# ICMI News July 2021

## 1. From the Desk of Jean-Luc Dorier, new ICMI Secretary General

After two terms as member-at-large in the ICMI EC, I let myself be convinced to be a candidate for the position of Secretary-General. Among other things, the perspective of traveling to various places and meeting colleagues around the world was something that appealed to me… that was without counting on Covid! The end of the term of the preceding ICMI EC was marked in a totally virtual manner, instead of the usual face-to-face meeting held immediately after the ICME closing ceremony. In fact, the report on ICME-14 had to be left for the next EC, because of the postponement of the Congress until 2021. And the new EC had to invent an equally new way of functioning. Instead of having one 3-day long annual meeting we had to switch to regular 2h long monthly meetings! Virtual meetings of course, with new EC member Marta just emerging from bed in Arizona at 5.30 in the morning and Vice-President Merrilyn longing to go to bed when the meeting ends at 00.30, Brisbane time. In normal life, a new EC would have had 3 days of work interspersed with shared meals and social events that create opportunities for these 14 people to get to know each other. But, usually, no such luxuries are entertained in online meetings, where work objectives must be made as precise and bare as possible to fit in with the etiquette of virtual interactions. So, on our first 2h virtual meeting in January we had to invent some kind of “getting to know you” social interaction in order to create a bit of humanity and team building, to use a popular expression of the time.

I must say that despite the circumstances, the new ICMI EC has gotten off to a great start after just six months of work. A liaison EC-member has been designated for each ICMI Affiliated Organization, as well as for the CANP project, the Klein Project, and International Mathematics Day. AMOR has found new volunteers, and thanks to the work of Núria Planas, the Celia Hoyles Unit has been launched. Under Anjum Halai’s leadership, the five CANP groups have been working on new perspectives (see in this newsletter). Open access publications relative to CANP have also been released. On the basis of the survey started during the term of the last EC and pursued by Jill Adler, Merrilyn Goos and Lena Koch, we have started thinking about launching a new ICMI Study (see the call for proposal in this and the previous ICMI newsletter). Moreover, volumes of some past ICMI Studies have been made available via open access and more are to come. Meanwhile, we have continued working on the organization of ICME-14, which is going to happen in very particular circumstances (see in this newsletter) and we are already making plans for ICME-15, to be held in Sydney in July 2024. We are also trying to maintain and strengthen our connection with all ICMI Country Representatives.

In many ways, this new ICMI EC has been much more productive in its first 6 months than any other before and this is largely due to the affordances of virtual meetings, which, thanks to the pandemic, are now an everyday occurrence. However, I would be the last to enjoy this new situation and I look forward to the possibility of a face-to-face meeting with the whole EC members in the near future.

Our community has developed a lot of energy in order to cope with the situation induced by this pandemic. We had to support schoolteachers and sometimes education authorities in our countries in order to provide high-quality remote teaching. We also had to face some difficulties in our teaching with students often in a very precarious financial and mental state. Everywhere, initiatives have been publicized and research projects have already grasped new issues raised by the global state of remote teaching throughout the whole world. This has been the case with CANP projects as well as in several of our affiliated organizations. There will also be a Discussion Group addressing these issues within ICME-14. Thinking about and shaping mathematics learning and teaching in tomorrow’s school and university is an enormous challenge now that this pandemic has forced us to see life differently.

We also had to adapt our way of working regarding international exchanges and conferences, workshops or congresses. The academic world, in which people are usually so keen to travel, has been suddenly totally shut down and we find ourselves working in improvised domestic situations with more or less good computers and uncertain internet connections… How do we survive? How much have inequalities increased as a result of this new state of our profession? What is tomorrow’s world going to look like?

Some say we will never travel again to big congresses that gather hundreds or thousands of academics, because technology can replace face-to-face interaction and it is better for the planet if we don’t travel. Some don’t believe that technology and remote virtual meetings are an adequate substitute for face-to-face meetings, in terms of creating social networks and good communication, especially the non-verbal kind. Even if we care about climate change, should academic travel be banished, especially considering what difference this would make compared to mass tourism? Is the hybrid, or blended, mode a sustainable solution for international meetings? Is it not the gateway to more inequalities?

So many questions and issues to deal with, in which ICMI has an important role to play. These will be a continuing and vivid source of debates and research works in the coming years, decade and probably decades. This is an enormous challenge for this first post-Covid ICMI Executive Committee.

## 2. News from IMU

### - A Belated Celebration of the Centennial of the IMU

The shared history of the International Mathematical Union (IMU) and the International Commission on Mathematical Instruction (ICMI) is a long and extensive one, beginning more than a century ago. Our common origin is the International Congresses of Mathematicians (ICMs), with the first ICM taking place in 1897 in Zürich, Switzerland.

It was at the ICM in Rome, Italy, in 1908, that the initiative to create ICMI as a distinct commission on mathematical instruction was taken in the form of a resolution of the General Assembly of the ICM. Its task; to report back to the next ICM regarding the teaching of mathematics. Needless to say, the extent and importance of mathematical instruction would demand a more long-term strategy than this initial construction. While world events in the 1930-40s subsequently disrupted activities, when international collaboration restarted in the aftermath of World War II, ICMI was organized as a standing commission of the IMU. Financially, ICMI depends fully on IMU membership dues but enjoys considerable autonomy within the IMU, running its own General Assemblies and quadrennial conference — the International Congress on Mathematical Education.

While ICMI was first established in 1908, it wasn’t until the ICM in Strasbourg, France, in 1920, that the decision to create the IMU was made. To celebrate this momentous event in the history of international collaboration in mathematics, the IMU decided – in joint cooperation with colleagues in France – to host an international conference at the same place and close to the exact date of creation a century earlier. The conference would provide the opportunity for mathematicians to come together and listen to a small number of high-level talks, as well as enjoy each other’s company and more informal discussions.

Unfortunately, the COVID-19 pandemic made it impossible to go through with the original plans to hold the conference in September 2020. However, with vaccines now becoming more widespread, infection rates are dropping, restrictions are slowly being lifted, and international travel is becoming feasible again. Thus, the IMU plans to host the belated celebration:

Mathematics without Borders, The Centennial of the International Mathematical Union, Strasbourg, 27–28 September 2021

Fortunately, all speakers have confirmed physical attendance in Strasbourg, regulations permitting. ICMI will be represented by a talk from its Secretary General Jean-Luc Dorier. For the full program, please refer to https://imucentennial.math.unistra.fr/

We hope to see many colleagues at the celebration in Strasbourg!

Helge Holden
Secretary General of the IMU

The 14th International Congress on Mathematical Education ICME-14 will be held from July 11-18, 2021.

Considering the current situation and potential development of COVID19, ICME-14 and ICMI decided in October, 2020 that ICME-14 would be held in a hybrid mode, i.e., it would be held simultaneously in Shanghai (face-to-face) as well as online.

Taking into account the many time zones around the world, the new schedule is divided into two parts: a 3.5h core time starting 19:30 Shanghai time (04:30 in Los Angeles, 06:30 in Mexico City, 07:30 in New York, 12:30 in London, 13:30 in Geneva, 17:00 in Delhi, 21:30 in Sydney and 23:30 in Auckland – all times using 24-hour clock). During the core time, the Opening and Closing ceremonies, one Plenary lecture, Plenary Panels 1-3, the Discussion groups, two sessions of each TSG, sessions to interact with the awardees and plenary speakers, as well as a Chinese art and cultural performance will be held. Between 14:30 and 18:00 Shanghai time the remaining program will be held. The Early Career Research Day will start at 08:30 Shanghai time.

For the time table details, please visit here.
The online conference tool Zoom will be used.

Online access

June 20, 2021 (Beijing Time) was the last day for registration and payment. The attending code will be issued before July 11 for the participants whose payment has been received.

The attendance code can be used on different devices, but not simultaneously.

## 4. ICME-14: Four Survey Teams' Presentations

Continuing with the practice of previous ICMEs, four Survey Teams have been set up. The organization of these teams is intended to strengthen the emphasis on new developments and progress in the area of each theme or issue since the last three or four ICMEs. Each Survey Team has worked for several years to survey the state-of-the-art with respect to a certain theme or issue, with particular concern in identifying and characterizing important new knowledge, recent developments, new perspectives, and emergent issues.

