referred to as the ''EBS RT Abstraction'' in this analysis/modeling report (AMR). The scope of this abstraction and report is limited to flow and transport processes. More specifically, this AMR does not discuss elements of the TSPA-SR and TSPA-LA that relate to the EBS but are discussed in other AMRs. These elements include corrosion processes, radionuclide solubility limits, waste form dissolution rates and concentrations of colloidal particles that are generally represented as boundary conditions or input parameters for the EBS RT Abstraction. In effect, this AMR provides the algorithms for transporting radionuclides using the flow geometry and radionuclide concentrations determined by other
Contextual Perspectives of School Mathematics: What Determines Mathematical Understanding?
White, Loren; Frid, Sandra
Results of a study into secondary school students' and teachers' conceptions of what mathematics is and the purposes of school mathematics are outlined. A total of about 220 first year engineering students and 600 high school students in Australia were involved in the surveys while 40 students, 19 teachers, 2 career counselors, and 2…
Mathematics as verbal behavior.
Marr, M Jackson
2015-04-01
"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. Copyright © 2015 Elsevier B.V. All rights reserved.
Lectures on Applications-Oriented Mathematics
Friedman, Bernard
2011-01-01
Meets the need for a program of short courses involving the essentials of a number of mathematical topics taken by physics and engineering students. Basically applications-oriented, the courses do include selected topics of abstract mathematics. While several courses can be used as practical appendices to conventional mathematics, others serve as introductions, providing motivation for self-study in areas of conceptual math.
Mathematical Literacy: A new literacy or a new mathematics?
Directory of Open Access Journals (Sweden)
Renuka Vithal
2006-10-01
Full Text Available Mathematical Literacy is a ‘hot’ topic at present in most countries, whether it is referred to by that name, or in some cases as Numeracy, or Quantitative Literacy, or Matheracy, or as some part of Ethnomathematics, or related to Mathematics in Society. Questions continue to be asked about what is meant by mathematics in any concept of Mathematical Literacy and the use of the very word ‘Literacy’ in its association with Mathematics has been challenged. Its importance, however, lies in changing our perspective on mathematics teaching, away from the elitism so often associated with much mathematics education, and towards a more equitable, accessible and genuinely educational ideal.
THE CONCEPT OF AGE IN SYSTEMS ANALYSIS
Directory of Open Access Journals (Sweden)
A. Dubi
2012-01-01
Full Text Available
ENGLISH ABSTRACT: This paper discusses the mathematical concept of ageing. It is shown that while in most cases a probabilistic definition of age is sufficient, in some cases a calendaric definition must be added in order to preserve the relationship between time and age.
AFRIKAANSE OPSOMMING: Hierdie artikel bespreek die wiskundige betekenis van veroudering. Daar word getoon dat alhoewel 'n waarskynlikheidsgebaseerde definisie van ouderdom meestal voldoende is, daar in sommige gevalle 'n tydgebaseerde definisie nodig is om die verwantskap tussen tyd en ouderdom te behou.
Pythagoras’ mystery in teaching mathematics
Directory of Open Access Journals (Sweden)
Chio, José Angel
2011-02-01
Full Text Available The article shows the cultural potentials of Mathematic for educating pupils. Reference is made to the mystic beliefs of Pythagoras that determined a conception of the world closely linked to the culture of
Pythagoras’ mystery in teaching mathematics
Chio, José Angel; López, Margarita; Sarduy, Delia
2011-01-01
The article shows the cultural potentials of Mathematic for educating pupils. Reference is made to the mystic beliefs of Pythagoras that determined a conception of the world closely linked to the culture of
Marti, E; Wang, X; Jambari, N N; Rhyner, C; Olzhausen, J; Pérez-Barea, J J; Figueredo, G P; Alcocer, M J C
2015-10-15
Insect bite hypersensitivity (IBH) is a seasonal recurrent skin allergy of horses caused by IgE-mediated reactions to allergens present in the saliva of biting insects of the genus Culicoides, and possibly also Simulium and Stomoxys species. In this work we show that protein microarrays containing complex extracts and pure proteins, including recombinant Culicoides allergens, can be used as a powerful technique for the diagnosis of IBH. Besides the obvious advantages such as general profiling and use of few microliters of samples, this microarray technique permits automation and allows the generation of mathematical models with the calculation of individual risk profiles that can support the clinical diagnosis of allergic diseases. After selection of variables on influence on the projection (VIP), the observed values of sensitivity and specificity were 1.0 and 0.967, respectively. This confirms the highly discriminatory power of this approach for IBH and made it possible to attain a robust predictive mathematical model for this disease. It also further demonstrates the specificity of the protein array method on identifying a particular IgE-mediated disease when the sensitising allergen group is known. Copyright © 2015 Elsevier B.V. All rights reserved.
The Mathematical State of the World
DEFF Research Database (Denmark)
Christensen, Ole Ravn; Skovsmose, Ole; Yasukawa, Keiko
2009-01-01
the concepts of “mathematical description” and “mathematical model” are inadequate to evaluate the use of mathematics in decision-making processes. As a result we develop a conceptual framework that is complex enough to match what goes on in scenarios involving applications of mathematics.......In this article we try to analyse the conditions for describing the world mathematically. We consider the role played by mathematics in discussing and analysing “the state of the world.” We use this discussion to clarify what it means to use a mathematical description. We illustrate why...
1979-12-01
abscess formation and tissue necrosis, its relationship to periodontal pockets was investigated. Specimens were obtained from maxillary and mandibular...of Organisms and Periodontal Pockets." (Abstract 4853). 10. SIMONSON, Lo Go, LAMDERTS, B. L. and JACROLA, Do R. - "Effects of Dextranases and other...the tip of the periodontal probe rests within epithelium, at or slightly apical to the coronal extent of the junctional epithelium. The purpose of
NPP life management (abstracts)
International Nuclear Information System (INIS)
Litvinskij, L.L.; Barbashev, S.V.
2002-01-01
Abstracts of the papers presented at the International conference of the Ukrainian Nuclear Society 'NPP Life Management'. The following problems are considered: modernization of the NPP; NPP life management; waste and spent nuclear fuel management; decommissioning issues; control systems (including radiation and ecological control systems); information and control systems; legal and regulatory framework. State nuclear regulatory control; PR in nuclear power; training of personnel; economics of nuclear power engineering
1982-12-01
Third Molars in Naval Personnel,- (Abstract #1430) 7. A. SEROWSKI* and F. AKER --"The Effect of Marine and Fresh-Water Atmospheric Environments on...record to determine changes in surface coverage or other outcomes -- extraction, endodontic therapy , crown placement -- which occurred over time. The...MR0412002-0443. 0 e5 History of Retention and Extraction of Third Molars in Naval Personnel. D. C. SCHROEDER*, J. C. CECIL and M. E. COHEN. Naval
Energy Technology Data Exchange (ETDEWEB)
NONE
2017-06-15
The volume includes abstracts of the Annual DEGRO Meeting 2017 covering lectures and poster sessions with the following issues: lymphoma, biology, physics, radioimmunotherapy, sarcomas and rare tumors, prostate carcinoma, lung tumors, benign lesions and new media, mamma carcinoma, gastrointestinal tumors, quality of life, care science and quality assurance, high-technology methods and palliative situation, head-and-neck tumors, brain tumors, central nervous system metastases, guidelines, radiation sensitivity, radiotherapy, radioimmunotherapy.
