PRE-SERVICE ELEMENTARY TEACHERS AND THE FUNDAMENTAL AMBIGUITY OF DIAGRAMS IN GEOMETRY PROBLEM-SOLVING

Abstract: In elementary geometry problem-solving, in most cases two different points of view on diagrams are in interaction: as physical objects and as images of theoretical objects. An ongoing research is studying if, and how, pre-service elementary teachers are conscious of this double status. It appears that most of them do not have a clear view of it, which leads to a number of confusions and may prevent them helping their pupils in an effective way in their learning of geometry. Three years ago, we started a research at the IUFM1 Orléans-Tours about the initial training of preservice elementary teachers in geometry, after having observed that, like many secondary students, they had difficulties in that area of mathematics, the crucial point seeming to be how they consider the diagrams used in geometry problem-solving [Parzysz & Jore 2002]