Table Of ContentSung Je Cho
Editor
Selected Regular
Lectures from the
12th International
Congress on
Mathematical
Education
Selected Regular Lectures
from the 12th International Congress
on Mathematical Education
Sung Je Cho
Editor
Selected Regular Lectures
from the 12th International
Congress on Mathematical
Education
123
Editor
SungJe Cho
SeoulNational University
Seoul
Korea,Republic of (SouthKorea)
ISBN978-3-319-17186-9 ISBN978-3-319-17187-6 (eBook)
DOI 10.1007/978-3-319-17187-6
LibraryofCongressControlNumber:2015935734
SpringerChamHeidelbergNewYorkDordrechtLondon
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Editor
Sung Je Cho, Seoul National University
Editors
Bill Barton, The University of Auckland
Gail Burrill, Michigan State University
Bernard R. Hodgson, Université Laval
Gabriele Kaiser, University of Hamburg
Oh Nam Kwon, Seoul National University
Hee-Chan Lew, Korea National University of Education
Editorial Board
Michèle Artigue, Université Paris Diderot—Paris 7
Évelyne Barbin, University of Nantes
Morten Blomhøj, IMFUFA Roskilde University
Jaime Carvalho e Silva, Universidade de Coimbra
Johann Engelbrecht, University of Pretoria
Mercy Kazima, University of Malawi
Masataka Koyama, Hiroshima University
Frederick Leung, The University of Hong Kong
Shiqi Li, East China Normal University
Cheryl E. Praeger, The University of Western Australia
Hyun Yong Shin, Korea National University of Education
K. (Ravi) Subramaniam, Homi Bhabha Centre for Science Education
Yuriko Yamamoto Baldin, Universidade Federal de São Carlos
Preface
Thisbookisaresultofthe12thInternationalCongressonMathematicalEducation
(ICME-12), which was held at Seoul, Korea from July 8, 2012 to July 15, 2012.
TheInternationalProgramCommittee(IPC-12)ofICME-12tookonthetaskof
acting as the editorial board to publish the Proceedings of the ICME-12 and
Selected Regular Lectures of the ICME-12 in two separate volumes. The
Proceedings of the ICME-12 is accessible through the Open Access Program by
Springer, the ICME-12 publisher.
Thesecondvolume,TheSelectedRegularLecturesfromtheICME-12contains
51 Regular Lectures. The Regular Lecturers were invited from different parts of
world by the IPC-12. The Regular Lectures covered a wide spectrum of topics,
themes, and issues. Originally, 78 Regular Lectures were planned but some of the
lecturerscouldnotmaketripstoICME-12.AmongthelecturesgivenatICME-12,
some of them are not contained in this volume for various reasons.
ICME-12 would not have been possible without the contribution from its
members and strategic partners. For the first time, all of the Korean mathematical
societiesunitedtobidandhostICME-12.ThesuccessofICME-12iscloselytiedto
the tireless efforts of all.
A considerable amount of the ICME-12 budget was funded through private
donations by mathematically minded individuals and businesses. ChunJae
Education Inc. was one of the largest contributors offunds and services. Printing
of the ICME-12 Program Booklets and Abstracts were paid for by ChunJae
Education Inc.
The Korean Ministry of Education helped to secure the balance of the budget
andassistedintheoperationofICME-12.TheCityofSeoul,KoreaFoundationfor
the Advancement of Science & Creativity, and Korea Tourism Organization were
significant funding bodies as well.
ThededicatedmembersoftheLocalOrganizingCommittee,skilledprofessional
conference organizers atMCI, and staffat theCOEX (Conventionand Exhibition)
wereintegralinthesuccessfulplanningandexecutionofICME-12.Thededication
shown by theLocalOrganizing Committee for the conference was second to none
and well beyond expectations.
vii
viii Preface
Finally, the Chief Editor would like to express his sincere thanks to all Regular
Lecturers.Withouttheireffortsanddedicationsthisvolumewasnotpossibleatall.
Also,theChiefEditorwouldliketothankallthemembersofIPC-12,whoreadall
or part of the Regular Lecture papers for improvements. It is needless to say that
without Professor Hee-chan Lew’sworkanddevotion,thisvolumecouldnothave
beencompleted.TheChiefEditorwouldliketoexpresshisheartfeltthankstohim.
