Mathematical Practices in a Social Learning Environment Guided by the Hypothetical Learning Trajectory for Quadrilaterals

Abstract

The purpose of the current article is to test and revise the hypothetical learning trajectory designed for teaching quadrilaterals by reporting the classroom mathematical practices emerged in a social learning environment developing preservice middle school mathematics teachers' understanding of quadrilaterals. Ten preservice teachers participated in five-week instructional sequence guided by the hypothetical learning trajectory designed by problem-based learning strategy about quadrilaterals. This teaching experiment study by a case study focused on their learning and understanding of quadrilaterals through argumentations. Hence, the qualitative data collected through whole class and peer group discussions, field notes, written worksheets, group meetings, and interviews were analysed by three-phase methodology of Rasmussen and Stephan (2008) based on Toulmin's model of argumentation (1969).  Three mathematical practices emerged through the five-week instructional sequence: reasoning on definitions of quadrilaterals, reasoning on relationship between quadrilaterals and reasoning on properties of quadrilaterals. Moreover, it was observed that preservice teachers developed their learning and understanding of quadrilaterals by the hypothetical learning trajectory.