# 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.

## Keywords

Digital technologies Mathematical problem-solving Conjectures Dynamic geometry system (DGS)## Notes

### Acknowledgement

This report is part of a wider project that deals with teachers and students’ use of digital technologies in extending both mathematics and didactic knowledge. We acknowledge the support received from research projects with reference numbers Conacyt-168543 (México) and EDU2015-65270-R (National I+D+I Plan of MEC-Spain) during the development of this research.

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