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An instructional unit for prospective teachers' conceptualization of geometric transformations as functions

This study explored prospective middle school mathematics teachers' developing understanding of geometric transformations through designing and implementing an instructional unit in a technology supported classroom environment. The instructional unit including seven activities was developed by considering past research on learners' pre-existing difficulties related to geometric transformations and research on learners' developing understanding of geometric transformations as functions. This instructional unit involving a hypothetical learning trajectory was tested and refined in two iterations. The data were obtained through the Transformation Geometry Questionnaire (TGQ) administered both before and after the instructional unit, the task-based interviews, classroom observations involving pairwise and whole class discussions, and the activity sheets completed by the participants during the course of instruction. The analysis of data showed that the participants were at or below the level of action conception prior to the implementation. During and after the implementation of the instructional unit, all the participants displayed progress in the action-object continuum. Thus, the instructional unit proved useful in helping participants conceptualize geometric transformations as functions and in integrating their knowledge of functions and geometric transformations. The implications for developing participants' understanding of geometric transformations were discussed.