Energy Technology Data Exchange (ETDEWEB)
NONE
2014-05-15
The proceedings of the SPR 2014 meeting include abstracts on the following topics: Body imaging techniques: practical advice for clinic work; thoracic imaging: focus on the lungs; gastrointestinal imaging: focus on the pancreas and bowel; genitourinary imaging: focus on gonadal radiology; muscoskeletal imaging; focus on oncology; child abuse and nor child abuse: focus on radiography; impact of NMR and CT imaging on management of CHD; education and communication: art and practice in pediatric radiology.
International Nuclear Information System (INIS)
2014-01-01
The proceedings of the SPR 2014 meeting include abstracts on the following topics: Body imaging techniques: practical advice for clinic work; thoracic imaging: focus on the lungs; gastrointestinal imaging: focus on the pancreas and bowel; genitourinary imaging: focus on gonadal radiology; muscoskeletal imaging; focus on oncology; child abuse and nor child abuse: focus on radiography; impact of NMR and CT imaging on management of CHD; education and communication: art and practice in pediatric radiology.
International Nuclear Information System (INIS)
Bianchi, E.; Bender, C.; Culetu, H.; Fried, H.; Grossmann, A.; Hofmann, R.; Le Bellac, M.; Martinetti, P.; Muller, B.; Patras, F.; Raffaeli, B.; Vitting Andersen, J.
2013-01-01
The object of this workshop is to consolidate and publicize new efforts in non-perturbative field theories. This year the presentations deal with quantum gravity, non-commutative geometry, fat-tailed wave-functions, strongly coupled field theories, space-times two time-like dimensions, and multiplicative renormalization. A presentation is dedicated to the construction of a nucleon-nucleon potential from an analytical, non-perturbative gauge invariant QCD. This document gathers the abstracts of the presentations
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
Interactive whiteboard in mathematics education
Cendelín, Jan
2013-01-01
Title: Interactive whiteboard in mathematics education Author: Bc. Jan Cendelín Department:Department of Mathematics Education Supervisor: RNDr. Antonín Slavík, Ph.D., Department of Mathematics Education Abstract: The development of modern technology is very fast. Almost everyone uses the technology at work and at home as well. So it is not unexpected that the technology gets into education at schools. This thesis focuses on the education of modern mathematics, and especially on the use of th...
The Constructivist Mathematics Classroom
Jones, Karrie; Jones, Jennifer L.; Vermette, Paul J.
2010-01-01
By examining how people learn, the educational theories of Dewey, Piaget, Vygotsky and Bruner can be synthesized to give this set of core Constructivist principles. Principles of effective mathematics teaching: (1) allows learning that is "active" and "reflective". Students are required to transfer key concepts to new situations; (2) allows…
Sax, Linda J.; Kanny, M. Allison; Riggers-Piehl, Tiffani A.; Whang, Hannah; Paulson, Laura N.
2015-01-01
Math self-concept (MSC) is considered an important predictor of the pursuit of science, technology, engineering and math (STEM) fields. Women's underrepresentation in the STEM fields is often attributed to their consistently lower ratings on MSC relative to men. Research in this area typically considers STEM in the aggregate and does not account…
DEFF Research Database (Denmark)
Thorsteinsson, Uffe
1999-01-01
Discussion about concept in industrial companies. A method for mapping of managerial concept in specific area is shown......Discussion about concept in industrial companies. A method for mapping of managerial concept in specific area is shown...
Trinajstić, Nenad; Gutman, Ivan
2002-01-01
A brief description is given of the historical development of mathematics and chemistry. A path leading to the meeting of these two sciences is described. An attempt is made to define mathematical chemistry, and journals containing the term mathematical chemistry in their titles are noted. In conclusion, the statement is made that although chemistry is an experimental science aimed at preparing new compounds and materials, mathematics is very useful in chemistry, among other things, to produc...
The Philosophy of Mathematics Education
DEFF Research Database (Denmark)
mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards......This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical...... research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also...
Making Meaning of Creativity and Mathematics Teaching
DEFF Research Database (Denmark)
Misfeldt, Morten
2014-01-01
. One reason is that it is not clear what relation such creative and innovative skills have to mathematics, and how we should teach them. In this paper, I review different conceptions of creativity in mathematics education and investigate what mathematical innovation and creativity “are......Creativity and innovation are important 21st-century skills, and mathematics education contributes to the development of these skills. However, it is far from clear how we as mathematics educators should respond to the need to contribute to our students’ development of creativity and innovation......” in the mathematical classroom. I show how different conceptions of mathematical innovation and creativity dominate different parts of the mathematics education literature, and explain how these differences can be viewed as framing mathematical creativity toward different domains....
Functional Abstraction of Stochastic Hybrid Systems
Bujorianu, L.M.; Blom, Henk A.P.; Hermanns, H.
2006-01-01
The verification problem for stochastic hybrid systems is quite difficult. One method to verify these systems is stochastic reachability analysis. Concepts of abstractions for stochastic hybrid systems are needed to ease the stochastic reachability analysis. In this paper, we set up different ways
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
THE MATHEMATICS-LANGUAGE SYMBIOSIS: THE LEARNERS ...
African Journals Online (AJOL)
JONATHAN
2016-07-01
Jul 1, 2016 ... will touch some basic concepts in grammar or language. The consequence is that such ..... programming. The concept of the function ..... mathematical problems solving are closely related to language. They share the idea that ...
Koreuber, Mechthild
2015-09-01
,,She [Noether] then appeared as the creator of a new direction in algebra and became the leader, the most consistent and brilliant representative, of a particular mathematical doctrine - of all that is characterized by the term ‚Begriffliche Mathematik‘.“ The aim of this paper is to illuminate this "new direction", which can be characterized as a conceptual [begriffliche] perspective in mathematics, and to comprehend its roots and trace its establishment. Field, ring, ideal, the core concepts of this new direction in mathematical images of knowledge, were conceptualized by Richard Dedekind (1831-1916) within the scope of his number theory research and associated with an understanding of a formation of concepts as a "free creation of the human spirit". They thus stand for an abstract perspective of mathematics in their entirety, described as 'modern algebra' in the 1920s and 1930s, leading to an understanding of mathematics as structural sciences. The establishment of this approach to mathematics, which is based on "general mathematical concepts" [allgemein-mathematische Begriffe], was the success of a cultural movement whose most important protagonists included Emmy Noether (1882-1935) and her pupil Bartel L. van der Waerden (1903-1996). With the use of the term 'conceptual', a perspective is taken in the analysis which allows for developing connections between the thinking of Dedekind, the "working and conceptual methods" [Arbeits- und Auffassungsmethoden] of Noether as well as the methodological approach, represented through the thought space of the Noether School as presented under the term "conceptual world" [Begriffswelt] in the Moderne Algebra of van der Waerden. This essay thus makes a contribution to the history of the introduction of a structural perspective in mathematics, a perspective that is inseparable from the mathematical impact of Noether, her reception of the work of Dedekind and the creative strength of the Noether School.
