Developing mathematical practices in a social context: a hypothetical learning trajectory to support preservice middle school mathematics teachers’ learning of triangles

Uygun, Tuğba
The purpose of the current study was to document preservice middle school mathematics teachers’ (PMSMT) classroom mathematical practices emerged through six-week instructional sequence about triangles. In this respect, the research question of “What are the classroom mathematical practices that are developed within design research environment using problem-based learning for teaching triangles to preservice middle school mathematics teachers?” guided the present study. In order to answer this research question and document the mathematical practices, a hypothetical learning trajectory and instructional sequence lasting six weeks related to triangles were formed. The hypothetical learning trajectory for the instructional sequence was performed for PMSMT to document their classroom mathematical practices about triangles. The classroom mathematical practices were analyzed benefiting from collective learning activity of whole class discussions including individual learning and social aspects of the environment by using emergent perspective. Focusing on taken-as-shared knowledge identified by Toulmin’s argumentation model, the classroom mathematical practices were extracted. The classroom mathematical practices encouraging PMSMT’s learning of triangles in the present study were: PMSMT’s reasoning on (a) the formation of a triangle, (b) the elements of triangles and their properties, and (c) congruence and similarity. Based on these mathematical practice, PMSMT improved their understanding of the concept triangles benefiting from other geometry concepts such as transformation geometry, geometric constructions and argumentations. In this respect, they examined the properties and elements of triangles and related properties by developing their conceptual understanding.