Mathematical Knowledge
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Mathematical Knowledge
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Author : Mary Leng
language : en
Publisher: OUP Oxford
Release Date : 2007-11-15
Mathematical Knowledge written by Mary Leng and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-15 with Philosophy categories.
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
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Author : Tim Rowland
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-06
Mathematical Knowledge In Teaching written by Tim Rowland and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-06 with Education categories.
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 Origins Of Mathematical Knowledge In Childhood
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Author : Catherine Sophian
language : en
Publisher: Routledge
Release Date : 2017-09-25
The Origins Of Mathematical Knowledge In Childhood written by Catherine Sophian and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-25 with Education categories.
This book examines the origins and development of children's mathematical knowledge. It contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the concept of number builds upon more basic concepts of equality, inequality, and less-than and greater-than relations, which derive from comparisons between unenumerated quantities such as lengths. The concept of number combines these basic comparative concepts with the concept of a unit of measure, which allows one quantity to be described as a multiple of another. Sophian examines these alternative accounts of children's developing mathematical knowledge in the light of research: on children's counting; on their reasoning about continuous quantities such as length and area; on the development of the concept of unit; on additive and multiplicative reasoning; and on knowledge about fractions. In the closing chapters, Sophian draws out the developmental and the educational implications of the research and theory presented. Developmentally, the comparison-of-quantities position undermines the idea that numerical knowledge develops through domain-specific learning mechanisms in that it links numerical development both to physical knowledge about objects, which is the starting point for the concept of unit, and to the acquisition of linguistic number terms. Instructionally, the comparison-of-quantities perspective diverges from the counting-first perspective in that it underscores the continuity between whole-number arithmetic and fraction learning that stems from the importance of the concept of unit for both. Building on this idea, Sophian advances three instructional recommendations: First, instruction about numbers should always be grounded in thinking about quantities and how numbers represent the relations between them; second, instruction in the early years should always be guided by a long-term perspective in which current objectives are shaped by an understanding of their role in the overall course of mathematics learning; and third, instruction should be directly toward promoting the acquisition of the most general mathematical knowledge possible. The Origins of Mathematical Knowledge in Childhood is intended for researchers, professionals, and graduate students in developmental psychology, educational psychology, and mathematics education, and as a supplementary text for advanced undergraduate courses in cognitive development, educational psychology, and mathematics education.
Mathematical Knowledge
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Author : Mark Steiner
language : en
Publisher:
Release Date : 1975
Mathematical Knowledge written by Mark Steiner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Logic, Symbolic and mathematical categories.
The Growth Of Mathematical Knowledge
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Author : Emily Grosholz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
The Growth Of Mathematical Knowledge written by Emily Grosholz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Philosophy categories.
Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics.
Forms Of Mathematical Knowledge
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Author :
language : en
Publisher:
Release Date : 1999
Forms Of Mathematical Knowledge written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Mathematical Knowledge For Primary Teachers
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Author : Andrew Davis
language : en
Publisher: Taylor & Francis
Release Date : 2017-02-17
Mathematical Knowledge For Primary Teachers written by Andrew Davis and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-17 with Education categories.
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.
Quantitative Measures Of Mathematical Knowledge
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Author : Jonathan Bostic
language : en
Publisher: Routledge
Release Date : 2019-04-29
Quantitative Measures Of Mathematical Knowledge written by Jonathan Bostic and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-29 with Education categories.
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
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Author : Paul Ernest
language : en
Publisher: Routledge
Release Date : 2016-12-07
Constructing Mathematical Knowledge written by Paul Ernest and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-07 with categories.
This book provides a panorama of complimentary and forward looking perspectives on the learning of mathematics and epistemology from some of the leading contributors to the field. It explores constructivist and social theories of learning, and discusses the role of the computer in the light of these theories. It brings analyses from psychoanalysis, Hermeneutics and other perspectives to bear on the issues of mathematics and learning. It enquires into the nature of enquiry itself, and an important emergent theme is the role of language. Finally it relates the history of mathematics to its teaching and learning. The book both surveys current research and indicates orientations for fruitful work in the future.
The Nature Of Mathematical Knowledge
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Author : Philip Kitcher
language : en
Publisher: Oxford University Press, USA
Release Date : 1984
The Nature Of Mathematical Knowledge written by Philip Kitcher and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Electronic books categories.
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.