Overview

Chemists, working with only mortars and pestles, could not get very far unless they had mathematical models to explain what was happening "inside" of their elements of experience -- an example of what could be termed mathematical learning.

This volume contains the proceedings of Work Group 4: Theories of Mathematics, a subgroup of the Seventh International Congress on Mathematical Education held at Université Laval in Québec. Bringing together...
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Theories of Mathematical Learning

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Overview

Chemists, working with only mortars and pestles, could not get very far unless they had mathematical models to explain what was happening "inside" of their elements of experience -- an example of what could be termed mathematical learning.

This volume contains the proceedings of Work Group 4: Theories of Mathematics, a subgroup of the Seventh International Congress on Mathematical Education held at Université Laval in Québec. Bringing together multiple perspectives on mathematical thinking, this volume presents elaborations on principles reflecting the progress made in the field over the past 20 years and represents starting points for understanding mathematical learning today. This volume will be of importance to educational researchers, math educators, graduate students of mathematical learning, and anyone interested in the enterprise of improving mathematical learning worldwide.
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Product Details

  • ISBN-13: 9781136485541
  • Publisher: Taylor & Francis
  • Publication date: 4/3/2013
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 544
  • File size: 6 MB

Table of Contents

Preface
1 Emergent and Sociocultural Views of Mathematical Activity 3
2 Negotiation of Mathematical Meaning in Classroom Processes: Social Interaction and Learning Mathematics 21
3 Emergent Mathematical Environments in Children's Games 51
4 Negotiating the Negotiation of Meaning: Comments on Voigt 1992 and Saxe and Bermudez 1992 69
5 Negotiating Mathematical Meanings in and out of School 77
6 Social Interaction and Individual Cognition 85
7 Learning Mathematics as a Meaningful Activity 91
8 Learning Mathematics as Participation in Classroom Practice: Implications of Sociocultural Theory for Educational Reform 115
9 Cultural Processes and Learning: Expectations, Actions, and Outcomes 131
10 Traditions of School Mathematics in Japanese and American Elementary Classrooms 149
11 Theories of Mathematics Education: The Role of Cognitive Analyses 179
12 A Conception of Knowledge Acquisition and Its Implications for Mathematics Education 197
13 The Theory of Conceptual Fields 219
14 Learning About Fractions 241
15 Imagery and the Development of Mathematical Reasoning 267
16 Cognition, Mathematics, and Education 285
17 Theory of Mathematics Education: The Contributions of Constructivism 303
18 Aspects of Radical Constructivism and Its Educational Recommendations 307
19 Phenomenography and Children's Experience of Division 315
20 Varieties of Constructivism: A Framework for Comparison 335
21 The Construction of Conceptual Schemes in Mathematics 351
22 Constructing Mathematical Conventions Formed by the Abstraction and Generalization of Earlier Ideas: The Development of Initial Fraction Ideas 381
23 A Joint Perspective on the Idea of Representation In Learning and Doing Mathematics 397
24 Young Children Invent Methods of Proof: The Gang of Four 431
25 Constructivism and Its Consequences for Training Teachers 449
26 Is the Metaphor of Mental Object Appropriate for a Theory of Learning Mathematics? 467
27 On the Nature of a Model of Mathematical Learning 477
Author Index 499
Subject Index 507
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