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Connecting Mathematics and Mathematics Education Collected Papers on Mathematics Education as a Design Science

Connecting Mathematics and Mathematics Education

Erich Christian Wittmann

Connecting Mathematics and Mathematics Education Collected Papers on Mathematics Education as a Design Science

123

Erich Christian Wittmann Department of Mathematics Technical University of Dortmund Dortmund, Germany

ISBN 978-3-030-61569-7 ISBN 978-3-030-61570-3 https://doi.org/10.1007/978-3-030-61570-3

(eBook)

© The Editor(s) (if applicable) and The Author(s) 2021. This book is an open access publication. Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Foreword

One of us, who had the good fortune of meeting Trevor Fletcher in the symposium on the centennial of L’Enseignement Mathématique held in Genève in October of 2000, received a piece of excellent advice from this notable mathematics educator, namely, that a fundamental task of the teacher of mathematics is to let students experience the intellectual life that the teacher really lives. Fletcher placed this quote (from E.E. Moise) at the forefront of his paper of 1975 that bears the title “Is the teacher of mathematics a mathematician or not?” [Schriftenreihe des Instituts für Didaktik der Mathematik Bielefeld, 6 (1975), 203–218]. Everybody began with a world “without mathematics”, this term to be t