Teachers modify geometry problems: From proof to investigation

We explored transformations that teachers made to modify geometry proof problems into investigation problems and analyzed how these transformations differ in teachers who use a dynamic geometry environment (DGE) in their classes and those who do not. We devised a framework for the analysis of problem transformations and types of teacher-generated problems. We introduce distinctions between static and dynamic transformations of geometry problems. By observing differences in the transformations the teachers made and the types of problems they produced, we suggest that teachers who use DGE in their classes develop a better understanding of geometry investigation tasks and have no difficulty in transforming proof problems into investigation discovery problems through teaching. Furthermore, we suggest that working with DGE leads to more changes in the givens of the problems and to more dynamic transformations of a problem. From the differences we found in relation to the various problems used in this study, we conclude that problem transformations are problem dependent. Finally, we argue that problem transformation is teachable but requires special training.