International Nuclear Information System (INIS)
1978-01-01
This volume contains the program and abstracts of the conference. The following topics are included: metal vapor molecular lasers, magnetohydrodynamics, rare gas halide and nuclear pumped lasers, transfer mechanisms in arcs, kinetic processes in rare gas halide lasers, arcs and flows, XeF kinetics and lasers, fundamental processes in excimer lasers, electrode effects and vacuum arcs, electron and ion transport, ion interactions and mobilities, glow discharges, diagnostics and afterglows, dissociative recombination, electron ionization and excitation, rare gas excimers and group VI lasers, breakdown, novel laser pumping techniques, electrode-related discharge phenomena, photon interactions, attachment, plasma chemistry and infrared lasers, electron scattering, and reactions of excited species
Clark, Allan
1984-01-01
This concise, readable, college-level text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems.Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results needed for Galois theory as well as the Sylow theorems, the Jordan-Holder theorem, and a complete treatment of the simplicity of alternating groups. Chapter III (Field Theory)
Energy Technology Data Exchange (ETDEWEB)
NONE
2017-05-15
The conference proceedings SPR 2017 include abstracts on the following issues: gastrointestinal radiography - inflammatory bowel diseases, cardiovascular CTA, general muscoskeletal radiology, muscoskeletal congenital development diseases, general pediatric radiology - chest, muscoskeletal imaging - marrow and infectious disorders, state-of-the-art body MR imaging, practical pediatric sonography, quality and professionalism, CT imaging in congenital heart diseases, radiographic courses, body MT techniques, contrast enhanced ultrasound, machine learning, forensic imaging, the radiation dos conundrum - reconciling imaging, imagining and managing, the practice of radiology, interventional radiology, neuroradiology, PET/MR.
International Nuclear Information System (INIS)
Entsua-Mensah, Clement
1994-01-01
Ghana Energy Abstracts 1994 is the first issue of an annual publication of the Energy information Centre. The aim is to combine in one publication the country' s bibliographic output on energy so as to provide a valuable source of reference for policy makers, planners,and researchers. It covers the broad spectrum of energy including; energy conservation, energy resource management, petroleum and renewable energy resources.The documents listed comprise research reports, baseline studies,conference proceedings, periodical articles dissertations and theses. Keywords and author indexes have been provided to facilitate easy reference. (C.E.M)
Parameterized Dataflow (Extended Abstract
Directory of Open Access Journals (Sweden)
Dominic Duggan
2016-10-01
Full Text Available Dataflow networks have application in various forms of stream processing, for example for parallel processing of multimedia data. The description of dataflow graphs, including their firing behavior, is typically non-compositional and not amenable to separate compilation. This article considers a dataflow language with a type and effect system that captures the firing behavior of actors. This system allows definitions to abstract over actor firing rates, supporting the definition and safe composition of actor definitions where firing rates are not instantiated until a dataflow graph is launched.
International Nuclear Information System (INIS)
2015-01-01
The volume includes the abstracts of the ESPR 2015 covering the following topics: PCG (post graduate courses): Radiography; fluoroscopy and general issue; nuclear medicine, interventional radiology and hybrid imaging, pediatric CT, pediatric ultrasound; MRI in childhood. Scientific sessions and task force sessions: International aspects; neuroradiology, neonatal imaging, engineering techniques to simulate injury in child abuse, CT - dose and quality, challenges in the chest, cardiovascular and chest, muscoskeletal, oncology, pediatric uroradiology and abdominal imaging, fetal and postmortem imaging, education and global challenges, neuroradiology - head and neck, gastrointestinal and genitourinary.
International Nuclear Information System (INIS)
Wilson, Michael L.
2001-01-01
Drift seepage refers to flow of liquid water into repository emplacement drifts, where it can potentially contribute to degradation of the engineered systems and release and transport of radionuclides within the drifts. Because of these important effects, seepage into emplacement drifts is listed as a ''principal factor for the postclosure safety case'' in the screening criteria for grading of data in Attachment 1 of AP-3.15Q, Rev. 2, ''Managing Technical Product Inputs''. Abstraction refers to distillation of the essential components of a process model into a form suitable for use in total-system performance assessment (TSPA). Thus, the purpose of this analysis/model is to put the information generated by the seepage process modeling in a form appropriate for use in the TSPA for the Site Recommendation. This report also supports the Unsaturated-Zone Flow and Transport Process Model Report. The scope of the work is discussed below. This analysis/model is governed by the ''Technical Work Plan for Unsaturated Zone Flow and Transport Process Model Report'' (CRWMS MandO 2000a). Details of this activity are in Addendum A of the technical work plan. The original Work Direction and Planning Document is included as Attachment 7 of Addendum A. Note that the Work Direction and Planning Document contains tasks identified for both Performance Assessment Operations (PAO) and Natural Environment Program Operations (NEPO). Only the PAO tasks are documented here. The planning for the NEPO activities is now in Addendum D of the same technical work plan and the work is documented in a separate report (CRWMS MandO 2000b). The Project has been reorganized since the document was written. The responsible organizations in the new structure are the Performance Assessment Department and the Unsaturated Zone Department, respectively. The work plan for the seepage abstraction calls for determining an appropriate abstraction methodology, determining uncertainties in seepage, and providing
Energy Technology Data Exchange (ETDEWEB)
NONE
2016-05-15
The volume on the meeting of pediatric radiology includes abstract on the following issues: chest, cardiovascular system, neuroradiology, CT radiation DRs (diagnostic reference levels) and dose reporting guidelines, genitourinary imaging, gastrointestinal radiology, oncology an nuclear medicine, whole body imaging, fetal/neonates imaging, child abuse, oncology and hybrid imaging, value added imaging, muscoskeletal imaging, dose and radiation safety, imaging children - immobilization and distraction techniques, information - education - QI and healthcare policy, ALARA, the knowledge skills and competences for a technologist/radiographer in pediatric radiology, full exploitation of new technological features in pediatric CT, image quality issues in pediatrics, abdominal imaging, interventional radiology, MR contrast agents, tumor - mass imaging, cardiothoracic imaging, ultrasonography.
Energy Technology Data Exchange (ETDEWEB)
NONE
2015-05-10
The volume includes the abstracts of the ESPR 2015 covering the following topics: PCG (post graduate courses): Radiography; fluoroscopy and general issue; nuclear medicine, interventional radiology and hybrid imaging, pediatric CT, pediatric ultrasound; MRI in childhood. Scientific sessions and task force sessions: International aspects; neuroradiology, neonatal imaging, engineering techniques to simulate injury in child abuse, CT - dose and quality, challenges in the chest, cardiovascular and chest, muscoskeletal, oncology, pediatric uroradiology and abdominal imaging, fetal and postmortem imaging, education and global challenges, neuroradiology - head and neck, gastrointestinal and genitourinary.
