The New Life of ICMI: Pursuing Autonomy and Identifying New Areas of Action

Abstract

Since 1969, the life of ICMI was marked by the International Congresses on Mathematical Education (ICMEs). These congresses gave voice to ICMI’s Executive Committee, its President and its Secretary, and also featured the principal topics and actors within mathematics education from an international perspective. The congresses became an important date in the life of researchers, teachers and people involved in various ways in mathematics education. In this chapter, the life of ICMI will be intertwined with the organization of the ICMEs in order to analyse its evolution, also with the aid of interviews released by prominent actors on the ICMI scene.

1 Introduction

As seen in Chap. 2 (Furinghetti and Giacardi, this volume), Hans Freudenthal’s presidency marks a turning point in the life of ICMI, both from the point of view of the organizational structure and from the point of view of action. This gradually resulted on the one hand in a greater autonomy from the community of mathematicians, and on the other hand in the Commission’s definition of its cultural identity. To analyse this evolution, we take the International Congresses on Mathematical Education (ICMEs) as a timepiece: after the first one in 1969 and the second in 1972 they became four-year appointments and marked the life of ICMI. They gave voice to ICMI’s Executive Committee—starting from its President and its Secretary—and also featured the principal topics and actors within mathematics education from an international perspective. The congresses became an important date in the life of researchers, teachers and people involved in various ways in mathematics education. It is unavoidable to intertwine the life of ICMI with the organization of the ICMEs. Indeed,

The ICMI’s primary responsibility is to plan for the ICME’s, which entails choosing from among host country bids, appointing an international program committee to form the scientific program and select presenters, and overseeing progress of the congress preparations (Bass and Hodgson 2004, p. 642).

In the interview released to Schubring (2008), Heinz Kunle, co-founder (as he himself reminds us) with Hans Georg Steiner of the Zentrum für Didaktik der Mathematik (Centre of Didactics of Mathematics) in Karlsruhe and of the Zentralblatt für Didaktik der Mathematik, chair of the German national subcommission of ICMI since 1970, and national representative after Heinrich Behnke, stated that ICMI relied heavily on the national commissions for the organization of the ICMEs, in order to know the mainstreams of research and projects in each country and decide about the topics to be faced in the plenaries and in the working groups.

The present chapter covers the period from the first ICME in 1969 to ICME-11 in 2008, the year of ICMI’s centennial. Its purpose is to outline the main characteristics of the four-year interval identified by each ICME, with reference also to ICMI activities, to the ICMI studies, to research trends, and to journals.

The website on the history of ICMI (Furinghetti and Giacardi 2008) presents not only the portraits of the officers and a rich timeline, but also a brief description of the ICMEs, interviews, documents (including the Terms of Reference), see (Furinghetti and Giacardi 2010; Bass 2008). We will often refer to the interviews as well as to the ICME proceedings, reminding that the latter do not have a uniform structure; for instance, results of individual working groups within an ICME were often published separately. The contents of the website are at the base of our reconstruction of the period under consideration, together with various papers that cover the same topic such as the history of the first 75 years of ICMI outlined by Geoffrey Howson (1984) and the brief note on the ICMI sketched by Bass and Hodgson (2004). The relationship between ICMI and the community of mathematicians is illustrated in the book on the history of the International Mathematical Union (IMU) by Olli Lehto (1998). The events are framed by the emerging of mathematics education as an academic discipline, as outlined by different authors (Kilpatrick 2008; Hodgson 2009; Furinghetti et al. 2013). Hodgson and Niss (2018) give an “insiders’ view” of the latest half century of the Commission. Their work provides important information and serves as a guide. Indeed, the two authors occupied leading positions within ICMI for a long period and their knowledge and experience are irreplaceable. The column “Once upon a time... Historical vignettes from the ICMI Archive,” launched in the ICMI Newsletter of March 2019 (p. 6–7) provides first-hand information and documents from the ICMI Archives gathered by their curator Bernard Hodgson.

For information about the ICMI officers who passed away in the first century of the life of ICMI, we refer to the portraits published in this book. We will provide some information for the other officers and members at large.

We start with some general observations:

• ICMI’s Executive Committee (EC) is elected 1 year before the ICME (2 years in the case of ICME-1), while the organization of an ICME necessarily requires some years. So an ICME cannot be seen as an expression of the Executive Committee that is in force during its holding, but rather as a bridge between two ECs (with exception of ICME-1, which completely represented ICMI’s President Freudenthal).

• ICMI is an official commission of the International Mathematical Union. This still defines the official position of ICMI. Furthermore, the majority of the funding of ICMI comes from IMU. Up to 2006 the Terms of Reference of ICMI have been established by the General Assembly of IMU, which was also responsible for the election of the Executive Committee, the administrative leadership of ICMI. Once these elections and budget matters were settled, ICMI worked with a large degree of autonomy (Bass and Hodgson 2004). According to new Terms of Reference in 2007, the Executive Committee of ICMI is elected by the General Assembly of ICMI itself, see (https://www.mathunion.org/icmi/terms-reference-icmi).

• Appointments of members of the Executive Committee have often been influenced by political issues (Hodgson and Niss 2018). Moreover, giving a look to the officers of ICMI within a committee, we see the attempt to gradually (and slowly) approach geographic balance, with a particular attention to developing countries, and gender equity. We also observe that mathematicians usually managed the appointment of the ECs, while that of the IPCs of the various ICMEs was more frequently the prerogative of mathematics educators.

2 ICME-1, Lyon 1969. Freudenthal’s Mark on Mathematics Education

In the period 1967–1970, ICMI was chaired by Freudenthal (Netherlands). The Vice-Presidents were Edwin Moise (USA) and Sergei L. Sobolev (USSR); André Delessert (Switzerland) had been elected Secretary and the other members were Behnke (Germany), André Revuz (France) and Bryan Thwaites (UK). Henri Cartan (France), President of IMU, was Member ex officio.

It was Maurice Glaymann, deeply involved in the reforms for the teaching of mathematics in France and first director of the IREM (Institut de Recherche sur L’enseignement des Mathématiques) in Lyon, to propose to have the venue of the ICME-1 in Lyon (interview to Glaymann, Artigue 2008a, part 1)

Chapter 2 (Furinghetti and Giacardi, this volume) analyses the reasons that led to this first ICME. The volume of the proceedings was edited by the editorial board of Educational Studies in Mathematics (Editorial Board of ESM 1969; see Fig. 3.1). It shows no date of publication, nor a list of participants. The contents of this volume are also published in the same year in Educational Studies in Mathematics (2: 135–418). Glaymann tells that the participants were over thousand, and included a large number of teachers (Artigue 2008a, part 1). According to the ICMI Bulletin 5, 20–24, which analyses the geographical distribution of the participants, these were 655 from 42 countries (https://www.math.uni-bielefeld.de/icmi/bulletin/ICMI_05_04_1975.pdf; also see Becker 1970).

Fig. 3.1

Frontispiece of the proceedings of ICME-1

All the papers of the congress are also published in Educational Studies in Mathematics (1969–1970, Vol. II, 134–418). Presenting the contents of the book, the editors regret that the address of Zoltan P. Diènes, “La mathématique a l’école primaire,” could not be inserted.

Concluding his allocution during the congress, Freudenthal invites the participants

To use this week of scientific and social events as a great opportunity to exchange experiences and ideas, to meet people from nearby and far away, and to enjoy all good things that this country and this city can offer you (Editorial Board of ESM, 1969, p. 6)

So, internationalization was growing.

The contents of the proceedings show continuity with topics born within the CIEAEM (Commission Internationale pour l’Étude et l’Amélioration de l’Enseignement des Mathématiques). In the contributions to ICME-1, we find mention of games, worksheets, films, manipulatives, and the “modern” overhead projector, which allowed lessons to be prepared in advance, to perform movements and overlapping. The use of the above-mentioned tools and of concrete materials is linked with a new methodology that includes working groups and classroom discussion. Frédérique Papy presented the Minicomputer, proposed for primary school. The presence of Dienes is further evidence of the interest of the ICMI community in concrete materials, such as Dienes’s logic blocks, and the beginning of a real interest in primary school. A clear reference to the role of computers in school mathematics is in the contribution by Thwaites (Furinghetti et al. 2008). About this new technology we note that a panel was dedicated to CAI (Computer-Aided Instruction), see (L’Enseignement Mathématique 1970, s. 2, 16, p. 116).

Thwaites was an applied mathematician from Southampton University (UK), and a member of the ICMI Executive Committee. He was involved with the curriculum reforms of the 1960s in his country, and was one of the founders of the School Mathematics Project (SMP). Thwaites observes in the interview he gave to Hodgson that

as the end of the 60s came, and the 70s came, there was a greater emphasis on [...] what one might almost call ‘individual scholarship’, in the field of mathematical education. Mathematical education itself became a kind of academic subject [...] in a way that it wasn’t certainly in the 50s or really in the early 60s. (Hodgson 2008b, part 1)

This observation by Thwaites can be found in the fifth point of the resolutions of the congress, which state that

• 1. The modernization of the teaching of mathematics should be pursued in all countries, both in content and method. “Content and method are inseparable and should be kept continually under scrutiny”.¹

• 2. Collaboration between teachers of mathematics and those of other disciplines should be encouraged.

• 3. Each country should be more fully informed of activities in the other countries. “In particular, the ‘advanced’ countries should continue to collaborate with the developing countries in the search for solutions appropriate to them”.

• 4. It is necessary for the teacher of mathematics to pursue further professional study during his employment.

• 5. The theory of mathematical education is becoming a science in its own right. The new science should receive places in the Universities or Research Institutes.

The first International Congress on Mathematical Education makes the following recommendations to I.C.M.I.:

• 1. To study the problems of national information, in particular that of the creation of an information bulletin;

• 2. To pay more attention, in the next congress, to pre-school education, elementary education, mathematical education for young people of all ages, and adult education (Editorial Board of ESM, 1969, p. 284).

