Exploring Candidates' Initial Images of Similar Figures

This article investigates preservice candidates' knowledge of similar figures while engaged in teacher-related mathematical tasks (TRMT) with the primary goal of developing a lesson plan on similar figures. This investigation was part of a larger study investigating candidate knowledge of what and how to teach proportional reasoning concepts while engaged in TRMT. The data collection and TRMT cycle included individual discussions and reflections, group planning and discussions, and group presentations. Individual candidates also wrote their teaching philosophies and math autobiographies, which were reviewed. While candidates appeared to grasp many of the aspects of the concept of similar figures and similarity, there was a lack of precision and strength in their representations. The knowledge base of the candidates in both mathematics and teaching varied. As the study progressed, candidates relied heavily on their subject matter knowledge to justify their images and ideas.