Constructing Knowledge for Teaching Secondary Mathematics

MATHEMATICS TEACHER EDUCATION VOLUME 6 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

Orit Zaslavsky • Peter Sullivan Editors

Constructing Knowledge for Teaching Secondary Mathematics Tasks to Enhance Prospective and Practicing Teacher Learning

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Editors Prof. Orit Zaslavsky New York University NY 10003 USA Technion—Israel Institute of Technology Haifa 32000 Israel [email protected]

Prof. Peter Sullivan Faculty of Education Monash University Wellington Road, 3800 Clayton, Victoria Australia [email protected]

ISBN 978-0-387-09811-1     e-ISBN 978-0-387-09812-8 DOI 10.1007/978-0-387-09812-8 Springer New York Dordrecht Heidelberg London © Springer Science+Business Media, LLC 2011 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. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Contents

 etting the Stage: A Conceptual Framework for Examining S and Developing Tasks for Mathematics Teacher Education �����������������������    1 Orit Zaslavsky and Peter Sullivan Part I I nstructional Alternatives via a Virtual Setting: Rich Media Supports for Teacher Development ���������������������������������������������������������������   23 Daniel Chazan, Patricio Herbst and Hagit Sela  lassifying and Characterising: Provoking Awareness of the Use C of a Natural Power in Mathematics and in Mathematical Pedagogy ��������   39 John Mason  esigning Tasks that Challenge Values, Beliefs and Practices: D A Model for the Professional Development of Practicing Teachers �����������   57 Malcolm Swan  edagogical, Mathematical, and Epistemological Goals P in Designing Cognitive Conflict Tasks for Teacher Education �������������������   73 Irit Peled and Anat Suzan  orking Mathematically on Teaching Mathematics: Preparing W Graduates to Teach Secondary Mathematics �����������������������������������������������   89 Anne Watson and Liz Bills  idactical Variability in Teacher Education �������������������������������������������������   103 D Jarmila Novotná and Bernard Sarrazy  ridging Between Mathematics and Education Courses: B Strategy Games as Generators of Problem Solving and Proving Tasks ����   117 Nitsa Movshovitz-Hadar v

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Contents

Part II  ediating Mathematics Teaching Development and Pupils’ M Mathematics Learning: The Life Cycle of a Task ����������������������������������������   143 Barbara Jaworski, Simon Goodchild, Stig Eriksen and Espen Daland  earning from the Key Tasks of Lesson Study ��������������������������������������������   161 L Catherine Lewis, Shelley Friedkin, Elizabeth Baker and Rebecca Perry  athematical Problem Solving: Linking Theory and Practice ������������������   177 M Berinderjeet Kaur and Tin Lam Toh Part III Guiding Mathematical Inquiry in Mobile Settings ��������������������������������������   191 Michal Yerushalmy and Galit Botzer  echnology Integration in Secondary Mathematics: Enhancing T the Professionalisation of Prospective Teachers �������������������������������������������   209 Merrilyn Goos  athematical Machines: From History to Mathematics Classroom ���������   227 M Michela Maschietto and Maria G. Bartolini Bussi Part IV  sing Video Episodes to Reflect on the Role of the Teacher U in Mathematical Discussions ��������������������������������������������������������������������������   249 João Pedro da Ponte  ensitivity to Student Learning: A Possible Way to Enhance S Teachers’ and Students’ Learning? ���������������������������������������������������������������   263 Ulla Runesson, Angelika Kullberg and Tuula Maunula Overcoming Pedagogical Barriers Associated with Exploratory Tasks in a College Geometry Course �������������������������������������������������������������   279 Norma Presmeg  sing a Model for Planning and Teaching Lessons as Part U of Mathematics Teacher Education ���������������������������������������������������������������   291 Peter Sullivan, Robyn Jorgensen and Judith Mousley  uilding Optimism in Prospective Mathematics Teachers �������������������������   307 B Gaye Williams Index �����������������������������������������������������������������������������������������������������������������   325

