Table Of ContentInternational Handbook of Mathematics Teacher Education: Volume 2
International Handbook of
Mathematics Teacher Education
(Second Edition)
Series Editor:
Olive Chapman
University of Calgary
Calgary, Alberta
Canada
This second edition of the International Handbook of Mathematics Teacher Education
builds on and extends the first edition (2008) in addressing the knowledge, teaching
and learning of mathematics teachers at all levels of teaching mathematics and
of mathematics teacher educators, and the approaches/activities and programmes
through which their learning can be supported. It consists of four volumes based on
the same themes as the first edition.
Volume 1: Knowledge, Beliefs, and Identity in Mathematics Teaching and
Teaching Development
Despina Potari, National and Kapodistrian University of Athens, Athens, Greece and
Olive Chapman, University of Calgary, Calgary, Canada (eds.)
paperback: 978-90-04-41886-8, hardback: 978-90-04-41885-1,
ebook: 978-90-04-41887-5
Volume 2: Tools and Processes in Mathematics Teacher Education
Salvador Llinares, University of Alicante, Alicante, Spain and Olive Chapman,
University of Calgary, Calgary, Canada (eds.)
paperback: 978-90-04-41897-4, hardback: 978-90-04-41895-0,
ebook: 978-90-04-41896-7
Volume 3: Participants in Mathematics Teacher Education
Gwendolyn M. Lloyd, Pennsylvania State University, Pennsylvania, USA and
Olive Chapman, University of Calgary, Calgary, Canada (eds.)
paperback: 978-90-04-41922-3, hardback: 978-90-04-41921-6,
ebook: 978-90-04-41923-0
Volume 4: The Mathematics Teacher Educator as a Developing Professional
Kim Beswick, University of New South Wales, Sydney, Australia and Olive Chapman,
University of Calgary, Calgary, Canada (eds.)
paperback: 978-90-04-42420-3, hardback: 978-90-04-42419-7,
ebook: 978-90-04-42421-0
International Handbook
of Mathematics Teacher
Education: Volume 2
Tools and Processes in Mathematics
Teacher Education
(Second Edition)
Edited by
Salvador Llinares and Olive Chapman
(cid:3461)(cid:3454)(cid:3458)(cid:3453)(cid:3454)(cid:3463)(cid:3)(cid:95)(cid:3)(cid:3451)(cid:3464)(cid:3468)(cid:3469)(cid:3464)(cid:3463)
Cover illustration: Photograph by Salvador Llinares
All chapters in this book have undergone peer review.
The Library of Congress Cataloging-in-Publication Data is available online at
http://catalog.loc.gov
ISBN 978-90-04-41897-4 (paperback)
ISBN 978-90-04-41895-0 (hardback)
ISBN 978-90-04-41896-7 (e-book)
Copyright 2020 by Koninklijke Brill NV, Leiden, The Netherlands.
Koninklijke Brill NV incorporates the imprints Brill, Brill Hes & De Graaf,
Brill Nijhoff, Brill Rodopi, Brill Sense, Hotei Publishing, mentis Verlag, Verlag
Ferdinand Schöningh and Wilhelm Fink Verlag.
All rights reserved. No part of this publication may be reproduced, translated,
stored in a retrieval system, or transmitted in any form or by any means, electronic,
mechanical, photocopying, recording or otherwise, without prior written
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This book is printed on acid-free paper and produced in a sustainable manner.
