Symbolizing, Modeling and Tool Use in Mathematics Education

1. Front Matter

   Pages N1-iv

   PDF

2. Introduction and Overview

   1. Introduction and Overview

      • Koeno Gravemeijer, Richard Lehrer, Bert Van Oers, Lieven Verschaffel

      Pages 1-5

3. Preamble: From Models to Modeling

   1. Preamble: From Models to Modeling

      • Koeno Gravemeijer

      Pages 7-22

4. Emergent Modeling

   1. Front Matter

      Pages 23-23

      PDF

   2. Informal Representations and Their Improvements

      • Bert van Oers

      Pages 25-28

   3. The Mathematization of Young Children’s Language

      • Bert van Oers

      Pages 29-58

   4. Symbolizing Space into Being

      • Richard Lehrer, Carrie Pritchard

      Pages 59-86

   5. Mathematical Representations as Systems of Notations-In-Use

      • Luciano R. De Lenos Meira

      Pages 87-103

   6. Students’ Criteria for Representational Adequacy

      • Andrea A. diSessa

      Pages 105-129

   7. Transitions in Emergent Modeling

      • Norma Presmeg

      Pages 131-137

5. The Role of Models, Symbols and Tools in Instructional Design

   1. Front Matter

      Pages 139-139

      PDF

   2. Introduction to Section II

      • Koeno Gravemeijer

      Pages 141-143

   3. Emergent Models as an Instructional Design Heuristic

      • Koeno Gravemeijer, Michelle Stephan

      Pages 145-169

   4. Modeling, Symbolizing, and Tool Use in Statistical Data Analysis

      • Paul Cobb

      Pages 171-195

   5. Didactic Objects and Didactic Models in Radical Constructivism

      • Patrick W. Thompson

      Pages 197-220

   6. Taking into Account Different Views

      • Christoph Selter

      Pages 221-227

6. Models, Situated Practices, and Generalization

   1. Front Matter

      Pages 229-229

      PDF

   2. Introduction to Section III

      • Lieven Verschaffel

      Pages 231-232

   3. On Guessing the Essential Thing

      • Ricardo Nemirovsky

      Pages 233-256

   4. Everyday Knowledge and Mathematical Modeling of School Word Problems

      • Lieven Verschaffel, Brian Greer, Erik de Corte

      Pages 257-276

The almost universal rejection of the notion of symbols as `carriers of meaning' has created the need to find an alternative for the use of models as embodiments of mathematical concepts. By taking its point of departure as a concern for the way students actually use tools and symbols, and for what these signify for them, this book explores the option of building on symbolizing, modelling and tool use as personally meaningful activities of students. This theme is approached from different angles and different perspectives. One dimension is that of setting, varying from the study of informal, spontaneous activity of students, to an explicit focus on instructional design, and goals and effects of instruction. Another dimension is the theoretical framework of the researcher, varying from constructivism, to activity theory, cognitive-psychology and instructional-design theory. This book will appeal to a wide audience, varying from researchers, instructional designers, educators, and graduate students.

• Lehrer
• education
• instructional design
• mathematics education
• modeling
• learning and instruction

• Freudenthal Institute/Department of Educational Sciences, Utrecht University, Utrecht, The Netherlands

  Koeno Gravemeijer

• Peabody College, Vanderbilt University, Nashville, USA

  Richard Lehrer

• Department of Education and Curriculum, Free University Amsterdam, Amsterdam, The Netherlands

  Bert Oers

• Center for Instructional Psychology and Technology, University of Leuven, Leuven, Belgium

  Lieven Verschaffel

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