Save today: Get 40% off titles in Popular Science!

Open Access This content is freely available online to anyone, anywhere at any time.

Connecting Mathematics and Mathematics Education

Collected Papers on Mathematics Education as a Design Science

Authors: Wittmann, Erich Christian

Free Preview
  • 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
see more benefits

Buy this book

eBook  
  • ISBN 978-3-030-61570-3
  • This book is an open access book, you can download it for free on link.springer.com
Hardcover $59.99
price for USA in USD
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.


About the authors

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.

Table of contents (14 chapters)

Table of contents (14 chapters)
  • Unfolding the Educational and Practical Resources Inherent in Mathematics for Teaching Mathematics

    Pages 1-24

    Wittmann, Erich Christian

  • Teaching Units as the Integrating Core of Mathematics Education

    Pages 25-36

    Wittmann, Erich Christian

  • Clinical Interviews Embedded in the “Philosophy of Teaching Units”—A Means of Developing Teachers’ Attitudes and Skills

    Pages 37-47

    Wittmann, Erich Christian

  • The Mathematical Training of Teachers from the Point of View of Education

    Pages 49-60

    Wittmann, Erich Christian

  • When Is a Proof a Proof?

    Pages 61-76

    Wittmann, Erich Christian

Buy this book

eBook  
  • ISBN 978-3-030-61570-3
  • This book is an open access book, you can download it for free on link.springer.com
Hardcover $59.99
price for USA in USD
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Connecting Mathematics and Mathematics Education
Book Subtitle
Collected Papers on Mathematics Education as a Design Science
Authors
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s)
eBook ISBN
978-3-030-61570-3
DOI
10.1007/978-3-030-61570-3
Hardcover ISBN
978-3-030-61569-7
Edition Number
1
Number of Pages
XX, 318
Number of Illustrations
139 b/w illustrations, 61 illustrations in colour
Topics