Investigating mathematics teacher educators’ specialised knowledge for teaching geometric transformations

Abstract

In this study, three mathematics teacher educators’(MTEs) specialised knowl edge for geometric transformations was explored. In this regard, MTEs’ mathematical knowledge about geometric transformations including the definitions and properties and their’ pedagogical content knowledge regarding the thinking ways of students about geometric transformations, the teaching strategies to develop students’ understandings and to overcome students’ difficulties were examined. Data were collected qualitatively in one-hour long structured interviews. Results showed that all participants defined geometric transformations in two ways: namely, as a motion and as a function. MTEs pointed that motion conception of geometric transformations is seen in school curricula; while, the function understanding is mostly delayed until the university level. MTEs also defined geometric transformations by using APOS theory in which they consid ered motion understanding at the action level, and function understanding both at the process level and the object level. Results further pointed to what MTEs consider as important in terms of the difficulties learners might possibly have and what strategies might be useful to overcome them. Particularly, results indicated that MTEs consider learners’ need to get used to studying with different functions in different spaces as well as their understanding of plane, R2 , as important to conceptualize the domain and the range of geometric transformations as the whole plane. In addition, Results further showed that MTEs consider that reflection is the easiest transformation for the learners and rotation is the hardest one. Thus, they recommend that it might be a good strategy to start teaching transformations with reflection.