In that period, besides the founding of the new journal Educational Studies in Mathematics in 1968, other journals appeared explicitly devoted to mathematics education: in 1969, the German Zentralblatt für Didaktik der Mathematik (now ZDM –The International Journal on Mathematics Education); in 1970, the USA Journal for Research in Mathematics Education, and the British International Journal of Mathematical Education in Science and Technology (IJMEST). The first two journals cited had links with ICMI: Educational Studies signed a contract with UNESCO (Lehto 1998, p. 259) clearly with ICMI’s assistance (Hodgson 2019); Zentralblatt had ICMI as co-editor (Redaktionskomitee. 1969).

Important international and national initiatives make evident the ferment of those years: after the SMP in the 1960s, in 1968 the above-mentioned Zentrum für Didaktik der Mathematik (Center for the Didactics of Mathematics) was founded in Karlsruhe by Steiner and Kunle, followed in 1973 by the IDM (Institut für Didaktik der Mathematik) founded at Bielefeld University by Heinrich Bauersfeld, Michael Otte and Steiner (see Schubring 2018). In 1969, the first IREMs were established in Lyon, Paris and Strasbourg. Many countries were presenting new syllabi inspired by New Math or by new methodologies. In 1971, Freudenthal himself founded the Institut Ontwikkeling Wiskunde Onderwijs (IOWO, Institute for the Development of Mathematics Teaching) (Furinghetti et al. 2013).

Even though Freudenthal’s presidency lasted only one term, as was usual in those days, he introduced many novelties into ICMI and in mathematics education, so that his influence lasted long time after his presidency. For instance, Thwaites underlines Freudenthal’s predominance over the other people’s view (see Hodgson 2008b, part 1) and Revuz considers him the best President of ICMI at all (interview to Revuz, Artigue 2008c, part 1). “So, it is fair to use the term the “Freudenthal Era”—in the spirit of Bass (2008)—for the years 1967–1980” (Hodgson and Niss 2018, p. 232).

Undoubtedly, such a dominant character had to cause some problems in the relations with IMU. In a letter written on October 15, 1970, to IMU Secretary Frostman, Cartan wrote that Freudenthal caused him worries (Cartan 1970). The reason for Cartan’s worries was that Freudenthal wanted the outgoing ICMI Executive Committee to appoint the International Programme Committee for ICME-2 with only 2 months left of his presidency (Furinghetti and Giacardi, this volume; Furinghetti et al. 2020). This inaugurated some tension between the ICMI President and the IMU leadership, arising again from time to time in the years to come (Hodgson and Niss 2018).

In 1970 and in 1972, the second and third volume of UNESCO’s New Trends in Mathematics Teaching were published (volume I had been published in 1966) (UNESCO 1970, 1972). These books were the result of a cooperation between ICMI and UNESCO and appeared in the UNESCO series devoted to the teaching of basic sciences; the aim was to foster the improvement of mathematics education at all levels and in all regions of the world. The two first volumes consisted of a blend of reprinted materials (as summary or critical reports) and original papers. As stated in the preface of the third volume, a general overview was lacking; moreover the papers were printed either in English or in French, often without even a summary in the other language (UNESCO, 1972, p. 6). It was therefore decided that the third volume be composed of scholarly analyses of the trends in various aspects of an overall educational area (e.g. mathematics education) and published in at least English, French and Spanish. Volume 3 was prepared and discussed during a two-week meeting in Royaumont in September 1971. The contributions referred to all educational levels, from kindergarten to university and to the main mathematical areas (algebra, geometry, analysis etc.) and were assigned to leading experts from different countries (Alan Bishop, Howard Fehr, Freudenthal, Claude Gaulin, Glaymann, Brian Griffiths, M. Hastad, Jeremy Kilpatrick, Anna Zofia Krygowska, A. D. Nijdam, Zolzistaw Opial, Georges Papy, Revuz, Steiner, Willy Servais, János Surányi).

We will see in the following that UNESCO was involved in different ICMI initiatives. As clarified by Jacobsen (1993), UNESCO is not a funding organization, having a reduced budget, so cooperation with ICMI depended upon common purposes. The main areas of cooperation were, besides the editions of the series “New trends in mathematics teaching,” the international meetings cosponsored by the two organizations all over the world and particularly in developing countries (Christiansen 1978).

The interest of UNESCO in the diffusion of scientific culture is evidenced, among other things, by the creation of a mathematics education post, which Bent Christiansen occupied from 1972 to 1976, and Edward C. Jacobsen from 1976 to 1992.

3 ICME-2, Exeter 1972. The Season of the Projects

The period 1971–1974 was chaired by James Lighthill (UK), with Vice-Presidents Shōkichi Iyanaga (Japan) and Surányi (Hungary). The Secretary was Edwin A. Maxwell (UK) and members were Henry O. Pollak (USA) and Sobolev (USSR). As decided by the General Assembly of IMU in 1970, ex officio members were not only the President of IMU (Komaravolu Chandrasekharan (Switzerland)), but also Freudenthal (Netherlands) as Past President of ICMI, Otto Frostman (Sweden) as Secretary of IMU, and André Lichnerowicz (France) as Representative of IMU in the International Council of Scientific Unions (ICSU) Committee on the Teaching of Science (CTS).²

ICME-2 was held in Exeter, 29 August - 2 September 1972.³ The proceedings were edited by Howson. As written on the back cover, the book surveys the work of the conference, and presents a picture of developing trends in mathematical education.

Moreover, we read that there were around 1400 participants from 73 countries (1384 participants and 76 countries, according to ICMI Bulletin 5, 1975: 20–24). The frontispiece shows the photos of George Pólya and Jean Piaget (Fig. 3.2). The proceedings open with a message of Prince Philip, Duke of Edinburgh, who stresses the important work of mathematics educators, in that “it requires real genius to light a flicker of understanding in the minds of those to whom mathematics is a clouded mystery”(Howson 1973, p. V).

Fig. 3.2

Frontispiece of the proceedings of ICME-2

Not all the congress papers appear in the proceedings. As Howson tells, the committee made a selection, also with the idea to give guidelines for further publications in the field (interview to Howson, Hodgson 2008a, part 1).

In his presidential address, Lighthill underlines the importance of the ICMEs:⁴

before their creation the study of mathematical teaching methods and curricula was supplemented and strengthened, among others, by international discussion every four years in the educational section of the International Congress of Mathematicians. Those useful discussions were, nevertheless, rather limited in scope and in the number of interested persons involved (Lighthill 1973, p. 88).

If ICME-1 was the expression of ICMI’s President Freudenthal, ICME-2 can be seen as the expression of the English component of the program and the organizing committee, which included Lighthill himself, Thwaites, Trevor Fletcher and above all Howson. Several English projects had a major part in this congress, SMP in particular (Hodgson 2008b, part 1). In the introduction to the proceedings of ICME-2, Howson discusses the role of laboratories and concrete materials, and the need to reflect on the use of the related teaching methodologies. In Howson’s opinion, educators look at the 1960s as the period of New Math, but the main long-lasting idea of that period was the emergence of new styles of teaching and a more systemic transfer of teaching materials and ideas in the various countries (Howson 1973).

One of the working groups—a new format introduced in ICME 2—deals with the use of television and films in the teaching of mathematics. The tradition already existed, but it was revived thanks to new technologies seen as necessary in mathematics education. At ICME-2, a WG explicitly addressed technology, and we also find Seymour Papert’s “turtle geometry,” aimed at primary school (Furinghetti et al. 2008). From that time on, the programs of ICME always encompassed official activities linked to computers.

Another important feature, already present in ICME-1, were Piaget’s theories. At ICME-2, the written contribution of Piaget, who did not attend the conference, still outlines the analogy of Bourbaki’s three mother structures with the structures of thinking; he ascribes the failure of Modern Mathematics in school to the use of traditional teaching methods based on oral transmission. Both WGs on “Pre-school and primary mathematics” and on “Structure and activity” are linked to Piaget’s experiences. According to Mary Sime, the value of Piaget’s tests is educational rather than diagnostic, because the formation of concepts happens through the use of suitable materials. In his turn, Efraim Fischbein (present in the first two ICMEs) considers that Piaget’s theory is the most important reference in the psychogenetic field, proposing a compromise between the theories of Piaget and Bruner (Howson 1973).

In the introduction to the proceedings, Howson stresses the importance that Piagetian psychology had for elementary school. He also observes that the WG for “the psychology of learning mathematics” was the most attended. According to Howson, the topic dealt with “underpins the whole of mathematics education” (Howson 1973, p. 15). Here we see the premises for the creation in 1976 at ICME-3 of the Study Group PME affiliated to ICMI.

The invited lecture by Pólya comments about a list of quotations about the learning of mathematics, which underline the role of conjectures and intuition before proving.

The two photographs on the cover of the proceedings of ICME-2 summarize the two main issues that emerged in the ICMI community: new methods of doing mathematics in the classroom (Pólya’s photo) and the interlacement with psychology (Piaget’s photo).

The discussion about the identity of mathematics education, or didactics of mathematics—the preferred nomenclature in some countries—continued. Krygowska, for example, in her contribution to the Working Group on teacher training for prospective secondary teachers, which was chaired by Steiner, identified four aspects of didactics of mathematics: a synthesis of the appropriate mathematical, educational, cultural and environmental ideas; an introduction to research; the nature and situation of the child; and practical experience (see Howson 1973). A call for more in-depth research in mathematics education was also present in the plenary of the mathematician Hassler Whitney, who had in mind the failure of New Math.

At ICME-2, New/Modern Math is still a matter of discussion, with positions against and in favour of it. The important contribution by René Thom (1973) stresses the contradiction of a teaching that is heuristic in principle, but is based on abstract mathematics. Thom thinks Piaget too much confident in the potentialities of mathematical formalism: Modern Mathematics has not produced new theorems and, as far as education is concerned, does not produce new knowledge. It has eliminated Euclidean geometry in favour of algebra, but it is exactly Euclidean geometry that connects natural language and abstraction. Because of Thom’s contribution, many authors date the end of Modern Mathematics back to ICME-2 (Furinghetti et al. 2008).

