The purpose of this thesis is to investigate the teaching of proportionality to 11 to 16-year old pupils registered in special-needs schools including pupils with more severe learning disabilities. Studies related to the teaching of mathematics have shown that the understanding of proportionality by pupils up to middle school age and more particularly by children with significant learning difficulties is often inappropriate. In order to find out if an adjustment can be made without any impact on the knowledge requirements, we experimented a teaching plan concerning the learning of proportionality by children with special-needs in the context of our study. We insist on the importance of the organization of the different types of knowledge within this teaching plan and also on the relevance of backgrounds and values of numerical didactical parameters. Analysis of our observations is carried out with statistical implicative analysis, Theory of Didactical Situations and with the frame of the double approach used to analyse the practices of teachers. The implementation of such a teaching plan requires, for teachers, mathematical knowledge. In order to reactivate this knowledge, we propose a symbolic scheme for each resolving technique applied to problems involving direct proportionality.
