Middle school students’ generalizations about properties of geometric transformations in a dynamic geometry environment

Making generalization is fundamental to mathematics and a crucial component of mathematical thinking. To help learners become more proficient at constructing mathematical generalizations, it is vital to better understand the forms that the constructive process might take in various mathematical contexts. The study reported here aimed to offer an empirically grounded theory of forms of generalization middle students made as they engaged in explorations regarding geometric transformations within a dynamic geometry environment. Based on their sources, participants’ statements about properties of geometric transformations were categorized into four types: context-bounded properties, perception-based generalizations, process-based generalizations, and theory-based generalizations. Although these forms of generalizations are different in their construction process, with appropriate pedagogical support generalizations of the same type and different types of generalizations can build on each other. DGS mediated the construction of these forms of generalizations based on how learners used it.