The Executive Committee decided to endorse formally the following resolutions proposed by working groups:

From the working group on “Mathematics in Developing Countries”:

“That all possible encouragement and assistance should be given to developing countries to make changes in their mathematical syllabuses and curricula”. The cultural background of the pupils and the needs of national development are to be taken into account.

From the working group on “Links with other Subjects at Secondary level”: The congress recommends that action be taken in providing support (including financial): to enable teachers of different areas to work together; to publish what has been done in the direction of interdisciplinarity; to encourage individuals and institutions to develop new teaching materials which cross disciplinary boundaries; to produce source materials suitable for use in secondary schools on topics linking mathematics with other subjects.

Moreover the Congress agrees that steps be taken by ICMI to establish a center for the interchange and dissemination of information on all matters of interest in Mathematics Education; and to encourage cooperation between journals in different languages (Howson 1973).

During Lighthill’s term of office, in 1972, the ICMI Bulletin was established as a rather informal means of communication within the “ICMI family” (Hodgson and Niss 2018), appearing in average two times a year. The Bulletin lists the many conferences and symposia organized by ICMI, and thus the many interests that were developing in the field: for instance, the interest toward primary education, testified by the ICMI Symposium about the teaching of mathematics in primary education, held in 1973 in Eger, Hungary (ICMI Bulletin, 2, 1973, p. 5).

Moreover a new policy of holding Regional Symposia “to facilitate wider discussion of mathematical education outside those areas of Europe and America where international meetings on the subject have mainly been held hitherto” (L’Enseignement Mathématique 1975, s. 2, 21, p. 330) was adopted, and numerous symposia were held with the co-sponsorship of the ICMI. Examples are the symposia held jointly with UNESCO, in Nairobi, Kenya (September 1–11, 1974) on “Interactions between linguistics and mathematical education,” and the regional conference about the development of a mathematics integrated curriculum for developing countries, held in New Delhi (India) in December 1975. Still in 1975, the fourth Interamerican conference on Mathematical Education was organized by IACME (Interamerican Committee on Mathematical Education, affiliated to ICMI in 1974) in Caracas Venezuela.

At the IMU General assembly in Canada in 1974, the President Chandrasekharan stated that IMU, as a member of ICSU, is committed to the principle of the free circulation of scientists and that the object of the world mathematical community should be of encouraging the growth of mathematics in the disadvantaged areas of the world. In relation to this, the adopted resolutions expressed the Assembly’s “great appreciation of the activities of ICMI in every aspect of mathematical education, particularly in developing countries, and its hope that this work will grow, and that the mathematical needs of other disciplines will be taken into consideration” (quoted in Lehto 1998, p. 182). IMU also became less dependent on subventions from ICSU and UNESCO due to a different politics regarding the unit contributions, fixed at 600 Swiss Francs (Lehto 1998, p. 182).

4 ICME-3, Karlsruhe 1976. The Birth of Affiliated Study Groups

The term 1975–1978 was chaired by Iyanaga (Japan), the Vice-Presidents were Christiansen (Denmark) and Steiner (Germany). The Secretary was Yukiyoshi Kawada (Japan), the members of the EC⁵ were Edward G. Begle (USA) and Lev D. Kudrjavcev (USSR). There also were four ex officio members: Lighthill (UK) as Past President of ICMI, Deane Montgomery (USA) as President of IMU, Jacques-Louis Lions (France) as Secretary of IMU, and Freudenthal (Netherlands) as Representative of IMU in CTS/ICS.

Iyanaga summarizes as follows the period 1975–1978:

In the wake of the success of the Bourbaki movement, the reform movement of mathematical instruction began in the early 1950s particularly in the U.S. by the SMSG (School Mathematics Study Group) directed by Begle. But the excess of this tendency was warned by mathematicians like André Weil or Morris Kline. In the international politics, on the other hand, the Soviet Union took a quite separate position from the “West” at the time. I believe that the general background of the period 1975–78 was largely like this.

Fortunately, the tradition of the ICMI is rather apolitical (Iyanaga 2001).

The ICME-3 took place in Karlsruhe, from August 16 to 21. The International program committee was chaired by Steiner. The proceedings were edited by Hermann Athen and Kunle (1977) Howson tells—in the mentioned interview by Hodgson—that the congress was very well organized, also thanks to a financial support from UNESCO, being Christiansen the UNESCO representative for high school mathematics (Hodgson 2008a, b, part 4).

In the already mentioned interview by Schubring, Kunle recalls the organization of ICME-3. The preparation lasted 3 years, and much was due to Steiner’s international relations. Germany was well represented in the congress. An interesting aspect concerns the choice of the official languages, which was decided to be four: German, French, English and Russian.⁶ This required to find experts in at least two languages for the chairing of the different sessions in order to help with some translations.

Indeed, as also Lehto underlines, in the ICMEs language was a much bigger problem than at the ICMs: “Mathematics education imposed greater linguistic demands on the speaker and hearer than did the presentation of mathematics. Mathematics educators lacked largely the international terminology and vocabulary of the mathematician and could not resort with equal facility to a universal set of symbols” (Lehto 1998, p. 260). Moreover, we can add that teachers have generally fewer opportunities for international contacts.

Kunle tells that there were about 200 participants from USA, 80 from Japan, 70–80 from Africa. There were also many teachers, and also meetings among teachers. A novelty was the creation of a logo (Fig. 3.3) for the congress, inspired to the hosting city, to mathematics and to ICMI. The proceedings reflected the structure of the whole program, with the main lectures, the sections and poster sessions, the panel discussion, the working groups (still called Exeter working groups), study groups, workshops, the projects, films and exhibitions. The Survey reports and the list of participants were in separate booklets. The main work of the congress was focused on 13 sections, each opened by a survey report. The proceedings contain only a summary of the results, which were later collected in Vol. IV of the series published by UNESCO, New trends in mathematics teaching (1979), prepared by the ICMI. As was the case for volume 3 of the same series, it was decided to link the papers of the fourth volume to the results of a conference (in this case the sections of ICME-3), with further meetings before and after the congress (UNESCO 1979, p. 2). The intense work of collaboration between ICMI and UNESCO that brought to the edition of what can be considered the true proceedings of ICME-3 is well described by Christiansen (1978). The planning of the volume started at the end of 1974 with an Advisory Meeting in Paris. It was decided that the volume should deal with broad topics of interest for mathematics teachers and educators: thirteen themes were identified, some of which were divided according to school levels. For each theme, a section should be established at the Karlsruhe Congress, the report being prepared by an international specialist, and later developed for Vol. IV of the series published by UNESCO.

Fig. 3.3

The logo for ICME-3

A particular role was also played by the projects: in the proceedings of ICME-3, the presentation of 15 projects is mentioned, among them SMP, IOWO, the Open university, IREMs. Many of them were already present in Exeter.

The Resolutions of the congress can be summarized as follows:

• (a) ICMI should continue and increment its cooperation with other associations devoted to furthering mathematical and scientific education.

• (b) National Subcommittees if ICMI should be reactivated. In fact many countries are not active in both matters of national concern and in international cooperation and contacts.

• (c) Internationally composed committees, working groups and study groups have been established in order to study and further particular areas of research in mathematical education, as HPM or PME. These are invited to continue their work. Moreover it is recommended that the theme “Women and Mathematics” be an explicit theme of ICME 1980.

An important moment of the congress was the establishing of the first Study Groups affiliated to ICMI: HPM (the International Study Group on the relations between the History and Pedagogy of Mathematics) and PME (the International Group for the Psychology of Mathematics Education). As to the first one, its history started with a working group at ICME-2 in 1972, where “there occurred a confluence between growing interest within the mathematics education community (seen notably in the NCTM’s celebrated 31st Yearbook of 1969, Historical Topics for the Mathematics Classroom) and an increased readiness of international bodies to take such interests and concerns on board” (Fasanelli and Fauvel 2008). Also concerning PME “the impetus to develop an organization with a psychological focus on mathematics education began much earlier when, in 1969 at the first International Congress on Mathematics Education […], Fischbein was invited by then ICME President Freudenthal to chair and organize a round table on the psychological problems of mathematics education. Fischbein, a cognitive psychologist and, at that time head of the department of Educational Psychology at the University of Bucharest (later he served as head of the Science Education Department at Tel Aviv University), was keen to take up Freudenthal’s call to improve mathematics education in schools by going beyond philosophical discussions of mathematics teaching and learning to advocating empirical scientific research in the field” (Nicol and Lerman 2008).

In 2008, ICMI’s organization included five permanent Affiliated Study Groups, each focusing on a specific field of interest and study in mathematics education consistent with the aims of the commission. The Affiliated Study Groups are neither appointed by ICMI nor operate on behalf or under the control of ICMI. They are thus independent of ICMI for their work, also in terms of finances, but they collaborate with ICMI on specific activities, such as the ICMI Studies or components of the program of the ICMEs. They present reports on their activities to the General Assembly of the ICMI (Bass and Hodgson 2004).

In 1977, the first conference of the Affiliated Group PME took place in Utrecht, with the opening address of Freudenthal (Freudenthal 1978). In the same issue of Volume 9 (1978), the lectures of the conference were published.

During those same years, the ICMI Secretary was the Japanese Kawada, who initiated the Southeast Asian Conference on Mathematical Education (SEACME) series in 1978 with the inaugural conference in Manila. This conference, sponsored by ICMI and SEAMS (Southeast Asian Mathematical Society), was very important for the involvement of the Eastern countries in the international movement of math education (see Lim-Teo 2008).

Whilst secondary education received most of the attention in the first 50 years of ICMI, primary and tertiary education now entered the field of interest as well. The already mentioned volume of UNESCO (1979), reflecting the Sections of ICME-3, contains chapters devoted to all school levels. Moreover, it contains chapters on the goals of mathematics teaching (by Ubiratan D’ Ambrosio), on applications (by Pollak) and on algorithms (by Arthur Engel), which went beyond the teaching of established mathematical areas and topics.