International Nuclear Information System (INIS)
2016-01-01
The volume on the meeting of pediatric radiology includes abstract on the following issues: chest, cardiovascular system, neuroradiology, CT radiation DRs (diagnostic reference levels) and dose reporting guidelines, genitourinary imaging, gastrointestinal radiology, oncology an nuclear medicine, whole body imaging, fetal/neonates imaging, child abuse, oncology and hybrid imaging, value added imaging, muscoskeletal imaging, dose and radiation safety, imaging children - immobilization and distraction techniques, information - education - QI and healthcare policy, ALARA, the knowledge skills and competences for a technologist/radiographer in pediatric radiology, full exploitation of new technological features in pediatric CT, image quality issues in pediatrics, abdominal imaging, interventional radiology, MR contrast agents, tumor - mass imaging, cardiothoracic imaging, ultrasonography.
The Joy of Mathematics Discovering Mathematics All Around You
Pappas, Theoni
1993-01-01
Part of the joy of mathematics is that it is everywhere-in soap bubbles, electricity, da Vinci's masterpieces, even in an ocean wave. Written by the well-known mathematics teacher consultant, this volume's collection of over 200 clearly illustrated mathematical ideas, concepts, puzzles, and games shows where they turn up in the "real" world. You'll find out what a googol is, visit hotel infinity, read a thorny logic problem that was stumping them back in the 8th century. THE JOY OF MATHEMATICS is designed to be opened at random…it's mini essays are self-contained providing the reader
Selection of Learning Media Mathematics for Junior School Students
Widodo, Sri Adi; Wahyudin
2018-01-01
One of the factors that determine the success of mathematics learning is the learning media used. Learning media can help students to create mathematical abstract mathematics that is abstract. In addition to media, meaningful learning is a learning that is adapted to the students' cognitive development. According to Piaget, junior high school…
ProofJudge: Automated Proof Judging Tool for Learning Mathematical Logic
DEFF Research Database (Denmark)
Villadsen, Jørgen
2015-01-01
Today we have software in many artefacts, from medical devices to cars and airplanes, and the software must not only be efficient and intelligent but also reliable and secure. Tests can show the presence of bugs but cannot guarantee their absence. A machine-checked proof using mathematical logic...... pen and paper because no adequate tool was available. The learning problem is how to make abstract concepts of logic as concrete as possible. ProofJudge is a computer system and teaching approach for teaching mathematical logic and automated reasoning which augments the e-learning tool NaDeA (Natural...
ProofJudge: Automated Proof Judging Tool for Learning Mathematical Logic
DEFF Research Database (Denmark)
Villadsen, Jørgen
2016-01-01
Today we have software in many artefacts, from medical devices to cars and airplanes, and the software must not only be efficient and intelligent but also reliable and secure. Tests can show the presence of bugs but cannot guarantee their absence. A machine-checked proof using mathematical logic...... using pen and paper because no adequate tool was available. The learning problem is how to make abstract concepts of logic as concrete as possible. ProofJudge is a computer system and teaching approach for teaching mathematical logic and automated reasoning which augments the e-learning tool Na...
Mathematical Modeling and Pure Mathematics
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…
Mathematics and engineering in real life through mathematical competitions
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.
Annas, Suwardi; Djadir; Mutmainna Hasma, Sitti
2018-01-01
on is an activity to organize a mathematical concept that has been previously owned into a new mathematical structure. Activites in abstraction are recognizing, organizing and constructing. Recognizing is a process of identifying a mathematical structure that had existed before. Organizing is a process of using structural knowledge to be assembled into a solution of a problem and constructing is a process of organizing the characteristics of the object into a new structure that does not exist. In abstraction process, the students use attributes to address the object, including routine attribute, nonroutine attributes, and meaningless attributes. This research applied descriptive qualitative research which aimed to describe the abstraction ability of students from high, moderate, and low groups to construct a relation within triangle. In collecting the data, this research used students’ pre-ability math test, abstraction test, and guided interview. The sampling technique in this research was based on the students’ scores in pre-ability math test, which were divided into three groups. Two students from each group were opted as the subjects of this research. Questions of the test are based on the indicators of steps in abstraction activity. Thus, based on the data gained in this research, researcher determined the tendency of attributes used in each abstraction activity. The result of this research revealed that students from high, moderate and low groups were prone to use routine attributes in recognizing triangles. In organizing the characteristics within triangles, high group tended to organize the triangle correctly, while the moderate and low groups tended to organize the triangle incorrectly. In constructing relation within triangles, students in high, moderate and low groups construct it incompletely.
Bottle Caps as Prekindergarten Mathematical Tools
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,…
Bingo! Select Games for Mathematical Thinking
Jackson, Christa; Taylor, Cynthia; Buchheister, Kelley
2013-01-01
Games can both generate excitement among students and motivate them to participate in mathematics. Although games have been used primarily to "review" mathematical concepts at the middle school level, games should, and often do, have other instructional purposes. When teachers use mathematical games as an instructional strategy, they are…
Descartes’s mathematical thought
Sasaki, Chikara
2003-01-01
Covering both the history of mathematics and of philosophy, Descartes's Mathematical Thought reconstructs the intellectual career of Descartes most comprehensively and originally in a global perspective including the history of early modern China and Japan. Especially, it shows what the concept of "mathesis universalis" meant before and during the period of Descartes and how it influenced the young Descartes. In fact, it was the most fundamental mathematical discipline during the seventeenth century, and for Descartes a key notion which may have led to his novel mathematics of algebraic analysis.
Mathematics for physics with calculus
Das, Biman
2005-01-01
Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful-and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.
The challenge of computer mathematics.
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.
Conceptualising inquiry based education in mathematics
DEFF Research Database (Denmark)
Blomhøj, Morten; Artigue, Michéle
2013-01-01
of inquiry as a pedagogical concept in the work of Dewey (e.g. 1916, 1938) to analyse and discuss its migration to science and mathematics education. For conceptualizing inquiry-based mathematics education (IBME) it is important to analyse how this concept resonates with already well-established theoretical...... frameworks in mathematics education. Six such frameworks are analysed from the perspective of inquiry: the problem-solving tradition, the Theory of Didactical Situations, the Realistic Mathematics Education programme, the mathematical modelling perspective, the Anthropological Theory of Didactics...
DOE Fundamentals Handbook: Mathematics, Volume 1
International Nuclear Information System (INIS)
1992-06-01
The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations
DOE Fundamentals Handbook: Mathematics, Volume 2
International Nuclear Information System (INIS)
1992-06-01
The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Energy Technology Data Exchange (ETDEWEB)
Sahin, S [Gazi University, Technical Education Faculty, Ankara (Turkey)
2007-07-01
In this book Conference Program and Abstracts were included 13th International Conference on Emerging Nuclear Energy Systems which held between 03-08 June 2007 in Istanbul, Turkey. The main objective of International Conference series on Emerging Nuclear Energy Systems (ICENES) is to provide an international scientific and technical forum for scientists, engineers, industry leaders, policy makers, decision makers and young professionals who will shape future energy supply and technology , for a broad review and discussion of various advanced, innovative and non-conventional nuclear energy production systems. The main topics of 159 accepted papers from 35 countries are fusion science and technology, fission reactors, accelerator driven systems, transmutation, laser in nuclear technology, radiation shielding, nuclear reactions, hydrogen energy, solar energy, low energy physics and societal issues.
