Traditions in German-Speaking Mathematics Education Research ICME-13 Monographs
Total Page：16
File Type：pdf, Size：1020Kb
ICME-13 Monographs Hans Niels Jahnke Lisa Hefendehl-Hebeker Editors Traditions in German-Speaking Mathematics Education Research ICME-13 Monographs Series editor Gabriele Kaiser, Faculty of Education, Didactics of Mathematics, Universität Hamburg, Hamburg, Germany Each volume in the series presents state-of-the art research on a particular topic in mathematics education and reflects the international debate as broadly as possible, while also incorporating insights into lesser-known areas of the discussion. Each volume is based on the discussions and presentations during the ICME-13 conference and includes the best papers from one of the ICME-13 Topical Study Groups, Discussion Groups or presentations from the thematic afternoon. More information about this series at http://www.springer.com/series/15585 Hans Niels Jahnke • Lisa Hefendehl-Hebeker Editors Traditions in German-Speaking Mathematics Education Research Editors Hans Niels Jahnke Lisa Hefendehl-Hebeker Faculty of mathematics Faculty of mathematics University of Duisburg-Essen University of Duisburg-Essen Essen, Germany Essen, Germany ISSN 2520-8322 ISSN 2520-8330 (electronic) ICME-13 Monographs ISBN 978-3-030-11068-0 ISBN 978-3-030-11069-7 (eBook) https://doi.org/10.1007/978-3-030-11069-7 Library of Congress Control Number: 2018966112 © The Editor(s) (if applicable) and The Author(s) 2019. 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, adap- tation, 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 publi- cation 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, express 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 Preface The papers contained in the present volume are expanded versions of those pre- sented during the sessions on ‘German-Speaking Traditions in Mathematics Education Research’ at the 13th International Congress on Mathematics Education (ICME 13) 2016, in Hamburg. Exactly forty years earlier in 1976, ICME 3 took place in the German city of Karlsruhe. It was quite natural then to ask what developments had taken place in German mathematics education research since 1976, what ideas and activities became characteristic, who proved to be influential, how were German-speaking mathematics educators influenced by the international community and how did they interact with it. ‘German-speaking traditions’ clearly encompass more than those of Germany alone. Austria and Switzerland belong to the family, as does the former German Democratic Republic (GDR), which has its own traditions that are still influential. Nevertheless, in preparing ICME 13, we decided, for the sake of clarity, to adopt an approach in which Germany would be our main focus while we would include cross references, some substantial, to Austria, Switzerland and the former GDR. Our overview on German-speaking traditions is basically organized in chapters on eight fields of research: Subject-matter Didactics (‘Stoffdidaktik’); Design Science and Design Research; Mathematical Modelling; Mathematics and Bildung 1810–1850; Allgemeinbildung, Mathematical Literacy and Competence Orientation; Theories of and in mathematics education; Classroom Studies in a Sociological Perspective; Educational Research on Learning and Teaching of Mathematics and Large-Scale Studies in Mathematics Education Research. In the introductory chapter (Chap. 1), ‘Educational Research on Mathematics—A Short Survey of Its Development in German Speaking Countries’, we try to provide a historical per- spective so that the reader might gain a better understanding of how these different fields of didactical research are interrelated. Looking at the eight themes above, one realizes the profound changes in German-speaking mathematics education research that have taken place during the last forty years. The only themes that could have appeared in the programme of the Karlsruhe Congress in 1976 are subject-matter didactics, design science (with qualifications) and the two chapters on Allgemeinbildung. All other topics, v vi Preface especially modelling, theory traditions, classroom studies and empirical research represent for Germany completely new fields of activity. Today, they define the stage on which German mathematics educators have to act. That said, more tra- ditional fields nearer to mathematics, subject-matter analysis and elementarization, are still alive and we hope they will continue to be areas of intense work so that the common ground of mathematics and education will not be lost. The development of a scientific discipline in any tradition is a complex and many-sided subject. To give it a fair overview is not possible in a single voice. At ICME 13, therefore, we aimed always to present our themes as far as possible in a dialogical and communicative manner, involving numerous colleagues not only from German-speaking countries but also from other parts of the world. The book of course is organized in unified and polished chapters; however, the attentive reader will find throughout the text hints of the different contributions and views of this diverse group, thus sensing, we hope, the communicative nature of the whole enterprise. A great number of colleagues worked on and contributed to this book. We would like to express our profound gratitude to them. Essen, Germany Hans Niels Jahnke November 2018 Lisa Hefendehl-Hebeker Contents 1 Educational Research on Mathematics—A Short Survey of Its Development in German Speaking Countries ............ 1 Uwe Gellert, Lisa Hefendehl-Hebeker, Hans Niels Jahnke and Timo Leuders 2 Subject-Matter Didactics ................................. 25 Lisa Hefendehl-Hebeker, Rudolf vom Hofe, Andreas Büchter, Hans Humenberger, Axel Schulz and Sebastian Wartha 3 Design Science and Design Research: The Significance of a Subject-Specific Research Approach .................... 61 Marcus Nührenbörger, Bettina Rösken-Winter, Michael Link, Susanne Prediger and Anna Susanne Steinweg 4 Mathematical Modelling ................................. 91 Katrin Vorhölter, Gilbert Greefrath, Rita Borromeo Ferri, Dominik Leiß and Stanislaw Schukajlow 5 Mathematics and Bildung 1810 to 1850 ..................... 115 Hans Niels Jahnke with a reaction by Michael N. Fried 6 Allgemeinbildung, Mathematical Literacy, and Competence Orientation ............................. 141 Rolf Biehler with a reaction by Mogens Niss 7 Theories of and in Mathematics Education ................... 171 Angelika Bikner-Ahsbahs and Andreas Vohns 8 Classroom Studies—Sociological Perspectives ................. 201 Uwe Gellert and Götz Krummheuer vii viii Contents 9 Educational Research on Learning and Teaching Mathematics .......................................... 223 Timo Leuders and Andreas Schulz 10 Large-Scale Studies in Mathematics Education Research ........ 249 Kristina Reiss, Andreas Obersteiner, Aiso Heinze, Ursula Itzlinger-Bruneforth and Fou-Lai Lin Chapter 1 Educational Research on Mathematics—A Short Survey of Its Development in German Speaking Countries Uwe Gellert, Lisa Hefendehl-Hebeker, Hans Niels Jahnke and Timo Leuders Abstract In German speaking countries, educational thinking and theorizing on mathematics teaching and learning originated with the establishment of compulsory education for all children and the creation of a school system. Though first efforts go back to the 18th century it does make sense to start this survey with the beginning of the 19th century, with the implication that educational research on mathematics has a history of about two hundred years in German speaking countries. During the 19th century a more and more sophisticated system of publication (journals and books) on mathematics education emerged, the education of mathematics teachers had become more professional and teacher training had developed into one of the main obligations of university teaching. However, didactics of mathematics as an academic discipline is a comparably new achievement. Its establishment began approximately fifty years ago, predominately by creating professorships and opportunities of graduation at universities.