In 1978, the BACOMET (Basic Components of Mathematics Education) group was initiated by Christiansen, Howson and Otte, elaborating research for improving teacher education.

5 ICME-4, Berkeley 1980. ICME Crosses the Ocean

Whitney (USA) was the President of ICMI in the period 1979–1982, Vice-Presidents were Christiansen (Denmark) and Ubiratan D’Ambrosio (Brazil). The Secretary was Peter Hilton (USA), and members were Stanley H. Erlwanger (Canada), Bernhard H. Neumann (Australia) and Zbigniew Semadeni (Poland). The ex officio members were Iyanaga (Japan) as Past President of ICMI, Lennart Carleson (Sweden) as President of IMU, Lions (France) as Secretary of IMU. The representative of IMU in CTS/ICSU was Christiansen, who was already in the EC as Vice-President.⁷

After the Indian Ram Behari (appointed as an officer in 1955) and the Japanese Yasuo Akizuki (appointed in 1959), Iyanaga and Kawada we see again a step forward toward internationalization with the appointment of the Brazilian D’Ambrosio from South America and Neumann from Australia as members of the ICMI EC.

The congress ICME-4 was held in Berkeley, California, USA, August 10–16. The proceedings were edited by Marilyn J. Zweng, Thomas Green, Kilpatrick, Pollak, and Marilyn Suydam (1983). According to the introduction to the proceedings, attendance was about 1800 full and 500 associate members from about 90 countries. In the acknowledgments, Zweng states that it is the first time in the history of ICMEs that all submitted papers were published. To stay within page limits, the editors often had to delete several pages or paragraphs of the submitted papers, without the approval of the authors. The chair of the International Program committee was Pollak. Pollak was an applied mathematician, director of the mathematics group at Bell Labs. He was, throughout his career, interested in mathematics education, with a major focus on mathematical modelling, a field he did much to implant in the school curriculum (Bass 2008, p. 14). He was also an active participant in the School Mathematics Study Group (SMSG) directed by Begle, one of the main American expressions of the “New Math” movement. He was active in ICMI affairs, serving on its Executive Committee in 1971–74 and in 1983–86 (Bass 2008).

The volume of the proceedings consists of thematic chapters, each with short contributions; it is not possible to distinguish within working and study groups, mini-conferences etc. One of the chapters is devoted to critical variables in mathematical educations, in memory of Begle. A version of the plenary by Freudenthal appeared in Educational Studies in Mathematics, 12, 1981, 133–150. Pólya was not able to attend the conference, and his short address was delivered by Gerald L. Alexanderson.

For the first time, no resolutions appear, there is no Presidential Address (at least not in the proceedings), and ICMI is not even mentioned. The logo of the congress is shown in Fig. 3.4.

Fig. 3.4

The logo for ICME-4

We still find echoes of the debate about New Math, in particular in the discussion about the movement Back to Basics, contained in Chap. 2 “Universal Basic Education” (Sobel 1983). Pólya’s brief abstract in the proceedings does not refer to problem-solving. But Pólya’s problem-solving—which arises from the tradition of mathematicians reflecting on their own work—was the argument of one of the 38 chapters and would become a dominant theme in the successive ICMEs and in mathematics education up to the present day.

According to Lehto, the period 1979–1982 suffered from a lack of adequate administration. Lehto considers the professional competence of Whitney and Hilton “in striking contrast to the Commission’s inefficient administration” (Lehto 1998, p. 258). The ICMI Bulletin even ceased to appear. Undoubtedly, the term of Whitney as President and Hilton as Secretary was a problematic one with reference to the relations between IMU and ICMI, and also to ICMIs internal relationships. In the minutes of a meeting of the IMU Executive Committee held in 1980, we can read: “The EC expresses concern about the lack of communications between IMU and ICMI.” And again in 1981: “Much concern concerning the difficulties that arose in the [ICMI] EC.” (IMU EC Minutes 1980, p. 14, and 1981, p. 25, quoted in (Hodgson and Niss 2018, p. 234)).

Indeed during Whitney’s term the EC met only rarely; moreover Hilton felt that his role as Secretary be confused with that of a clerk rather than that of an organizer and decision-making executive officer. He expressed this in a letter to IMU Secretary Lions: “It is clear to me that I was expected by some of my colleagues on the EC to act purely in a ‘secretarial’ capacity”(Hilton 1980). That perception had led Hilton to present his resignation from his office. However, this resignation did not materialize and Hilton finally remained as the ICMI Secretary till the end of his term. Another controversial theme was due to the fact that members of the ICMI EC put forward as their candidate for the next President the Danish mathematics educator Christiansen, ICMI Vice-President for two terms since 1975. Instead, the IMU President Carleson, in a letter to the ICMI EC at the end of 1981, expressed the desire to have as next President a well-known mathematician with established interests in education. Reporting the letter, Hodgson and Niss comment—paraphrasing Clemenceau⁸—that for the IMU officers “mathematics education was far too important to be left to the mathematics educators” (Hodgson and Niss 2018, p. 235).

Important events in that period were the creation of the journals For the Learning of Mathematics (FLM) and Recherches en Didactique des Mathématiques (RDM), both in 1980.

In 1980, the ICMI General Assembly set up an IMO (International Mathematical Olympiad) Site Committee. Its task was to ensure that annual IMOs were held to assist the host country. It was customary that the appointments of the members to the Site Committee followed nominations by the IMO jury. “Although ICMI has no responsibility for financing and organizing the Olympiads, a link was thus created between it and the IMOs” (Lehto 1998, p. 263).

In 1982, new terms were adopted by the General Assembly of IMU, there is no longer mention to members at large; moreover, the ex officio members are said to belong to the EC. The rest is quite unchanged:

• (a) The Commission shall consist of

  • 1. the members of an Executive Committee as specified in (b) below, elected by IMU, and

  • 2. one national delegate from each member nation as specified in (d) below.

• (b) The Executive Committee consists of four officers, namely, President, two Vice-Presidents, and Secretary, and of three further members. Furthermore, the outgoing President of ICMI, the President and the Secretary of IMU, and the representative of IMU at CTS (ICSU) are members ex-officio of the E.C.

• (c) In all other respects the Commission shall make its own decisions as to its internal organization and rules of procedure.

• (d) Any National Adhering Organization wishing to support or encourage the work of the Commission may create, or recognize, in agreement with its National Committee, a National Sub-Commission for ICMI to maintain liaison with the Commission in all matters pertinent to its affairs. The National Adhering Organization in question shall designate one member of the said Sub-Commission, if created, to serve as a delegated member of ICMI as mentioned in (a).

The new terms were to be implemented by the next President (ICMI Bulletin, 13, February 1983, 5).

6 ICME-5, Adelaide 1984. The Birth of Ethnomathematics

The next President, for the period 1983–1986, was Jean-Pierre Kahane (France), Vice-Presidents were Christiansen (Denmark) and Semadeni (Poland). The Secretary was Howson (UK). Other members were Bienvenido F. Nebres (Philippines), Michael F. Newman (Australia), Pollak (USA). The ex officio members were Whitney (USA) as Past President of ICMI, Jürgen Moser (Switzerland) as President of IMU, Lehto (Finland) as Secretary of IMU and Henri Hogbe-Nlend (Cameroon) as the representative of IMU in CTS/ICSU.

The 1984 ICME congress was held in Adelaide, Australia, August 24–30 (logo in Fig. 3.5). The proceedings were edited by Marjorie Carss (1986).

Fig. 3.5

From the frontispiece of the proceedings of ICME-5

In the interview by Artigue, Kahane mentions with great interest the Australian Mathematical Competitions (Artigue 2008b, part 2). Indeed, they were directed to a large number of students and were based on the principle that every student can find a challenge somewhere (Kahane, ICMI Bulletin 47). May be that this can be one of the reasons for the attribution to Adelaide of the organization of ICME-5. But no particular reference to the competitions appears in the proceedings, with the exception of a dedicated Topic Area, which anyway existed also in previous ICMEs. Only, on that occasion, a first proposal for a Federation of National Competitions was made (in 1994, the Federation would become affiliated to ICMI). According to the Foreword, attendance numbered more than 1800 participants from over 70 countries. In the proceedings, there is the list of participants. In addition to the working sessions, there were three major plenary addresses, several specially invited presentations, and over 420 individual papers in the form of short communications, either as posters or brief talks. In addition, there were a variety of exhibits, film and video presentations, and workshops. In all, more than half of those attending the congress made a direct contribution to the scientific program.

Most of the presentations and papers prepared for ICME 5 are not included in the proceedings. The Presidential Address by Kahane is in fact a plenary about “Mesures et dimensions.” In the Public Forum, as well as in the Specially Invited Presentations, some local situations about the teaching of mathematics are presented. The other two main invited addresses are held respectively by Pollak on the effects of technology on the curriculum and Phillip Davis about the nature of proof. Plenary lectures were held by Kilpatrick (“Reflection and recursion”), Renfrey Potts (“Discrete mathematics”), and d’Ambrosio (“Sociocultural bases of mathematical education”).

This latter lecture represents a milestone, namely, the beginning of ethnomathematics. Some days before, the first Satellite meeting of HPM had taken place in Adelaide and d’Ambrosio had underlined the need to develop three separate histories of mathematics: “history as taught in schools, history as developed through the creation of mathematics, and the history of that mathematics which is used in the street and the workplace. In the plenary at ICME 5 he introduced the concept of ‘ethno mathematics’ as compared to ‘learned mathematics’ to deal with these differences (see Fasanelli and Fauvel 2008).”

According to Hodgson and Niss (2018) the—perhaps implicit—mandate of Kahane and Howson was to put ICMI back on track, or at least to revitalize ICMI (also see the interview to Kahane, Artigue 2008b).