International Nuclear Information System (INIS)
Sahin, S.
2007-01-01
In this book Conference Program and Abstracts were included 13th International Conference on Emerging Nuclear Energy Systems which held between 03-08 June 2007 in Istanbul, Turkey. The main objective of International Conference series on Emerging Nuclear Energy Systems (ICENES) is to provide an international scientific and technical forum for scientists, engineers, industry leaders, policy makers, decision makers and young professionals who will shape future energy supply and technology , for a broad review and discussion of various advanced, innovative and non-conventional nuclear energy production systems. The main topics of 159 accepted papers from 35 countries are fusion science and technology, fission reactors, accelerator driven systems, transmutation, laser in nuclear technology, radiation shielding, nuclear reactions, hydrogen energy, solar energy, low energy physics and societal issues
Computational Abstraction Steps
DEFF Research Database (Denmark)
Thomsen, Lone Leth; Thomsen, Bent; Nørmark, Kurt
2010-01-01
and class instantiations. Our teaching experience shows that many novice programmers find it difficult to write programs with abstractions that materialise to concrete objects later in the development process. The contribution of this paper is the idea of initiating a programming process by creating...... or capturing concrete values, objects, or actions. As the next step, some of these are lifted to a higher level by computational means. In the object-oriented paradigm the target of such steps is classes. We hypothesise that the proposed approach primarily will be beneficial to novice programmers or during...... the exploratory phase of a program development process. In some specific niches it is also expected that our approach will benefit professional programmers....
IEEE conference record -- Abstracts
International Nuclear Information System (INIS)
Anon.
1994-01-01
This conference covers the following areas: computational plasma physics; vacuum electronic; basic phenomena in fully ionized plasmas; plasma, electron, and ion sources; environmental/energy issues in plasma science; space plasmas; plasma processing; ball lightning/spherical plasma configurations; plasma processing; fast wave devices; magnetic fusion; basic phenomena in partially ionized plasma; dense plasma focus; plasma diagnostics; basic phenomena in weakly ionized gases; fast opening switches; MHD; fast z-pinches and x-ray lasers; intense ion and electron beams; laser-produced plasmas; microwave plasma interactions; EM and ETH launchers; solid state plasmas and switches; intense beam microwaves; and plasmas for lighting. Separate abstracts were prepared for 416 papers in this conference
Imbs, Diane-Charlotte; El Cheikh, Raouf; Boyer, Arnaud; Ciccolini, Joseph; Mascaux, Céline; Lacarelle, Bruno; Barlesi, Fabrice; Barbolosi, Dominique; Benzekry, Sébastien
2018-01-01
Concomitant administration of bevacizumab and pemetrexed-cisplatin is a common treatment for advanced nonsquamous non-small cell lung cancer (NSCLC). Vascular normalization following bevacizumab administration may transiently enhance drug delivery, suggesting improved efficacy with sequential administration. To investigate optimal scheduling, we conducted a study in NSCLC-bearing mice. First, experiments demonstrated improved efficacy when using sequential vs. concomitant scheduling of bevacizumab and chemotherapy. Combining this data with a mathematical model of tumor growth under therapy accounting for the normalization effect, we predicted an optimal delay of 2.8 days between bevacizumab and chemotherapy. This prediction was confirmed experimentally, with reduced tumor growth of 38% as compared to concomitant scheduling, and prolonged survival (74 vs. 70 days). Alternate sequencing of 8 days failed in achieving a similar increase in efficacy, thus emphasizing the utility of modeling support to identify optimal scheduling. The model could also be a useful tool in the clinic to personally tailor regimen sequences. © 2017 The Authors CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals, Inc. on behalf of American Society for Clinical Pharmacology and Therapeutics.
Newton, Lawrence R.
This project (1) identifies basic and functional mathematics skills (shop mathematics skills), (2) provides pretests on these functional mathematics skills, and (3) provides student learning projects (project sheets) that prepare metal trades students to read, understand, and apply mathematics and measuring skills that meet entry-level job…
The possibilities of a modelling perspective for school mathematics
Directory of Open Access Journals (Sweden)
Dirk Wessels
2009-09-01
complex teaching methodology requires in-depth thinking about the role of the teacher, the role of the learner, the nature of the classroom culture, the nature of the negotiation of meaning between the teacher and individuals or groups, the nature of selected problems and material, as well as the kind of integrative assessment used in the mathematics classroom. Modelling is closely related to the problem-centred teaching approach, but it also smoothly relates to bigger and longer mathematical tasks. This article gives a theoretical exposition of the scope and depth of mathematical modelling. It is possible to introduce modelling at every school phase in our educational sytem. Modelling in school mathematics seems to make the learning of mathematics more effective. The mastering of problem solving and modelling strategies has deﬁnitely changed the orientation, the competencies and performances of learners at each school level. It would appear from research that learners like the application side of mathematics and that they want to see it in action. Genuine real life problems should be selected, which is why a modelling perspective is so important for the teaching and mastering of mathematics. Modelling should be integrated into the present curriculum because learners will then get full access to involvement in the classroom, to mathematisation, to doing problems, to criticising arguments, to ﬁnding proofs, to recognising concepts and to obtaining the ability to abstract these from the realistic situation. Modelling should be given a full opportunity in mathematics teacher education so that our learners can get the full beneﬁt of it. This will put the mathematical performances of learners in our country on a more solid base, which will make our learners more competitive at all levels in the future.
Primary Mathematics. A Saxon Teacher's Resource Booklet.
1997
Saxon's primary mathematics series is a "hands-on," success-oriented program which emphasizes manipulatives and mental math. The series addresses the multisensory approach to teaching. Its use enables all children to develop a solid foundation in the language and basic concepts of mathematics. Concepts are presented in carefully…
The Psychological Basis of Learning Mathematics.
Ruberu, J.
1982-01-01
Mathematics is a hierarchial build-up of concepts and the process of this systematic building up of concepts is of prime importance in the study of mathematics. Although discovery approaches are currently used, there are limitations. Ausubel's "meaningful learning" approach is suggested as an alternative to discovery learning in…
Applied mathematics made simple
Murphy, Patrick
1982-01-01
Applied Mathematics: Made Simple provides an elementary study of the three main branches of classical applied mathematics: statics, hydrostatics, and dynamics. The book begins with discussion of the concepts of mechanics, parallel forces and rigid bodies, kinematics, motion with uniform acceleration in a straight line, and Newton's law of motion. Separate chapters cover vector algebra and coplanar motion, relative motion, projectiles, friction, and rigid bodies in equilibrium under the action of coplanar forces. The final chapters deal with machines and hydrostatics. The standard and conte
Problem Posing with Realistic Mathematics Education Approach in Geometry Learning
Mahendra, R.; Slamet, I.; Budiyono
2017-09-01
One of the difficulties of students in the learning of geometry is on the subject of plane that requires students to understand the abstract matter. The aim of this research is to determine the effect of Problem Posing learning model with Realistic Mathematics Education Approach in geometry learning. This quasi experimental research was conducted in one of the junior high schools in Karanganyar, Indonesia. The sample was taken using stratified cluster random sampling technique. The results of this research indicate that the model of Problem Posing learning with Realistic Mathematics Education Approach can improve students’ conceptual understanding significantly in geometry learning especially on plane topics. It is because students on the application of Problem Posing with Realistic Mathematics Education Approach are become to be active in constructing their knowledge, proposing, and problem solving in realistic, so it easier for students to understand concepts and solve the problems. Therefore, the model of Problem Posing learning with Realistic Mathematics Education Approach is appropriately applied in mathematics learning especially on geometry material. Furthermore, the impact can improve student achievement.
