This article is a follow-up to an earlier article (Bednarz and Janvier, 1982) which presented the results of a research study on the understanding of numeration by primary school children. That study pointed out the main difficulties children meet in learning numeration, presented a theoretical framework that made explicit a conception of numeration different from the one considered in current mathematics teaching, and also proposed a reference framework utilizable for learning and evaluating this notion. The experimentation in a classroom announced at the end of the article, was undertaken from 1980 to 1983 with the same group of children from the time they were in first grade (6–7 years old) to the third grade (8–9 years). The theoretical and reference frameworks developed in the former research study proved to be effective for developing a constructivist approach leading children to build a meaningful and efficient symbolism of number.
This article is mainly devoted to presenting the results of this three year longitudinal study (part C). At first, we shall characterize briefly our intervention based on a constructivist approach of numeration (part A). Also we shall describe the conditions under which the experimentation was carried out, and the means used to evaluate the impact on the pupils (part B).