Kahane (1926–2017) was a French mathematician of the first rank. During his long career at the University of Orsay, he extensively contributed to the development of mathematics knowledge in many fields such as analysis and probability. He also played a role in mathematics education: the French Minister of Education asked him to chair what came to be called the “Commission Kahane,” charged to bring recommendations for revision of the mathematics programs in the French schools (see https://smf.emath.fr/publications/jean-pierre-kahane-numero-special-gazette). Bur, already before, as ICMI President he had shown interest and deep understanding in topics that concerned the role of computers in mathematics education (Kahane 1987), in mathematics as a service subject (Kahane 1986a, b) and in general in the developments of mathematics education (Kahane 1988a). These topics provided the subject for the first ICMI studies. More than that, Kahane was “a thinker and communicator of philosophical depth, elegance, and eloquence” (Bass 2008, p. 20), qualities that made him an exemplary President of ICMI, from 1983 through 1990.

One of the first decisions, took in Adelaide, was that the program committee for the next ICME be elected by the Executive Committee of ICMI (interview to Howson, Hodgson 2008 a, part 4), thus becoming international rather than local.⁹ As a consequence, ICME becomes even more emanation of ICMI.

One of the problems of such a decision was a financial one, as it required travelling—other kinds of communication were not easy at that time—and ICMI did not have big incomes. The travel expenses also concerned the meeting of the EC, which became more frequent than before, namely about twice a year. Even more frequent were the meetings between Howson and Kahane (Hodgson 2008a, part 4).

Kahane tried to involve more people in ICMI and he had the merit to establish good relationships with IMU and obtain a wider support. As Howson tells, the fact of taking on responsibilities like a major involvement of the EC helped in gaining a stable recognition from IMU. Christiansen, who had been Kahane’s competitor for the presidency of ICMI, admitted that he would never have reached what Kahane managed to do (Interview to Howson, Hodgson 2008a, part 4).

Another novelty of the Kahane-Howson term was the series of the ICMI studies, starting in 1984. The ICMI studies replaced the former tradition of the international inquiries (Furinghetti and Giacardi 2010). In general, an ICMI study focuses on an issue of current interest in mathematics education. Here too, an international program committee is established, which launches the Study through a Discussion Document published in L’Enseignement Mathématique and in other journals; researchers submit their contributions on the theme of the Study; on the basis of the contributions received, the Committee delivers the invitations to the ICMI Study meeting to about 80 participants; at the end, a book (the ICMI Study volume) is published to disseminate the results. The whole process lasts about 3 years. Kahane tells that the idea had already been discussed with Whitney, in 1982 (Kahane 2001).

The first ICMI Studies dealt with the following topics:

• 1. The Influence of computers and informatics on mathematics and its teaching (Strasbourg, France, 1985).

• 2. School mathematics in the 1990s (Kuwait, 1986).

• 3. Mathematics as a service subject (Udine, Italy, 1987).

• 4. Mathematics and cognition (book prepared by PME, an Affiliated Study Group of ICMI), 1990.

The first one was held in Strasbourg, France, in March 1985. The resulting book was edited by Robert F. Churchhouse, Bernard Cornu, Howson, Kahane, van Lint, François Pluvinage, Antony Ralston, and Masaya Yamaguti in 1986 as first volume of the ICMI Study Series, published by Cambridge University Press. A second edition was published by UNESCO in 1992, edited by Bernard Cornu and Anthony Ralston (Science and Technology Education No. 44).¹⁰

The second ICMI Study was not launched by a discussion document, the Study Volume was prepared by the editors Howson and Bryan Wilson following a closed international seminar held in Kuwait in February 1986. It was again published by Cambridge University Press as volume 2 of the ICMI Study Series.

The third Study Conference was held in Udine, Italy, in April 1987, see (Kahane 1986a, b). The Study Volume was published in 1988, edited by Howson, Kahane, Pierre Lauginie and Elisabeth de Turckheim. Moreover, a volume of Selected Papers on the Teaching of Mathematics as a Service Subject was published by Springer Verlag in 1988, edited by Richard R. Clements, Lauginie and de Turckheim (CISM Courses and Lectures No. 305).

Also the fourth study was not the result of a general study conference, the Study Volume was prepared under the responsibility of PME and published by Cambridge University Press in 1990, edited by Pearla Nesher and Jeremy Kilpatrick.

The themes 1, 2, 4 of the ICMI studies exactly reflected the wishes respectively of Kahane, Howson and Christiansen (Hodgson 2008a, part 4)

And so, this first study served me as a model for what followed. The principle of the studies was this, as stated in English in the prefaces of the first studies. It is a question of identifying subjects that are, if not ‘on fire,’ at least ripe for a serious international study. And that we preside over such a study, that we provide the state of the art, but that we never make recommendations. The principle is that the study should provide a survey of the problems, and possibly the elements of solutions, but never a solution with an ‘ICMI’ label (from the interview to Kahane by Artigue, translated in Bass 2008, p.19).

Many other activities such as conferences and working sessions were organized, edited and published by the Affiliated Study Groups of ICMI (see ICMI website: https://www.mathunion.org/icmi/organization/affiliated-organizations).

Under Kahane’s presidency, old links were renewed and strengthened: in 1983, Kahane and Howson joined the editorial board of L’Enseignement Mathématique (hereafter EM), which then started publishing discussion documents for the newly instituted ICMI Studies.

In 1987, a new study group was affiliated to ICMI, namely the IOWME – The International Organization of Women and Mathematics Education. According to Nancy Shelley, the history of the group started as early as in 1976 at ICME-3 in Karlsruhe, at a meeting arranged during the course of that congress to discuss the question of “Women and Mathematics.” The calling of that meeting was initiated by two Australian women, Jan Kennedy and Nancy Shelley, who were struck by the lack of representation of women as speakers, panel members or presiders, despite the fact that nearly 50% of those attending the congress were women. As Shelley (2008) put it

Eight years later, a somewhat more enlightened view is taken about women and the study of mathematics, and it is now acknowledged that much human potential is being lost by the fact that so few women consider mathematics to be a subject for them to study. It may, therefore, be a surprise to some to learn what the reaction was to the calling of that first meeting, to holding it, and to its outcomes. For the record, however, it needs to be told.

As a subcommission of IMU, ICMI has always been apolitical and succeeded in staying out, for instance, of the long debate over China’s entry into the IMU. But surely the organization since 1969 of international congresses on mathematics education increased ICMI’s sovereignty. Lehto (1998) observed that this became manifest in 1986, when a movement began to bar the Republic of South Africa from the activities mounted under ICMI auspices. This would have been in violation of the non-discrimination policy of the ICSU, to which IMU and thus ICMI belong. The decision finally taken by the Executive Committee was that ICMI, as well as the affiliated study groups, should abide by ICSU’s rules.

Nevertheless, the EC condemned the apartheid policies of the South African regime and, in the ICMI Bulletin of June 1986, members of the EC expressed their different opinions about changing or keeping ICSU’s rules. Christiansen was in favour of changing the rules and considered South African apartheid not as a political issue, but as a question of human rights. Howson, though understanding Christiansen’s opinion, believed however that, on balance, ICMI had more to lose than to gain from banning South Africans (Lehto 1998, p. 261).

7 ICME-6, Budapest 1988. The Legacy of Tamás Varga

For the first time ICMI President and Secretary had the opportunity for a long-term planning. Indeed, in the period 1987–1990, both Kahane and Howson were reconfirmed. The remaining members of the EC changed: the new Vice-Presidents were Lee Peng-Yee (Singapore) and Emilio Lluis (Mexico). Members were Hiroshi Fujita (Japan), Kilpatrick (USA), Mogens Niss (Denmark) and the ex officio members were Ludwig Faddeev (USSR) as President of IMU, Lehto (Finland) as Secretary of IMU, Jacobus H. van Lint (Netherlands) as representative of IMU in CTS/ICSU.

ICME-6 was held in Budapest, July 27 to August 30. The chair of the Hungarian Organizing Committee was Janos Szendrei, the chair of the IPC and of the Janos Bolyai Mathematical Society was Akos Csaszar. The proceedings were edited by Ann and Keyth Hirst (1988) (see the frontispiece in Fig. 3.6). No date of printing is indicated. According to the Foreword, there were 2414 registered participants from 74 countries.

Fig. 3.6

Frontispiece of the proceedings of ICME-6

The general pattern used in Adelaide was followed (in particular, the action groups are the same as the fifth congress). The reports of the Action and Theme Groups and of the topic Areas form the major part of the volume. An additional aspect of the groups’ work was the provision, in a number of cases, of a related Survey Lecture.

The congress included also national presentations, exhibitions, poster presentations and short oral communications. Two books of abstracts were prepared for congress participants. The editors also write that the range of topics in these presentations was wide, the use of video materials was represented, but little emphasis was given to computers.

An invisible architect of this conference was the well-known mathematics educator Tamas Varga. Varga had played a particular role at ICME-2 in Exeter in that he was one of the reviewers who decided about the papers to be accepted in the proceedings (Howson contribution delivered by video at the conference Varga 100, Budapest 2019). Moreover, Howson met him often when travelling to Budapest during the organization of ICME-6. But he died in November 1987. The Topic Area 5 about “Comparative Education,” in which Varga appears as Hungarian coordinator together with Douglas Quadling, became in fact a meeting in the congress dedicated to him, in recognition of his outstanding contributions to international cooperation in mathematics education (Quadling 1988).

Another eminent Hungarian was remembered with more emphasis in the President’s address, namely Pólya, died in 1985 (Kahane 1988b).

Of particular importance was the Fifth Day Special about “Mathematics, Education and Society,” the question of the interrelation between mathematics education and educational policies became the issue of a whole day. The contributions to this point were published in a separate book (Keitel et al. 1989) with the support of UNESCO.

The ICMI studies launched in this period were the numbers

• 5. The Popularization of Mathematics (Leeds, UK, 1989), edited by Howson and Kahane and published in 1990 by Cambridge University Press;

• 6. Assessment in Mathematics Education (Calonge, Spain, 1991). Two volumes were edited by Mogens Niss and published by Kluwer in 1993, appearing as volume 1 and 2 of the New ICMI Study Series (NISS): Cases of Assessment in Mathematics Education, and Investigations into Assessment in Mathematics Education.