Mathematics is always invisible, Professor Dowling
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.
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.)
Areepattamannil, Shaljan; Khine, Myint Swe; Melkonian, Michael; Welch, Anita G; Al Nuaimi, Samira Ahmed; Rashad, Fatimah F
2015-10-01
Drawing on data from the 2012 Program for International Student Assessment (PISA) and employing multilevel modeling as an analytic strategy, this study examined the relations of adolescent children's perceptions of their parents' attitudes towards mathematics to their own attitudes towards mathematics and mathematics achievement among a sample of 5116 adolescents from 384 schools in the United Arab Emirates. The results of this cross-sectional study revealed that adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children not only to study but also for their career tended to report higher levels of intrinsic and instrumental motivation to learn mathematics, mathematics self-concept and self-efficacy, and mathematics work ethic. Moreover, adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children's career tended to report positive intentions and behaviors toward mathematics. However, adolescents who perceived that their parents considered mathematics was important for their children's career tended to report higher levels of mathematics anxiety. Finally, adolescents who perceived that their parents considered mathematics was important for their children to study performed significantly better on the mathematics assessment than did their peers whose parents disregarded the importance of learning mathematics. Copyright © 2015 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.
Contents, Abstracts and Keywords
Institute of Scientific and Technical Information of China (English)
2012-01-01
The Ethnic Minority Rights from the Angle of Multiculturalism Zhou Shaoqing（1） Abstract： Historically, multiculturalism was closely related to the ethnic minority rights. Currently there are two features in the research on multiculturalism and the ethnic minority rights. One is that most researchers do not strictly distinguish the different dimensions of multiculturalism, the other is that they tend to regard only multiculturalism as a theory of the ethnic minority rights, and less attach its importance to the multi-ethnie state construction. The thesis argues that multiculturalism has at least five dimensions, such as fact, theory, ideology, policy, and normative principle. The concept of the ethnic minority rights in each dimension has its special meaning and effect. The ethnic minority rights protection and the multi-ethnic state construction are two different aspects in the same historical process. Multiculturalism is not only a theory of the ethnic minority rights, but also an important supportive theory of the multi-ethnic state construction.
1998-09-23
the First Hypothesis of Plato’s Parmenides and the Undecidable Sentence of Kurt Godel 155 D. Drai Concepts of validity 156 M. L Zelbert, Logical...account of mathematics in the "Tractatus". -154- LC Book of Abstracts A Comparison Between the First Hypothesis of Plato’s Parmenides and the...42)(05)43129386 svandova@jumbo.ped.muni.cz in the second half of the twentieth century there has been a revival of interest in Plato’s Parmenides
Yakubova, Gulnoza; Hughes, Elizabeth M; Shinaberry, Megan
2016-07-01
The purpose of this study was to determine the effectiveness of a video modeling intervention with concrete-representational-abstract instructional sequence in teaching mathematics concepts to students with autism spectrum disorder (ASD). A multiple baseline across skills design of single-case experimental methodology was used to determine the effectiveness of the intervention on the acquisition and maintenance of addition, subtraction, and number comparison skills for four elementary school students with ASD. Findings supported the effectiveness of the intervention in improving skill acquisition and maintenance at a 3-week follow-up. Implications for practice and future research are discussed.
Aigner, Martin; Spain, Philip G
2010-01-01
Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" unde
Pappas, Theoni
1997-01-01
In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre ? in short, the human background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics?Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions
Stroud, K A
2013-01-01
A groundbreaking and comprehensive reference that's been a bestseller since it first debuted in 1970, the new seventh edition of Engineering Mathematics has been thoroughly revised and expanded. Providing a broad mathematical survey, this innovative volume covers a full range of topics from the very basic to the advanced. Whether you're an engineer looking for a useful on-the-job reference or want to improve your mathematical skills, or you are a student who needs an in-depth self-study guide, Engineering Mathematics is sure to come in handy time and time again.
Introduction to the theory of abstract algebras
Pierce, Richard S
2014-01-01
Intended for beginning graduate-level courses, this text introduces various aspects of the theory of abstract algebra. The book is also suitable as independent reading for interested students at that level as well as a primary source for a one-semester course that an instructor may supplement to expand to a full year. Author Richard S. Pierce, a Professor of Mathematics at Seattle's University of Washington, places considerable emphasis on applications of the theory and focuses particularly on lattice theory.After a preliminary review of set theory, the treatment presents the basic definitions
Exponentially Convergent Algorithms for Abstract Differential Equations
Gavrilyuk, Ivan; Vasylyk, Vitalii
2011-01-01
This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for the practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as the partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which
Exoplanets and Multiverses (Abstract)
Trimble, V.
2016-12-01
(Abstract only) To the ancients, the Earth was the Universe, of a size to be crossed by a god in a day, by boat or chariot, and by humans in a lifetime. Thus an exoplanet would have been a multiverse. The ideas gradually separated over centuries, with gradual acceptance of a sun-centered solar system, the stars as suns likely to have their own planets, other galaxies beyond the Milky Way, and so forth. And whenever the community divided between "just one' of anything versus "many," the "manies" have won. Discoveries beginning in 1991 and 1995 have gradually led to a battalion or two of planets orbiting other stars, very few like our own little family, and to moderately serious consideration of even larger numbers of other universes, again very few like our own. I'm betting, however, on habitable (though not necessarily inhabited) exoplanets to be found, and habitable (though again not necessarily inhabited) universes. Only the former will yield pretty pictures.
International Nuclear Information System (INIS)
Lumsden, M.D.; Argyriou, D.N.; Inosov, D.
