Mathematics Education and Technology-Rethinking the Terrain The 17th ICMI Study

489 Pages·6.586 MB·English

by  Hoyles, Celia(Editor);Lagrange, Jean-Baptiste(Editor)

New ICMI Study Series
VOLUME 13
Published under the auspices of the International Commission on
Mathematical Instruction under the general editorship of
Michèle Artigue, President Bernard R. Hodgson, Secretary-General
For other titles published in this series, go to
www.springer.com/series/6351
Information on the ICMI Study program and on the resulting publications can be obtained
at the ICMI website http://www.mathunion.org/ICMI/ or by contacting the ICMI Secretary-
General, whose email address is available on that website.
Celia Hoyles • Jean-Baptiste Lagrange
Editors
Mathematics Education
and Technology-Rethinking
the Terrain
The 17th ICMI Study
Editors
Celia Hoyles Jean-Baptiste Lagrange
London Knowledge Lab IUFM de Reims and Didirem
Institute of Education Paris 7
University of London France
London [email protected]
UK
[email protected]
ISBN 978-1-4419-0145-3 e-ISBN 978-1-4419-0146-0
DOI 10.1007/978-1-4419-0146-0
Springer New York Dordrecht Heidelberg London
Library of Congress Control Number: 2009936312
© Springer Science+Business Media, LLC 2010
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Contents
1 Introduction ................................................................................................ 1
Celia Hoyles and Jean-Baptiste Lagrange
Section 1 Design of Learning Environments and Curricula
2 Introduction to Section 1 ........................................................................... 15
Celia Hoyles and Nathalie Sinclair
3 Designing Software for Mathematical Engagement
through Modeling ....................................................................................... 19
Jere Confrey, Celia Hoyles, Duncan Jones, Ken Kahn,
Alan P. Maloney, Kenny H. Nguyen, Richard Noss and Dave Pratt
4 Designing Digital Technologies and Learning Activities
for Different Geometries ........................................................................... 47
Keith Jones, Kate Mackrell and Ian Stevenson
5 Implementing Digital Technologies at a National Scale ......................... 61
Nathalie Sinclair, Ferdinando Arzarello, Maria Trigueros Gaisman
and Maria Dolores Lozano, with Valentina Dagiene, Emran Behrooz
and Nicholas Jackiw
Section 2 Learning and Assessing Mathematics with and through
Digital Technologies
6 Introduction to Section 2 ........................................................................... 81
Paul Drijvers, Maria-Alessandra Mariotti, John Olive
and Ana Isabel Sacristán
v
vi Contents
7 Integrating Technology into Mathematics Education:
Theoretical Perspectives .......................................................................... 89
Paul Drijvers, Carolyn Kieran and Maria-Alessandra Mariotti,
with Janet Ainley, Mette Andresen, Yip Cheung Chan,
Thierry Dana-Picard, Ghislaine Gueudet, Ivy Kidron,
Allen Leung and Michael Meagher
8 Mathematical Knowledge and Practices Resulting
from Access to Digital Technologies ....................................................... 133
John Olive and Katie Makar, with Verónica Hoyos,
Liew Kee Kor, Olga Kosheleva and Rudolf Sträßer
9 The Influence and Shaping of Digital Technologies
on the Learning – and Learning Trajectories – of
Mathematical Concepts ........................................................................... 179
Ana Isabel Sacristán, Nigel Calder, Teresa Rojano,
Manuel Santos-Trigo, Alex Friedlander and Hartwig Meissner, with
Michal Tabach, Luis Moreno and Elvia Perrusquía
10 Micro-level Automatic Assessment Supported by Digital
Technologies .............................................................................................. 227
Chris Sangwin, Claire Cazes, Arthur Lee and Ka Lok Wong
11 Technology, Communication and Collaboration: Re-thinking
Communities of Inquiry, Learning and Practice .................................. 251
Ruth Beatty and Vince Geiger
Section 3 Teachers and Technology
12 Introduction to Section 3 ......................................................................... 287
Lulu Healy and Jean-Baptiste Lagrange
13 Working with Teachers: Context and Culture ...................................... 293
Anne Berit Fuglestad, Lulu Healy, Chronis Kynigos
and John Monaghan
14 Teachers and Teaching: Theoretical Perspectives
and Issues Concerning Classroom Implementation ............................. 311
Merrilyn Goos and Sophie Soury-Lavergne, with Teresa Assude,
Jill Brown, Chow Ming Kong, Derek Glover, Brigitte Grugeon,
Colette Laborde, Zsolt Lavicza, Dave Miller and Margaret Sinclair
15 Teacher Education Courses in Mathematics
and Technology: Analyzing Views and Options .................................... 329
Brigitte Grugeon, Jean-Baptiste Lagrange and Daniel Jarvis,
with Mara Alagic, Mili Das and Diana Hunscheidt
Contents vii
Section 4 Implementation of Curricula: Issues of Access and Equity
16 Introduction to Section 4 ......................................................................... 349
Colleen Vale and Cyril Julie, with Chantal Buteau and Jim Ridgway
17 Some Regional Developments in Access and Implementation
of Digital Technologies and ICT ............................................................. 361
Cyril Julie, Allen Leung, Nguyen Chi Thanh, Linda S. Posadas,
Ana Isabel Sacristán and Alexei Semenov
18 Technology for Mathematics Education: Equity, Access
and Agency ................................................................................................ 385
Helen J. Forgasz, Colleen Vale and Sonia Ursini
19 Factors Influencing Implementation of Technology-Rich
Mathematics Curriculum and Practices ................................................ 405
Teresa Assude, Chantal Buteau and Helen J. Forgasz
Section 5 Future Directions
20 Introduction to Section 5 ......................................................................... 423
Celia Hoyles and Jean-Baptiste Lagrange
21 Design for Transformative Practices ...................................................... 425
Douglas Butler, Nicholas Jackiw, Jean-Marie Laborde,
Jean-Baptiste Lagrange and Michal Yerushalmy
22 Connectivity and Virtual Networks for Learning ................................. 439
Celia Hoyles, Ivan Kalas, Luc Trouche, Laurent Hivon,
Richard Noss and Uri Wilensky
23 The Future of Teaching and Learning Mathematics
with Digital Technologies ......................................................................... 463
Michèle Artigue
Author Index .................................................................................................... 477
Subject Index .................................................................................................... 485
Contributors
Janet Ainley
School of Education, University of Leicester, Leicester, UK
Mara Alagic
Wichita State University, Wichita, Kansas, USA
Mette Andresen
Navimat, University College Capital, Copenhagen, Denmark
Michèle Artigue

