From Royaumont to Lyon: Applications and modelling during the sixties

At the Royaumont Seminar (1959) the New Math reform was officially launched. In the decade between Royaumont and the first ICME congress in Lyon (1969), many mathematics educators were involved in actions to facilitate the implementation of the New Math reform. The New Math advocates were convinced that a deep knowledge and understanding of the structures of modern mathematics was a prerequisite to arrive at substantial applications, but in actual classroom practices the applied side of mathematics was often completely neglected. But already at the Royaumont Seminar there were alternative voices who pleaded for taking the role of applications seriously (Niss, Blum, & Galbraith, 2007). We investigate the arguments for integrating applications in mathematics education, as well as the kind of (new) applications that were envisaged, at the Royaumont Seminar and in the decade thereafter, a period which is still not well documented in the recent history of modelling and applications, possibly with the exception of a study by Gispert (2003). Although there was some attention for applications in the post Royaumont era, the debate was almost always about how the New Math curricula should be set up. In 1967 applications, but also the didactics of mathematics, with even more emphasis, were explicitly addressed at the ICMI colloquium How to teach mathematics so as to be useful. There Freudenthal raised in his opening address the question Why to teach mathematics so as to be useful? (1968). From then on, applications (and modelling) gained interest, not only at school, but also in math educational research and development.