Tasks in Primary Mathematics Teacher Education

Tasks in Primary Mathematics Teacher Education

MATHEMATICS TEACHER EDUCATION VOLUME 4 SERIES EDITOR Andrea Peter-Koop, University of Oldenburg, Germany Patricia Wilson, University of Georgia, United States EDITORIAL BOARD Andy Begg, Auckland University of Technology, New Zealand Chris Breen, University of Cape Town, South Africa Francis Lopez-Real, University of Hong Kong, China Jarmila Novotna, Charles University, Czechoslovakia Jeppe Skott, Danish University of Education, Copenhagen, Denmark Peter Sullivan, Monash University, Monash, Australia Dina Tirosh, Tel Aviv University, Israel SCOPE The Mathematics Teacher Education book series presents relevant research and innovative international developments with respect to the preparation and professional development of mathematics teachers. A better understanding of teachers cognitions as well as knowledge about effective models for preservice and inservice teacher education is fundamental for mathematics education at the primary, secondary and tertiary level in the various contexts and cultures across the world. Therefore, considerable research is needed to understand what facilitates and impedes mathematics teachers professional learning. The series aims to provide a significant resource for teachers, teacher educators and graduate students by introducing and critically reflecting new ideas, concepts and findings of research in teacher education. For other titles published in this series, go to http://www.springer.com /series/6327

Barbara Clarke Barbro Grevholm Richard Millman Editors Tasks in Primary Mathematics Teacher Education Purpose, Use and Exemplars ABC

Editors Barbara Clarke Monash University Faculty of Education Wellington Road Clayton VIC 3800 Australia barbara.clarke@education.monash.edu.au Richard S. Millman Georgia Institute of Technology Center for Education Integrating Science, Mathematics & Computing (CEISMC) Atlanta, GA 30332-0282 USA millman@ms.uky.edu Barbro Grevholm University of Agder Faculty of Engineering and Science Department of Mathematical Sciences NO-4604 Kristiansand Norway barbro.grevholm@uia.no ISBN: 978-0-387-09668-1 e-isbn: 978-0-387-09669-8 DOI: 10.1007/978-0-387-09669-8 Library of Congress Control Number: 2008938622 c Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper springer.com

Preface The idea for this book emerged from discussions at the Research Study Conference 15 organised by the International Commission for Mathematical Instruction. The study focused on professional education and development of teachers of mathematics and brought together invited participants from around the world. The authors in this book are a selection of presenters at that study conference, who subsequently contributed chapters with examples and elaborations of tasks used in primary mathematics teacher education. The authors first provided outlines that were subsequently reviewed by the editorial group and then after a second review process revised to produce the chapters you will find here. This book is organised in three sections. The first section presents chapters with tasks for teachers and teacher educators that indicate the cyclic character of the work. The second section concerns tasks as a tool for developing mathematical knowledge for teaching. The third section is related to tasks as a tool for developing knowledge through and for practice. These three categories are of course overlapping but help to focus key aspects of the purpose of the tasks. Each section begins with an overview and the book ends with a concluding chapter. The chapters in this book describe tasks that have been used successfully in mathematics teacher education for primary teachers in a range of contexts and countries. These tasks are often exemplars of broader categories of tasks or illustrative of techniques for developing particular understandings. While the tasks have a practical and experiential focus, a theoretical or research-based justification is included for each of them. We do not see this as a book about how mathematics teacher education is conducted in a particular country or institution or about the policy for that but rather as a book about research-driven practices. The primary audience for this book will be mathematics teacher educators who focus on the preparation of elementary/primary teachers. The tasks are applicable across a range of contexts. While the tasks themselves are a useful resource, the rationales and discussions of the nature and purpose of such tasks can provide richer understanding of the role of tasks in primary mathematics teacher education tasks as the meta-level focus. v

vi Preface We acknowledge with much thanks the work of Nike Prince whose careful attention to the final editing, thoughtful liaising with authors and organised management of the development of the manuscript made a very important contribution to this book. Barbara Clarke, Barbro Grevholm, and Richard Millman

Contents Function, Form and Focus: The Role of Tasks in Elementary Mathematics Teacher Education... 1 Barbro Grevholm, Richard Millman, and Barbara Clarke Section A Tasks as a Tool for Exploring the Cyclical Nature of Learning and Developing Reflection in the Teaching of Mathematics Using Lesson Study to Develop an Appreciation of and Competence in Task Design... 11 Joanne Lieberman Reflecting on the Process of Task Adaptation and Extension: The Case of Computational Starters... 25 Theresa J. Grant and Jane-Jane Lo Tasks for Primary Student Teachers: A Task of Mathematics Teacher Educators... 37 Victoria Sánchez and Mercedes García The Mathematics Teaching Portfolio: A Reflective Tool for Developing Professional Growth and Improving Classroom Practices... 51 Rose Spanneberg Section B Tasks as a Tool for Developing Mathematical Knowledge for Teaching Pushing Probability and Statistics Tasks in a New Direction... 71 Dan Canada Logic in Wonderland: Alice s Adventures in Wonderland as the Context of a Course in Logic for Future Elementary Teachers... 85 Nitsa Movshovitz-Hadar and Atara Shriki vii

