**Citation for the 2009 ICMI Hans Freudenthal Award to Professor **Yves Chevallard

It is with great pleasure that the ICMI Awards Committee hereby announces that the Hans Freudenthal Medal for 2009 is given to Professor Yves Chevallard, IUFM d’Aix-Marseille, France, in recognition of his foundation and development over the last two and a half decades of a very original, fruitful and influential research programme in mathematics education. The first part of the programme, developed in the 1980s, was focused on the notion of didactical transposition of mathematical knowledge from outside school to inside the mathematics classroom, a transposition which also transforms the very nature of mathematical knowledge. This idea has been further developed, in the 1990s and beyond, into a more general study of the varying institutional characteristics and cultures within which mathematics is being practised in terms of different praxeologies (combining praxis and logos). This gave rise to the so-called anthropological theory of the didactic (ATD) which offers a tool for modelling and analysing a diversity of human activities in relation to mathematics. On that basis Yves Chevallard has developed an entirely new approach to teacher training focusing on the needs and problems of the profession operating in what he calls “clinics for training" which are also cumulatively establishing “archives for training".

It is a characteristic feature of Yves Chevallard’s work and impact that he continues to collaborate closely with colleagues in France and Spain and that his work has had a great impact internationally, and not the least so in Latin America. This is reflected in a large number of doctoral dissertations that have been written in various countries about, or within the framework of, his theory. International conferences on ATD have been held in 2005, 2007, and 2010, each of which has gathered about a hundred researchers from Europe, America, Africa, and Asia. In some countries, including Chile and Mexico, Yves Chevallard’s work also has exerted a direct influence on curriculum development and in-service teacher training.

Yves Chevallard graduated from l’Ecole Normale Supérieure in Paris (rue d’Ulm) in 1967 and earned agrégation in mathematics in 1970. After having taught mathematics at a lycée (high school) in Marseille, he moved - in 1972 – to Université d’Aix-Marseille II, first as an assistant and then, from 1986, as a 1st class maître de conférences (associate professor), working at the department of mathematics. With a background as a researcher in mathematical logic he turned his attention towards issues of mathematics education, greatly stimulated by the work of Guy Brousseau, whom he calls his mentor. During the years 1984-1991 Yves Chevallard was the Director of IREM d’Aix-Marseille (IREM: Institut de recherches sur l’enseignement des mathématiques). After having been declared qualified for directing research in 1990 Yves Chevallard was appointed full university professor in 1991 at the newly created IUFM d’Aix-Marseille (IUFM: Institut universitaire de formation des maîtres), and promoted to the 1st class in 1999, where he was also chair of the scientific and pedagogical council 1991-2006. He is still working at this institution.

Yves Chevallard has served on a number of posts in the academic community in general and in the community of researchers in mathematics education in particular, mainly in France. Thus he was a member of national council of universities in France (CNU) 1982-1990. He has been member of the administrative council of IUFM d’Aix-Marseille since 1991, and is currently a member of the joint laboratory council UMR ADEF which gathers researchers from three scientific institutions in France. Yves Chevallard founded and directed (1994-2000) the journal Skholê published at IUFM d’Aix-Marseille. He was the editor-in-chief of Recherches en didactique des mathématiques, 2000-2002 and currently is a member of its scientific committee as well as of the editorial committee of Éducation et didactique. He was also for a number of years a member of the scientific committee of the book series Raisons éducatives, published by the University of Geneva. He was responsible for the units of education and didactics and for initiation of research in mathematics education at the University of Provence 2007-09 and has been a visiting professor at universities in Germany and Spain.

La transposition didactique – du savoir savant au savoir enseigné (1985, extended edition in 1991, Spanish translation in 1997) is his internationally most well-known work. A joint book in Spanish with Marianna Bosch and Josep Gascón, Estudiar matemáticas. El eslabón perdido entre la enseñanza y el aprendizaje (1997) provides what Yves Chevallard calls “a midway summary" of ATD. Moreover, several of his more than a hundred publications in journals and anthologies have reached an international audience, even though the far majority of them are written in French.

In summary, Yves Chevallard, who continues to be very prolific in his academic work, is an eminently worthy recipient of the Hans Freudenthal Medal 2009.