Overview
- 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
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
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.
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Authors and Affiliations
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: https://doi.org/10.1007/978-3-030-61570-3
Publisher: Springer Cham
eBook Packages: Education, Education (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s) 2021
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, general