viii Contents Tasks using Video Clips of Children in a Content Mathematics Course for Future Elementary School Teachers... 105 Richard Millman, Kelly Svec, and Dana Williams Teacher Tasks for Mathematical Insight and Reorganization of What it Means to Learn Mathematics... 113 George Gadanidis and Immaculate Namukasa Teaching and Understanding Mathematical Modelling through Fermi-Problems... 131 Andrea Peter-Koop A Research-Based Workshop Design for Volume Tasks... 147 Mariana Sáiz and Olimpia Figueras Task-Based Lessons: The Central Focus of a Mathematics Content Course for Future Elementary Teachers... 161 Anne R. Teppo Section C Tasks as a Tool for Developing Knowledge through and for Practice The Use of Relational Games in Initial Teacher Education: Bringing the Classroom into the Lecture Theatre... 177 Solange Amorim Amato Using Mathematically Rich Tasks to Deepen the Pedagogical Content Knowledge of Primary Teachers... 197 George Ashline and Regina Quinn From Professional Tasks in Collaborative Environments to Educational Tasks in Mathematics Teacher Education... 215 José Carrillo and Nuria Climent The Analysis of Classroom-Based Processes as a Key Task in Teacher Training for the Approach to Early Algebra... 235 Nicolina A. Malara and Giancarlo Navarra Outdoor Mathematical Experiences: Constructivism, Connections, and Health... 263 Meg Moss From Teacher Education to Teacher Practice: A Gap Affecting the Implementation of Tasks... 275 Pedro Palhares, Alexandra Gomes, Paulo Carvalho, and Valter Cebolo Concluding Remarks... 285 Barbara Clarke, Barbro Grevholm, and Richard Millman

Contents ix Author Notes...291 Author Index...297 Subject Index...303

Contributors Solange Amato, Lecturer, Faculty of Education, University of Braslia, Brasil George Ashline, Professor of Mathematics, Saint Michaels College, Vermont, USA Dan Canada, Associate Professor, Department of Mathematics, Eastern Washington University, USA José Carrillo, Assistant Professor, Faculty of Educational Sciences, University of Huelva, Spain Paulo Carvalho, Institute of Child Studies, University of Minho, Portugal Valter Cebolo, Institute of Child Studies, University of Minho, Portugal Barbara Clarke, Associate Professor and Associate Dean of Staff, Faculty of Education, Monash University, Australia Nuria Climent, University of Huelva, Spain Olimpia Figueras, Researcher, Mathematics Education Department of the Center for Research and Advanced Studies of the National Poly-technique Institute (Cinvestav), Mexico George Gadanidis, Associate Professor, Faculty of Education, The University of Western Ontario, Canada Mercedes García, Professor, Department of Didactic of Mathematics, University of Seville, Spain Alexandra Gomes, Assistant Professor, Institute of Child Studies, University of Minho, Portugal Theresa Grant, Professor, Department of Mathematics, Western Michigan University, USA xi

xii Contributors Barbro Grevholm, Professor of Mathematics Education, University of Agder, Norway Joanne Lieberman, Assistant Professor, Mathematics and Statistics Department, California State University Monterey Bay, USA Jane-Jane Lo, Associate Professor, Department of Mathematics, Western Michigan University, USA Nicolina A. Malara, Professor, Department of Mathematics, Faculty of Science, University of Modena & Reggio Emilia, Italy Richard Millman, Director, Center for Education Integrating Science, Mathematics and Computing, and Professor of the Practice of Mathematics, Georgia Institute of Technology, USA Meg Moss, Associate Professor of Mathematics and Teacher Education Coordinator, Pellissippi State Technical Community College in Knoxville, TN, USA Nitsa Movshovitz-Hadar, Emeritus Professor of Mathematics Education, Technion Israel Institute of Technology, Israel Immaculate Namukasa, Assistant Professor, Faculty of Education, University of Western Ontario, Canada Giancarlo Navarra, Department of Mathematics, University of Modena & Reggio E, Italy Pedro Palhares, Assistant Professor, Institute of Child Studies, University of Minho, Portugal Andrea Peter-Koop, Professor of Mathematics Education, University of Oldenburg, Germany Regina Quinn, Project Director and co-pi of the Vermont Mathematics Partnership, USA Mariana Sáiz, Professor, Learning and Teaching of sciences, humanities and arts, Universidad Pedagógica Nacional México City, Mexico Victoria Sánchez, Professor, Department of Didactic of Mathematics, University of Seville, Spain Atara Shriki, Oranim Academic College of Education, Israel Rose Spanneberg, Director, Rhodes University Mathematics Education Project (RUMEP), South Africa Kelly Svec, Student, University of Kentucky, USA Anne Teppo, Independent scholar who collaborates with other mathematics educators around the world Dana Williams, Graduate, University of Kentucky, USA