The duo Kahane–Howson was very appreciated (Lehto 1998) and, in particular, Kahane praised Howson: “We had a very good and active Executive Committee, full of ideas and easy to chair, because everything was thought, planned and prepared by Geoffrey Howson” (Kahane 2001, p.1; also see Kahane 1988a).

The year 1990 was the year of the retirement of Kahane as ICMI President. Bass (2008) lists the particularly insightful observations on mathematics and mathematics education that he offered in that occasion:

In no other living science is the part of presentation, of the transformation of disciplinary knowledge to knowledge as it is to be taught (transformation didactique), so important at a research level.

In no other discipline, however, is the distance between the taught and the new so large.

In no other science has teaching and learning such social importance.

In no other science is there such an old tradition of scientists’ commitment to educational questions (Bass 2005, p. 417).

But Kahane’s farewell message also pointed to open problems, as the fact that contacts between the ICMI Executive Committee and the National Representatives were far from satisfactory. According to him, it was not always clear who the National Representatives are, how they react to the ICMI Bulletin, if they do pass on the information (Kahane 1990).

8 ICME-7, Quebec 1992. The Solidarity Program

The period 1991–1994 was chaired by Miguel de Guzmán (Spain) with Mogens Niss (Denmark) as Secretary, Vice-Presidents were Kilpatrick (USA) and Peng-Yee (Singapore). The three members were Yuri L. Ershov (Russia), Eduardo Luna (USA) and Anna Sierpinska (Canada). Ex officio members were Kahane (France) as Past President of ICMI, Lions (France) as President of IMU, Jacob Palis (Brazil) as Secretary of IMU and van Lint (Netherlands) as Representative of IMU in CTS/ICSU. For the first time, the Executive committee includes a woman: Anna Sierpinska.

ICME-7 was held in Québec-city from August 17 to 23 (see the logo in Fig. 3.7). Attendance was about 3500 participants from 94 countries. The proceedings were edited by Gaulin, Hodgson, David Wheeler, John Egsgard (1994), while David Robitaille, Wheeler and Carolyn Kieran (1994) edited the selected lectures. The first and the second volume (containing the lectures) have a preface describing the structure (plenaries, topic groups, working groups, etc.) and the organization that is becoming the norm for the ICME congresses. In the presidential address, de Guzmán stresses the need for a Solidarity Program and a Solidarity Fund in Mathematics Education. In his concluding address, the Secretary-General Niss reminds the audience that the ICMEs are held on behalf of and under the auspices of ICMI. He gives a survey on the activities of ICMI and underlines the complexity of the field of mathematics education. Moreover, we observe the complex organization of such an event. There is an International Program committee (IPC) appointed by ICMI and a National Organizing Committee run by the host country. David Wheeler chaired the IPC, Hodgson chaired the National Organizing Committee, while Gaulin chaired the Local Organizing Committee. In addition, Robitaille chaired the Executive Committee.

Fig. 3.7

The logo of ICME-7

A relevant role was played by Gaulin. ICME-7 can be seen in many ways as “his” congress. “Even the fact that ICMI accepted the invitation of the Canadian community to host the congress in Québec is undoubtedly connected to Claude himself and to his deep and practical knowledge of the ICMI culture, tradition and expectations. He knew exactly what it means to organize an ICME and all the details that need to be attended. He was the mainspring behind the setting-up, in Canada and more particularly in Québec, of an infrastructure ensuring the success of the enterprise” (Dionne and Hodgson 2020, p. 15/ section 11).

The Solidarity Program in Mathematics Education, strongly desired by de Guzmán, was based on two points:

The first objective of the Solidarity Fund was to increase, in a variety of ways, the commitment and involvement of mathematics educators around the world in order to help the progress of mathematics education in those parts of the world where there is a need for it that justifies international assistance and where the economic and socio-political contexts do not permit adequate and autonomous development. This initiative thus aims to foster solidarity in mathematics education between well-defined quarters in developed and less-developed countries. Particular emphasis is placed on projects that enable the activation of a self-sustainable infrastructure within mathematics education in the region, country, or province at issue. Central to this program of international assistance was the establishment of a fund to provide financial support for the approved projects. The Solidarity Fund is based on voluntary donations from individuals and organizations and is kept separate from the ICMI’s general funds.

The second component of the ICMI Solidarity Program aims at having a balanced representation from all over the world among the presenters and the general participants in activities such as the ICMI Studies or the ICME’s (Bass and Hodgson 2004).

In 1994, one more study group was affiliated to ICMI, namely the WFNMC – The World Federation of National Mathematics Competitions. As Peter Kenderov states, WFNMC was founded through the inspiration of Peter O’Halloran from Australia, who realized that there was a need “for an international organization to exchange ideas and information on mathematics competitions as well as to give encouragement to those mathematicians and teachers who are involved with the competitions.” The proposal had already been made at ICME-5 in Adelaide, Australia, in 1984 (Kenderov 2008). Also see the paper by Kahane in (ICMI Bulletin 47, 1999).

Three more ICMI studies were launched in that period:

• 7. Gender and Mathematics Education (Höör, Sweden, 1993); the Study Volume was published by Kluwer Academic Publishers in 1996, and edited by Gila Hanna with the title Towards Gender Equity in Mathematics Education, (New ICMI Study Series 3). A separate book with the Proceedings of the Study Conference was published by Lund University Press in 1995 (outside the ICMI studies series) edited by Barbro Grevholm and Hanna.

• 8. What is Research in Mathematics Education and what are its Results? (College Park, USA, 1994). The proceedings were edited in 1998 by Sierpinska and Kilpatrick with the title Mathematics Education as a Research Domain: A Search for Identity (2 voll., NISS 4)

• 9. Perspectives on the Teaching of Geometry for the 21st Century (Catania, Italy, 1995). The Study Volume was published in 1998 and edited by Carmelo Mammana and Vinicio Villani with the same title (NISS 5).

With reference to the Study no. 7, Kahane remembers an episode (interview to Kahane, Artigue 2008b; also mentioned in Pollak, Niss, and Kahane 2004): in 1993, at Höör in Sweden, before the ICMI Study on Gender and Mathematics Education, there was a special session in the morning, prepared by the organizers in order to emphasize that there was a problem in the gender composition of the ICMI Executive Committee. All members of the EC who were present were invited to sit on the platform, all men, in front of an audience of women.¹¹ The lesson was clear, and the ICMI EC was renewed later with a fair participation of women.

In 1992, Jacobsen, having reached UNESCO’s retirement age, left the mathematics education post at UNESCO after 18 years. In this long period, UNESCO’s collaboration with ICMI had continued by helping in the organization and financing of ICMEs and especially the ICMI regional groups in Latin America, Southeast Asia, and Africa (IACME, SEAMS, and AMU) (Jacobsen 1993). It was Jacobsen who decided to replace in the 1980s the series “New Trends in Mathematics Teaching” with more frequent studies on mathematics education, merged into the series “Science and Technology Education,” which was published in English and Spanish (Jacobsen 1996). These latter volumes stemmed out from different occasions, for instance Mathematics for All came out from Theme Group 1 at ICME 5 (Damerow et al. 1986) and Mathematics, Education and Society summarized the special day at ICME 6 on the political dimension of mathematics education (Keitel et al. 1989, see above).

The involvement of UNESCO through Jacobsen favoured the success of the regional conferences and brought to major cooperation with the local governments. A result was, for instance, the creation of a Faculty of Education at the University of Botswana. Jacobsen was awarded in 2011 by IACME of the Luis Santaló Medal for his international commitment to mathematics education.

9 ICME-8, Sevilla 1996. Regular Lectures, for All Tastes

The period 1995–1998 featured again de Guzmán (Spain) as President and Niss (Denmark) as Secretary. Vice-Presidents were Kilpatrick (USA) and Sierpinska (Canada). The members were Colette Laborde (France), Gilah Leder (Australia), Carlos E. Vasco (Colombia), Zhang Dianzhou (China). The ex officio members were David Mumford (USA) as President of IMU and Palis (Brazil) as Secretary of IMU.

Attendance to the ICME-8 Congress was about 3500 participants from 98 countries (see the logo in Fig. 3.8). The proceedings were edited by Claudi Alsina, José María Alvarez, Niss, Antonio Pérez, Luis Rico, and Anna Sfard (Alsina et al. 1998a, b). In the preface to the second volume (the Selected Lectures), Hodgson (for the Editing Committee: Alsina, Alvarez, C. Laborde and Pérez) reports that the IPC decided to maintain the practice introduced at ICME-7 of having a significant number of lectures. Therefore, in addition to the plenary lectures, the working groups and topic groups, there were about sixty invited Regular Lectures, a selection of which (33) was published in Volume 2. This large number was necessary as they reflected the many research areas in which mathematics educators were split.

Fig. 3.8

The logo of ICME-8

Two more ICMI studies were launched in that period:

• 10. The Role of the History of Mathematics in the Teaching and Learning of Mathematics (Luminy, France, 1998). The Study Volume was published in the year 2000, edited by John Fauvel and Jan van Maanen with the title History in Mathematics Education: The ICMI Study  (NISS 6).

• 11. Teaching and Learning of Mathematics at University Level (Singapore, 1998). The proceedings were edited by Derek Holton and published in 2002 (NISS 7). Selected papers presented at the Study Conference were published as a special issue of the International Journal for Mathematical Education in Science and Technology (31: 1-160, 2000).

Pursuing the goal of having a balanced representation at the ICMEs, ICMI implemented—starting with ICME-8—a general policy of forming for each ICME an ICME Solidarity Fund established by setting aside 10% of the registration fees in order to provide grants to congress delegates from non-affluent countries. Bass and Hodgson (2004) report that at each of the recent ICMEs, some 100 to 150 participants from economically challenged regions of the world have thus been given financial support to facilitate their presence at the congress. Another way to involve non-affluent countries is through the organization of the ICMI Regional Conferences, which continued despite the acquired international nature of ICMI’s position. These meetings are supported morally by the ICMI and sometimes with modest financial contributions as well. In 1999, the SEACME-8 – eighth South East Asian Conference on Mathematical Education was organized in Quezon City, Philippines.

