Analyzing preservice secondary mathematics teachers' prompts in dynamic geometry environment tasks

The purpose of this study was to analyze the prompts that preservice secondary mathematics teachers used for the acquisition of mathematics knowledge in dynamic geometry environment tasks. The participants, four preservice secondary mathematics teachers who were enrolled in a computer-supported mathematics education course, designed a dynamic geometry environment task based on a high school mathematics curriculum learning outcome. The main data sources were the participants' task documents and the transcripts of interviews that were conducted with the participants to examine the details of their tasks. The techno-pedagogic mathematics task design model was used to analyze the data. The results indicated that the focus of the designs was to help students realize the invariant properties of geometric figures that were embodied by robust construction steps in the tasks. The preservice teachers utilized several capabilities of the dynamic geometry environment (e.g. measuring, dragging, and changing the input box value) to help students discern these properties and expected students to make a generalization based on inductive reasoning. However, since students were directed to build robust constructions, the mathematical activities prompted by the preservice teachers were limited to observing, finding, generalizing, and explaining the previously constructed invariant features in the tasks.