Exploring the Thinking Experiences of Preservice Mathematics Teachers in Learning Geometric Transformation Proofs

Abstract

This study aimed to explore the thinking experiences of preservice mathematics teachers in learning geometric transformation proofs, focusing on four categories of thinking: personalization, contextualization, depersonalization, and decontextualization. Employing a qualitative approach with a phenomenological design, the study involved 24 preservice mathematics teachers in a mathematics education program who had completed a course on Geometric Transformations. Data were collected through written test tasks and in-depth interviews and analyzed thematically.  The data analysis followed a four-stage phenomenological procedure: bracketing, to suspend researcher assumptions; intuiting, to immerse in participants’ experiences; thematizing, to identify recurring patterns; and describing, to construct a comprehensive understanding of the phenomenon. The findings identified seven key themes that reflect the thinking experiences of preservice mathematics teachers. Through an in-depth analysis of these themes, it was revealed that the participants’ reasoning predominantly remained at the stages of personalization and contextualization. Depersonalized and decontextualized thinking was not identified, suggesting that the transition toward formal and abstract mathematical reasoning had not yet occurred. The findings suggest possible cognitive obstacles experienced by preservice teachers in transitioning toward formal reasoning, based on interview responses. However, the exploration of these challenges was limited to data gathered through interviews. Future studies are recommended to conduct deeper investigations through classroom observations and analysis of instructional materials to better understand how these thinking difficulties emerge.