A Journey in Mathematics Education Research

1. Front Matter

   Pages i-xxiv

   PDF

2. Introduction

   • Erna Yackel, Koeno Gravemeijer

   Pages 1-5

3. Radical Constructivism

   1. Front Matter

      Pages 7-7

      PDF

   2. Introduction

      • Paul Cobb

      Pages 9-17

   3. The Constructivist Researcher as Teacher and Model Builder

      • Paul Cobb, Leslie P. Steffe

      Pages 19-30

4. Social Constructivism

   1. Front Matter

      Pages 31-31

      PDF

   2. Introduction

      • Paul Cobb, Erna Yackel

      Pages 33-40

   3. Young Children’s Emotional Acts While Engaged in Mathematical Problem Solving

      • Paul Cobb, Erna Yackel, Terry Wood†

      Pages 41-71

5. Symbolizing and Instructional Design – Developing Instructional Sequences to Support Students’ Mathematical Learning

   1. Front Matter

      Pages 73-73

      PDF

6. Symbolizing and Instructional Design - Developing Instructional Sequences to Support Students’ Mathematical Learning

   1. Introduction

      • Paul Cobb, Koeno Gravemeijer, Erna Yackel

      Pages 75-84

   2. Learning from Distributed Theories of Intelligence

      • Paul Cobb

      Pages 85-105

7. Classroom Mathematical Practices

   1. Front Matter

      Pages 107-107

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   2. Introduction

      • Paul Cobb, Michelle Stephan, Janet Bowers

      Pages 109-115

   3. Participating in Classroom Mathematical Practices

      • Paul Cobb, Michelle Stephan, Kay McClain, Koeno Gravemeijer

      Pages 117-163

8. Diversity and Equity

   1. Front Matter

      Pages 165-165

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   2. Introduction

      • Paul Cobb, Lynn Liao Hodge, Melissa Gresalfi

      Pages 167-177

   3. Culture, Identity, and Equity in the Mathematics Classroom

      • Paul Cobb, Lynn Liao Hodge

      Pages 179-195

9. The Institutional Setting of Mathematics Teaching and Learning

   1. Front Matter

      Pages 197-197

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   2. Introduction

      • Paul Cobb, Chrystal Dean, Teruni Lamberg, Jana Visnovska, Qing Zhao

      Pages 199-206

   3. The Collective Mediation of a High-Stakes Accountability Program: Communities and Networks of Practice

      • Paul Cobb, Kay McClain

      Pages 207-230

Our objective is to publish a book that lays out the theoretical constructs and research methodologies within mathematics education that have been developed by Paul Cobb and explains the process of their development. We propose to do so by including papers in which Cobb introduced new theoretical perspectives and methodologies into the literature, each preceded by a substantive accompanying introductory paper that explains the motivation/rationale for developing the new perspectives and/or methodologies and the processes through which they were developed, and Cobb’s own retrospective comments. In this way the book provides the reader with heretofore unpublished material that lays out in considerable detail the issues and problems that Cobb has confronted in his work, that, from his viewpoint, required theoretical and methodological shifts/advances and provides insight into how he has achieved the shifts/advances. The result will be a volume that, in addition to explaining Cobb’s contributions to the field of mathematics education, also provides the reader with insight into what is involved in developing an aggressive and evolving research program. When Cobb confronts problems and issues in his work that cannot be addressed using his existing theories and frameworks, he looks to other fields for theoretical inspiration. A critical feature of Cobb’s work is that in doing so, he consciously appropriates and adapts ideas from these other fields to the purpose of supporting processes of learning and teaching mathematics; He does not simply accept the goals or motives of those fields. As a result, Cobb reconceptualizes and reframes issues and concepts so that they result in new ways of investigating, exploring, and explaining phenomena that he encounters in the practical dimensions of his work, which include working in classrooms, with teachers, and with school systems. The effect is that the field of mathematics education is altered. Other researchers have foundhis "new ways of looking" useful to them. And they, in turn, adapt these ideas for their own use. The complexity of many of the ideas that Cobb has introduced into the field of mathematics education can lead to a multiplicity of interpretations by practitioners and by other researchers, based on their own experiential backgrounds. Therefore, by detailing the development of Cobb’s work, including the tensions involved in coming to grips with and reconciling apparently contrasting perspectives, the book will shed additional light on the processes of reconceptualization and thus help the reader to understand the reasons, mechanisms, and outcomes of researchers’ constant pursuit of new insights.

• Equity and Identity
• Institutional Setting of Mathematics
• Instructional Design
• Mathematical Practices
• Mathematics Teaching and Learning
• Radical Constructivism
• Social Constructivism
• Symbolizing

• Tel Aviv, Israel

  Anna Sfard

• , Eindhoven School of Education, Eindhoven University of Eindhoven, Eindhoven, Netherlands

  Koeno Gravemeijer

• Dyer, USA

  Erna Yackel

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