The Proceedings of the 12th International Congress on Mathematical Education: Intellectual and attitudinal challenges

Front matter

Sung Je Cho Editor

Intellectual and Attitudinal Challenges

A Springer Open

Preface

This book is the result of the 12th International Congress on Mathematical Education (ICME-12), which was held at Seoul, Korea from July 8, 2012 to July 15, 2012.

The International Program Committee (IPC-12) of ICME-12 took on the task of 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. All conference materials and volumes are accessible through the Open Access Program by Springer, the ICME-12 publisher.

The Proceedings volume of ICME-12 contains the Opening and Award Ceremonies, four Plenary Lectures and three Plenary Panels, four ICMI Awardees Lectures, three Survey Teams reports, five National Presentations, abstracts of 55 Regular Lectures, reports of 37 Topic Study Groups, reports of 17 discussion Groups, Closing Ceremony, and lists of participants. The Selected Regular Lectures volume of ICME-12 contains the full versions of lectures.

The 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 societies united to bid and host the ICME-12. The successes of ICME-12 is closely tied to 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 contributor of funds 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 and assisted in the operation of ICME-12. The City of Seoul, Korea Foundation for the Advancement of Science and Creativity, and Korea Tourism Organization were significant funding bodies as well.

The dedicated members of the Local Organizing Committee, skilled professional conference organizers at MCI, and staff at the COEX (Convention and Exhibition) were integral in the successful planning and execution of ICME-12. The dedication shown by the Local Organizing Committee for the conference was second to none and well beyond expectation.

viii Preface

Finally, the Editor would like to express his sincere thanks to all the members of IPC-12, Korean government agencies, private donors, lecturers, members of Survey Teams, and organizers of Topics Study Groups and Discussion Groups. Gratitude also is extended to the more than 3,000 worldwide attendees who contributed to the success of the ICME-12 by sharing their expertise via paper presentations or participating in discussions. Without Prof. Hee-chan Lew’s work and devotion, this extensive volume could not have been completed. The Editor would like to express his heartfelt thanks to him. The Editor believes that the world mathematical society is closer than before and leading towards more productive and friendly mathematics classrooms around the world.

Seoul, Korea Sung Je Cho Editor

Part I Opening Ceremonies Ingrid Daubechies

Bill Barton

Congratulatory Remarks: Minister of Education Ju Ho Lee

Carolyn Kieran

Part II Plenary Lectures Etienne Ghys

Whither the Mathematics/Didactics Interconnection?

Evolution and Challenges of a Kaleidoscopic Relationship

Bernard R. Hodgson x Contents

Mathematics Education in the National Curriculum—with Lee Don-Hee

Quality Teaching of Mathematical Modelling: What Do We Know, What: Can We: Do? 24-54 beat Ga chee See eda eed hee 73 Werner Blum

Part III Plenary Panels Konrad Krainer, Feng-Jui Hsieh, Ray Peck and Maria Teresa Tatto

Frederick K.S. Leung, Kyungmee Park, Yoshinori Shimizu and Binyan Xu

Gilah C. Leder

Part IV Awardees Teaching Mathematics in Tomorrow’s Society: Yves Chevallard

Mathematics for All? The Case for and Against National Testing .... 189 Gilah C. Leder

Early Algebraic Thinking: Epistemological, Semiotic, Luis Radford

How We Think: A Theory of Human Decision-Making, Alan H. Schoenfeld

Contents xi Part V Survey Teams

Gail Burrill, Glenda Lappan and Funda Gonulates

School to University... 0... 0.0.0... 00... cee ee 265 Mike O.J. Thomas, Iole de Freitas Druck, Danielle Huillet,

Mi-Kyung Ju, Elena Nardi, Chris Rasmussen and Jinxing Xie

Paola Valero, Mellony Graven, Murad Jurdak, Danny Martin,

Tamsin Meaney and Miriam Penteado

Part VI National Presentations Sun-Hwa Park

Berinderjeet Kaur, Cheow Kian Soh, Khoon Yoong Wong,

Eng Guan Tay, Tin Lam Toh, Ngan Hoe Lee, Swee Fong Ng,

Jaguthsing Dindyal, Yeen Peng Yen, Mei Yoke Loh,

Hwee Chiat June Tan and Lay Chin Tan

Rick Scott

Part VII Regular Lectures xii Contents Part VIII Topic Study Groups Tamsin Meaney

