Basic Elements of Didactique

Abstract

Guy Brousseau was born in Morocco in 1933. Since his father was in the military, he wound up attending school in a number of different places. He was nonetheless quite successful, and earned himself admission to the École Normale d’Instituteurs (Normal School for Elementary Teachers) in Agen. He earned a baccalaureate degree there, and then a more advanced baccalaureate (with distinction in elementary mathematics) at the École Normale in Montpellier. This in turn led to his being given a scholarship to study mathematics in Toulouse in preparation for being admitted to an École Normale Supérieure. By the end of the year, however, he realized that this was not the direction he wanted to go. Much as he enjoyed the advanced mathematics and physics he was learning, his real fascination was with how children learn mathematics—not how children learn in general but very specifically how they learn mathematics. When one of his professors suggested that he belonged in the field of psychology he rejected the notion out of hand. In fact, even more specifically, he wanted to focus on how students learn mathematics in a classroom. He had, by this time, been exposed to the work of Piaget, and greatly admired many of his ideas and explorations, but felt that Piaget’s focus on individual children isolated from any group excluded some key learning dynamics. In pursuit of this fascination, he returned to Agen for a year to complete the studies required for a teaching certificate. At the end of the year he was given a position in a village school, teaching all of the village’s elementary age children. Shortly thereafter he married Nadine Labesque, whom he had met on his first day in Agen, and as a couple they were given a school in a slightly larger village. Nadine taught the younger half of the children, Guy the older. These years launched his experimental efforts, both in the classroom (his and Nadine’s) and out of it (for instance teaching a collection of farmers techniques for optimization and for computing areas.) He also continued learning about other people’s ideas by spending every spare moment in the nearby Tonneins or not-too-distant Toulouse. He gives a vivid description of himself standing in a bookstore voraciously consuming books (he bought enough to keep from being thrown out!) To avoid wasting any of his precious time, he developed a practice of invariably starting a book in the middle, so as to determine whether it had anything of interest and use to him. If he decided that it did, he generally figured out on his own what must have come before, only rarely actually going back and reading the early parts. In this way he acquired extensive knowledge of a wide range of material with remarkably little exposure to how the material is introduced to the more conventional reader who starts on page one.