This doctoral disertation in mathematics education focuses on two areas of unequal importance: Symbolic Expressions of Elementary Algebra ( " ESA " ) on the one hand and Discussions Around Problems ( " DAP " ) on the other hand. The main body of the thesis explains " the main features of plausible structural models of ESA. This work is not strictly a mathematics education study , which would more or less directly applicable to what happens in the classroom, but rather a fundamental research on the structure of symbolic expressions, designed to serve as a tool to further educational studies. This study is structured in three main parts. The first part (Chapters I-III) exposes the problem, and refers to existing work. The second part (chapter IV to VIII) present our proposals, namely a grammar of ESA. The third and final part (Chapter IX to XIII) is based on the results of surveys of students on meaning of the ESA. The annex includes two items : * "Finding a teaching approach in mathematics with adults " , in collaboration with Y. Paquelier and published in 1987 in the journal Education Permanente * " Some recent developments in research on the Discussion Around Problems " , in collaboration with Y. Paquelier , H. Lymberopoulos and H. Nikolakarou and published in 1988 in the Proceedings of the Twelfth Annual Conference of the International Group "Psychology of Mathematics Education " in Veszprém (Hungary).
