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  • Book
  • Open Access
  • © 2021

Connecting Mathematics and Mathematics Education

Collected Papers on Mathematics Education as a Design Science

  • Provides a comprehensive overview of mathematics education as a design science

  • Draws a clear distinction between “mathematics” (for specialists) and “well-understood” mathematics

  • Demonstrates how to fruitfully integrate mathematics into courses on mathematics education

  • Includes models for designing substantial learning environments in various topic areas

Buying options

Softcover Book USD 49.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)

Table of contents (14 chapters)

  1. Front Matter

    Pages i-xx
  2. Teaching Units as the Integrating Core of Mathematics Education

    • Erich Christian Wittmann
    Pages 25-36Open Access
  3. The Mathematical Training of Teachers from the Point of View of Education

    • Erich Christian Wittmann
    Pages 49-60Open Access
  4. When Is a Proof a Proof?

    • Erich Christian Wittmann
    Pages 61-76Open Access
  5. Mathematics Education as a ‘Design Science’

    • Erich Christian Wittmann
    Pages 77-93Open Access
  6. Designing Teaching: The Pythagorean Theorem

    • Erich Christian Wittmann
    Pages 95-160Open Access
  7. Standard Number Representations in the Teaching of Arithmetic

    • Erich Christian Wittmann
    Pages 161-189Open Access
  8. Developing Mathematics Education in a Systemic Process

    • Erich Christian Wittmann
    Pages 191-208Open Access
  9. The Alpha and Omega of Teacher Education: Organizing Mathematical Activities

    • Erich Christian Wittmann
    Pages 209-222Open Access
  10. Operative Proofs in School Mathematics and Elementary Mathematics

    • Erich Christian Wittmann
    Pages 223-238Open Access
  11. Back Matter

    Pages 287-318

About this book

This open access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the “design science conception” has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers.

The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level.

This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.


  • Relating Mathematics to Mathematics Education
  • Mathematics Education as a Design Science
  • Substantial Learning Environments
  • Integrating Theory and Practice
  • Curriculum Development
  • Developing mathematics education courses
  • Open Access


“Both teachers I interviewed were particularly interested in the examples of teaching units proposed in the book. These teachers’ reactions further confirm the validity of Wittmann’s vision of mathematics education as a design science. … I read their words as a wish to base their educational commitment … . This appears to me the main message of the book and a sensible output of the searching for common ground for mathematics and mathematics education … .” (Fulvia Furinghetti, Educational Studies in Mathematics, Vol. 111 (2), 2022)

Authors and Affiliations

  • Department of Mathematics, Technical University of Dortmund, Dortmund, Germany

    Erich Christian Wittmann

About the author

Erich Ch. Wittmann finished his studies of mathematics and physics at the University of Erlangen from 1959 to 1964 and his practical training as a teacher for the gymnasium in 1966 with the Bavarian State Examination and the PhD in mathematics in 1967. After three years in mathematical research at the Dept. of Mathematics/Erlangen he was appointed full professor of mathematics education at the University of Dortmund.  In 1987 he was co-founder of the developmental research project Mathe 2000. His international reputation has been acknowledged by the invitation to a plenary lecture at ICME 9.

Bibliographic Information

  • Book Title: Connecting Mathematics and Mathematics Education

  • Book Subtitle: Collected Papers on Mathematics Education as a Design Science

  • Authors: Erich Christian Wittmann

  • DOI:

  • Publisher: Springer Cham

  • eBook Packages: Education, Education (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s) 2021

  • License: CC BY

  • Hardcover ISBN: 978-3-030-61569-7Published: 10 December 2020

  • Softcover ISBN: 978-3-030-61572-7Published: 24 December 2021

  • eBook ISBN: 978-3-030-61570-3Published: 09 December 2020

  • Edition Number: 1

  • Number of Pages: XX, 318

  • Number of Illustrations: 139 b/w illustrations, 61 illustrations in colour

  • Topics: Mathematics Education, Teaching and Teacher Education, Curriculum Studies, Mathematics

Buying options

Softcover Book USD 49.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)