ICME-13 Monographs Brian Doig · Julian Williams · David Swanson · Rita Borromeo Ferri · Pat Drake Editors Interdisciplinary Mathematics Education The State of the Art and Beyond 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 Brian Doig • Julian Williams • David Swanson • Rita Borromeo Ferri • Pat Drake Editors Interdisciplinary Mathematics Education The State of the Art and Beyond Editors Brian Doig Julian Williams Faculty of Arts and Education Ellen Wilkinson Building Deakin University The University of Manchester Victoria, VIC, Australia Manchester, UK David Swanson Rita Borromeo Ferri Manchester Institute of Education Institut für Mathematik The University of Manchester Universität Kassel Manchester, UK Kassel, Hessen, Germany Pat Drake Victoria University Melbourne, VIC, Australia ISSN 2520-8322 ISSN 2520-8330 (electronic) ICME-13 Monographs ISBN 978-3-030-11065-9 ISBN 978-3-030-11066-6 (eBook) https://doi.org/10.1007/978-3-030-11066-6 Library of Congress Control Number: 2018966113 © The Editor(s) (if applicable) and The Author(s) 2019. This book is an open access publication. 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This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Contents 1 Introduction to Interdisciplinary Mathematics Education ........ 1 Brian Doig and Julian Williams Part I Conceptualising and Theorising Interdisciplinarity in Research, Policy and Practice Julian Williams 2 Introduction .......................................... 9 Julian Williams 3 Theoretical Perspectives on Interdisciplinary Mathematics Education ............................................ 13 Julian Williams and Wolff-Michael Roth 4 Integration from a Commognitive Perspective: An Experience with Mathematics and Music Students ...................... 35 M. Alicia Venegas-Thayer 5 Challenges and Opportunities for a STEM Interdisciplinary Agenda .............................................. 51 Russell Tytler, Gaye Williams, Linda Hobbs and Judy Anderson Part II Focus on Cross-Cutting Skills: A Glass Half-Full? Pat Drake 6 Introduction: A Glass Half Full? .......................... 85 Pat Drake 7 Developing Mathematical Reasoning Using a STEM Platform .... 93 Andrzej Sokolowski 8 Quantitative Reasoning and Its Rôle in Interdisciplinarity ....... 113 Robert Mayes v vi Contents 9 Modelling and Programming of Digital Video: A Source for the Integration of Mathematics, Engineering, and Technology ....... 135 Carlos A. LópezLeiva, Marios S. Pattichis and Sylvia Celedón-Pattichis Part III Case Studies in Inter-Disciplinarity: Mathematics as Tool and Mathematics as (Conscious) Generalisation David Swanson 10 Introduction .......................................... 157 David Swanson 11 Mathematics in an Interdisciplinary STEM Course (NLT) in The Netherlands ..................................... 167 Nelleke den Braber, Jenneke Krüger, Marco Mazereeuw and Wilmad Kuiper 12 Maths Adds up ........................................ 185 Maite Gorriz and Santi Vilches 13 The Successful Students STEM Project: A Medium Scale Case Study ........................................... 209 Linda Hobbs, Brian Doig and Barry Plant 14 “Draw What You See” Transcending the Mathematics Classroom ............................................ 229 Signe E. Kastberg, Rachel Long, Kathleen Lynch-Davis and Beatriz S. D’Ambrosio 15 Inter-disciplinary Mathematics: Old Wine in New Bottles? ...... 245 Brian Doig and Wendy Jobling Part IV Teacher Education and Teacher Development Rita Borromeo Ferri 16 Teacher Education and Teacher Development ................ 259 Rita Borromeo Ferri 17 Inclusion of Interdisciplinary Approach in the Mathematics Education of Biology Trainee Teachers in Slovakia ............ 263 Ivana Boboňová,Soňa Čeretková, Anna Tirpáková and Dagmar Markechová 18 Creating Academic Teacher Scholars in STEM Education by Preparing Preservice Teachers as Researchers ............. 281 Jennifer Wilhelm and Molly H. Fisher Contents vii Part V Conclusion to Interdisciplinary Mathematics Education Brian Doig 19 Conclusion to Interdisciplinary Mathematics Education ......... 299 Brian Doig and Julian Willams Chapter 1 Introduction to Interdisciplinary Mathematics Education Brian Doig and Julian Williams Abstract The purpose of this chapter is to preface, and introduce, the content of this book, but also to help clarify concepts and terms addressed, set the stage by summarising our previous work, and issue some caveats about our limitations. We will close with a discussion of the mathematics in Interdisciplinary Mathematics Education (IdME), which we see as a lacuna in the literature, and even in this book. Keywords Interdisciplinary · Mathematics · Education · Introduction 1.1 Origins and Context of This Volume The origins of this book emerged after some of us were invited to lead a Topic Study Group (TSG-22) at the International Conference on Mathematics Education in Hamburg in 2016 (ICME-13). Initially the suggestion was for a topic on Science, Technology, Engineering and Mathematics (STEM) education, a topic that has been increasingly prominent in educational policy, and practice, in the last decade. How- ever, we preferred to go to the concept of ‘interdisciplinarity’ as the focus of interest for several reasons. First, while much STEM-related work does involve interdisci- plinarity, much does not—it had emerged as a funding priority, and is often related more to political and economic expediencies, than to educational principles. Second, much STEM work does little to emphasise mathematics, and when it does so, it does not always relate the mathematics to the other disciplines or subjects involved. Third, much good interdisciplinary mathematics involves non-STEM disciplines, and we wanted to include the arts, music, and other disciplines that might be excluded from STEM. Finally, however, we hoped that “Interdisciplinary mathematics education” would include much STEM work, and even most of STEM work, that might be of contemporary interest. B. Doig Deakin University, Melbourne, Australia J. Williams (B) University of Manchester, Manchester M13 9PL, UK e-mail: [email protected] © The Author(s) 2019 1 B. Doig et al. (eds.), Interdisciplinary Mathematics Education, ICME-13 Monographs, https://doi.org/10.1007/978-3-030-11066-6_1 2 B. Doig and J. Williams 1.2 The State of the Art in 2016: What Next? Prior to the ICME-13 conference, the organisers were invited to produce a State of the art in the topic, which was published immediately prior to the conference, and is available freely on-line (see, Williams et al., 2016). This provided the base level of knowledge that all papers in Topic Group 22 built on, and many of the chapters in this book refer to it, so it is worth summarising some of its key points here. In the State of the art, the authors make clear that previous research in the topic suffers from several key problems, or even flaws. First, there is confusion over the key concepts and terms, making it hard for research to become cumulative. Much of the writing in the topic assumes that a discipline equates with a school curricu- lum subject, and that any form of collaboration, or integration, between subjects is therefore ‘interdisciplinary’, whereas, we prefer to use the term ‘curriculum inte- gration’ or ‘subject