Université Paris Diderot, Paris 7, France
Ferdinando Arzarello

Università degli Studi di Torino, Torino, Italy
Teresa Assude

University of Provence, Aix-en-Provence, France
Ruth Beatty

Ontario Institute for Studies in Education, University of Toronto, Toronto, ON,
Canada
Emran Behrooz

Isfahan Mathematics House, Isfahan, Iran
Jill Brown
Australian Catholic University, Melbourne, Australia
Chantal Buteau

Brock University, St. Catharines, ON, Canada
Douglas Butler

ICT Training Centre, Oundle, UK
Nigel Calder

Mathematics, Science and Technology Education, University of Waikato at
Tauranga, Tauranga, New Zealand
ix
x Contributors
Claire Cazes

Pierre and Marie Curie (UPMC), University Paris VI, Paris, France
Yip Cheung Chan
The Hong Kong Institute of Education, Hong Kong SAR
Chow Ming Kong
Tampines Junior College, Singapore
Jere Confrey
Friday Institute for Educational Innovation, College of Education, North Carolina
State University, Raleigh, North Carolina, USA
Valentina Dagiene

Matematikos ir Informatikos Institutas, Vilnius, Lithuania
Thierry Dana-Picard
Department of Mathematics, Jerusalém, College of Technology, Israel
Mili Das
Joint Director of Public Instruction (Teachers’ Training),
Government of West Bengal, Kolkata, India
Paul Drijvers

Freudenthal Institute for Science and Mathematics Education, Utrecht University,
Utrecht, The Netherlands
Helen J. Forgasz

Monash University, VIC, Australia
Alex Friedlander

Department of Science Teaching, The Weizmann Institute of Science, Rehovot,
Israel
Anne Berit Fuglestad

Department of Mathematical Sciences, University of Agder, Kristiansand, Norway
Maria Trigueros Gaisman

Instituto Tecnológico Autónomo de México, Mexico City, Mexico
Vince Geiger

Australian Catholic University, Brisbane, QLD, Australia
Derek Glover
University of Keele, Keele, UK
Merrilyn Goos

University of Queensland, Brisbane, QLD, Australia
Brigitte Grugeon

IUFM University of Amiens and Didirem, Paris 7, France
Ghislaine Gueudet
CREAD, IUFM Bretagne-Université de Brest, France
Contributors xi
Lulu Healy

Bandeirante University of São Paulo, São Paulo, Brazil
Laurent Hivon
IREM: Institute for Research on Mathematics Teaching, Orléans, France
Celia Hoyles

London Knowledge Lab, Institute of Education, University of London,
London, UK
Verónica Hoyos
National Pedagogical University, Mexico
Diana Hunscheidt
Carl von Ossietzky University Oldenburg, Oldenburg, Germany
Nicholas Jackiw

KCP Technologies in California, Emeryville, CA, USA
Daniel Jarvis

Faculty of Education, Nipissing University, North Bay, ON, Canada
Duncan Jones

Alder Coppice Primary School, Northway, Sedgley, Dudley, West Midlands, UK
Keith Jones

University of Southampton, Southampton, UK
Cyril Julie

School of Science and Mathematics Education, University of the Western Cape,
Bellville, South Africa
Ken Kahn

London Knowledge Lab, Institute of Education, University of London, London, UK
Ivan Kalas

Comenius University, Bratislava, Slovakia
Liew Kee Kor
MARA University of Technology, Kedah, MALAYSIA
Ivy Kidron
Department of Applied Mathematics, Jerusalem, College of Technology, Israel
Carolyn Kieran

Département de Mathématiques, Université du Québec à Montréal, Montréal,
QC, Canada
Chronis Kynigos

Educational Technology Lab, Department of Education, School of Philosophy,
University of Athens and RACTI, Athens, Greece
Olga Kosheleva
Department of Teacher Education, University of Texas at El Paso El Paso, USA