The survey teams will have 90 minutes to present their work at ICME-14 in a kind of sub-plenary format. They will present their work in parallel at 16:30─18:00 Shanghai Time (UCT+8), July 18, 2021.
After the conference, all surveys will be published.

ST 1. Research on university mathematics education

Chair: Chris RASMUSSEN (USA), Team members: Marianna BOSCH (Spain), Reinhard HOCHMUTH (Germany), Oh Nam KWON (Korea), Birgit LOCH (Australia), Mike THOMAS (New Zealand), María TRIGUEROS (Mexico)

The Work of Survey Team 1
It is an exciting time for research in university mathematics education. There are now several major conferences every year across the globe, as well as the fairly new International Journal of Research in Undergraduate Mathematics Education, now in its seventh year. The innovative work that is being done includes practical, research-based curricular innovations, new insights into teaching practices that support students’ deep engagement in mathematics, as well as theoretical and methodological advances that ground and guide this work. Members of the ICME community will find of great interest the many research-based innovations identified by the survey team, innovations that can inform and strengthen work in their own classrooms, departments, and institutions.

The survey team also identified areas of interest that are less well-researched. These nascent research areas represent exciting opportunities for members of the ICME community to conduct their own scholarly work and help advance the field at large. Two examples of areas that are ripe for new learning are the professional development of university faculty and collaborations among mathematicians, engineers, scientists, didacticians, and psychologists. So while there is now much research-based wisdom, there are also exciting opportunities for new research, and the survey team is looking forward to highlighting both these advances and areas of growth.

You can learn more about the work of the Research in University Mathematics Education Survey Team at our presentation, which is scheduled for 16:30─18:00 Shanghai Time (UCT+8), July 18, 2021.

ST 2. Early childhood mathematics education (up to age 7)

Chair: Elia ILIADA (Cyprus), Team members: Anna BACCAGLINI-FRANK (Italy), Nosisi FEZA (South Africa), Esther LEVENSON (Israel), Nanae MATSUO (Japan)

The work of Survey Team 2
The purpose of this survey is to establish an in-depth and comprehensive review of the state-of-the-art of the most important developments and contributions between 2012 and 2020, and of new perspectives and emerging challenges in early childhood mathematics education (up to age 7).

Over the past few years, there is an increasing growth of research in early childhood mathematics education within the field of mathematics education. This is evidenced by the great number of publications and the special interest or study groups in international mathematics education conferences which focus exclusively on the particular topic. The growing interest in early childhood mathematics education research is attributed to the prominent place of early childhood education in many countries all over the world and the existing evidence that a solid foundation for children’s mathematical development before entering school has a crucial role in their future learning. It is also noteworthy that the quality of early childhood mathematics education affects children’s later mathematical dispositions.

In this survey we identified six major research themes in recent literature on early childhood mathematics education. Three of these themes are content-oriented: Number sense and whole number development, geometry education and children’s competences in other content domains. A cognition-oriented theme focuses on cognitive skills associated with mathematics learning and special education. Another theme that is systematically reviewed deals with the role of technologies in early mathematics teaching and learning. Finally, the sixth theme focuses on developments and trends in teacher-related issues.

Overall, our review showed a strong emphasis on number sense and development both in research and in curricula. We expect greater research attention on how to develop and assess children’s competences in geometry, spatial reasoning, pattern and structure, measurement, statistical reasoning, functional thinking and to promote these mathematical content domains in the curriculum and teachers’ education. Furthermore, our findings reveal that the focus of early childhood mathematics education research has been on prekindergarten, kindergarten and early primary school years. Considering that children begin to develop mathematical competences very early, we hope to see further and deeper investigations of the mathematical skills and development of children under four years of age, using appropriate research designs. More research is also needed on the learning opportunities in mathematics offered to this age group of children and on developing early childhood educators’ knowledge about toddlers as mathematics learners.

You can learn more about the work of Survey Team 2 at our presentation, which is scheduled for 16:30─18:00 Shanghai Time, July 18th, 2021.

ST 3. Teachers’ collective work as a regular school practice for teacher development
Chair: Birgit PEPIN (Netherlands), Team members:   Jehad ALSHWAIKH (Palestine), Hiroyuki NINOMIYA (Japan),
Gérard SENSEVY (France), Yudong YANG (China), Bill ATWEH (Australia), Zeger-jan KOCK (Netherlands)

The work of Survey Team 3
Whilst in many countries teacher professional development activities were previously mainly conducted at and by universities and teacher education institutions, nowadays they are often run by local or regional school boards and agencies at school level. This trend goes hand-in-hand with proposals that teachers become partners in the design of their curriculum, rather than ‘simply’ implementing the curriculum, supported by (government) approved textbooks. Moreover, due to the availability of an enormous amount of free educational resources on the web, teachers ask for guidance and support for choosing and appropriating those resources for their classroom, and the closest support lies at school level, with their colleagues (in their or neighbouring schools).

At the same time teachers’ collective work as regular school practice has a long history in several countries: Lesson Study in Japan and Teaching Research Groups in China are well known examples. However, varying forms of such practice exist in many countries and in varying educational contexts. Over time, and particularly in more recent years, these practices have been shared and researched leading to the evolution of a wide, yet dispersed, knowledge base.

This lies at the heart of the work of survey team 3, asking the following research question guiding the survey study:
What can be learnt from an examination of common features (of mathematics teachers’ collective work as regular school practice) as well as from variations in practices and their rationales in different national contexts?
To answer this question the team investigates

1. the nature of school-based mathematics teachers’ collective work as regular school practice, and how this relates to situation, culture and context;
2. the roles of the participants (coming from different communities) who engage collaboratively in such school-based collective work, and how they relate to each other;
3. the kinds of learning that can be observed (and evidenced) in school-based teacher collective work, and how the observed/evidenced learning relates to the collective aspect, context and goals of the work;
4. the methodological and theoretical perspectives/lenses that are used to guide and inform school-based teacher collective work, and perceived teacher learning, in such teams

At ICME the team will present the findings from the survey study.

Moreover, the team colleague from Japan will talk about ‘Japanese Teachers’ Collective Work as a Regular School Practice’, and the team colleague from China about ‘Chinese Lesson Study and its features’. In addition, the team conducted a survey (with questionnaires) in selected countries where mathematics teachers were asked about their collaborative professional development practices at school level. Results will be compared and juxtaposed with those found in the literature.

You can learn more about the work of the Survey Team 3 in terms of research in ‘Mathematics Teachers’ Collective work as Regular School-based Practice’ at the ICME presentation, which is scheduled for 16:30─18:00 Shanghai Time (UCT+8), July 18, 2021.

ST 4. The teaching and learning of mathematical modelling and interdisciplinary mathematics education
Chair: Gloria STILLMAN (Australia), Team members: Jussara de Loiola ARAÚJO (Brazil), Jonas ÄRLEBÄCK (Sweden), Angeles DOMINGUEZ (Mexico), Toshikazu IKEDA (Japan), Stanislaw SCHUKAJLOW (Germany)

The work of Survey Team 4
The theme of survey team 4 is the teaching and learning of mathematical modelling and interdisciplinary mathematics education with a focus on relations to the real world and connections and implications for STEM education. Our aim is to briefly present the relevance of this theme in mathematics education research as well as an overview of the work done by the Survey Team on this specific theme, which will be of interest for mathematics educators and mathematicians interested in education.

Overall, our review showed there was more evidence of interdisciplinary themes from the literature reviews of mathematical The literature review shows an interesting discrepancy between general emphasis and research focus: Although the introduction of many papers on modelling mentions interdisciplinarity (even more than mention relations to the real world), there is little evidence of this interdisciplinarity being a focus in the research proper as it is just assumed if you are doing modelling then it is interdisciplinary.

The use of mathematical modelling approaches was also strongly advocated in STEM integration but this was not the case in actual practice.  In contrast there were fewer references to relations to the real world in the mathematical modelling research literature but in these cases they were more likely to take more than a minor role in the research study. Definitions of what was considered as interdisciplinarity varied in research studies and in curricula.

