Handbook of International Research in Mathematics Education

www.Ebook777.com

Free ebooks ==> www.Ebook777.com

Handbook of International Research

in Mathematics Education

This third edition of the Handbook of International Research in Mathematics Education pro￾vides a comprehensive overview of the most recent theoretical and practical developments in

the field of mathematics education. Authored by an array of internationally recognized scholars

and edited by Lyn D. English and David Kirshner, this collection brings together overviews

and advances in mathematics education research spanning established and emerging topics,

diverse workplace and school environments, and globally representative research priorities.

New perspectives are presented on a range of critical topics including embodied learning,

the theory–practice divide, new developments in the early years, educating future mathematics

education professors, problem solving in a 21st-century curriculum, culture and mathematics

learning, complex systems, critical analysis of design-based research, multimodal technologies,

and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Hand￾book’s original themes for international research in mathematics education and remains in the

process a definitive resource for the field.

Lyn D. English is a professor of STEM in education within the Faculty of Education at

Queensland University of Technology, Australia. She is a fellow of the Academy of the Social

Sciences in Australia and the founding editor of the international journal Mathematical Think￾ing and Learning.

David Kirshner is a professor in the School of Education at Louisiana State University, USA,

and co-director of the Gordon A. Cain Center for Scientific, Mathematical, Engineering, and

Technological Literacy at that institution.

www.Ebook777.com

Free ebooks ==> www.Ebook777.com

This page intentionally left blank

www.Ebook777.com

Free ebooks ==> www.Ebook777.com

Handbook of International

Research in Mathematics

Education

Third Edition

Edited by

Lyn D. English and David Kirshner

www.Ebook777.com

Free ebooks ==> www.Ebook777.com

First published 2016

by Routledge

711 Third Avenue, New York, NY 10017

and by Routledge

2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN

Routledge is an imprint of the Taylor & Francis Group, an informa business

© 2016 Taylor & Francis

The right of the editors to be identified as the authors of the editorial material, and of the authors for their

individual chapters, has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and

Patents Act 1988.

All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any elec￾tronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording,

or in any information storage or retrieval system, without permission in writing from the publishers.

Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only

for identification and explanation without intent to infringe.

Library of Congress Cataloging-in-Publication Data

Handbook of international research in mathematics education /

[edited] by Lyn D. English and David Kirshner.— [3rd edition].

â•…â•…pages cm

Includes bibliographical references and index.

1. Mathematics—Study and teaching—Research. I. English, Lyn D. II. Kirshner, David, 1950–

QA11.2.H36 2015

510.71—dc23

2015007357

ISBN: 978-0-415-83203-8 (hbk)

ISBN: 978-0-415-83204-5 (pbk)

ISBN: 978-0-203-44894-6 (ebk)

