Symbolizing, Modeling and Tool Use in Mathematics Education

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

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

Table of contents

  1. Front Matter
    Pages N1-iv
  2. Introduction and Overview

    1. Koeno Gravemeijer, Richard Lehrer, Bert Van Oers, Lieven Verschaffel
      Pages 1-5
  3. Preamble: From Models to Modeling

    1. Koeno Gravemeijer
      Pages 7-22
  4. Emergent Modeling

    1. Front Matter
      Pages 23-23
    2. Richard Lehrer, Carrie Pritchard
      Pages 59-86
    3. Luciano R. De Lenos Meira
      Pages 87-103
    4. Andrea A. diSessa
      Pages 105-129
    5. Norma Presmeg
      Pages 131-137
  5. The Role of Models, Symbols and Tools in Instructional Design

    1. Front Matter
      Pages 139-139
    2. Koeno Gravemeijer
      Pages 141-143
    3. Koeno Gravemeijer, Michelle Stephan
      Pages 145-169
    4. Christoph Selter
      Pages 221-227
  6. Models, Situated Practices, and Generalization

    1. Front Matter
      Pages 229-229
    2. Lieven Verschaffel
      Pages 231-232
    3. Ricardo Nemirovsky
      Pages 233-256
    4. Lieven Verschaffel, Brian Greer, Erik de Corte
      Pages 257-276
    5. David Carraher, Analúcia Schliemann
      Pages 295-304
  7. Back Matter
    Pages 305-308

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.


Lehrer education instructional design mathematics education modeling

Editors and affiliations

  • Koeno Gravemeijer
    • 1
  • Richard Lehrer
    • 2
  • Bert Van Oers
    • 3
  • Lieven Verschaffel
    • 4
  1. 1.Freudenthal Institute/Department of Educational SciencesUtrecht UniversityUtrechtThe Netherlands
  2. 2.Peabody CollegeVanderbilt UniversityNashvilleUSA
  3. 3.Department of Education and CurriculumFree University AmsterdamAmsterdamThe Netherlands
  4. 4.Center for Instructional Psychology and TechnologyUniversity of LeuvenLeuvenBelgium

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6180-5
  • Online ISBN 978-94-017-3194-2
  • Buy this book on publisher's site