We will be presenting our findings in four threads where overall trends, issues and challenges will be illustrated and exemplified. The first thread is importance of a well understood relation between mathematics and the real world underpinning interdisciplinary work in mathematics education. This will be related to the way mathematical modelling is used to describe real world situations as well as produce artefacts in the non-mathematical world. The second thread addresses interdisciplinary research teams and interdisciplinary teaching teams and combinations of these in the research literature in our data. The composition of such teams and how they contribute to the corpus of knowledge about the effectiveness that such interdisciplinarity brings to modelling research will be illustrated. Our third thread examines and illuminates issues around relationships among mathematical modelling, mathematics, the real world and interdisciplinarity and the challenges these relationships bring. Our final thread focuses on the proposition that mathematical modelling is critical as a high-leverage topic to ensure mathematical depth in STEM integration and how STEM integration in this manner can motivate and support learning within all disciplines concerned. The success of productively exploring opportunities and tackling challenges of STEM integration rests on strong, broad and deep mathematical knowledge that can be applied and drawn upon when engaged in mathematical modelling.

You can learn more about the work of Survey Team 4 at our presentation, which is scheduled for Shanghai Time (UCT+8), July 18, 2021.

## 5. Once upon a time…

### .. Historical Vignettes from the Archives of ICMI: The Origins of the ICMEs

Bernard R. Hodgson,
Curator of the ICMI Archive

The 14th International Congress on Mathematical Education (ICME-14) will take place in Shanghai between July 11-18, 2021.  (Due to the COVID-19 pandemic, this congress has been delayed by a year and will be held in a hybrid “on site / at distance” mode.) This provides an opportune moment to reflect on the origins of the ICME congresses.

The ICME is to ICMI, the International Commission on Mathematical Instruction, what the International Congress of Mathematicians (ICM) is to the International Mathematical Union (IMU), the organisation of which ICMI is a commission.  It may thus be worth examining chronologically the genesis among this chain of acronyms: ICME—ICMI—ICM—IMU.

• ICM

It all started in the late 19th century with the ICM.  In his book surveying this series of congresses, Guillermo Curbera, former Curator of the IMU Archive, presents this beginning as a sound one:

“The International Mathematical Union is an offspring of the International Congress of Mathematicians. This is as it should be.  The reverse situation would have had all the weaknesses of a purely administrative decision.” [1, p. 305]

The first ICM was held in Zurich in 1897.  It was decided at the outset to use the name “congress of mathematicians”, and not “of mathematics”, thus stressing the importance given to the relationship between people.  This spirit is well captured in the welcome words of Adolf Hurwirtz at the opening reception of the first ICM:

“In the heart of a mathematician lives the necessity for communicating and expressing himself to his colleagues.  And each of us certainly knows by personal experience how stimulating personal scientific intercourse can be.” [2, p. 23]

The background to the Zurich ICM is discussed in a paper by June Barrow-Green, the current IMU Archive Curator, [3] and in more details in the fundamental book of Olli Lehto [4, pp. 1-11].  At the heart of the process leading to this first ICM was a general idea of “increasing internationalism” [ibid., p. 2]—as may suggest for instance the first Olympic games of the modern era organised in 1896—and a growing perception among leading mathematicians, especially in the last decade of the 19th century, of the importance of international collaboration in mathematics.  Many names could be mentioned on that account here, but those of Georg Cantor, Felix Klein, Charles Hermite or Henri Poincaré, to name just a few, possibly stand out as having played important roles, in some cases by using their reputation to foster such a collaboration.

Charles-Ange Laisant can also be seen as having been influential on that account.  In a report on the mathematics section of the congress of the French Association for the Advancement of Sciences held in Bordeaux in 1895, he writes that the idea of having international mathematical congresses held on a regular basis is gaining support, and that “quelques savants des plus illustres s’y sont attachés avec une véritable passion” [5, pp. 33-34].  (In Lehto’s translation, “some of the most brilliant scholars have exhibited real passion for it” [4, p. 7].)  Laisant stresses as the main goals of such gatherings the presentation of a general picture of the progress made, among various countries and in different branches of mathematics, in the time frame from one congress to the other, and the possibility for scholars working in analogous directions to meet and get to know each other [5, p. 34].

Closer to ICMI interests, Laisant also co-founded in 1899, jointly with Henri Fehr, the journal L’Enseignement Mathématique—which was to become a few years later, at the inception of ICMI, its official organ, with Fehr being the first ICMI Secretary-General.  In the initial paper that they signed for the first issue of the journal, Laisant and Fehr stress the importance for the “world of teaching” to be associated with the “great movement of scientific solidarity” exemplified by the recent inception of “international congresses, so brilliantly inaugurated in Zurich in 1897 and whose principle is henceforth well-established” [6, p. 2].

• ICMI

Following congresses held in Paris (1900)—of “Hilbert’s problems” fame—and Heidelberg (1904), the fourth ICM took place in Rome in 1908.  As discussed in a previous ICMI Archive vignette [7], it was on the occasion of the Rome ICM that ICMI was born—for the first time.  But the gestation had been underway for a while: already in 1905 David Eugene Smith, mathematician and teacher educator from the US, had proposed in L’Enseignement Mathématique [8, p. 469] the establishment of such a commission.  The General Assembly of the Rome ICM adopted a resolution entrusting mathematicians Klein, Fehr and George Greenhill to set up an international committee in order to study the teaching of mathematics at the secondary school, and to report at the next ICM in Cambridge (1912).  However, the mandate of that international committee was soon expanded, both in scope and in time.

The committee was known, in the first part of its life, as the International Commission on the Teaching of Mathematics—in close correspondence to the French, German or Italian versions of its name—but it eventually became the International Commission on Mathematical Instruction (ICMI), when reborn as an IMU commission after World War 2.  A special symposium celebrating the centennial of ICMI [9] was held in 2008 in Palazzo Corsini, the original birthplace of ICMI in Rome.  More information about the main episodes in the early life of ICMI can be found on the History of ICMI website, edited by Fulvia Furinghetti and Livia Giacardi [10].

• IMU

The next acronym in our series, in chronological order, is IMU.  As is the case for ICMI, there are so to say two “moments of birth” for the International Mathematical Union.  The first one took place at the ICM that convened in Strasbourg in 1920, right after World War 1 —in Lehto’s parlance [4, chap. 2], this was the “Old IMU”.  In line with that milestone, an IMU conference is now under preparation to celebrate this centennial [11]—a gathering which also, because of COVID, has been delayed by a year, to September 2021.

The first years in the life of IMU were somewhat uneasy, to a large extent as a repercussion of the tense political context in the aftermath of World War 1, and were later followed by a period of dormancy up to the end of World War 2.  The IMU as we know it today results from a series of actions taken in the late 1940s and early 1950s.  The narrative by Lehto [4] of the many episodes that then occurred covers some 50 pages.  It is summarised as follows on the IMU website:

“The years 1950-1952 are milestones in the history of IMU. The Constitutive Convention in 1950 in New York created IMU de facto. By the Statutes adopted there, IMU came into being in 1951 de jure, and in 1952 the General Assembly [held in Rome] inaugurated the activities of the new Union, elected its first President and Executive Committee and was readmitted to ICSU.” [12] (See also [4, p. 88].)

• ICME

This brings us to the final stage in our acronymic journey—in fact, its starting point: what about the ICME congresses, and how did they come to be?  The answer to this query is in fact short and precise: the International Congress on Mathematical Education can to a large extent be described as the outcome of the dynamism and vision of a sole man: Hans Freudenthal, member of the ICMI Executive Committee (EC) from 1963 to 1966, and ICMI President for the period 1967-1970.  The launching of a series of international congresses specific to ICMI remains one of his main legacies to both the Commission itself and the mathematics education community.