2012-01-01
The microscopic origin of unconventional superconductivity continues to attract the attention of the condensed matter community. Whereas rare-earth / actinide-based intermetallic and copper oxide-based high temperature superconductors are studied for more than twenty years, the iron-based superconductors have been in the focus of interest since their recent discovery. Inelastic neutron scattering experiments have been of particular importance for the understanding of the magnetic and superconducting properties of these compounds. With its 29 talks and 14 posters the workshop provided a forum for the 71 registered participants to review and discuss experimental achievements, recognize the observed synergy and differences as well as discuss theoretical efforts to identify the symmetry of the superconducting order parameter in addition to the coupling mechanisms of the Cooper pairs. The workshop covered different topics relevant for the study of unconventional superconductivity. Magnetization and lattice dynamics such as spin resonances, phonons, magnetic and other excitations as studied by spectroscopic methods were presented. Investigations of (doping, pressure and magnetic field dependent) phase diagrams, electronic states as well as vortex physics by the various diffraction techniques were also addressed. This document gathers only the abstracts of the papers. (authors)
International Nuclear Information System (INIS)
2013-06-01
ANIMMA 2013 is the third of a series of conferences devoted to endorsing and promoting scientific and technical activities based on nuclear instrumentation and measurements. The main objective of ANIMMA conference is to unite the various scientific communities not only involved in nuclear instrumentation and measurements, but also in nuclear medicine and radiation. The conference is all about getting scientists, engineers and the industry to meet, exchange cultures and identify new scientific and technical prospects to help overcome both current and future unresolved issues. The conference provides scientists and engineers with a veritable opportunity to compare their latest research and development in different areas: physics, nuclear energy, nuclear fuel cycle, safety, security, future energies (GEN III+, GENIV, ITER, ...). The conference topics include instrumentation and measurement methods for: Fundamental physics; Fusion diagnostics and technology; Nuclear power reactors; Research reactors; Nuclear fuel cycle; Decommissioning, dismantling and remote handling; Safeguards, homeland security; Severe accident monitoring; Environmental and medical sciences; Education, training and outreach. This document brings together the abstracts of the presentations. Each presentation (full paper) is analysed separately and entered in INIS
Automated Supernova Discovery (Abstract)
Post, R. S.
2015-12-01
(Abstract only) We are developing a system of robotic telescopes for automatic recognition of Supernovas as well as other transient events in collaboration with the Puckett Supernova Search Team. At the SAS2014 meeting, the discovery program, SNARE, was first described. Since then, it has been continuously improved to handle searches under a wide variety of atmospheric conditions. Currently, two telescopes are used to build a reference library while searching for PSN with a partial library. Since data is taken every night without clouds, we must deal with varying atmospheric and high background illumination from the moon. Software is configured to identify a PSN, reshoot for verification with options to change the run plan to acquire photometric or spectrographic data. The telescopes are 24-inch CDK24, with Alta U230 cameras, one in CA and one in NM. Images and run plans are sent between sites so the CA telescope can search while photometry is done in NM. Our goal is to find bright PSNs with magnitude 17.5 or less which is the limit of our planned spectroscopy. We present results from our first automated PSN discoveries and plans for PSN data acquisition.
Mathematical Model for the Control of measles 1*PETER, OJ ...
African Journals Online (AJOL)
PROF HORSFALL
2018-04-16
Apr 16, 2018 ... 5Department of Mathematics/Statistics, Federal University of Technology, Minna, Nigeria ... ABSTRACT: We proposed a mathematical model of measles disease dynamics with vaccination by ...... Equation with application.
A new hierarchy of infinitary logics in abstract algebraic logic
Czech Academy of Sciences Publication Activity Database
Lávička, Tomáš; Noguera, Carles
2017-01-01
Roč. 105, č. 3 (2017), s. 521-551 ISSN 0039-3215 R&D Projects: GA ČR GA13-14654S EU Projects: European Commission(XE) 689176 - SYSMICS Institutional support: RVO:67985556 ; RVO:67985807 Keywords : Abstract algebraic logic * consequence relations * infinitary logics * completeness properties Subject RIV: BA - General Mathematics; BA - General Mathematics (UIVT-O) OBOR OECD: Pure mathematics; Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) (UIVT-O) Impact factor: 0.589, year: 2016 http://library.utia.cas.cz/separaty/2017/MTR/noguera-0469118.pdf
International Nuclear Information System (INIS)
J.T. Birkholzer
2004-01-01
This model report documents the abstraction of drift seepage, conducted to provide seepage-relevant parameters and their probability distributions for use in Total System Performance Assessment for License Application (TSPA-LA). Drift seepage refers to the flow of liquid water into waste emplacement drifts. Water that seeps into drifts may contact waste packages and potentially mobilize radionuclides, and may result in advective transport of radionuclides through breached waste packages [''Risk Information to Support Prioritization of Performance Assessment Models'' (BSC 2003 [DIRS 168796], Section 3.3.2)]. The unsaturated rock layers overlying and hosting the repository form a natural barrier that reduces the amount of water entering emplacement drifts by natural subsurface processes. For example, drift seepage is limited by the capillary barrier forming at the drift crown, which decreases or even eliminates water flow from the unsaturated fractured rock into the drift. During the first few hundred years after waste emplacement, when above-boiling rock temperatures will develop as a result of heat generated by the decay of the radioactive waste, vaporization of percolation water is an additional factor limiting seepage. Estimating the effectiveness of these natural barrier capabilities and predicting the amount of seepage into drifts is an important aspect of assessing the performance of the repository. The TSPA-LA therefore includes a seepage component that calculates the amount of seepage into drifts [''Total System Performance Assessment (TSPA) Model/Analysis for the License Application'' (BSC 2004 [DIRS 168504], Section 6.3.3.1)]. The TSPA-LA calculation is performed with a probabilistic approach that accounts for the spatial and temporal variability and inherent uncertainty of seepage-relevant properties and processes. Results are used for subsequent TSPA-LA components that may handle, for example, waste package corrosion or radionuclide transport
International Nuclear Information System (INIS)
1987-01-01
The document contains abstracts of 24 review papers, 24 invited papers, 24 oral contributions and 120 posters. 10 review papers summarize the status of laser fusion research and progress in high-power laser facilities in major world laboratories. Four papers review research programs (laser-matter interaction studies and X-ray source development) based on KrF laser systems. Other review papers discuss the problems of laser energy conversion into X-rays in laser-heated cavities, X-ray lasing at shorter wavelengths, optimization of targets for inertial fusion. Two review papers are devoted to light ion fusion. The subjects of most invited papers are special problems of current laser plasma research, such as hot electron generation, nonlinear resonance absorption, energy accumulation limits, pellet ignition, conversion of laser light into X-rays, high-pressure plasma generation. Three invited papers review laser plasma research in Czechoslovakia, Poland and Spain. One paper suggests a new method of producing muonic superdense matter. The remaining inivited papers deal with the progress in XUV lasers and with laser plasma applications for further laser development. Of the papers accepted for oral presentation 12 papers discuss various problems of laser-plasma interaction; 4 papers deal with laser targets, 4 papers with laser-initiated X-ray sources, 3 papers with the diagnostics of laser-produced plasma. The last oral contribution presents the main principles of the excimer laser theory. The largest group of posters is related to laser-plasma interaction and energy absorption problems, to laser-target interaction and various methods of laser plasma diagnostics. The other posters deal with plasma applications in laser development, plasma mirrors, Brillouin and Raman scattering, X-ray emission, harmonic generation, electron acceleration, production of high-Z plasmas and other related problems. (J.U.)
Formalizing the concept of sound.
Energy Technology Data Exchange (ETDEWEB)
Kaper, H. G.; Tipei, S.
1999-08-03
The notion of formalized music implies that a musical composition can be described in mathematical terms. In this article we explore some formal aspects of music and propose a framework for an abstract approach.
Kleene, Stephen Cole
1967-01-01
Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.