Mathematics Education at Tertiary Level and Access to Tertiary Level ¢ coe conos i Senen ede ee ade A E eee a A 385 Ansie Harding and Juha Oikkonen

Peter Taylor and Roza Leikin

Jean-Philippe Drouhard

Geoff Wake and Keiko Yasukawa

Mogens Niss

Teaching and Learning of Number Systems and Arithmetic Joana Brocardo and Geoffrey B. Saxe

JeongSuk Pang and Kees Buijs

Rakhi Banerjee and Luis Puig

Colette Laborde

Per Nilsson and Jun Li

Dani Ben-Zvi and Katie Makar

Victor Martinez-Luaces and Sunsook Noh

Contents xiii

Viviane Durand-Guerrier

Manuel Santos-Trigo and Zahra Gooya

Gert Kadunz and Michal Yerushalmy

Mathematical Applications and Modelling in the Teaching Jill Brown and Toshikazu Ikeda

Morten Misfeldt and Wei-Chi Yang

Marcelo C. Borba and Hans-Georg Weigand

Renaud Chorlay and Wann-Sheng Horng

Yeping Li and Hélia Oliveira

Gaye Williams and Hsin Mei Huang

Len Sparrow

Aihui Peng and Hikma Smida

In-Service Education, Professional Development Shuhua An and Andrea Peter-Koop

Sylvie Coppé and Ngai-Ying Wong

Motivation, Beliefs, and Attitudes Towards Mathematics and: Its Teachings)... 4.3 ee5 cee aps eked dae oe PE 523 Birgit Pepin and Ji-Won Son xiv Contents

Tracy Craig and Candia Morgan

Olof Steinthorsdottir and Veronique Lizan

Mathematics Education in a Multilingual Anjum Halai and Richard Barwell

Xuhua Sun and Lalina Coulange

Koeno Gravemeijer and Anita Rampal

Christine Suurtamm and Michael Neubrand

The Role of Mathematical Competitions and Other Challenging Mariade Losada and Ali Rejali

Fulvia Furinghetti

Pedro Palhares and Lawrence Shirley

Theoretical Issues in Mathematics Education: An Introduction to the Presentations... 0.0.0.0... 0.0000. 579 Angelika Bikner-Ahsbahs and David Clarke

Part IX Discussion Groups Current Problems and Challenges in Non-university James Roznowsk and Huei Wuan Low-Ee

Hartwig Meissner

Contents Xv

Avi Berman and Kazuyoshi Okubo

Nitsa Movshovitz-Hadar and Atara Shriki

Bjorn Smestad

Paul Ernest

Improving Teacher Professional Development Through Lesson Study: se eor sia wc bop Re ean TREE See ee CRA aes 609 Toshiakira Fujii and Akihiko Takahashi

Theory and Perspective of Mathematics Learning and Teaching Chun Chor Litwin Cheng

Using Technology to Integrate Geometry and Algebra Scott Steketee

New Challenges in Developing Dynamic Software Zsolt Lavicza and Balazs Koren

Axelle Faughn and Barbara Pence

Kim Beswick and Olive Chapman

The Role of Mathematics Education in Helping to Produce William Finzer

Mathematical Modeling in Connecting Concepts to Real World Application... 1.0.0... 0.0.0... eee ee eee 639 Zhonghe Wu and Lijun Ye xvi Contents

Mathematics and Culture in Micronesia: An Exploration A.J. (Sandy) Dawson

Dirk Huylebrouck

Yew Hoong Leong and Rungfa Janjaruporn

Erratum to: Congratulatory Remarks: Minister of Education Ju Ho Lee

Congratulatory Remarks: President of Korea

Good morning, distinguished ladies and gentlemen. I offer my heartful congratulations to the opening of the 12th International Congress on Mathematical Education (ICME).

I am very pleased to welcome President William Barton of the International Commission on Mathematical Instruction (ICMI), President Ingrid Daubechies of the International Mathematical Union (IMU) and all the mathematical educators here.

As the largest festivities in the realm of mathematical instructions, the ICME has made great contributions to mathematical instruction and popularization of math over the past half century.

Considering the significance of the ICME, I sent a letter to the ICMI requesting to hold the Congress in Korea 9 years ago when I was the Mayor of Seoul.

Today, I am glad to see my wish has come true. Let me take this opportunity to thank all the people who have devoted in preparing for this meeting.

Distinguished educator,

To me, mathematics is a magnificent journey of human reason in search of a clue for the mystery surrounding the universe.