Freudenthal was highly critical of the way issues pertaining to the teaching and learning of mathematics were being addressed in the ICM sections on education (or on teaching, as they were usually called).  In Utrecht in August 1967, the first year of his presidency, at a meeting of the ICMI EC jointly with ICMI ‘members-at-large’ and national delegates (in agreement with the Terms of reference of the time—see [13]), he expressed the strong conviction that ICMI should take action in that connection.  As one can read in the report of ICMI Secretary-General André Delessert:
“Mr. President considers [in French: M. le Président estime] that the principle of ICMI reports at the quadrennial Congress of Mathematicians is wrong.  National reports are generally unusable. He advocates the idea of an ICMI Congress, held a year prior to the IMU Congress, where invited talks and personal communications would be presented.” [14, p. 245]

The “principle of an ICMI Congress in 1969” was immediately adopted, and the French delegate to ICMI, Maurice Glaymann [recently deceased at age 90], proposed to have it take place in France [ibid.].  During the following two years, Freudenthal clearly played a strong and essential role in the concretization of this project.

It is highly peculiar that after the 1967 Utrecht meeting, the preparation of the first ICME happened without ICMI keeping IMU informed of its project.  Lehto even speaks of a “break of contact between the IMU Executive Committee and ICMI” [4, p. 172].  I have already mentioned this absence of communication in an earlier ICMI Archive vignette, quoting a letter of IMU President Henri Cartan complaining that ICMI has had no consultation with IMU when deciding to have an international congress independent of the ICM [15, p. 9].  In a similar vein, Cartan, late in 1968, writes to IMU Secretary Otto Frostman: “I saw Freudenthal two days ago. (…) I insisted on the fact that we really want to be informed of all projects and all activities of ICMI” [16].

Under an item concerning the IMU-ICMI relations during the IMU EC meeting held in May 1968, one reads in the minutes:
The President and the Secretary complain of a lack of information about the activities of ICMI.  It was recalled that the President of IMU is a member ex officio of every Committee of the Union.  (…)  It seems that ICMI decided to hold an international congress in Paris in 1969” [17, pp. 3-4].

(NB:  The last part of this quotation appears in [4, p. 259], but with an incorrect reference to the source.)  As a consequence, it was then decided by the IMU EC that “the President of the Union will write to Professor Freudenthal (President of ICMI), in order to ask for better information and to keep good relationship between IMU and ICMI.  A personal contact will be useful.” [ibid., p. 4]

Eventually the tension provoked by the creation of the ICMI congresses waned.  In the minutes of the following IMU EC held in May 1969, a mere three months prior to the first ICME congress, one finds the following comments under the item ‘Report on ICMI relations’:
The E.C. was informed by the President about the forthcoming International Congress on Mathematical Education in Lyon, August 24-30, 1969.  The E.C. welcomed the idea that Professor Cartan attend at least a part of the Congress without formally committing IMU in any way.” [18, p. 4]

In a report of the IMU EC on the year 1969, one reads that the ICME-1 congress, “attended by about 655 active participants, was a big success thanks to the high level of the 21 addresses delivered by outstanding educators, a large number of panel discussions and free communications, and thanks to the excellent organisation” [19, p. 4].  Brief information is also given there on the next ICME congress, scheduled to be held in 1972 [ibid. p. 5].  A personal account of the first ICME was given in ICMI News [20] by Geoffrey Howson, former ICMI Secretary-General (1983-1990).

The ICME-1 Proceedings quickly appeared both as a book and as a double issue of Educational Studies in Mathematics [21], a new journal launched at the initiative of Freudenthal with the assistance of ICMI [4, p. 259].  It may be reminded here that the very creation of ESM was still another source of tension between IMU and ICMI during Freudenthal’s presidency, as seen for instance in the following comment in March 1968 of Cartan to Georges De Rham, his predecessor as IMU President:
You see that Freudenthal’s projects are materialising, although we have hardly been informed.  I would like to know if you think that an initiative of IMU President should be taken towards Freudenthal, if only to remind him that ICMI has an official organ, L’Enseignement Mathématique.” [22]

The closing words on this episode may belong to Lehto.  Regarding the creation by ICMI of the ICMEs, he comments on a tongue-in-cheek tone: “From the point of view of the Executive Committee of the IMU, the child had come of age and behave accordingly.  Yet the parent was understanding.” [4, p. 259]  But more importantly there was an explicit will to foster the relationship between IMU and ICMI, as can be seen by a comment from the May 1969 IMU EC meeting:
It was agreed by the E.C. that IMU continues its policy of paying special attention to educational questions through ICMI, in order to ensure that the creative mathematician and the educator do not work isolated for each other.” [18, p. 4]

The inception of the ICME series, half a century ago, definitely serves as a landmark in the history of ICMI.  Quoting again Lehto: “The introduction of ICMEs independently of the IMU meant an essential increase in ICMI’s sovereignty as a [commission] of the Union” [4, p. 261].

NB: The interested reader may easily access the books by Curbera [1] and Lehto [4], as well as the Proceedings of the 1897 ICM [2], all of which are freely downloadable from the IMU website [www.mathunion.org].  The Proceedings of the ICMI centennial symposium [9] can be found on the ICMI website [www.mathunion.org/icmi].

Sources
[1]  Curbera, G.P. (2009). Mathematicians of the world, unite! The International Congress of Mathematicians—A human endeavor. Wellesley, MA : A.K. Peters.  [www.mathunion.org/organization/imu-history]
[2]  Hurwitz, A. (1898).  Excerpts from “Verlauf des Kongresses: Empfangsabend”.  In Ferdinand Rudio (Ed.), Verhandlungen des Ersten Internationalen Mathematiker-Kongresses (pp. 22-23). (Zürich, 9-11 August 1897)  Leipzig: B.G. Teubner.  [www.mathunion.org/icm/proceedings]
(English translation from the German taken from [1, p. 1])
[3]  Barrow-Green, J. (1994).  International Congresses of Mathematicians from Zurich 1897 to Cambridge 1912.  The Mathematical Intelligencer 16(2), pp. 38-41.
[4]  Lehto, O. (1998). Mathematics without borders: A history of the International Mathematical Union. New York : Springer.  [www.mathunion.org/organization/imu-history]
[5]  Laisant, C.-A. (1896).  Les mathématiques au congrès de l’Association française pour l’avancement des sciences à Bordeaux.  Revue générale des sciences pures et appliquées 7(1), pp. 31-34.
[6]  Laisant, C.-A. & Fehr, H. (1899). L’Enseignement Mathématique.  L’Enseignement Mathématique 1, pp. 1-5.  (Translated from the French)
[7]  Hodgson, B.R. (2019).  The (first) ICMI birth certificate.  (“Once upon a time…  Historical vignettes from the ICMI Archives”)  ICMI News (March 2019) pp. 6-7.  [www.mathunion.org/icmi/publications/icmi-newsletter/icmi-newsletter-archive]
[8]  Smith, D.E. (1905). Opinion sur les réformes à accomplir dans l’enseignement des mathématiques.  L’Enseignement Mathématique 7, pp. 469-471.
[9]  Menghini, M., Furinghetti, F., Giacardi, L., & Arzarello, F. (Eds.). (2008). The first century of the International Commission on Mathematical Instruction (1908-2008). Reflecting and shaping the world of mathematics education. Rome: Istituto della Enciclopedia Italiana.  [www.mathunion.org/icmi/conferences/other-icmi-conferences]
[10]  Furinghetti, F., & Giacardi, L. (Eds.), The first century of the International Commission on Mathematical Instruction (1908-2008).  [www.icmihistory.unito.it]  (Accessed on June 1, 2021)
[11]  Mathematics without Borders: The Centennial of the International Mathematical Union.  [www.mathunion.org]  [indico.math.cnrs.fr/event/5375/]  (Accessed on June 1, 2021)
[12]  International Mathematical Union. IMU history.  [www.mathunion.org/organization/imu-history]  (Accessed on June 1, 2021)
[13]  Hodgson, B.R. (2020).  A dilemma related to the ICMI Terms of reference.  (“Once upon a time…  Historical vignettes from the ICMI Archives”)  ICMI News (November 2020) pp. 6-8.  [www.mathunion.org/icmi/publications/icmi-newsletter/icmi-newsletter-archive]
[14]  Delessert, A. (1967).  Compte rendu de la séance de la C.I.E.M. (Utrecht, 26 août 1967)  L’Enseignement Mathématique 13, pp. 243-246.  (Translated from the French)
[15]  Hodgson, B.R. (2019).  Episodes from the Freudenthal era.  (“Once upon a time…  Historical vignettes from the ICMI Archives”)  ICMI News (July 2019) pp. 8-10.  [www.mathunion.org/icmi/publications/icmi-newsletter/icmi-newsletter-archive]
[16]  Cartan, H. (1968).  Letter to Otto Frostman, IMU Secretary, 4 October.  IMU Archive/ SF 1 / Ser 6.5 / F3.  [Box 6F – Presidents and Secretaries, 1966-1975]  (Translated from the French)
[17]  IMU EC Minutes (1968).  Minutes of the 24th meeting of the Executive Committee of the International Mathematical Union. (Paris, May 6-7, 1968).  IMU Archive / SF 1 / Ser 6 / F24  [Box 4B (IMU EC minutes, 1963-1974)].
[18]  IMU EC Minutes (1969).  Minutes of the 25th meeting of the Executive Committee of the International Mathematical Union. (Pisa, May 16-17, 1969).  IMU Archive / SF 1 / Ser 6 / F24  [Box 4B (IMU EC minutes, 1963-1974)].
[19]  IMU (1971).  Report of the Executive Committee of the International Mathematical Union to the National Adhering Organizations (1 January – 31 December 1969).  Bulletin of the International Mathematical Union.  Internationale Mathematische Nachrichten 97 (Jan. 1971) pp. 1-7.  [www.mathunion.org/membership/imu-bulletins]
[20]  Howson, G. (2008).  Historical vignettes: How the first ICME congress was born.  ICMI News 3 (April 2008) item 10.  [www.mathunion.org/icmi/publications/icmi-newsletter/icmi-newsletter-archive]
[21]  Editorial Board of Educational Studies in Mathematics (Eds.). (1969). Proceedings of the First International Congress on Mathematical Education. (International Commission on Mathematical Education [sic], ICMI). Dordrecht: D. Reidel. [Also in Educational Studies in Mathematics, 2 (1969) 135-418.]
[22]  Cartan, H. (1968).  Letter to Georges De Rham, former IMU President, 2 March.  IMU Archive/ SF 1 / Ser 6.5 / F3.  [Box 6F – Presidents and Secretaries, 1966-1975]  (Translated from the French)

