Mathematical Knowledge

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Mathematical Knowledge

Mary Leng,Alexander Paseau,Michael Potter,Michael D. Potter
Mathematical Knowledge Book PDF

Author : Mary Leng,Alexander Paseau,Michael Potter,Michael D. Potter
Publisher : Oxford University Press
Page : 199 pages
File Size : 48,6 Mb
Release : 2007-11-15
Category : Mathematics
ISBN : 9780199228249

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Mathematical Knowledge by Mary Leng,Alexander Paseau,Michael Potter,Michael D. Potter Pdf

What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions. Written by some of the world's leading philosophers of mathematics, psychologists, and mathematicians, Mathematical Knowledge gives a lively sense of the current state of debate in this fascinating field.

Mathematical Knowledge in Teaching

Tim Rowland,Kenneth Ruthven
Mathematical Knowledge in Teaching Book PDF

Author : Tim Rowland,Kenneth Ruthven
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 54,6 Mb
Release : 2011-01-06
Category : Education
ISBN : 9789048197668

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Mathematical Knowledge in Teaching by Tim Rowland,Kenneth Ruthven Pdf

The quality of primary and secondary school mathematics teaching is generally agreed to depend crucially on the subject-related knowledge of the teacher. However, there is increasing recognition that effective teaching calls for distinctive forms of subject-related knowledge and thinking. Thus, established ways of conceptualizing, developing and assessing mathematical knowledge for teaching may be less than adequate. These are important issues for policy and practice because of longstanding difficulties in recruiting teachers who are confident and conventionally well-qualified in mathematics, and because of rising concern that teaching of the subject has not adapted sufficiently. The issues to be examined in Mathematical Knowledge in Teaching are of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing more effective approaches to characterizing, assessing and developing mathematical knowledge for teaching.

The Nature of Mathematical Knowledge

Philip Kitcher
The Nature of Mathematical Knowledge Book PDF

Author : Philip Kitcher
Publisher : Oxford University Press, USA
Page : 300 pages
File Size : 42,5 Mb
Release : 1984
Category : Electronic books
ISBN : 9780195035414

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The Nature of Mathematical Knowledge by Philip Kitcher Pdf

This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified.

Quantitative Measures of Mathematical Knowledge

Jonathan Bostic,Erin Krupa,Jeffrey Shih
Quantitative Measures of Mathematical Knowledge Book PDF

Author : Jonathan Bostic,Erin Krupa,Jeffrey Shih
Publisher : Routledge
Page : 254 pages
File Size : 52,9 Mb
Release : 2019-04-29
Category : Education
ISBN : 9780429942242

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Quantitative Measures of Mathematical Knowledge by Jonathan Bostic,Erin Krupa,Jeffrey Shih Pdf

The aim of this book is to explore measures of mathematics knowledge, spanning K-16 grade levels. By focusing solely on mathematics content, such as knowledge of mathematical practices, knowledge of ratio and proportions, and knowledge of abstract algebra, this volume offers detailed discussions of specific instruments and tools meant for measuring student learning. Written for assessment scholars and students both in mathematics education and across educational contexts, this book presents innovative research and perspectives on quantitative measures, including their associated purpose statements and validity arguments.

Constructing Mathematical Knowledge

Paul Ernest
Constructing Mathematical Knowledge Book PDF

Author : Paul Ernest
Publisher : Routledge
Page : 295 pages
File Size : 45,6 Mb
Release : 2012-10-12
Category : Education
ISBN : 9781136364723

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Constructing Mathematical Knowledge by Paul Ernest Pdf

First published in 1994. This book and its companion volume, Mathematics, Education and Philosophy: An International Perspective are edited collections. Instead of the sharply focused concerns of the research monograph, the books offer a panorama of complementary and forward-looking perspectives. They illustrate the breadth of theoretical and philosophical perspectives that can fruitfully be brough to bear on the mathematics and education. The empathise of this book is on epistemological issues, encompassing multiple perspectives on the learning of mathematics, as well as broader philosophical reflections on the genesis of knowledge. It explores constructivist and social theories of learning and discusses the rile of the computer in light of these theories.

Mathematical Knowledge and the Interplay of Practices

José Ferreirós
Mathematical Knowledge and the Interplay of Practices Book PDF

Author : José Ferreirós
Publisher : Princeton University Press
Page : 358 pages
File Size : 43,9 Mb
Release : 2015-12-22
Category : Science
ISBN : 9781400874002

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Mathematical Knowledge and the Interplay of Practices by José Ferreirós Pdf

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Naturalizing Logico-Mathematical Knowledge

Sorin Bangu
Naturalizing Logico Mathematical Knowledge Book PDF

Author : Sorin Bangu
Publisher : Routledge
Page : 319 pages
File Size : 55,8 Mb
Release : 2018-02-01
Category : Mathematics
ISBN : 9781351998444

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Naturalizing Logico-Mathematical Knowledge by Sorin Bangu Pdf

This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.