For the past long history, mathematics has been the engine of civilization, striving to liberate humanity from famine, poverty and ignorance.

I hope the rational and creative thinking of young people will be enhanced through math. In this way, they will make the future of humanity better.

I expect all the participants will be able to freely exchange diverse and expert views for the advancement of mathematics at this very meaningful meeting.

As a post script, I would like to remind you that the International Expo is now being held in the southern port city of Yeosu. Please tour the Expo by all means and carry home fond memories of the beautiful natural and cultural landmarks of Korea’s South Coast.

xvii xviii Congratulatory Remarks: President of Korea

Korea has hosted many international events, buy I personally attach extraordinary importance to this congress because the ICME can be described as a “math education forum of Olympic proportions”. Once again, welcome to Korea.

Thank you very much.

Lee Myung-bak 10th President of the Republic of Korea Seoul, Republic of Korea

Part I Opening Ceremonies Opening Address: President of IMU

Ingrid Daubechies

It is a great pleasure for me to have the opportunity to address you, during this opening ceremony for the 12th International Congress on Mathematical Education, in my capacity as President of the International Mathematical Union, or IMU.

Officially, that is, with respect to the International Council for Science (or ICSU), which itself reports to UNESCO, IMU is the umbrella organization concerned with matters of global interest to mathematicians worldwide. The International Commission on Mathematical Instruction (or ICMI for brevity), which organizes the quadrennial ICME meetings, is the most important sub-organization of the IMU. In fact, and as ICMI President Bill Barton likes to remind me goodhumoredly, ICMI is older than the IMU itself, since it was created in 1908—IMU was created only in 1920, and even then it was an earlier incarnation that stopped functioning in the 1930s; in its present version, it was reborn in 1951.

An extremely important charge for the IMU is to organize the prestigious quadrennial International Congresses of Mathematicians, or ICMs, the first one of which dates back to 1893; it is probably no exaggeration to state that the IMU was first started to ensure a regular and orderly organization of the ICMs. This is similar to the role ICMI plays with respect to the ICME congresses, which are all held under ICMI’s auspices and principles. Once the ICME series hit its quadrennial rhythm, it became customary to hold the ICMs and ICMEs in interleaved evennumbered years, keeping stride nicely with the World Cup in Soccer/Football and the Olympic Games, which one could view as a “warm-up” for our more serious pursuits. The next ICM will thus take place in 2014, coincidentally in this very same city, in this very same Conference Center.

Over the years, IMU has come to stand for much more than just the umbrella organization ensuring continuity for the ICMs. In the past few decades, IMU has become more concerned with assisting developing countries build up their own

I. Daubechies (XI) Duke University, Durham, USA e-mail: ingrid @math.duke.edu

© The Author(s) 2015 3 S.J. Cho (ed.), The Proceedings of the 12th International Congress on Mathematical Education, DOI 10.1007/978-3-319-12688-3_1

4 I. Daubechies strong mathematics communities. IMU is also solidly and seriously invested in helping develop and sustain excellent mathematics education everywhere, and at all levels—although the work of my colleagues on the Executive Committee of the IMU, as well as my own, is anchored in mathematics research, we all realize fully the importance of teaching mathematical insights, understanding and skills in the best possible way, and we are committed to help ICMI as much as we can in pursuing this goal. These are not empty words—we are acting on our beliefs! The following are just two examples. In setting up the new stable central Secretariat for the IMU, it was viewed as an essential and core part of its charge that it provides a stable administrative support and archival role for ICMI as well. On a different note, IMU is also actively helping ICMI in finding and providing funding for the very important CANP workshops, which build networking for mathematics educators in less developed regions in the world.

I am personally thrilled by this tighter connection between mathematical researchers and experts on, or researchers in, mathematical education. Whether we decide to contribute to mathematical research, or whether we decide to invest our creative energy in mathematics education—you and I, ICME or ICM participants, we are ALL mathematicians, united in our love for mathematics. It was a proud moment in my life when my son announced his decision to become a high school teacher in mathematics; he now teaches in one of the inner city schools in Chicago, and works hard to ignite and keep alive an interest in mathematics among his students, bringing to this the energy and drive that he could easily have taken to graduate school. I respect and value the commitment and engagement of teachers like him, and I encourage all professional research mathematicians to do likewise.

Dear ICME-12 Participants, fellow mathematicians, focused on bringing the best possible mathematics education to future generations, I salute you!