Typeset in Galliard

by Apex CoVantage, LLC

v

Acknowledgments ix

List of Reviewers xi

SECTION I

Priorities in International Mathematics Education Research 1

1 Changing Agendas in International Research in Mathematics Education 3

LYN D. ENGLISH AND DAVID KIRSHNER

2 Perspectives on Priority Mathematics Education: Unpacking and

Understanding a Complex Relationship Linking Teacher Knowledge,

Teaching, and Learning 19

CHARALAMBOS Y. CHARALAMBOUS AND DEMETRA PITTA-PANTAZI

3 Approaches to Embodied Learning in Mathematics 60

SUSAN GEROFSKY

4 Configuring Learning Theory to Support Teaching 98

DAVID KIRSHNER

SECTION II

Democratic Access to Mathematics Learning 151

5 Young Children’s Access to Powerful Mathematics Ideas: A Review

of Current Challenges and New Developments in the Early Years 153

JOAN MOSS, CATHERINE D. BRUCE, AND JANETTE BOBIS

6 Powerful Ideas in Elementary School Mathematics 191

DAVID W. CARRAHER AND ANALÚCIA D. SCHLIEMANN

Contents

vi Contents

7 Students’ Access to Mathematics Learning in the Middle

and Junior Secondary Schools 219

TERESA ROJANO

8 Mathematical Structure, Proof, and Definition in Advanced

Mathematical Thinking 239

JOANNA MAMONA-DOWNS AND MARTIN L.N. DOWNS

9 Reform as an Issue for Mathematics Education Research: Thinking

About Change, Communication, and Cooperation 257

MICHAEL N. FRIED AND MIRIAM AMIT

10 Prospective Mathematics Teachers’ Learning and Knowledge

for Teaching 275

JOÃO PEDRO DA PONTE AND OLIVE CHAPMAN

11 Educating Future Mathematics Education Professors 297

JEREMY KILPATRICK AND DENISE A. SPANGLER

SECTION III

Transformations in Learning Contexts 311

12 Problem Solving in a 21st-Century Mathematics Curriculum 313

LYN D. ENGLISH AND JULIE GAINSBURG

13 Critical Issues in Culture and Mathematics Learning 336

PETER APPELBAUM AND CHAROULA STATHOPOULOU

14 Mathematics Education and Democracy: An Open Landscape of Tensions,

Uncertainties, and Challenges 359

OLE SKOVSMOSE AND MIRIAM GODOY PENTEADO

15 Toward a Sociology of Mathematics Education: Examining Democratic

Access in U.S. Schools 374

CELIA ROUSSEAU ANDERSON AND WILLIAM F. TATE

16 Mathematics Learning In and Out of School: Towards Continuity

or Discontinuity? 395

GUIDA DE ABREU AND SARAH CRAFTER

17 Perspectives on Complex Systems in Mathematics Learning 416

BRENT DAVIS AND ELAINE SIMMT

Contents vii

SECTION IV

Advances in Research Methodologies 433

18 Researching Mathematical Meanings for Teaching 435

PATRICK W. THOMPSON

19 Measurement Challenges in Mathematics Education Research 462

ROSEMARY CALLINGHAM

20 Design Research: An Analysis and Critique 481

PAUL COBB, KARA JACKSON, AND CHARLOTTE DUNLAP

21 The Intertwining of Theory and Practice: Influences on Ways

of Teaching and Teachers’ Education 504

ANNALISA CUSI AND NICOLINA A. MALARA

22 Knowledge Creation Through Dialogic Interaction Between the Practices

of Teaching and Researching 523

KENNETH RUTHVEN AND SIMON GOODCHILD

SECTION V

Influences of Advanced Technologies 541

23 Foundations for the Future: The Potential of Multimodal Technologies

for Learning Mathematics 543

STEPHEN J. HEGEDUS AND DAVID O. TALL

24 Statistical Software and Mathematics Education: Affordances

for Learning 563

JANE WATSON AND NOLEINE FITZALLEN

25 The Use of Digital Technology in Mathematical Practices: Reconciling

Traditional and Emerging Approaches 595

LUIS MORENO-ARMELLA AND MANUEL SANTOS-TRIGO

26 Computerized Environments in Mathematics Classrooms:

A Research-Design View 617

RINA HERSHKOWITZ, MICHAL TABACH, AND TOMMY DREYFUS

27 E-Textbooks in/for Teaching and Learning Mathematics: A Potentially

Transformative Educational Technology 636

BIRGIT PEPIN, GHISLAINE GUEUDET, MICHAL YERUSHALMY, LUC TROUCHE,

AND DANIEL I. CHAZAN

viii Contents

28 Digital Technologies in the Early Primary School Classroom 662

NATHALIE SINCLAIR AND ANNA BACCAGLINI-FRANK

Final Comment 687

29 Mathematics Education Research: A Strategic View 689

HUGH BURKHARDT

Index 713

ix

The publication of this third edition of the Handbook of International Research in Mathemat￾ics Education would not have been possible without the commitment of the authors, many

of whom are new contributors to this edition. David and I extend our sincere thanks to our

authors, who willingly made improvements to their chapters on receiving reviewers’ feedback.

To the reviewers, we extend our heartfelt thanks. Your thoughtful, constructive reviews were

invaluable to all of us as we worked towards producing a third edition Handbook of scholarly

distinction. Throughout the book’s development David and I established a strong partnership

that never wavered even through sometimes rocky waters. I was very fortunate in securing

David as my co-editor and remain forever grateful for his reasoned and insightful advice on

all aspects of the book. I also gratefully acknowledge the Australian Research Council, who

funded some of the research I address in Chapters 1 and 12. We further acknowledge the pro￾fessional input from Jessica Leder, who skillfully assisted us with the formatting of the book.

Finally, we thank the production team at Taylor & Francis, including Catherine Bernard and

Trevor Gori, for their support during the production process.

In Memoriam

David and I wish to express our deepest sympathy for the recent passing of one of our chap￾ter authors, Dr. Martin Downs, who co-authored chapter 8 with Joanna Mamona-Downs. I

have known both Joanna and Martin for many years, and have fond memories of the times

we shared at various international conferences. Martin’s passing is indeed a great loss to our

international community. As a Group theorist, Martin had deep insights into the essence of

mathematical structures as evident in his and Joanna’s chapter. Martin’s rich work in this field

continues to generate increasing interest from scholars globally. His memory will be kept alive

not only through the editions of this Handbook but also through the lectures, papers, and

mathematical conversations his research will continue to inspire.

Lyn D. English

David Kirshner

Acknowledgments

This page intentionally left blank

xi

Dor Abrahamson

Anna Baccaglini-Frank

Claire Berg

Alan Bishop

Hugh Burkhardt

Beatriz D’Ambrosio

Thomas Dick

Ed Dubinsky

Julie Gainsburg

Peter Gates

Simon Goodchild

Keono Gravemeijer

Jim Greeno

Barbro Grevholm

Anthony Harradine

Kate Highfield

Karen Hollerbrands

Gert Kadunz

Mandy Jansen

Jane-Jane Lo

Luis Moreno-Armella

Reviewers

Nicholas Mousoulides

Nitsa Movshovitz-Hadar

Patricia Moyer-Packenham

Na’ilah Nasir

Helena Osana

Efi Paparistodemou

Despina Potari

Arthur Powell

Bob Reys

Ornella Robutti

Annie Selden

Elaine Simmt

Adrian Simpson

Nathalie Sinclair

Denise Spangler

Bharath Sriraman

Paola Sztajn

Michal Tabach

Brendan Tangney

Patrick Thompson

Margaret Walshaw

This page intentionally left blank

Section I

Priorities in International

Mathematics Education Research