Mathematical Knowledge for Primary Teachers

Jennifer Suggate,Andrew Davis,Maria Goulding
Mathematical Knowledge for Primary Teachers Book PDF

Author : Jennifer Suggate,Andrew Davis,Maria Goulding
Publisher : Routledge
Page : 490 pages
File Size : 49,8 Mb
Release : 2010-04-05
Category : Education
ISBN : 9781135165000

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Mathematical Knowledge for Primary Teachers by Jennifer Suggate,Andrew Davis,Maria Goulding Pdf

Now in its fourth edition, the bestselling text Mathematical Knowledge for Primary Teachers provides trainee teachers with clear information about the fundamental mathematical ideas taught in primary schools. With rigorous and comprehensive coverage of all the mathematical knowledge primary teachers need, the text goes beyond rules and routines to help readers deepen their understanding of mathematical ideas and increase their confidence in teaching these ideas. Fully updated to incorporate recommendations of the Williams review, new sections are included covering talk for learning in mathematics, with an emphasis placed on the language and vocabulary used in arithmetic contexts. Throughout the book, knowledge is linked to the TDA standards for Qualified Teacher Status, and features include: ‘Check’ questions to test the reader’s understanding ‘Challenges’, to increase teachers’ confidence and stretch their mathematical abilities ‘Links with the classroom’ to emphasise the relevance of ideas to the classroom context Straightforward coverage from theory to practice for all aspects of the Mathematics framework. The book is accompanied by e-resources, which contain further visual activities and support, designed to scaffold and support the reader’s own understanding. Essential reading for all practising and trainee primary teachers, this book is ideal for those who wish to increase their mathematical understanding and confidence in presenting mathematics in the classroom.

Forms of Mathematical Knowledge

Dina Tirosh
Forms of Mathematical Knowledge Book PDF

Author : Dina Tirosh
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 50,8 Mb
Release : 2013-03-14
Category : Education
ISBN : 9789401715843

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Forms of Mathematical Knowledge by Dina Tirosh Pdf

What mathematics is entailed in knowing to act in a moment? Is tacit, rhetorical knowledge significant in mathematics education? What is the role of intuitive models in understanding, learning and teaching mathematics? Are there differences between elementary and advanced mathematical thinking? Why can't students prove? What are the characteristics of teachers' ways of knowing? This book focuses on various types of knowledge that are significant for learning and teaching mathematics. The first part defines, discusses and contrasts psychological, philosophical and didactical issues related to various types of knowledge involved in the learning of mathematics. The second part describes ideas about forms of mathematical knowledge that are important for teachers to know and ways of implementing such ideas in preservice and in-service education. The chapters provide a wide overview of current thinking about mathematics learning and teaching which is of interest for researchers in mathematics education and mathematics educators. Topics covered include the role of intuition in mathematics learning and teaching, the growth from elementary to advanced mathematical thinking, the significance of genres and rhetoric for the learning of mathematics and the characterization of teachers' ways of knowing.

The Construction of New Mathematical Knowledge in Classroom Interaction

Heinz Steinbring
The Construction of New Mathematical Knowledge in Classroom Interaction Book PDF

Author : Heinz Steinbring
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 40,8 Mb
Release : 2006-03-30
Category : Education
ISBN : 9780387242538

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The Construction of New Mathematical Knowledge in Classroom Interaction by Heinz Steinbring Pdf

Mathematics is generally considered as the only science where knowledge is uni form, universal, and free from contradictions. „Mathematics is a social product - a 'net of norms', as Wittgenstein writes. In contrast to other institutions - traffic rules, legal systems or table manners -, which are often internally contradictory and are hardly ever unrestrictedly accepted, mathematics is distinguished by coherence and consensus. Although mathematics is presumably the discipline, which is the most differentiated internally, the corpus of mathematical knowledge constitutes a coher ent whole. The consistency of mathematics cannot be proved, yet, so far, no contra dictions were found that would question the uniformity of mathematics" (Heintz, 2000, p. 11). The coherence of mathematical knowledge is closely related to the kind of pro fessional communication that research mathematicians hold about mathematical knowledge. In an extensive study, Bettina Heintz (Heintz 2000) proposed that the historical development of formal mathematical proof was, in fact, a means of estab lishing a communicable „code of conduct" which helped mathematicians make themselves understood in relation to the truth of mathematical statements in a co ordinated and unequivocal way.