And I wish you a wonderful Congress.

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Opening Address: President of ICMI

Bill Barton

Honourable Mr Lee, Minister of Education

Professor Sung Je Cho, Convenor of this wonderful conference

ICMI Colleagues and friends

Our moment has arrived. Isn’t this wonderful!

I am delighted to be here, to open the 12th International Congress of Mathematics Education—to be honest, it is a moment I have been looking forward to for more than 4 years. Our community is very fortunate to have attracted a conference bid from Korea, and our Korean friends are already proving to us that we made a very good decision to accept their bid.

These few minutes are my opportunity to address the wider ICMI community about the things that I believe are important about mathematics education on the international stage. I cannot detail all the many, many activities of ICMI as an organisation: ICMI Studies, Regional conferences, Affiliated organisations, and on and on. I urge everyone in this room to find out who their ICMI country representative is, and ensure that they become part of their national network. You should also subscribe to the ICMI Newsletter (on line) or become a Facebook Friend. We survive as an organisation through your participation.

I wish to mention three topics: our major development project; the Klein Project; and finally some comments on how our community communicates.

Since the last ICME in Mexico, ICMI as an organisation has changed dramatically. We have extended our development activities significantly. It is no longer true that we are primarily an organisation of professionals in mathematics education. Now we spend at least half our efforts and resources on worldwide development activities. A major part of this effort is the Capacity and Networking Project, that we call CANP.

B. Barton (È<) Former President of International Commission on Mathematical Instruction, University of Auckland, Auckland, New Zealand

© The Author(s) 2015 5 S.J. Cho (ed.), The Proceedings of the 12th International Congress on Mathematical Education, DOI 10.1007/978-3-319-12688-3_2

6 B. Barton

The aim of CANP is to support developing regions to form self-sustaining networks of mathematics educators, mathematicians, government officials, and, of course, teachers. What ICMI does is to organise a two-week Workshop in a different region every year. Last year the first was held in Mali, this year the second will be held in Costa Rica, and next year it will be Cambodia. A region of four or five countries is selected, and a Scientific Committee is formed of four people from the international community and four from the region. The Workshop is usually about fifty people representing all the groups in the network. The focus of the Workshop is secondary teacher education, but the aim is really to get key people in the region working together. Funds for each CANP programme are raised separately, we have had significant support from IMU, UNESCO, CIMPA and other organisations.

My second topic is the Klein Project. I invite everyone to turn ON their smartphones or open their computers—please go to the Klein Project Blog <http:// blog.kleinproject.org> ... or at least write this down, and log in at your first opportunity. The Klein Project is a worldwide project to produce writing on contemporary mathematics for secondary school teachers. Note: it is not designed for use in classrooms, but for the pleasure and satisfaction of teachers. In the Klein Blog you will find Klein Vignettes—these are short (4—6 pages) on a contemporary topic, written for secondary school mathematics teachers.

Over the next months you will see the Klein Blog grow—both with new Vignettes, but also as we translate the Vignettes into any and every language. This is a major task for our community, and I seek your help to offer to translate the Vignettes into your languages.

Eventually there will also be a Klein Project book—a small volume aimed at secondary teachers, that they will be able to dip into in the spare moments of their busy teaching lives. A book that will sustain and inspire teachers mathematically.

Please will you have a look, feed back to the project with your reactions, offer to help write more materials, and, most importantly, spread the Blog address amongst your secondary teacher friends and networks—or anyone whom you think would be interested.

I mention the Klein Project not because it is ICMI’s only project—it is not, we have several others—but because it illustrates for me an very important point: that ICMI works more closely than ever with IMU, the world body of mathematicians. The Klein Project is a joint project with IMU, and every piece of writing is the result of collaborations between mathematics teachers, educators, and mathematicians.

And lest you think that ICMI is focused only on secondary teachers and mathematicians, let me quickly say: “Look out for the next ICMI Study announcement—it will be on Primary Mathematics”. Watch for the announcement in December.

Finally, allow me to note that ICMI is changing in another respect—it is changing in the way the world is changing. New technologies, new modes of communication, new groupings, new social imperatives, new problems to be solved and questions to be answered. ICMI must and does change, and in particular we

Opening Address: President of ICMI 7 change in the way we communicate. We have a Facebook page, we have a bank of digitised publications, we have an ever increasing website. In what new ways will we meet and communicate in four years time? We need the new members of our community to lead us in this matter—and I call on you all to embrace the movement forward into new worlds.