## 6. ICME-1 Experience by Jerry Becker

In the ICMI Newsletter published one year ago in July 2020, in the historical vignette, Celia Hoyles had a note about the ICMEs and her experience participating in the second one (ICME 2 at Exeter University). In her message, she clearly expressed her feeling that the conference (congress) was transformational for her as a teacher attendee, and it was no exaggeration to state that very clearly, she said. And I agree completely with her regarding the potential learning from the ICMEs.

In my case, I had the good fortune of participating in the first conference (ICME-1), in Lyon, France. It was transformational for me, too, in that I met Prof. Erich Wittmann of Dortmund University of Germany at the congress. We learned that we shared a strong interest in several topics and issues in mathematics education. Subsequently, we were in regular communication through international airmail and again meeting in later conferences - at ICMEs and other regional and local conferences. We shared and critiqued each other’s work.

In one case, we separately noticed an extremely interesting article by Douglas Quadling and Alistair Macintosh on linear mappings and arithmogons in the English journal Teaching Mathematics in the Secondary School. We began a conversation when we noticed the topic could be developed in a manner that we thought would represent an excellent elementary school mathematics curriculum topic, with a focus on mathematical thinking and reasoning and providing, in the process, students' practice on computation or practice skills (avoiding drill!). The topic ended up as part of a German primary school curriculum, and a topic that is part of teacher professional development in a course I teach at my university and each summer at the University of Chicago in the United States.
And now more than 50 years later, our shared interests and exchanges continue. The congress provided a context and opportunity to meet and subsequently work towards and exchange in an excellent collaboration over many years.

I noticed very recently that the works of Prof. Wittmann are now available as an open access publication, freely available.  The link is https://link.springer.com/book/10.1007/978-3-030-61570-3

Our professional exchanges over these years was launched consequent to our meeting at ICME-1 in Lyon, France in 1959!

I hope we can all meet in connection with ICME-14. All good wishes.
Jerry Becker

Note from the editors: Pr. Jerry Becker is now the only scholar to have participated in all the ICMEs held so far and he will participate in ICME-14. ICMI is highly grateful for his contribution to the community.

## 7. Capacity and Network Project

Creating networks and reaching out to the critical mass in the mathematics education community is a potent strategy to maximize the impact of reform in mathematics education.

The Capacity and Networking Project (CANP)  is a step in this direction. A key purpose of CANP is to create networks in low and middle income countries to enhance mathematics education at all levels. It aims to develop the educational capacity of those responsible for mathematics teachers, and create sustained and effective regional networks of teachers, mathematics educators and mathematicians, also linking them to international support.

### - Creating Networks and Impact in Mathematics Education

Since 2010 ICMI has supported five CANPs, each with the common purpose of advancing mathematics education but differing in its approach and methodology. The community of mathematics educators across the five CANPs is a significant resource because working at the grassroots level they provide insights into key issues and challenges in supporting mathematics education. Under the new ICMI Executive Committee, there will be significant effort to consolidate and enhance the impact of CANP.  Each CANP has one ICMI EC member acting as a liaison person as noted below:

 CANP1 (Francophone Sub-Saharan African Region) EC-Liaison - Jean-Luc Dorier CANP2 (Central America and the Caribbean) EC-Liaison - Marta Civil CANP3 (South East Asia) EC- Liaison -Susanne Prediger CANP4 (East Africa) EC-Liaison - Mercy Kazima CANP5 (Andean Region and Paraguay) EC- Liaison- Patricio Felmer

Through sharing cross-national regional experiences, the CANP community aims to deepen and broaden the understanding of lessons learnt in the process of establishing the CANP and taking it forward towards sustainability. Towards this end, during ICME-14 being held in July 2021, all the five CANPs will come together in a Discussion Group. Specifically, the group will discuss the challenges arising as a result of the disruption caused by the pandemic. Discussions will be guided by the following key questions:

1. What did the CANP do in 2020? How (if at all) were your activities impacted by the pandemic? (focus on one or two innovations/activities).
2. What is planned for the CANP in 2021? Why?
3. What new questions arise for the mathematics education community?
4. What are the similarities and differences in the opportunities and challenges arising in the CANPs?
5. What is the impact of CANP on mathematics education in the region? How could the impact be sustained?

To conclude, CANP remains a significant initiative of ICMI, especially as it reaches out to under-represented communities in low and middle income countries. ICMI will continue to support CANP in such a way that ultimately each CANP becomes a sustainable entity able to support itself.

Join DG13. Discussion Group: Capacity and Network Project Sustainability and Future Directions
Wednesday July 14, 21:30-23:00 Shanghai time.

For further information on CANP please see https://www.mathunion.org/cdc/scholarships/capacity-networking-project-canp-project-support

If you have any questions, please contact Anjum Halai, ICMI VP and ICMI EC CANP Liaison person.

## 8. ERME in the Virtual Space

News from the Affiliated Regional Organization

Susanne Prediger & Carl Winsløw

Entering now the second year of the pandemic, ERME (the European Society for Research in Mathematics Education) is functioning in the virtual space. The former ERME president, Susanne Prediger, and the new ERME president, Carl Winsløw, can report:

Virtual Conference
Although the regular CERME 12, planned for 2021, was shifted to February 2022, the community kept in contact with a Virtual pre-CERME 12 event held in February 2021, that was brilliantly organized by Eirini Geraniou and Jeremy Hodgen and their team at University College London. All Thematic Working Groups held at least one session. The plenary lecture by Nathalie Sinclair (Simon Fraser University, Canada), the plenary panel on online mathematics education, and ERME’s general meeting, provided shared experiences for the more than 1400 registered participants from 77 different countries.

YERME YouTube Channel with Lectures and Workshops
A most active part of ERME live is currently organized by YERME, the Young Researchers in ERME. A series of online-workshops was started already in October 2019 and keeps on growing into a lovely digital library with interactive lectures or workshops recorded for later use. They are intended to let early-career researchers in mathematics education from all over Europe (and of course also the rest of the world) learn from experts in the field, with topics such as writing journal articles, mathematics education research journals, literature reviews, interdisciplinary research, and revising papers after reviews.