Mathematical Knowledge for Primary Teachers

Andrew Davis,Maria Goulding,Jennifer Suggate
Mathematical Knowledge for Primary Teachers Book PDF

Author : Andrew Davis,Maria Goulding,Jennifer Suggate
Publisher : Routledge
Page : 419 pages
File Size : 55,5 Mb
Release : 2017-02-17
Category : Education
ISBN : 9781317219002

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Mathematical Knowledge for Primary Teachers by Andrew Davis,Maria Goulding,Jennifer Suggate Pdf

Now in its fifth edition, the best-selling text Mathematical Knowledge for Primary Teachers provides trainee teachers with clear information about the fundamental mathematical ideas taught in primary schools. With rigorous and comprehensive coverage of all the mathematical knowledge primary teachers need, the text goes beyond rules and routines to help readers deepen their understanding of mathematical ideas and increase their confidence in teaching these ideas. The book has been updated to incorporate changes in the National Curriculum and the associated tests. In addition, Chapter 1 has been expanded to discuss mathematical understanding in the light of the challenges posed by the current changes. These include the re-introduction of traditional calculation methods for multiplication and division, the early coverage of abstract fractions calculations and much more. Features include: ■ ‘Check’ questions to test the reader’s understanding ■ ‘Challenges’ to increase teachers’ confidence and stretch their mathematical abilities ■ ‘Links with the classroom’ to emphasise the relevance of ideas to the classroom context ■ Straightforward coverage from theory to practice for all aspects of the Mathematics Framework. The book is accompanied by eResources which contains further visual activities and support, designed to scaffold and support the reader’s own understanding. Essential reading for all practising and trainee primary teachers, this book is ideal for those who wish to increase their mathematical understanding and confidence in presenting mathematics in the classroom.

Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction

Judith T. Sowder,Randolph A. Philipp,Barbara E. Armstrong,Bonnie P. Schappelle
Middle Grade Teachers Mathematical Knowledge and Its Relationship to Instruction Book PDF

Author : Judith T. Sowder,Randolph A. Philipp,Barbara E. Armstrong,Bonnie P. Schappelle
Publisher : SUNY Press
Page : 240 pages
File Size : 53,5 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 0791438414

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Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction by Judith T. Sowder,Randolph A. Philipp,Barbara E. Armstrong,Bonnie P. Schappelle Pdf

The outcome of a two-year investigation, this book shows how teachers' understanding of the mathematics of number, quantity, and proportion influences how they teach and what their students learn of the concepts, skills, and reasoning associated with this mathematical domain of knowledge. It grew out of the recognition of the need to understand the complexities of helping teachers reconceptualize the mathematics they teach and the resulting effects in their classrooms. The book includes case studies of five teachers, from different types of school settings, illustrating changes in the teachers' teaching methods, expectations of students, and beliefs about the role of professional development.

Mathematical Knowledge and the Interplay of Practices

José Ferreirós
Mathematical Knowledge and the Interplay of Practices Book PDF

Author : José Ferreirós
Publisher : Princeton University Press
Page : 357 pages
File Size : 42,6 Mb
Release : 2015-12-22
Category : Science
ISBN : 9780691167510

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Mathematical Knowledge and the Interplay of Practices by José Ferreirós Pdf

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration

C. Lange
Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration Book PDF

Author : C. Lange
Publisher : IOS Press
Page : 610 pages
File Size : 40,9 Mb
Release : 2011-10-14
Category : Computers
ISBN : 9781614993452

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Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration by C. Lange Pdf

Mathematics is becoming increasingly collaborative, but software does not sufficiently support that: Social Web applications do not currently make mathematical knowledge accessible to automated agents that have a deeper understanding of mathematical structures. Such agents exist but focus on individual research tasks, such as authoring, publishing, peer-review, or verification, instead of complex collaboration workflows. This work effectively enables their integration by bridging the document-oriented perspective of mathematical authoring and publishing, and the network perspective of threaded discussions and Web information retrieval. This is achieved by giving existing representations of mathematical and relevant related knowledge about applications, projects and people a common Semantic Web foundation. Service integration is addressed from the two perspectives of enriching published documents by embedding assistive services, and translating between different knowledge representations inside knowledge bases. A usability evaluation of a semantic wiki that coherently integrates knowledge production and consumption services points out the remaining challenges in making such heterogeneously integrated environments support realistic workflows. The results of this thesis will soon also enable collaborative acquisition of new mathematical knowledge, as well as the contributions of existing knowledge collections of the Web of Data.

Platonism, Naturalism, and Mathematical Knowledge

James Robert Brown
Platonism Naturalism and Mathematical Knowledge Book PDF

Author : James Robert Brown
Publisher : Routledge
Page : 195 pages
File Size : 42,9 Mb
Release : 2013-06-17
Category : Philosophy
ISBN : 9781136580383

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Platonism, Naturalism, and Mathematical Knowledge by James Robert Brown Pdf

This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.