CONTENTS
Preface vii
Olive Chapman
List of Figures and Tables ix
Tools and Ways of Thinking in Mathematics Teacher Education:
An Introduction 1
Salvador Llinares
Part 1: Video, Tasks to Promote Reflective Skills and Lesson De-Brief
Conversations as Tools in Mathematics Teacher Education
1. Leveraging the Power of Video for Teacher Learning: A Design
Framework for Mathematics Teacher Educators 23
Elizabeth A. van Es, Miray Tekkumru-Kisa and Nanette Seago
2. (cid:55)(cid:68)(cid:86)(cid:78)(cid:86)(cid:3)(cid:51)(cid:85)(cid:82)(cid:80)(cid:82)(cid:87)(cid:76)(cid:81)(cid:74)(cid:3)(cid:51)(cid:85)(cid:82)(cid:86)(cid:83)(cid:72)(cid:70)(cid:87)(cid:76)(cid:89)(cid:72)(cid:3)(cid:48)(cid:68)(cid:87)(cid:75)(cid:72)(cid:80)(cid:68)(cid:87)(cid:76)(cid:70)(cid:86)(cid:3)(cid:55)(cid:72)(cid:68)(cid:70)(cid:75)(cid:72)(cid:85)(cid:86)(cid:182)(cid:3)(cid:53)(cid:72)(cid:192)(cid:72)(cid:70)(cid:87)(cid:76)(cid:89)(cid:72)(cid:3)
(cid:54)(cid:78)(cid:76)(cid:79)(cid:79)(cid:86)(cid:29)(cid:3)(cid:41)(cid:82)(cid:70)(cid:88)(cid:86)(cid:3)(cid:82)(cid:81)(cid:3)(cid:44)(cid:81)(cid:71)(cid:76)(cid:89)(cid:76)(cid:71)(cid:88)(cid:68)(cid:79)(cid:3)(cid:39)(cid:76)(cid:3445)(cid:72)(cid:85)(cid:72)(cid:81)(cid:70)(cid:72)(cid:86)(cid:3) (cid:24)(cid:24)
(cid:49)(cid:68)(cid:263)(cid:68)(cid:3)(cid:57)(cid:82)(cid:81)(cid:71)(cid:85)(cid:82)(cid:89)(cid:105)
3. Learning to Teach Mathematics: The Lesson De-Brief Conversation 85
Julian Brown, Laurinda Brown, Alf Coles and Tracy Helliwell
Part 2: Technological Tools and Technological Mediation in
Mathematics Teacher Education
4. Technology as a Curricular Instrument 111
Angel Ruiz
5. Digital Curriculum Resources in/for Mathematics Teacher
Learning: A Documentational Approach Perspective 139
Ghislaine Gueudet and Birgit Pepin
6. Prospective and Practicing Teachers and the Use of Digital
Technologies in Mathematical Problem-Solving Approaches 163
Manuel Santos-Trigo
7. Computational Modelling in Elementary Mathematics Teacher
Education 197
George Gadanidis, Janette M. Hughes, Immaculate Namukasa
and Ricardo Scucuglia
v
CONTENTS
8. Technology Tools for Mathematics Teacher Learning: How Might
(cid:55)(cid:75)(cid:72)(cid:92)(cid:3)(cid:54)(cid:88)(cid:83)(cid:83)(cid:82)(cid:85)(cid:87)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:39)(cid:72)(cid:89)(cid:72)(cid:79)(cid:82)(cid:83)(cid:80)(cid:72)(cid:81)(cid:87)(cid:3)(cid:82)(cid:73)(cid:3)(cid:38)(cid:68)(cid:83)(cid:68)(cid:70)(cid:76)(cid:87)(cid:92)(cid:3)(cid:73)(cid:82)(cid:85)(cid:3)(cid:54)(cid:83)(cid:72)(cid:70)(cid:76)(cid:191)(cid:70)(cid:3)(cid:55)(cid:72)(cid:68)(cid:70)(cid:75)(cid:76)(cid:81)(cid:74)(cid:3)
Assignments? 223
Patricio Herbst, Daniel Chazan and Amanda Milewski
Part 3: Conceptual Instrumentation in Mathematics Teacher
Education: Learning to Use Theories to Analyze Teaching
9. The Fractal Complexity of Using Theories in Mathematics Teacher
Education: Issues and Debates, Opportunities and Limitations 255
Elisabeta Eriksen and Annette Hessen Bjerke
10. Controlled Implementations: Teaching Practice to Practicing
Mathematics Teachers 285
Paola Sztajn, Lara Dick, Reema Alnizami, Dan Heck and
Kristen Malzahn
11. Noticing as a Tool to Analyze Mathematics Instruction and Learning 311
Julie Amador
12. Theoretical Lenses to Develop Mathematics Teacher Noticing:
Learning, Teaching, Psychological, and Social Perspectives 337
(cid:38)(cid:72)(cid:81)(cid:72)(cid:76)(cid:71)(cid:68)(cid:3)(cid:41)(cid:72)(cid:85)(cid:81)(cid:105)(cid:81)(cid:71)(cid:72)(cid:93)(cid:3)(cid:68)(cid:81)(cid:71)(cid:3)(cid:37)(cid:68)(cid:81)(cid:3)(cid:43)(cid:72)(cid:81)(cid:74)(cid:3)(cid:38)(cid:75)(cid:82)(cid:92)
13. Transcending Contemporary Obsessions: The Development of a
Model for Teacher Professional Development 361
Paulino Preciado-Babb, Martina Metz, Brent Davis and
Soroush Sabbaghan
Part 4: Crosscutting Issues on Tools and Processes in Mathematics
Teacher Education
14. Using Professional Development Contexts to Structure
Prospective Teacher Education 393
José Carrillo, Nuria Climent, Luis C. Contreras and Miguel Montes
15. From Tools to Resources in the Professional Development of
Mathematics Teachers: General Perspectives and Crosscutting Issues 421
Abraham Arcavi
Index 441
vi
PREFACE
It is an honor to follow Terry Wood, series editor of the first edition of the four
volume International Handbook of Mathematics Teacher Education (2008), as se-
ries editor of this second edition of the Handbook. As Terry indicated, she, Barbara
Jaworski, Sandy Dawson and Thomas Cooney played key roles in opening up the
field of mathematics teacher education “to establish mathematics teacher education
as an important and legitimate area of research and scholarship” (Wood, 2008, p. vii).
