ICME-13 Monographs Philip Clarkson · Wee Tiong Seah · JeongSuk Pang Editors Values and Valuing in Mathematics Education Scanning and Scoping the Territory 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 congress 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 Philip Clarkson • Wee Tiong Seah • JeongSuk Pang Editors Values and Valuing in Mathematics Education Scanning and Scoping the Territory Editors Philip Clarkson Wee Tiong Seah Australian Catholic University Melbourne Graduate School of Education Fitzroy, VIC, Australia The University of Melbourne Melbourne, VIC, Australia JeongSuk Pang Department of Elementary Education Korea National University of Education Chungbuk, Korea (Republic of) ISSN 2520-8322 ISSN 2520-8330 (electronic) ICME-13 Monographs ISBN 978-3-030-16891-9 ISBN 978-3-030-16892-6 (eBook) https://doi.org/10.1007/978-3-030-16892-6 Library of Congress Control Number: 2019935990 © The Editor(s) (if applicable) and The Author(s) 2019. This book is an open access publication. 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Bishop This volume is dedicated to Alan Bishop in recognition of his pioneering work on which many of the present contributions build. Contents 1 Scanning and Scoping of Values and Valuing in Mathematics Education ............................................ 1 Philip Clarkson, Wee Tiong Seah and JeongSuk Pang 2 A Conversation with Alan Bishop .......................... 11 Philip Clarkson 3 Student and/or Teacher Valuing in Mathematics Classrooms: Where Are We Now, and Where Should We Go? ............. 25 Monica E. Carr 4 Values of the Japanese Mathematics Teacher Community ....... 53 Douglas Lyman Corey and Hiroyuki Ninomiya 5 Democratic Actions in School Mathematics and the Dilemma of Conflicting Values .................................... 69 Annica Andersson and Lisa Österling 6 Valuing in Mathematics Learning Amongst Ghanaian Students: What Does It Look Like Across Grade Levels? ............... 89 Ernest Kofi Davis, Monica E. Carr and Ernest Ampadu 7 What Do Pāsifika Students in New Zealand Value Most for Their Mathematics Learning? ................................. 103 Julia Hill, Jodie Hunter and Roberta Hunter 8 The Role of Value Alignment in Levels of Engagement of Mathematics Learning ................................ 115 Penelope Kalogeropoulos and Philip Clarkson 9 Exploring Teachers’ Values and Valuing Process in School-Based Lesson Study: A Brunei Darussalam Case Study .............. 129 Nor Azura Abdullah and Frederick Koon Shing Leung vii viii Contents 10 Why Mathematics Is Valuable for Turkish, Turkish Immigrant and German Students? A Cross-Cultural Study ............... 143 Yüksel Dede 11 Mathematical Values Through Personal and Social Values: A Number Activity in a Japanese Kindergarten ............... 157 Nagisa Nakawa 12 Socially Open-Ended Problems for Enriching Student Learning with Mathematical Models and Social Values ................. 171 Takuya Baba and Isao Shimada 13 Values in Mathematics Learning: Perspectives of Chinese Mainland Primary and Secondary Students .................. 185 Qiaoping Zhang 14 Methodological Issues in the Investigation of Values in Mathematics ........................................ 197 Yip-Cheung Chan and Ngai-Ying Wong 15 The Elementary Mathematics Teachers’ Values Underlying Teacher Noticing: The Context of Polygons .................. 209 Fatma Nur Aktaş, Esra Selcen Yakıcı-Topbaş and Yüksel Dede Contributors Nor Azura Abdullah Faculty of Education, The University of Hong Kong, Pokfulam, Hong Kong SAR, China Fatma Nur Aktaş Department of Mathematics and Science Education, Gazi Education Faculty, Gazi University, Ankara, Turkey Ernest Ampadu University of Ghana, Accra, Ghana Annica Andersson University of South-Eastern Norway (USN), Borre, Norway Takuya Baba Hiroshima University, Higashi-Hiroshima, Hiroshima, Japan Monica E. Carr Melbourne Graduate School of Education, The University of Melbourne, Melbourne, VIC, Australia Yip-Cheung Chan Department of Curriculum and Instruction, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China Philip Clarkson Australian Catholic University, Fitzroy, VIC, Australia Douglas Lyman Corey Brigham Young University, Provo, UT, USA Ernest Kofi Davis School of Educational Development and Outreach, College of Education Studies, University of Cape Coast, Cape Coast, Ghana Yüksel Dede Department of Mathematics and Science Education, Gazi Education Faculty, Gazi University, Ankara, Turkey Julia Hill Institute of Education, Massey University Albany, Auckland, New Zealand Jodie Hunter Institute of Education, Massey University Albany, Auckland, New Zealand Roberta Hunter Institute of Education, Massey University Albany, Auckland, New Zealand ix x Contributors Penelope Kalogeropoulos Faculty of Education, Monash University, Clayton Campus, Melbourne, VIC, Australia Frederick Koon Shing Leung The University of Hong Kong, Pokfulam, Hong Kong SAR, China Nagisa Nakawa Kanto Gakuin University, Yokohama, Kanagawa, Japan Hiroyuki Ninomiya Saitama University, Saitama, Japan Lisa Österling Stockholm University, Stockholm, Sweden JeongSuk Pang Korea National University of Education, Cheongju, South Korea Wee Tiong Seah The University of Melbourne, Melbourne, VIC, Australia Isao Shimada Nippon Sport Science University, Setagaya, Japan Ngai-Ying Wong The Education University of Hong Kong, Tai Po, Hong Kong SAR, China Esra Selcen Yakıcı-Topbaş Gazi University, Ankara, Turkey Qiaoping Zhang The Education University of Hong Kong, Tai Po, Hong Kong SAR, China Chapter 1 Scanning and Scoping of Values and Valuing in Mathematics Education Philip Clarkson, Wee Tiong Seah and JeongSuk Pang Abstract Although the ideas of values and valuing have been totemic notions in education for forever, when applied to mathematics they become quite problematic. Even today for many mathematic teachers and learners, mathematics is a value-free space. For them, school mathematics is learning the skills of manipulating num- bers before moving to the more abstract ideas of algebra, and occasionally delving into geometry and measurement ideas. Likewise teaching mathematics in schools is ensuring students get good marks on the tests and examinations using whatever peda- gogical techniques ensure this. Although in schools this is still the prevailing attitude to mathematics, nevertheless for some decades there has been a growing counter position in mathematics education research that problematizes and challenges this orthodoxy. It has argued that at a fundamental level there are mathematical values that underpin the doing of mathematics, and indeed the same is true for mathematics pedagogy. This chapter briefly explores a number of these notions as it introduces the various chapters in this volume. Keywords Values · Valuing · Mathematics education · Mathematics · Mathematics teaching · Mathematics learning P. Clarkson (B) Australian Catholic University, Locked Bag 4115, Fitzroy MDC, VIC 3065, Australia e-mail: [email protected] W. T. Seah The University of Melbourne, Melbourne, VIC, Australia e-mail: [email protected] J. Pang Korea National University of Education, Cheongju, South Korea e-mail: [email protected] © The Author(s) 2019 1 P. Clarkson et al. (eds.), Values