Video-recordings of all webinars and interviews are published on the  YERME youtube channel here; https://www.youtube.com/channel/UCnOxT-aoAFHNV5u_nPAxUXA/featured.

We thank Dorota Lembrér and Dilan Şahin-Gür for their commitment in organizing this highly valuable YERME YouTube channel!

Returning to normal
Even if we successfully use the virtual space for keeping communication, collaboration and cooperation alive, we eagerly aspire to return to normal meetings – naturally, taking necessary precautions, as required by the situation. First, 84 doctoral students and 10 senior scholars are scheduled to work together at the 11th ERME summer school (YESS11) held in Brixen, Italy, in August 2021. And then we all look forward to the next real CERME conference, to be held in Bolzano, Italy (February, 2-6, 2022). The deadline for paper submission will be September, 15, 2021. More information can be found here: https://www.cerme12.it/

## 9. News from CIEAEM

CIEAEM 72: a restricted online meeting
Gilles Aldon*, Cristina Sabena**
*IFÉ ENS de Lyon, S2HEP, president of CIEAEM - **Università di Torino. Secretary of CIEAEM

The CIEAEM is a meeting place in which researchers, teachers of primary and secondary schools, and teacher trainers are invited to share with others their experiences, ideas and perceptions of mathematics and mathematics education. The last two face to face conferences, in 2018 in Mostaganem (Algeria) and in 2019 in Braga (Portugal) provided an opportunity for discussion around questions that overcome mathematics education but which are of great importance if we want to stay faithful to the philosophy and the aim of CIEAEM, which “emphasizes  that  links  between  research  and practice [which] have to be re-constructed continuously by mutual efforts, and that changes in mathematics education [which] have to be nourished  by  both,  practice  and  theory,  by  critique  and  transformation  of  practice  as  well  as  critique  and  application  of research into educational development”

(CIEAEM manifesto, available on line at https://www.cieaem.org/index.php/en/). Living together, living in an increasingly complex world, were the themes of these conferences; during the working groups the discussion based on research and pragmatic studies tried to respond to the challenges that this reality poses to mathematics educators. As for each CIEAEM conference, the work has been summarized in the proceedings that are published by the Italian Journal Quaderni di Ricerca in Didattica in special issue 3, 2019 and  special issue 7, 2020.

Every four years, and in the years in which the ICME conference takes place, the commission members organize a restrictive meeting, the goal of which is to take stock of the work done in the previous four years and to prepare for future years. In 2020 this conference should have been held in Volos (Greece). But, as with all the conferences around the world, it has been impossible to meet and we postponed this meeting by one year.

Unfortunately, even during this year 2021 the health situation did not allow us to organize a face-to-face meeting. This is the reason why we decided to meet virtually in May 2021 on the 3rd, the 10th and the 12th. Two of these three meetings were internal to the commission and the discussion focused on the life of the commission. So, future conferences were on the agenda: Philadelphia (Arcadia University, USA) in 2022, Praha (Charles University, Czech Republic, ) in 2023 and Malmö (Malmö University, Sweden) in 2024 are the next towns and universities which are going to welcome our international meeting. The management of the new website was also on the agenda, including the publication of CIEAEM Newsletters. Twice a year, the CIEAEM Newsletter informs about the different events and works that commission members carry out; for example, in the two last Newsletters (June 2020 and January 2021, available at https://www.cieaem.org/index.php/en/resources-en/cieaem-newsletter), written during the pandemic period, testimonies of the educational situation in commission members’ countries give a very interesting landscape of the effects of the pandemic on education worldwide. The meeting was also an opportunity to present to the whole commission the current state of the new book, The role of the history of Mathematics in the Teaching /Learning process, which will complete the CIEAEM sourcebook collection in the Springer ‘Advances in Mathematics Education’ Series (https://www.cieaem.org/index.php/en/resources-en/cieaem-source-book-en). The editorial committee of this book was able to communicate the agreement of Springer and will thus very quickly propose an agenda for the writing of the various chapters to the authors who already wrote the proposal.

The third part of the May 2021 meeting was devoted to a scientific discussion. It focused on a reflection on methodologies and was introduced by a talk given by Sandra Racionero-Plaza (University of Barcelona) and Aito Gómez González (University of Rovira i Virgili) titled Communicative Methodology: researching with, rather than on, Roma community. This lecture illustrates why and how the speakers work with and for the Roma community through Communicative Methodology. In order to have a positive impact working with vulnerable groups, as for instance the Roma community, it is necessary to develop methodologies to assess to what extent social science research is having direct impact on improving those groups’ living conditions. Many social science researchers are developing methodologies through which we can directly work with citizens, constructing together deeper knowledge and, in so doing, transforming the reality for the better. Within a communicative perspective and applying Communicative Methodology, knowledge is constructed in close and egalitarian intersubjective dialogue with the potential participants from the very beginning of the research process until the end. Through this lecture, the speakers showed how by applying the specific methodology in different research processes over the last 20 years with and for the Roma community, a great scientific, political and social impact has been achieved. It was highlighted how these studies were organized, and in particular, how this knowledge was built based on the application of communicative data collection techniques and communicative data analysis.

After the talk, the participants discussed issues raised by the conference and attempted to answer the following questions:

• How does the presentation echo the methodologies you use in your own research?
• In educational research, what difficulties can be encountered when using "cooperative" methods?
• Could we discuss the application of Communicative Methodology in Mathematics Education?

Discussions in small groups were very fruitful and allowed participants to share their own practices in terms of methodology, particularly when working with teachers. To paraphrase the title of the conference, discussions showed that CIEAEM research is conducted with, rather than on, teachers.

During the ICME 14, the CIEAEM will seize the opportunity given by the organizers who offered a time slot for Affiliated Organizations. The presentation of the CIEAEM will focus on the issues that have been discussed in our conferences, and mainly on how our research practice has changed during this pandemic time. We will propose a workshop based on the workshops organized during CIEAEM conferences and we will discuss the issues to obtain answers that are coherent with the world in which we live, while maintaining an epistemological and ethical vigilance towards the fundamental humanistic values that have presided over the creation and development of the CIEAEM:

• creating links between scientific knowledge and craft wisdom,
• reinforcing the collaboration of mathematics education research and practice.

During the session, participants will be asked to share their experience and will be involved in discussing live issues related to mathematics education in the 21st century, in a way similar to the working groups during the CIEAEM conferences.

We will draw on the proceedings of previous conferences as well as on the publications resulting from the work of the commission. The CIEAEM sourcebooks are based on the work reported and discussed at the annual CIEAEM conferences and mix theoretical research texts and chapters describing pedagogical experiences; they are always related to the themes of the conferences, augmenting the texts already published in the proceedings. The first (Gellert & al. 2015) offers fresh insight and understanding of the many ways in which children, youth and adults may find their paths to mathematics. The second (Aldon et al., 2017) offers fresh insight and understanding of the many ways in which technological resources can improve the teaching and learning of mathematics. The next book (Romero et al., forthcoming), through different key aspects arising from the significance of history of mathematics, the study of the history of mathematics and its relation to mathematical education, and the use of history in the teaching of mathematics and in the process of training mathematicians, deeply discusses how the historical perspective brings us closer to mathematics as a human science.

Aldon, G., Hitt, F., Bazzini, L., & Gellert, U. (Eds.) (2017). Mathematics and technology. Springer.
Gellert, U., Giménez Rodríguez, J., Hahn, C., & Kafoussi, S. (Eds.) (2015). Educational paths to mathematics. Springer.
Romero S., Serradó A., Appelbaum P., Aldon G. (forthcoming). The role of the history of Mathematics in the Teaching/Learning process. Springer.

ICMI AMOR project is a long-term project and aims at building online resources reflecting significant and influential research in mathematics education at an international level. ICMI Felix Klein and Hans Freudenthal Awardees are asked to prepare online lectures which are put together in units.  Each unit is devoted to one awardee and consists of a series of 8 to 12 modules between 10 and 30 minutes up to a total of 120-180 mins of videos. Recently a new unit by Anna Sfard, recipient of the Hans Freudenthal Award 2009 was finalized and can be found here.

## 11. Anti-racism and Anti-discrimination in Publications

ICMI has received a request from a group of editors of mathematics education journals to publish a statement on anti-racism and anti-discrimination in publications.