The field has grown significantly since the late 1980s “when Barbara Jaworski initi-
ated and maintained the first Working Group on mathematics teacher education at
PME [Psychology of Mathematics Education conference]” (p. vii) and over the last
10 years following the first edition of the Handbook. So, the editorial team, I and
the four volume editors (Kim Beswick, Salvador Llinares, Gwendolyn Lloyd, and
Despina Potari), of this second edition is honored to present it to the mathematics
education community and to the field of teacher education in general.
This second edition builds on and extends the topics/ideas in the first edition
while maintaining the themes for each of the volumes. Collectively, the authors
looked back beyond and within the last 10 years to establish the state-of-the-art
and continuing and new trends in mathematics teacher and mathematics teacher
educator education, and looked forward regarding possible avenues for teachers,
teacher educators, researchers, and policy makers to consider to enhance and/or fur-
ther investigate mathematics teacher and teacher educator learning and practice, in
particular. The volume editors provide introductions to each volume that highlight
the subthemes used to group related chapters, which offer meaningful lenses to see
important connections within and across chapters. Readers can also use these sub-
themes to make connections across the four volumes, which, although presented
separately, include topics that have relevance across them since they are all situated
in the common focus regarding mathematics teachers.
I extend special thanks to the volume editors for their leadership and support in
preparing this handbook. I feel very fortunate to have had the opportunity to work
with them on this project. Also, on behalf of myself and the volume editors, sincere
thanks to all of the authors for their invaluable contributions and support in working
with us to produce a high-quality handbook to inform and move the field of mathe-
matics teacher education forward.
Volume 2, Tools and Processes in Mathematics Teacher Education, edited by Sal-
vador Llinares, describes and analyze various promising tools and processes, from
different perspectives, aimed at facilitating the mathematics teacher learning and
development. It provides insights of how mathematics teacher educators think about
vii
PREFACE
and approach their work with teachers. Thus, as the second volume in the series,
it broadens our understanding of the mathematics teacher and their learning and
teaching.
REFERENCE
Wood, T. (Series Ed.), Jaworski, B., Krainer, K., Sullivan, P., & Tirosh, D. (Vol. Eds.). (2008).
International handbook of mathematics teacher education. Rotterdam, The Netherlands:
Sense Publishers.
Olive Chapman
Calgary, AB
Canada
viii
FIGURES AND TABLES
FIGURES
2.1. Ternary diagram for shifts in Stance (diagram by Adrian Simpson) 71
2.2. Kate’s and Lisa’s development of Stance in the video-intervention 72
2.3. Changes in topic in Kate’s and Lisa’s responses to tasks (ordered
chronologically; 01 – pre-task, 03 – post-task, 04/06 – observation
of the teaching of others at the LS/US teaching practice) 73
2.4. Kate’s and Lisa’s results in the tasks across the video-intervention
(100% is the maximum number of points for each task) 74
2.5. Nature of Kate’s and Lisa’s reflection across the tasks 76
4.1. The five emphases of the school mathematics curriculum in
Costa Rica 118
4.2. The curriculum syllabi in three columns, the third one with specific
suggestions (translated from the Spanish) 121
4.3. Frontpage project’s website. Three of the main sections:
Mini MOOCs, blended courses, documents 122
4.4. Mini MOOCs (thumbs of eight courses within the edX platform) 129
5.1. A schema of a documentational genesis 143
5.2. A screen of the French Digital Educational Resources Bank. For the
keyword “proportionality,” 271 resources are available, and can be
used to build lessons 144
5.3. The “Chinese abacus at school” training path 147
5.4. LaboMEP, choosing interactive exercises about functions 151
5.5. A screenshot from the PRIMAS platform 156
6.1. Drawing a midpoint of a given segment 172
6.2. Drawing a perpendicular line to a segment from a given point 173
6.3. Points C, D and E are on the circle with centre at A and FH,
FG and GH are tangents lines to the circle 173
6.4. The loci of midpoints when tangent points move along the circle 174
6.5. Connecting the midpoint property to draw the equilateral triangle 175
6.6. Representing the problem geometrically 177
6.7. The locus of the slope of line EH provides key information to
solve the task 178
6.8. Generating a family of triangles by moving vertex C on the circle 179
6.9. Point Q has the same x-coordinate as point C (the mobile point)
and as y-coordinate the area of triangle ABC. The locus of point
Q when point C is moved on the circumference shows the area
variation of the family of generated triangles 180
ix
