High School Teachers’ Use of a Dynamic Geometry System to Formulate Conjectures and to Transit from Empirical to Geometric and Algebraic Arguments in Problem-Solving Approaches

Abstract

The aim of the study is to analyse and discuss ways of reasoning that high school teachers develop in a problem-solving environment that fosters the systematic use of digital technologies. Results indicate that they relied on a dynamic geometry system's affordances to initially make sense of problem statements to formulate a set of conjectures or relationships that involve mathematical parameters' behaviours. Initially these conjectures were empirically validated or through visual and quantitative arguments; but later the same arguments were a source to think with an algebraic support. Throughout the activities, the participants engaged in mathematical reflection to reconcile visual, geometric and algebraic or analytical approaches.