But face-to-face communication will, in my opinion, always be highly valued. Being able to Skype my grandchildren or my research colleagues on the other side of the world only makes me want to actually see them and spend time with them so much more.

And this is why we are here. To greet and see and talk to each other. To make new friends and affirm old ones. And we do this with great pleasure at the same time as we work hard to improve the learning of mathematics in classrooms at all levels in every country.

Thus I regard it as one of the greatest honours of my career to declare the 12th International Congress on Mathematics Education Officially open.

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Welcome Address: Chair of IPC

I would like to express my utmost gratitude to His Excellency Lee Myung-bak, the President of the Republic of Korea for preparing a welcoming message for us despite his busy schedule.

Your Excellency Lee Ju Ho, Minister of Education, Science, and Technology, Professor Ingrid Daubechies, the President of IMU, Professor Bill Barton, the President of ICMI, Ladies and Gentlemen, distinguished guests and participants from all around the world, I would like to extend my warmest welcome to you all.

We, the Korean Mathematics Society and Korean Mathematics Education Society, are very proud to host the 12th International Congress on Mathematical Education. Our International Programme Committee has worked tirelessly through two face-to-face meetings and numerous internet discussions. It is needless to say that this Congress would not be possible without the dedicated and coordinated efforts of members of the various committees, presenters and participants. We thank all of you for making this a reality.

Mathematics has been at the heart of human culture, philosophy, technology and advancement since the dawn of civilization. We cannot think of our modern society apart from mathematics because mathematics influences every facet of our daily lives. Due to the far reaching effects of mathematics in our world, mathematics education may be one of the most efficient ways to influence betterment of mankind. For the week starting today, we are gathered here to nurture and cultivate the mathematics educational environment for our future generation so that they may become significant part of the solution and advancement of our society.

S.J. Cho (È<)

International Programme Committee of ICME-12, Seoul National University, Seoul, Republic of Korea e-mail: sungjcho @ snu.ac.kr

© The Author(s) 2015 9 S.J. Cho (ed.), The Proceedings of the 12th International Congress on Mathematical Education, DOI 10.1007/978-3-3 19-12688-3_3

It is our sincere hope that this Congress would inspire wider and tighter mathematics education research network as well as inviting and stimulating mathematics classrooms all over the world.

Thank you,

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Congratulatory Remarks: Minister of Education and Science, and Technology

Ju Ho Lee

First of all, congratulations on the opening of the 12th International Congress on Mathematical Education.

I am glad that this important math event is being held in Korea this year.

Also, it is a great pleasure to welcome math education researchers and math teachers from more than 100 countries.

With the aim of transforming Korea into a nation of great science and technology capacity, and a nation of outstanding human talent, the Ministry of Education, Science and Technology of Korea is focusing on three important points in designing and implementing its policies.

The three points are “creativity”, “convergence”, and “human talent”. Creativity enables us to think outside the box, convergence allows us to go beyond the traditional boundaries between disciplines, and finally human talent builds the very foundation that make all these possible.

Without a doubt, these are the most essential elements in today’s knowledge-based society.

Math is the very subject that can foster much needed creativity and convergence, and is becoming a core factor in raising national competitiveness.

Math is behind everything.

The ICT revolution would have been impossible without the binary system.

The technology behind the CT scans can be traced back to simultaneous equations.

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

An erratum of the original chapter can be found under DOI 10.1007/978-3-319-12688-3_80

J.H. Lee (%4) Former Minister of Education, Science and Technology, KDI School of Public Policy and Management, Seoul, Republic of Korea

© The Author(s) 2015 11 S.J. Cho (ed.), The Proceedings of the 12th International Congress on Mathematical Education, DOI 10.1007/978-3-319-12688-3_4

ICMI Awards Report

Carolyn Kieran

A wonderful part of the opening session of the ICME congresses is the ICMI Awards ceremony. The 2012 ceremony, which was presided over by Prof. Carolyn Kieran, the chair of the ICMI Awards Committee, was no exception. Congress participants shared in congratulating the recipients of the 2009 and 2011 competitions for the Klein and Freudenthal awards. The Korean Minister of Education, Science, and Technology, the Honorable Mr. Ju-Ho Lee, did us the honor of presenting each award.

In 2000, the International Commission on Mathematical Instruction decided to create two prizes given in recognition of outstanding achievement in mathematics education research:

e the Felix Klein Award, which honours lifetime achievement in our field, and e the Hans Freudenthal Award, which honours a major cumulative programme of research.