Contributors

Elizabeth Baker  Mills College Lesson Study Group, Oakland, USA e-mail: [email protected] Maria G. Bartolini Bussi  Dipartimento di Matematica Pura e Applicata, Università di Modena e Reggio Emilia, Modena, Italy e-mail: [email protected] Liz Bills  Department of Education, University of Oxford, OX2 6PY, Oxford, UK e-mail: [email protected] Galit Botzer  Faculty of Education, Institute for Research of Alternatives in Education, University of Haifa, Haifa, Israel e-mail: [email protected] Daniel Chazan  University of Maryland, College Park, USA e-mail: [email protected] Espen Daland  University of Agder, Kristiansand, Norway e-mail: [email protected] Stig Eriksen  University of Agder, Kristiansand, Norway e-mail: [email protected] Shelley Friedkin  Mills College Lesson Study Group, Oakland, USA e-mail: [email protected] Simon Goodchild  University of Agder, Kristiansand, Norway e-mail: [email protected] Merrilyn Goos  Teaching and Educational Development Institute, The University of Queensland, St Lucia, QLD 4072, Australia e-mail: [email protected] Patricio Herbst  University of Michigan, Ann Arbor, USA e-mail: [email protected] Barbara Jaworski  Loughborough University, Loughborough, UK e-mail: [email protected] vii

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Contributors

Robyn Jorgensen  Griffith University, Brisbane, QLD, Australia e-mail: [email protected] Berinderjeet Kaur  National Institute of Education, Nanyang Technological University, Singapore e-mail: [email protected] Angelika Kullberg  Department of Education, University of Gothenburg, Gothenburg, Sweden e-mail: [email protected] Catherine Lewis  Mills College Lesson Study Group, Oakland, USA e-mail: [email protected] Michela Maschietto  Dipartimento di Matematica Pura e Applicata, Università di Modena e Reggio Emilia, Modena, Italy e-mail: [email protected] John Mason  Open University, Milton Keynes, UK University of Oxford, Oxford, UK e-mail: [email protected] Tuula Maunula  Department of Education, University of Gothenburg, Gothenburg, Sweden e-mail: [email protected] Judith Mousley  Deakin University, Geelong, 3217 Australia e-mail: [email protected] Nitsa Movshovitz-Hadar  Technion—Israel Institute of Technology, Haifa 32000, Israel e-mail: [email protected] Jarmila Novotná  Faculty of Education, Department of Mathematics and Mathematics Education, Charles University in Prague, Czech Republic e-mail: [email protected] Irit Peled  Faculty of Education, Department of Mathematics Education, University of Haifa, Haifa, Israel e-mail: [email protected] Rebecca Perry  Mills College Lesson Study Group, Oakland, USA e-mail: [email protected] João Pedro da Ponte  Instituto de Educação, Universidade de Lisboa, Lisboa, Portugal e-mail: [email protected] Norma Presmeg  Mathematics Department, Illinois State University, Normal, IL, USA e-mail: [email protected] Ulla Runesson  School of Education and Communication, University of Jönköping, Sweden e-mail: [email protected]

Contributors

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Bernard Sarrazy  Laboratoire Culture, Education, Société, Université Bordeaux Segalen, Bordeaux, France e-mail: [email protected] Hagit Sela  University of Maryland, College Park, USA e-mail: [email protected] Peter Sullivan  Faculty of Education, Monash University, Wellington Road, 3800 Clayton, VIC, Australia e-mail: [email protected] Anat Suzan  Faculty of Education, Department of Mathematics Education, University of Haifa, Haifa, Israel e-mail: [email protected] Malcolm Swan  Centre for Research in Mathematics Education, School of Education, University of Nottingham, Nottingham, England e-mail: [email protected] Tin Lam Toh  National Institute of Education, Nanyang Technological University, Singapore e-mail: [email protected] Anne Watson  Department of Education, University of Oxford, OX2 6PY, Oxford, UK e-mail: [email protected] Gaye Williams  Faculty of Arts and Education, Deakin University, Geelong, 3217 Australia e-mail: [email protected] Michal Yerushalmy  Faculty of Education, Institute for Research of Alternatives in Education, University of Haifa, Haifa, Israel e-mail: [email protected] Orit Zaslavsky  Technion—Israel Institute of Technology, Haifa 32000, Israel New York University, NY 10003, USA e-mail: [email protected]