The Development Of Multiplicative Reasoning In The Learning Of Mathematics

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The Development Of Multiplicative Reasoning In The Learning Of Mathematics

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Author : Guershon Harel
language : en
Publisher: State University of New York Press
Release Date : 1994-06-28

The Development Of Multiplicative Reasoning In The Learning Of Mathematics written by Guershon Harel and has been published by State University of New York Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-06-28 with Education categories.

Two of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating. This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework.

The Development Of Multiplicative Reasoning In The Learning Of Mathematics

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Author : Guershon Harel
language : en
Publisher: SUNY Press
Release Date : 1994-06-28

The Development Of Multiplicative Reasoning In The Learning Of Mathematics written by Guershon Harel and has been published by SUNY Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-06-28 with Education categories.

Two of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating. This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework.

Providing A Foundation For Teaching Mathematics In The Middle Grades

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Author : Judith T. Sowder
language : en
Publisher: SUNY Press
Release Date : 1995-01-01

Providing A Foundation For Teaching Mathematics In The Middle Grades written by Judith T. Sowder and has been published by SUNY Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Mathematics categories.

This book provides middle school teachers with a firm pedagogical foundation based on the manner in which students learn the mathematics being taught.

Learning Mathematics

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Author : Paul Cobb
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Learning Mathematics written by Paul Cobb 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 2013-03-09 with Education categories.

This volume emphasizes students' inferred mathematical experiences as the starting point in the theory-building process. The book addresses conceptual constructions, including multiplicative notions, fractions, algebra, and the fundamental theorem of calculus, and theoretical constructs such as the crucial role of language and symbols, and the importance of dynamic imagery.

Early Algebraization

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Author : Jinfa Cai
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-24

Early Algebraization written by Jinfa Cai 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 2011-02-24 with Education categories.

In this volume, the authors address the development of students’ algebraic thinking in the elementary and middle school grades from curricular, cognitive, and instructional perspectives. The volume is also international in nature, thus promoting a global dialogue on the topic of early Algebraization.

A Study Of Proportional Reasoning As It Relates To The Development Of Multiplication Concepts

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Author : Judith Flowers
language : en
Publisher:
Release Date : 1998

A Study Of Proportional Reasoning As It Relates To The Development Of Multiplication Concepts written by Judith Flowers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Advanced Mathematical Thinking

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Author : David Tall
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11

Advanced Mathematical Thinking written by David Tall 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 2006-04-11 with Education categories.

Advanced Mathematical Thinking has played a central role in the development of human civilization for over two millennia. Yet in all that time the serious study of the nature of advanced mathematical thinking – what it is, how it functions in the minds of expert mathematicians, how it can be encouraged and improved in the developing minds of students – has been limited to the reflections of a few significant individuals scattered throughout the history of mathematics. In the twentieth century the theory of mathematical education during the compulsory years of schooling to age 16 has developed its own body of empirical research, theory and practice. But the extensions of such theories to more advanced levels have only occurred in the last few years. In 1976 The International Group for the Psychology of Mathematics (known as PME) was formed and has met annually at different venues round the world to share research ideas. In 1985 a Working Group of PME was formed to focus on Advanced Mathematical Thinking with a major aim of producing this volume. The text begins with an introductory chapter on the psychology of advanced mathema- cal thinking, with the remaining chapters grouped under three headings: • the nature of advanced mathematical thinking, • cognitive theory, and • reviews of the progress of cognitive research into different areas of advanced mathematics.

Developing Essential Understanding Of Ratios Proportions And Proportional Reasoning For Teaching Mathematics In Grades 6 8

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Author : Joanne Elizabeth Lobato
language : en
Publisher: National Council of Teachers of English
Release Date : 2010

Developing Essential Understanding Of Ratios Proportions And Proportional Reasoning For Teaching Mathematics In Grades 6 8 written by Joanne Elizabeth Lobato and has been published by National Council of Teachers of English this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Curriculum planning categories.

"A series for teaching mathematics."--P. [1] of cover.

Second Handbook Of Research On Mathematics Teaching And Learning

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Author : Frank K. Lester
language : en
Publisher: IAP
Release Date : 2007-02-01

Second Handbook Of Research On Mathematics Teaching And Learning written by Frank K. Lester and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-01 with Education categories.

The audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics. The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment. Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.

Mathematical Reasoning

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Author : Raymond Nickerson
language : en
Publisher: Taylor & Francis
Release Date : 2011-02-25

Mathematical Reasoning written by Raymond Nickerson and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-25 with Psychology categories.

The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.