Kahane (Interview to Kahane, Artigue 2008b, part 3) praised very much the work of the duo de Guzmán–Niss, while Hyman Bass praised the dedication, skill, and efficacy in advancing the work of ICMI of the secretaries Howson, Niss, and later Hodgson. “Each of them, in his own right, has been a major international figure in mathematics education. One cannot overestimate the debt that the ICMI community owes them, as each of the ICMI Presidents will readily bear witness” (Bass 2008 p. 23).

10 ICME-9, Tokyo 2000. Grants to Support Mathematics Education

In the period 1999–2002, the President was Hyman Bass (USA), with Bernard R. Hodgson (Canada) as Secretary. Vice-Presidents were Néstor Aguilera (Argentina) and Artigue (France). Four more members composed the EC: Leder (Australia), Yukihiko Namikawa (Japan), Igor F. Sharygin (Russia), Jian-Pan Wang (China). Ex officio members were de Guzmán (Spain) as Past President of ICMI, Palis (Brazil) as President of IMU, Phillip Griffiths (USA) as Secretary of IMU.

The participants to the ICME-9 conference were about 2300 from more than 70 countries (the logo is shown in Fig. 3.9). The proceedings were edited by Hiroshi Fujita, Yoshihiko Hashimoto, Hodgson, Peng Yee Lee, Stephen Lerman, and Toshio Sawada (Fujita et al. 2004). The International Program Committee was chaired by Fujita, the National Organizing Committee was chaired by Ken-Ichi Sugiyama. The congress was supported by the Science Council of Japan, led by Rector Yoshikawa.

Fig. 3.9

The logo of ICME-9

In the presidential address, Bass states:

the great challenges now facing mathematics education around the world demand a much deeper and more sensitive involvement of disciplinary mathematicians than we now have, both in the work of educational improvement and in research on the nature of teaching and learning. There are many things that have impeded such boundary crossing and collaboration, such as the need to reconcile language, epistemology, norms of evidence, and, in general, all of the intellectual and attitudinal challenges that face multidisciplinary research and development. ICME-9 brings together people who know and understand different things, to learn from each other, and hopefully to foster collaboration (Fujita et al. 2004, p. XV)

In his closing remarks, the Secretary Hodgson observes that a great part of grant funds for non-affluent countries comes from individual domestic donations, the majority of these from persons not participating in ICME 9 but wishing to support mathematics education (Fujita et al. 2004, p. 391).

In the meeting of April 2002 in Paris, new Terms of Reference for ICMI were approved by the Executive Committee of the International Mathematical Union. Among the modifications is a change in nomenclature regarding the position of “Secretary,” which was now designated by the term “Secretary-General,” as it was in the past (see ICMI Bulletin 51, 2002: 8–12). Moreover, the members of ICMI are now countries and not individuals. The ICMEs are explicitly mentioned as the place where the Commission shall meet every 4 years. So the General Assembly of the Commission consists of.

• (a) the members of the Executive Committee, as specified in (3) below, and

• (b) one Representative from each member country of ICMI, as specified in (5) below.

The General Assembly of ICMI shall normally meet once in every 4 years, during the International Congress on Mathematical Education.

…

3. The Executive Committee of the Commission consists of the following members, elected by IMU: Nine members, including the four officers, namely, the President, two Vice-Presidents, and the Secretary General. Ex-officio members: The outgoing President of ICMI, the President and the Secretary of IMU. Co-opted members: In order to provide for missing coverage or representation, the ICMI Executive Committee may co-opt up to two additional members.

There is no longer reference to the representative of the Committee on the Teaching of Science in ICSU.

In 2003 a new study group was affiliated to ICMI, the International Study Group for Mathematical Modelling and Applications (ICTMA). According to Ken Houston, Peter Galbraith, Gabriele Kaiser, all began in 1973 with the McLone Report. This work surveyed what recent mathematics graduates were doing in their employment, how relevant their education was to their work, and how satisfied their employers were with their performance. Some years later, in the UK David Burghes, who could well be described as the Father of ICTMA, decided to try to enliven the school mathematics curriculum by working with teachers to produce interesting modelling investigations for pupils at secondary level. There were many influences from many directions, and things began to happen (Houston et al. 2008).

Two new ICMI Studies, the numbers 12 and 13, were launched in these years, namely:

• 12. The Future of the Teaching and Learning of Algebra (Melbourne, Australia, 2001). The Study Volume was published by in 2004, edited by Kaye Stacey, Helen Chick and Margaret Kendal (NISS 8).

• 13. Mathematics Education in Different Cultural Traditions: A Comparative Study of East-Asia and the West (Hong Kong, 2002). The Study Volume was published by Springer in 2006, edited by Frederick K.S. Leung, Klaus-D. Graf and Francis J. Lopez-Real (NISS 9).

The tradition of regional conferences continued, with the organization of several conferences: the All-Russian Conference on Mathematical Education (Dubna, Russia, 2000); the ICMI-EARCOME-2 – Second ICMI East Asia Regional Conference on Mathematics Education (Singapore, 2002); the XI-IACME – 11th Inter-American Conference on Mathematics Education (Blumenau, Brazil, 2003), and the Espace Mathématique Francophone (EMF) (Tozeur, Tunisia, 2003).

In October 2000, in Geneva, the 100 years of the journal L’Einseignement Mathematique were celebrated. Founded in 1899 by Charles-Ange Laisant and Henri Fehr, this journal played an important role as official organ of ICMI within the international community of mathematics educators. This role diminished with time, but the meeting was an important occasion to rethink at the evolution of mathematics education, looking at the teaching of specific mathematical topics (Coray et al. 2003).

On the occasion of the 50th issue of ICMI Bulletin, de Guzmán reflects on the meaning of ICMI, asking “what would be nowadays the main tasks in which ICMI could be involved in a natural way?” (De Guzmán 2001). Undoubtedly, the “star activity” of ICMI is the International Congress on Mathematical Education (ICME), notwithstanding the fact that someone questions the need for such an energy-consuming activity and asks if it still has the meaning and the impact it should have, considering the other activities as the “ever more influential” ICMI studies and the meeting organized by the affiliated groups.

But, according to de Guzmán, there are two problems which appear much more important nowadays and which concern both ICMI and the International Mathematical Union (IMU). These two problems should be at the center of the regular activities of both bodies:

The main problem with which ICMI should be concerned, as an organism responsible for the health of mathematics education at a global level, as well as IMU, as an organism which has to attend to the good state of the mathematical activity, is the huge gap in many places around the world between those members of the mathematical community whose main activities are related to education, and those whose main occupation is the furtherance of mathematical research, be it oriented towards its more theoretical or its more applied aspects.

…

For a number of years, a traditional standpoint adopted by the community of those involved in mathematical research (especially university faculty) towards theoretical and practical pedagogical issues, which are of deep concern to another important segment of the mathematical community - such as mathematicians interested by the processes of mathematical learning or those interested in their daily tasks in identifying ways to facilitate this learning at any level -, has been to look at those issues with contempt. Maybe they disregard pedagogical studies and occupations on the basis that they constitute a field of second or third category, where it is very easy to decide at any time what are the appropriate options and where one who has taught for a few years has as much authority as anyone to express a valid opinion (De Guzmán 2001, p. 1).

To solve this gap, it is necessary, according to de Guzmán, to fully recognize that ICMI is the education commission of IMU. The risk of a split into two different organizations must be avoided. This risk is not negligible, as ICMI had a relatively vigorous life before IMU existed.

11 ICME-10, Copenhagen 2004. The ICMI Awards

The term 2003–2006 was again chaired by Bass (USA), with Vice-Presidents Jill Adler (South Africa) and Michèle Artigue (France). The Secretary-General was still Hodgson (Canada). The other members were Carmen Batanero (Spain), Nikolai Dolbilin (Russia), Maria Falk De Losada (Colombia), Peter L. Galbraith (Australia), Petar S. Kenderov (Bulgaria), Frederick Koon-Shing Leung (Hong Kong). Ex officio members were John Ball (UK), President of IMU, and Phillip Griffiths (USA), Secretary of IMU. We observe that Africa had its first officer, Jill Adler.

ICME-10 was held in Copenhagen in 2004, from July 4 to 11 (the logo is shown in Fig. 3.10). Participants numbered about 2300, from nearly 100 different countries. The chair of the IPC was Niss, who also edited the proceedings. Morten Blomhøj chaired the Local Organizing Committee. The proceedings included 64 papers based on the regular lectures (out of 74). According to the editor’s foreword, it has not been possible to include reports on several other important congress activities such as the five national presentations by Korea, Mexico, Romania, and Russia, and the Nordic host countries (Denmark, Finland, Iceland, Norway, and Sweden), the 46 workshops, the 12 sharing experiences groups, the more than 220 posters, the five ICMI Affiliated Study Groups, and the several informal meetings. The closing address was given, as usual, by the Secretary-General of ICMI, Bernard Hodgson. Among the various innovations of this congress, he particularly mentions the creation of five so-called Survey Teams, each having as a mandate to survey the state-of-the-art with respect to a certain theme or issue, paying particular attention to the identification and characterization of new knowledge, recent developments, new perspectives and emergent issues (Niss 2008).

Fig. 3.10

The logo of ICME-10

ICME-10 also featured the first awarding of two medals in mathematics education research, inaugurated by ICMI (officially assigned in 2003). The Felix Klein Medal for lifetime achievement was awarded to Guy Brousseau from France. The Hans Freudenthal Medal for a major program of research was awarded to Celia Hoyles of the UK (information about these awards and citations of the work of the laureates can be found on the ICMI website, http://www.mathunion.org/ICMI/).¹²

ICME-10 was also the occasion to launch a travelling exhibition titled “Why Mathematics?” on which ICMI was collaborating with UNESCO. This international exhibition on mathematical objects and phenomena was aimed particularly at young people, their parents, and their teachers and would later travel to various places.