Huckstep, Peter
2002-01-01
Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)
Batchelder, William H
2010-09-01
Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.
Kodaira, Kunihiko
1996-01-01
This is the translation from the Japanese textbook for the grade 11 course, "General Mathematics". It is part of the easier of the three elective courses in mathematics offered at this level and is taken by about 40% of students. The book covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.
Mathematics for sustainability
Roe, John; Jamshidi, Sara
2018-01-01
Designed for the 21st century classroom, this textbook poses, refines, and analyzes questions of sustainability in a quantitative environment. Building mathematical knowledge in the context of issues relevant to every global citizen today, this text takes an approach that empowers students of all disciplines to understand and reason with quantitative information. Whatever conclusions may be reached on a given topic, this book will prepare the reader to think critically about their own and other people’s arguments and to support them with careful, mathematical reasoning. Topics are grouped in themes of measurement, flow, connectivity, change, risk, and decision-making. Mathematical thinking is at the fore throughout, as students learn to model sustainability on local, regional, and global scales. Exercises emphasize concepts, while projects build and challenge communication skills. With no prerequisites beyond high school algebra, instructors will find this book a rich resource for engaging all majors in the...
Principles of mathematical modeling
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...
Zorich, Vladimir A
2015-01-01
VLADIMIR A. ZORICH is professor of mathematics at Moscow State University. His areas of specialization are analysis, conformal geometry, quasiconformal mappings, and mathematical aspects of thermodynamics. He solved the problem of global homeomorphism for space quasiconformal mappings. He holds a patent in the technology of mechanical engineering, and he is also known by his book Mathematical Analysis of Problems in the Natural Sciences . This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems...
Murray, James D
1993-01-01
The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...
Parshall, Karen Hunger
2002-01-01
Although today's mathematical research community takes its international character very much for granted, this "global nature" is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians and mathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only develo...
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.
Brain Functors: A Mathematical Model of Intentional Perception and Action
Directory of Open Access Journals (Sweden)
David Ellerman
2016-03-01
Full Text Available Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics - with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it is split into two parts, a left and a right semiadjunction. Semiadjunctions (essentially a formulation of universal mapping properties using hets can then be combined in a new way to define the notion of a brain functor that provides an abstract model of the intentionality of perception and action (as opposed to the passive reception of sense-data or the reflex generation of behavior.
The materiality of mathematics: presenting mathematics at the blackboard.
Greiffenhagen, Christian
2014-09-01
Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.
Where mathematics come from how the embodied mind brings mathematics into being
Lakoff, George
2001-01-01
This book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms.
Contemplating Symbolic Literacy of First Year Mathematics Students
Bardini, Caroline; Pierce, Robyn; Vincent, Jill
2015-01-01
Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…
The tools of mathematical reasoning
Lakins, Tamara J
2016-01-01
This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.
Preservice Mathematics Teachers' Metaphorical Perceptions towards Proof and Proving
Ersen, Zeynep Bahar
2016-01-01
Since mathematical proof and proving are in the center of mathematics; preservice mathematics teachers' perceptions against these concepts have a great importance. Therefore, the study aimed to determine preservice mathematics teachers' perceptions towards proof and proving through metaphors. The participants consisted of 192 preservice…
Keles, Oguz; Tas, Isil; Aslan, Durmus
2016-01-01
The aim of this study was to identify the thoughts of pre-service teachers, who play an important role in the early preschool experience of children in mathematics, towards the concepts of mathematics and education of mathematics with the help of metaphors. The study group of the research consists of a total of 227 pre-service teachers at the…
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…
The method of abstraction in the design of databases and the interoperability
Yakovlev, Nikolay
2018-03-01
When designing the database structure oriented to the contents of indicators presented in the documents and communications subject area. First, the method of abstraction is applied by expansion of the indices of new, artificially constructed abstract concepts. The use of abstract concepts allows to avoid registration of relations many-to-many. For this reason, when built using abstract concepts, demonstrate greater stability in the processes. The example abstract concepts to address structure - a unique house number. Second, the method of abstraction can be used in the transformation of concepts by omitting some attributes that are unnecessary for solving certain classes of problems. Data processing associated with the amended concepts is more simple without losing the possibility of solving the considered classes of problems. For example, the concept "street" loses the binding to the land. The content of the modified concept of "street" are only the relations of the houses to the declared name. For most accounting tasks and ensure communication is enough.
Concrete and abstract visualizations in history learning tasks
Prangsma, M.E.; van Boxtel, C.A.M.; Kanselaar, G.; Kirschner, P.A.
2009-01-01
Background: History learning requires that students understand historical phenomena, abstract concepts and the relations between them. Students have problems grasping, using and relating complex historical developments and structures. Aims: A study was conducted to determine the effects of tasks
49. Annual meeting of the Deutsche Gesellschaft fuer Neuroradiologie. Abstracts
International Nuclear Information System (INIS)
2014-01-01
The conference proceedings of the 48. Annual meeting of the Deutsche Gesellschaft fuer Neuroradiologie contain abstracts on the following issues: neuro-oncological imaging, multimodal imaging concepts, subcranial imaging, spinal codes, interventional neuroradiology.
Advance Organizers: Concret Versus Abstract.
Corkill, Alice J.; And Others
1988-01-01
Two experiments examined the relative effects of concrete and abstract advance organizers on students' memory for subsequent prose. Results of the experiments are discussed in terms of the memorability, familiarity, and visualizability of concrete and abstract verbal materials. (JD)
Mathematics for natural scientists fundamentals and basics
Kantorovich, Lev
2016-01-01
This book, the first in a two part series, covers a course of mathematics tailored specifically for physics, engineering and chemistry students at the undergraduate level. It is unique in that it begins with logical concepts of mathematics first encountered at A-level and covers them in thorough detail, filling in the gaps in students' knowledge and reasoning. Then the book aids the leap between A-level and university-level mathematics, with complete proofs provided throughout and all complex mathematical concepts and techniques presented in a clear and transparent manner. Numerous examples and problems (with answers) are given for each section and, where appropriate, mathematical concepts are illustrated in a physics context. This text gives an invaluable foundation to students and a comprehensive aid to lecturers. Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.
Anku, Sitsofe E.
1997-09-01
Using the reform documents of the National Council of Teachers of Mathematics (NCTM) (NCTM, 1989, 1991, 1995), a theory-based multi-dimensional assessment framework (the "SEA" framework) which should help expand the scope of assessment in mathematics is proposed. This framework uses a context based on mathematical reasoning and has components that comprise mathematical concepts, mathematical procedures, mathematical communication, mathematical problem solving, and mathematical disposition.
Mathematical Snippets Exploring mathematical ideas in small bites
Pappas, Theoni
2008-01-01
From nutritional labels and box office statistics to terabytes and megapixels, the 21st century world is awash in numbers. How can the average Joe or Jane make sense of all that data? The key, Theoni Pappas argues, is math. In Mathematical Snippets, she draws readers into the fascinating world of math without overwhelming them with mind-numbing equations. Short, engaging sections on everything from golf to game theory introduce mathematical concepts and celebrate math's impact on daily life.