ICMI will discuss the issue at the next ICMI EC meeting and make recommendations.

## 12. In Memoriam - Ubiratan D'Ambrosio

We have recently received the sad news that Ubiratan D’Ambrosio passed away on May 12, 2021. An eminent specialist of ethnomathematics, he was very well-known and appreciated by many of us in the ICMI community. In 2005 he received the second Felix Klein Award in recognition of the role he has played in the development of mathematics education as a field of research and development throughout the world, above all in Latin America. It also recognized Ubiratan D'Ambrosio's pioneering role in the development of research perspectives which are sensitive to the characteristics of social, cultural, and historical contexts in which the teaching and learning of mathematics take place, as well as his insistence on providing quality mathematics education to all, not just to a privileged segment of society.

Instead of a formal obituary, we have decided to publish a more personal tribute to this man of exception. Thanks to Daniel Clark Orey for his tribute.

Jean-Luc Dorier, ICMI Secretary-General

Saudades… indeed, there is no better word to describe how we are all feeling right now.

I don’t think I could have written this last week, my emotions were far too raw, and I was overwhelmed by the love and recognition our dear mentor, colleague and academic father, Ubiratan D’Ambrosio, was receiving from all over the world. One can go to any number of sites and newsletters and read his many, many honors… I won’t do that here. I think he would appreciate it, to be honest. Maybe it is his spirit of creative insubordination coming through that I feel as I write this.

We last spoke with Ubi and Maria José a week before he passed, and I must confess, we spoke with them more than I do my own biological parents, always with the same reverence, love, and respect, with the need for feedback and advice about our work, yet with a growing trepidation as he became more and more frail, that at his age and time, each call could be the last one. Over the last couple of years, we became more and more cognizant that each moment with Ubiratàn had become more and more precious. Time with Ubi was treasured, and will always be. And so it was, a week or so before we found that he was hospitalized for a serious infection we had spoken; all of us were happy that soon my husband Milton too would be vaccinated and that we could meet in São Paulo in a few months. We spoke about his upcoming talk to our master’s program here in Ouro Preto, and other things… and then, like that, a week later, he was gone. It is so very, very painful to speak of one’s mentor, teacher, father in the past tense. This is saudades.

A story.

I first met Ubi at the annual meeting of the Northern California Mathematics Council at Asilomar, perhaps it was 1996. Though much earlier, I had heard of him through my doctoral advisor Patrick Scott at the University of New Mexico as he translated one of Ubi’s first books into English for the International Study Group in Ethnomathematics (ISGEm) community, which they founded together. After his keynote, I found him sitting by himself, something I became used to, as he loved to sit after a talk and just enjoy people, taking pictures, signing books, and encouraging new voices. But at Asilomar, he was enjoying, as he told me years later, the anonymity. I went over to him and introduced myself. I ended up spending the entire weekend with him, walking on the beach discussing Latin American politics, ethnomathematics, and mathematics education. He invited me to write a Fulbright application to work with them in Brazil, and I did, and ended up working with the ethnomathematics and mathematical modeling group at the Pontificia Universidade Católica de Campinas, where he introduced me to Milton and his work. I know he helped hundreds of new voices just like this.

One more story.

One trip to São Paulo, with our son visiting, we had dinner with him and Maria José in their home. Milton and I were dying to see his Felix Klein medal, yet we were far too embarrassed to ask. After a few drinks, we encouraged our son to ask instead, and Ubi took us all downstairs to his office, rummaged through a drawer, and there it was… I remember going back to the hotel later and sending an email to Bea D’Ambrosio in Ohio, that we had found it. She was non-plussed, as I guess she too hadn’t been able to ask or find it. We told her which drawer it was in and so, on her next trip home, she let us know it was still there! It was our own little joke between all of us! But it showed just how humble and real Ubiratan was.

Milton and I cannot remember if he ever mentioned a negative word about anyone, ever. Even about those who attacked his work. That alone, as an academician, is no mean feat. His work with ethnomathematics, non-killing mathematics, and mathematics for peace, was such that he walked the talk. His life remains a monument, a legacy, indeed a powerful example of his work. And we, those he has left behind, will continue his work, his lessons and try as best we can to implement his philosophy of peace, inclusion, of love, of a sense of true humanity and of course… creative insubordination.

We will miss you forever Ubiratan!

Daniel Clark Orey, Ph.D.
Professor, Departamento de Educação Matemática
Instituto de Ciências Exatas e Biológicas

Coordenador, O Grupo de Pesquisa de Etnomatemática na Universidade Federal de Ouro Preto
Professor Emeritus, California State University, Sacramento
Senior Fulbright Specialist – Nepal/Brasil
www.oreydc.com

## 13. In Memoriam - Gérard Vergnaud

by Michèle Artigue and Janine Rogalski

It is with great sadness that the ICMI community has learned of the death of Gérard Vergnaud, in Paris on June 6, 2021.

Gérard Vergnaud was born in 1933 in Doué-La-Fontaine, France, into a family of modest origins, which would have normally meant that his studies would have stopped after primary education. Fortunately, a primary teacher persuaded his parents to enter him in a scholarship exam, which allowed him to access secondary education. As he shared in the interview conducted for the preparation of the thematic afternoon at ICME-13 in 2016, his love for theater and mime led him, after graduating from HEC, a famous French business school, to take an interest in psychology. He enrolled in psychology at the Sorbonne University and took the course that Jean Piaget was teaching at the time. This was a real intellectual shock, which led him to prepare a thesis under the supervision of Piaget, on the problem solving activity of children from 4 to 10 years of age, which he defended in 1968. He mentioned in the same interview that it is also thanks to Piaget's support, that he joined the CNRS (National Center for Scientific Research) as early as 1963 as a research associate in Bresson's laboratory. He finally spent his entire career at the CNRS, where he successively led research teams in several laboratories, always linking research issues on cognitive development and the study of the role of education (for children) or training (for adults). He retired in 1999 but did not stop his scientific activity, becoming Emeritus Director of Research.

Gérard Vergnaud played a major role in the evolution of the relationship between cognitive developmental psychology and mathematics didactics, helping it move from the status of external reference to the role of participant in the study of all types of didactic phenomena, as Jean Brun expressed it in his contribution to the conference organized in France in 1993 in homage to the two founding fathers of French research in mathematics didactics, Guy Brousseau and Gérard Vergnaud (Brun, 1994). Vergnaud is indeed, according to him, the first psychologist to have placed the question of the contents of knowledge at the heart of developmental psychology, and to have affirmed the need for the psychologist not to remain a prisoner of their current description in order to be able to analyze the formation and functioning of knowledge in the individual subject (Brun, 1994, pp. 71-72). This was to become the basis of his major contribution to mathematics education, which is the theory of conceptual fields (Vergnaud, 1991, 2009). However, as he also explained in this interview, it was through a combination of circumstances that he came into contact with the world of education and the nascent didactic research. At the end of the 1960s, indeed, he accepted an invitation to replace a colleague as pedagogical counsellor for teachers in a primary school whose director wanted to introduce modern mathematics. He attended classes and helped teachers in choosing situations. In the interview panel at ICME-10, reflecting on this first engagement, he said: “I can add that the theory of conceptual fields was born at that time, even if it was only several years later that I could formalize it as a triplet of a set of situations, a set of operational invariants, and a set of symbolic and linguistic representations” (Artigue, d’Ambrosio, Hanna, Kilpatrick & Vergnaud, 2008, p. 108).

In the central place given to the notion of situation in this conceptualization, the meeting with Guy Brousseau, the founder of the theory of didactic situations, also played a role. It occurred in the early seventies. On this subject, in this same panel, Vergnaud said: "I was most impressed by the reflection and the experience of Guy Brousseau concerning didactic situations […]. Then I could match the concept of ‘scheme’, which I had borrowed from Piaget, with the concept of ‘class of situations’.” (ibidem, p. 108).  But his psychological approach to the notion of situation is substantially different from Brousseau's and the French didacticians who, like us, lived through this period, still remember the Homeric scientific debates that these differences of approach gave rise to during the sessions of the national didactic seminar or during the first summer schools of mathematics didactics, at the beginning of the 80s.