The ICMI studies launched in that period were the numbers

• 14. Applications and Modeling in Mathematics Education (Dortmund, Germany, February 2004). The Study Volume was published by Springer in 2007 with the title Modeling and Applications in Mathematics Education, and was edited by Werner Blum, Peter L. Galbraith, Hans-Wolfgang Henn and Mogens Niss (New ICMI Study Series 10).

• 15. Professional Education and Development of Teachers of Mathematics (Águas de Lindóia, Brazil, May 2005). The Study Volume published by Springer in 2009 had the same title and was edited by Ruhama Even and Deborah Loewenberg Ball (NISS 11).

• 16. Challenging Mathematics in and beyond the Classroom (Trondheim, Norway, June 2006). This is also the title of the Study Volume published by Springer in 2009, edited by Edward J. Barbeau and Peter J. Taylor (NISS 12).

• 17. Technology in Mathematics Education (Hanoi, Vietnam, December 2006). The Study Volume published by Springer, in 2010 was titled Mathematics Education and Technology - Rethinking the Terrain, and was edited by Celia Hoyles and Jean-Baptiste Lagrange (NISS 13).

Regional conferences held in the same period were the EARCOME-3, third ICMI East Asia Regional Conference on Mathematics Education (Shanghai, China, 2005), and EMF 2006 – Espace Mathématique Francophone (Sherbrooke, Canada, 2006).

At ICM-2006, the French Michèle Artigue became the first woman appointed as President of ICMI. Up to 2008, of the 107 officers, only nine were women. Former Vice-President Artigue was not only the first female ICMI President ever, but also the first ICMI President after Smith whose primary expertise is mathematics education rather than research mathematics. This was linked to the objective of changing the rules of ICMI, an objective that Bass had set for his presidency. As Bass tells (Bass 2020, section 10), one of his conditions to become President of ICMI was the change in the terms of reference, what indeed happened in 2007, when the election of ICMI’s EC became a task of the General Assembly of ICMI itself.

12 2008: The Centennial of ICMI in Rome and ICME-11 in Monterrey

The term 2007–2009 was chaired by Artigue (France), with Vice-Presidents Adler (South Africa) and Bill Barton (New Zealand). The Secretary-General was again Hodgson (Canada). The other members were Mariolina Bartolini Bussi (Italy), Jaime Carvalho e Silva (Portugal), Hoyles (UK), Kumaresan S. aka Kumaresan Somaskandan (India), Koon-Shing Leung (Hong Kong SAR), Alexei L. Semenov. Other members were Bass (USA), Past President of ICMI, László Lovász (Hungary), President of IMU and Martin Grötschel (Germany), Secretary of IMU.

Having in mind to pave the way for a smooth transition to the new governance structure, the new EC was established by the 2006 IMU General Assembly for a 3-year term, 2007–2009. To ensure continuity from the past to the future, Hodgson was exceptionally asked to serve as the Secretary-General for a third term, also a complete novelty (besides the first female President) since the time when Henri Fehr (1870–1954) served for decades as Secretary-General of the “Old ICMI” (Hodgson and Niss 2018, p. 14).

An important event preceded ICME-11. It was the celebration of the centennial of the foundation of ICMI. An international symposium entitled “The First Century of the International Commission on Mathematical Instruction. Reflecting and Shaping the World of Mathematics Education” was held in Rome from 5 to 8 March 2008. Once again, as it did in 1952, when ICMI was reconstituted as a subcommission of IMU, Palazzo Corsini, home of the Accademia Nazionale dei Lincei, provided the venue for the congress, along with Palazzo Mattei di Paganica, home of the Enciclopedia Italiana (the logo in Fig. 3.11) The congress was attended by about 180 participants representing 43 countries. The program included ten plenary lectures, eight parallel lectures, five working groups and a panel discussion. An afternoon was reserved for the Italian teachers and was broadcasted in Italian schools. The last day featured an excursion that recalled that of 1908, and took the participants to visit the Villa d’Este and Hadrian’s Villa in Tivoli (see Castelnuovo 1909).

Fig. 3.11

The logo of the Centennial

The conviction that history is a powerful means not only for giving an account of the past but also for building the future, inspired the activities of the symposium as well as the publication. The papers in the Proceedings touch on a wide variety of themes: the origins of the ICMI; its rebirth at the end of the 1960s and the emergence of the new field of research of mathematics education; the dialectic between rigor and intuition; the relationships between pure and applied mathematics and the emphasis to be given to each; the interactions between research and practice; the comparison between centres and peripheries of the world; the relationships between mathematics and mathematics teaching; the training of teachers; and the relationship of mathematics education to technology, society and other disciplines. It emerges that ICMI has mirrored the development of mathematics education as a field of study and practice, and stimulated new directions of research, opening new horizons (Menghini et al. 2008). On that occasion also the website mentioned before was established by Fulvia Furinghetti and Livia Giacardi (Furinghetti and Giacardi 2008).

Some months later, ICME-11 was held in Monterrey, Mexico, from July 6 to July 13 (the logo is shown in Fig. 3.12). For the first time an ICME was held in a developing (or “non-affluent”) country. The bid was made by the Mexican Mathematical Society with the support of the Ministry of Education. The Chair of the International Program Committee was Marcela Santillán, while Carlos Signoret chaired the Local Organizing Committee.

Fig. 3.12

The logo of ICME-11

No proceedings have been edited, some contributions and summaries are available online in the ICMI’s website (ICME-11 2008). On the congress website we read that between 2000 and 2500 professionals from 100 countries were expected:

www.mathunion.org/fileadmin/ICMI/Conferences/ICME/ICME11/www.icme11.org/index.html Retrieved 23 February 2021.

In her opening address, Artigue comments on the role of the ICMEs:

There is no doubt that, in the last decade, the number of conferences in mathematics education has exploded, leading to question what is the role, the specificity of a congress such as ICME.

As are the International Congresses of Mathematicians for mathematics, ICMEs are unique events for mathematics education. Why? This is not only due to their size, to the international representation they gather, but also because reflecting ICMI values, they address to all those involved in mathematics education all around the world: educational researchers, teachers of mathematics and teacher educators, mathematicians, curriculum designers, educational policy makers and administrators.

ICMI ambition is to provide them all with a unique forum for exchanging, discussing, disseminating ideas and realizations, a unique opportunity for accessing information about the most recent advances in the field of mathematics education, an information covering the multiplicity of its dimensions, and sensitive to the diversity of the voices that exist in it. This explains the diversity of proposed activities […].

(https://www.mathunion.org/fileadmin/ICMI/files/Digital_Library/ICMEs/Opening_Michele_Artique_President_ICMI.pdf, Retrieved 1 November 2020)

The IPC proposed to launch the academic activities of ICME-11 through a dialogue on issues of crucial interest for mathematics education. Artigue and Kilpatrick initiated the dialogue posing the following questions:

• What do we know that we did not know 10 years ago in mathematics education, and how have we come to know it?

• What kind of evidence is accessible, and what has to be looked for in mathematics education?

• What are the societal expectations regarding our field, and how do we situate ourselves regarding them?

• Up to what point can visions of teaching and learning mathematics and evidence in the field transcend the diversity of educational contexts and cultures?

• What are the main challenges that mathematics education faces today?

The paper that appears on the website collecting the materials of ICMI-11¹³ reflects the dialogue proposing the different positions of the two authors.

In the same year, the ICMI study 18 on Statistics Education in School Mathematics: Challenges for Teaching and Teacher Education, was organized jointly by ICMI and the International Association for Statistical Education (IASE). The study Conference was held in Monterrey, México, July 2008. The Study Volume was published by Springer in 2011, with the title Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education and was edited by Carmen Batanero, Gail Burrill, Chris Reading (New ICMI Study Series, 14).

In 2008, a new IMU/ICMI project came to life: the Klein Project, whose aim is to produce mathematics resources for secondary teachers on contemporary mathematics. It materializes through “vignettes,” which are a short, readable piece on a topic of contemporary mathematics (http://blog.kleinproject.org/?page_id=363).

The project was inspired by Felix Klein’s book Elementary Mathematics from a Higher Standpoint, first published 100 years earlier (in the year of the birth of ICMI). It aims at representing a stimulus for mathematics teachers, so to help them to make connections between the mathematics they teach, or could teach, and the field of mathematics, while taking into account the evolution of this field over the last century.

13 Conclusions

In the year of the centenary of ICMI, there are 84 member countries of ICMI, 68 of which are also members of IMU and 2 are associate members (ICMI Bulletin 2008, 62, p. 3). Each country, whether an IMU member or not, is invited to appoint a Representative to ICMI, who acts as a liaison between ICMI and the mathematics education community in the country. Of course, 84 is less than the half of the total countries in the world, but the effort to expand the presence of the ICMI in the world is undeniable. An example is the more recent CANP (Capacity & Networking Project), started in 2011 and promoted by ICMI, IMU, UNESCO and ICIAM (International Congress of Industrial and Applied Mathematics).

CANP aims to enhance mathematics education at all levels in developing countries so that their people are capable of meeting the challenges these countries face. It wants 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 (https://www.mathunion.org/icmi/news-and-events/2011-08-09/canp-project).

The CANP project, as well as the Klein project mentioned above, help to face two of the “evergreen” questions within ICMI: the relationship with mathematicians and the engagement of non-affluent countries.

The evolution of the organization of the successive ICMEs leads us to ask the question that Howson asked himself (Howson 2004, p. 1): “Since [ICME-1] there have been many changes, but have we arrived at a suitable form and balance, better than anything that has gone before?” And, in reference to the current context, another question arises: “What is the role of the ICMEs in this context?” De Guzmán wondered if such huge conferences still made sense, Artigue (indirectly) answered that they have, because they reflect ICMI values, and therefore address to all those involved in mathematics education all around the world. We can add that, being an ICME a large container for a wide variety of topics related to mathematics education, everybody finds their place in it. Probably this very diversity helps to keep the community of mathematics educators together.