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Symbolizing, Modeling and Tool Use in Mathematics Education

  • Book
  • © 2002

Overview

Editors:
  1. Koeno Gravemeijer

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

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  2. Richard Lehrer

    1. Peabody College, Vanderbilt University, Nashville, USA

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  3. Bert Oers

    1. Department of Education and Curriculum, Free University Amsterdam, Amsterdam, The Netherlands

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  4. Lieven Verschaffel

    1. Center for Instructional Psychology and Technology, University of Leuven, Leuven, Belgium

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Part of the book series: Mathematics Education Library (MELI, volume 30)

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Table of contents (18 chapters)

  1. Front Matter

    Pages N1-iv
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  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
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    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
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    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
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    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
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Keywords

About this book

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.

Editors and Affiliations

  • 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

Bibliographic Information

  • Book Title: Symbolizing, Modeling and Tool Use in Mathematics Education

  • Editors: Koeno Gravemeijer, Richard Lehrer, Bert Oers, Lieven Verschaffel

  • Series Title: Mathematics Education Library

  • DOI: https://doi.org/10.1007/978-94-017-3194-2

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2002

  • Hardcover ISBN: 978-1-4020-1032-3Published: 31 December 2002

  • Softcover ISBN: 978-90-481-6180-5Published: 05 December 2010

  • eBook ISBN: 978-94-017-3194-2Published: 09 March 2013

  • Series ISSN: 0924-4921

  • Series E-ISSN: 2214-983X

  • Edition Number: 1

  • Number of Pages: IV, 308

  • Topics: Mathematics Education, Learning & Instruction, Curriculum Studies

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