Prospective middle school mathematics teachers’ developing understanding of geometric transformations

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2017
Avcu, Seher
The purpose of this study was to explore prospective middle school mathematics teachers’ developing understanding of geometric transformations during the implementation of a seven-week instructional sequence designed to have them gain a mapping understanding of geometric transformations. This instructional sequence involved exploring geometric transformations in both static and dynamic geometry environments. Participants of the study were sixteen prospective middle school mathematics teachers. Design-based research was conducted to explore their developing understanding of geometric transformations during the implementation of instructional sequence and this development was evaluated by using APOS theory. Moreover, Transformation Geometry Questionnaire developed by the researcher was administered before and after the implementation of instructional sequence. Findings of the study showed that the participants had difficulties in defining, identifying and performing geometric transformations prior to study. During and after the implementation, they showed development in defining, identifying, and performing geometric transformations. This study also revealed that the participants were at or below the level of action conception prior to the implementation. Eight out of sixteen participants conceived geometric transformations as one to one and onto functions defined on the plane and thus they gained a complete object conception of geometric transformations at the end of the study. Seven participants reached an understanding that fell within a continuum between process and object conception at the end of the study. This study contributed to the literature by uncovering several critical ideas required for understanding geometric transformations as functions. Recommendations for future research were also presented.