Each award consists of a medal and a certificate, accompanied by a citation. The two awards are given in odd-numbered years. A six-person Awards Committee is responsible for selecting the awardees and for producing the citations explaining the merits of the awardees. The members, of whom only the Chair is known, are appointed by the President of ICMI and serve on the Committee for 8 years.

Scientific and scholarly quality is of course the fundamental characteristic involved in reviewing the candidates’ work and merits. The first Committee, which was appointed in 2002, agreed on four aspects of quality, four criteria of evaluation: impact, sustainability, depth, and novelty. These criteria have been maintained throughout the Committee’s work. Nevertheless, the field is influenced by social and cultural conditions, traditions, values, norms, and priorities. So, there are, inevitably, delicate balances to be struck between different dimensions, different traditions, different cultural and ethnic regions, and—indeed—different schools of

C. Kieran (DX) Université du Québec à Montréal, Montréal, QC, Canada

© The Author(s) 2015 13 S.J. Cho (ed.), The Proceedings of the 12th International Congress on Mathematical Education, DOI 10.1007/978-3-3 19-12688-3_5

14 C. Kieran thought. Past Klein awardees have been Guy Brousseau (2003), Ubiritan D’ Ambrosio (2005), and Jeremy Kilpatrick (2007). Past Freudenthal awardees have been Celia Hoyles (2003), Paul Cobb (2005), and Anna Sfard (2007).

At the 2012 ICMI Awards ceremony, the following four individuals were honored for their contributions to the field.

e The Felix Klein Medal for 2009: awarded to IAS Distinguished Professor and Professor Emerita Gilah C. Leder, La Trobe University, Bundoora, Victoria, Australia.

e The Hans Freudenthal Medal for 2009: awarded to Professor Yves Chevallard, IUFM d’Aix-Marseille, France.

e The Felix Klein Medal for 2011: awarded to the Elizabeth and Edward Connor Professor of Education and Affiliated Professor of Mathematics, Alan H. Schoenfeld, University of California at Berkeley, USA.

e The Hans Freudenthal Medal for 2011: awarded to Professor Luis Radford, Université Laurentienne, Sudbury, Canada.

Gilah Leder’s citation, which was read by ICMI President Bill Barton, acknowledged her more than thirty years of sustained, consistent, and outstanding lifetime achievement in mathematics education research and development. Her particular emphasis on gender success and equity in mathematics education, but also more broadly her work on assessment, student affect, attitudes, beliefs, and self-concepts in relation to mathematics education from school to university, as well as her research methodology, and teacher education, have contributed to shaping these areas and have made a seminal impact on all subsequent research.

Yves Chevallard’s citation, which was read by ICMI Vice-President Mina Teicher, recognized his foundational development of an original, fruitful, and influential research programme in mathematics education. The early years of the programme focused on the notion of didactical transposition of mathematical knowledge from outside school to inside the mathematics classroom, a transposition that also transforms the very nature of mathematical knowledge. The theoretical frame was further developed and gave rise to the anthropological theory of didactics (ATD), which offers a tool for modelling and analysing a diversity of human activities in relation to mathematics.

Alan Schoenfeld’s citation, which was read by ICMI Past-President Michéle Artigue, recognized his more than thirty years of scholarly work that has shaped research and theory development in mathematical learning and teaching. His fundamental theoretical and applied work that connects research and practice in assessment, mathematical curriculum, diversity in mathematics education, research methodology, and teacher education has made a seminal impact on subsequent research. Another significant component of his achievements has been the mentoring he has provided to graduate students and scholars, nurturing a generation of new scholars.

Luis Radford’s citation, which was read by ICMI Vice-President Angel Ruiz, acknowledged the outstanding contribution of the theoretically well-conceived and highly coherent research programme that he initiated and brought to fruition over

ICMI Awards Report 15 the past two decades. His development of a semiotic-cultural theory of learning, rooted in his interest in the history of mathematics, has drawn on epistemology, semiotics, anthropology, psychology, and philosophy, and has been anchored in detailed observations of students’ algebraic activity in class. His research, which has been documented in a vast number of scientific articles and in invited keynote presentations, has had a significant impact on the community.

The image of the four awardees standing on the stage together, receiving their medals and accompanying certificates from the Minister of Education—as well as the beautiful bouquets of flowers presented by young Koreans in traditional dress— is one that will stay with us for quite some time.

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.