## “Algebra, Additive and Multiplicative Structures. Is there any coherence at the early secondary level?”

**Presented By:** **Gérard Vergnaud, **Emeritus Director of Research, Centre National de la Recherche Scientifique (CNRS), France

Wednesday, April 6, 2011 from 4:30 p.m. – 5:30 p.m.

**Abstract:** Students’ understanding of the main additive and multiplicative relationships one can find in elementary mathematics is far from being satisfactory when they enter early secondary school. At the same time, they are introduced to elementary algebra. Their understanding of algebra is obviously influenced by their understanding of arithmetic; reciprocally, the learning of algebra may help them in understanding arithmetic better. It is an interesting challenge for researchers in mathematics education to draw a reliable picture of the difficulties met by students during that period of their schooling and therefore enable teachers to perceive more clearly both the basis and the obstacles that algebra finds in arithmetic. The picture should also point at concepts and operations of thinking that are specific to algebra. Prof. Gérard Vergnaud’s presentation aims at contributing to this picture.

**Bio:** Gérard Vergnaud is director emeritus of research at CNRS (Centre National de la Recherche Scientifique) in France. He was trained as a psychologist and completed his dissertation in 1968 with Jean Piaget. He coordinated the network of French research in mathematics education and physics for a long period. He was also President of the International Group “Psychology of Mathematics Education.” His research has focused on developing mathematical skills of students in elementary and secondary school. He also participated in the development of vocational education research. He has a doctorate honoris causa from the University of Geneva, and he is a member of the International Academy of Psychology in Russia.