Vergnaud's major contribution to the didactics of mathematics is, as written above, the theory of conceptual fields. It has nourished and still nourishes a large number of research studies in mathematics education, and well beyond. The theory is based on the idea that cognitive development cannot be understood by considering concepts as isolated entities: it is necessary to approach them in their interactions with other close concepts. Thus, the notion of conceptual field defined as a "set of situations and a set of concepts tied together" (Vergnaud, 2009, p. 86). The dialectical vision Vergnaud proposes between a notion of scheme inspired by Piaget and that of situation is the second pillar of the theory.  He defines a scheme, indeed, as the invariant organization of action for a class of situations, and distinguishes in it four components: goals, subgoals, and anticipations; rules of action; operational invariants (concepts in action or theorems in actions); possibilities of inferences. We cannot enter into details but would like to also mention the importance for Vergnaud of the distinction between two forms of knowledge, operational knowledge that makes it possible to act and predicative knowledge that makes it possible to formulate and justify action. The extensive research Vergnaud has carried out on the conceptual fields of additive and multiplicative structures is emblematic of this approach and has become an international reference (Vergnaud, 1982, 1983).

Gérard Vergnaud became involved in the activities of the ICMI community very early on. Together with Efraim Fischbein and Richard Skemp he was one of the founders of PME, one of the first two ICMI-affiliated study groups. The creation of PME followed the ICME-3 congress in Karlsruhe in 1976. In the interview panel at ICME-10, he told this anecdote which reveals his good living personality: during the Warwick meeting in 1979, “Alan Bell had written a draft of a constitution, but we had not been able to reach an agreement. I invited Alan Bell and Hartwig Meissner to my home in the suburbs of Paris. We had good food and good wines. We reached an agreement rather easily. The text of the first constitution of PME was adopted in Berkeley in 1980 without any discussion” (Artigue et al., 2008, p. 111).

Vergnaud himself organized two PME conferences, the first in Grenoble in 1981, and the second in Paris in 1989, at the time when France was celebrating the bicentenary of the 1789 revolution.

But Gérard Vergnaud's scientific contribution is not limited to the above, nor even to his contribution to mathematics education. From the nineties, increasingly interested in skills development and learning at work for adults, he contributed, with Pierre Pastré, Pierre Rabardel, Janine Rogalski and Renan Samurçay, to the emergence of professional didactics (a term introduced by Pierre Pastré in his doctoral thesis). In 1996, he joined the cognition laboratory of Paris 8 University and, from its creation by Pierre Rabardel, he participated to the C3U ergonomics team at the multidisciplinary Paragraphe laboratory. As stressed in the note his colleagues wrote after his death, his profound agreement with the researchers of this laboratory was both methodological, with the importance given to the analysis of complex activities in natural situations, and theoretical, with a developmental perspective, crossing the contributions of the Piagetian research current with those of the historico-cultural approach of Soviet psychology and Lev Vygotsky’s approach. In turn, this new field of professional didactics has become a resource for researchers in mathematics education studying teachers’ professional practices (Vandebrouck, 2013).

Gérard Vergnaud was not only an eminent scientist; all along his professional life, he has also been an activist, defending his vision of psychology research, pushing for the acknowledgement of the field of didactic research by the CNRS (obtaining the creation of the first didactic GDR in 1984), and also a researcher strongly engaged in trade union activities. He has established numerous relationships with research and research institutions all over the world, and supervised more than 80 doctoral theses! He was Doctor Honoris Causa from the University of Geneva (1995), Central State University of Buenos Aires (2011), and member of the International Academy of Psychological Sciences of Russia.

We are losing a great and unique researcher and human being, but were are sure that his writings will continue to inspire researchers in mathematics education and beyond for decades.

References:

Artigue, M., d’Ambrosio, U, Hanna, G., Kilpatrick, J., & Vergnaud, G. (2008). Plenary panel session moderated by Michèle Artigue. In M. Niss (Ed.), Proceedings of ICME-10 (pp. 105-122). IMFUA, Department of Science, System and Models, Roskilde University, Denmark.
Brun, J. (1994). Evolution des rapports entre la psychologie du développement et la didactique des mathématiques. In M. Artigue, R. Gras, C. Laborde & P. Tavignot (Eds.), Actes du Colloque Vingt ans de Didactique des Mathématiques en France (pp. 67-83). Grenoble: La Pensée Sauvage.
Vandebrouck, F. (Ed.) (2013). Mathematics classrooms. Students’ activities end teachers’ practices. Rotterdam: Sense Publishers.
Vergnaud, G. (1982). A classification of cognitive tasks and operations of thought involved in addition and subtraction problems. In T.P. Carpenter, J.M. Moser & T.A. Romberg (Eds.), Addition and substraction: a cognitive perspective (pp. 39-59). Hillsdale NJ: Lawrence Erlbaum.
Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 127-174). Academic Press.
Vergnaud, G. (1991). La théorie des champs conceptuels. Recherches en didactique des mathématiques, 10(2/3), 133-170.
Vergnaud, G. (2009). The theory of conceptual fields. Human Development, 52, 83–94.

http://www.cfem.asso.fr/cfem/ICME-13-didactique-francaise
https://ardm.eu/autres-annonces/deces-de-gerard-vergnaud/
See the website https://gerardvergnaud.wordpress.com/ gathering various of Vergnaud’s contributions.

## 14. In Memoriam - Nadine Brousseau

Nadine Brousseau2: Concerning the research on rational and decimal numbers, it has been a very very heavy work and very long. At first there was the first year… yes the first year… when we started, I mostly worked with Guy. He had everything in his head, I was listening, he was telling me “Here is what you are going to do tomorrow, here is what we are going to try to do. OK. And the next day: I had to execute. I was in my class with my students and I was trying to put in practice what had been prepared… And right after the lesson, I used to get a notebook and try to write everything that had just happened with the children. This allowed me to regroup all these lessons, the canvas of which I really had. And then after the lesson, we used to get together and see what did not and did work. We tried to do the review of the lesson. And, according to this review, I used to write my sheets afterwards. But there was also the sheet to be done before… Marie Hélène (Salin) talked about the didactical sheet, this didactical sheet was absolutely essential.
Guy Brousseau: From my own perspective… You were… what was excellent was the vision you had of what was going to happen, of what was possible or not. And if you did not conceive what could happen with the children, you let me know. It was precious, because that stopped us in the deliriums we could have caressed.

This quotation shows the very important role played by Nadine in the experimental process that underlined the theoretical work that Guy Brousseau had been able to achieve, which is now known as the theory of situations. From that, we can understand that this was not a just a mere canonical academic work that is easy to encapsulate in publications. On top of the barrier of language, this is a reason of the difficulty of access, especially for non-French native speakers, of the essence of Brousseaus' work, or should I say the Brousseaus’ work!

In the unit devoted to Guy Brousseau in the AMOR3 project, Annie Bessot and Claire Margolinas have tried to make this specificity more accessible by using different resources. Moreover, in Module 0, I have given some key aspects of Guy’s life and background, including his relation to Nadine (you can see the extract of the interview quoted above in French subtitled in English).

The fantastic work signed by Nadine and Guy on rational and decimal numbers has recently been published in an English revised version4 with the help of Virginia Warfield. This book accessible in English shows the importance of Nadine, in Guy’s work and makes explicit the fact that she was not just a wife, or even a teacher applying his ideas, but a real research partner and an essential collaborator in the very elaborated process of creation based on a specific role of experimentation and observation, which is characteristic of the theory of situation. Nadine was not the type to claim for fame and always insisted in staying in the shadow, yet she signed a few texts with Guy and even talked at some conferences. She has also been immortalised in lots of videos from the COREM, like the one from which the picture below is extracted when she was teaching the famous “Race to 20”.

Dear Guy, I know you must have been quite affected by the loss only 10 days ago of your dear friend Gérard Vergnaud, an intellectual challenger in your early days, with whom you share the paternity of the French school of research in Didactique des Mathématiques. Never would an expression such as your other half have been accurate to designate what Nadine represented for you. In the name of ICMI and of the whole community of mathematical education, let me offer you our sincere sympathy and condolences in this difficult moment.