The Chief Editor believes that the world mathematical education society is closer
than before and leading toward more productive and friendly mathematics class-
rooms around the world.
Sung Je Cho
Contents
Understanding the Nature of the Geometric Work
Through Its Development and Its Transformations. . . . . . . . . . . . . . . 1
Alain Kuzniak
Integration of Technology into Mathematics Teaching:
Past, Present and Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Adnan Baki
Developing Free Computer-Based Learning Objects for High
School Mathematics: Examples, Issues and Directions. . . . . . . . . . . . . 27
Humberto José Bortolossi
Doing Research Within the Anthropological Theory of the Didactic:
The Case of School Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Marianna Bosch
Curriculum Reform and Mathematics Learning:
Evidence from Two Longitudinal Studies . . . . . . . . . . . . . . . . . . . . . . 71
Jinfa Cai
Mathematical Problem Solving Beyond School: Digital
Tools and Students’ Mathematical Representations. . . . . . . . . . . . . . . 93
Susana Carreira
Constructing Abstract Mathematical Knowledge in Context . . . . . . . . 115
Tommy Dreyfus
Digital Technology in Mathematics Education:
Why It Works (Or Doesn’t). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Paul Drijvers
ix
x Contents
Mathematical Thinking Styles in School and Across Cultures . . . . . . . 153
Rita Borromeo Ferri
Learning to See: The Viewpoint of the Blind . . . . . . . . . . . . . . . . . . . 175
Lourdes Figueiras and Abraham Arcavi
Issues and Concerns About the Integration of ICT
into the Teaching and Learning of Mathematics in Africa:
Botswana Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Kgomotso Gertrude Garegae
Learning Mathematics in Secondary School: The Case
of Mathematical Modelling Enabled by Technology . . . . . . . . . . . . . . 203
Jonaki B. Ghosh
Doing Mathematics in Teacher Preparation: Giving Space
and Time to Think, Reflect, Share and Feel . . . . . . . . . . . . . . . . . . . . 223
Frédéric Gourdeau
Resources at the Core of Mathematics Teachers’ Work. . . . . . . . . . . . 235
Ghislaine Gueudet
The Mathematics Education Reform Movement in Indonesia. . . . . . . . 253
Sutarto Hadi
Emotions in Problem Solving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Markku S. Hannula
Hands that See, Hands that Speak: Investigating Relationships
Between Sensory Activity, Forms of Communicating
and Mathematical Cognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Lulu Healy
Freudenthal’s Work Continues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
Marja Van den Heuvel-Panhuizen
Teachers Learning Together: Pedagogical Reasoning
in Mathematics Teachers’ Collaborative Conversations. . . . . . . . . . . . 333
Ilana Seidel Horn
Transforming Education Through Lesson Study:
Thailand’s Decade-Long Journey. . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Maitree Inprasitha
Contents xi
Dialectic on the Problem Solving Approach: Illustrating
Hermeneutics as the Ground Theory for Lesson Study
in Mathematics Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
Masami Isoda
History, Application, and Philosophy of Mathematics
in Mathematics Education: Accessing and Assessing Students’
Overview and Judgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
Uffe Thomas Jankvist
Implications from Polya and Krutetskii . . . . . . . . . . . . . . . . . . . . . . . 405
Wan Kang
Constructionism: Theory of Learning or Theory of Design? . . . . . . . . 417
Chronis Kynigos
Mobile Linear Algebra with Sage. . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
Sang-Gu Lee
Discernment and Reasoning in Dynamic Geometry Environments . . . . 451
Allen Leung
Riding the Third Wave: Negotiating Teacher and Students’
Value Preferences Relating to Effective Mathematics Lesson. . . . . . . . 471
Chap Sam Lim
Learning Mathematics by Creative or Imitative Reasoning . . . . . . . . . 487
Johan Lithner
Features of Exemplary Lessons Under the Curriculum Reform
in China: A Case Study on Thirteen Elementary
Mathematics Lessons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507
Yunpeng Ma and Dongchen Zhao
Teachers, Students and Resources in Mathematics Laboratory . . . . . . 527
Michela Maschietto
The Common Core State Standards in Mathematics. . . . . . . . . . . . . . 547
William McCallum
From Practical Geometry to the Laboratory Method:
The Search for an Alternative to Euclid in the History
of Teaching Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561
Marta Menghini
