Abstract:

The purpose of the research is to examine the development of elementary mathematics teachers’ use of multiple representation and translations between representations throughout the implementations of hypothetical learning trajectories. The research was designed as a teacher development experiment and two elementary school mathematics teachers participated in the process. This research was completed in 10 weeks and the process was carried out in 3 different stages as “planning, teaching experiment and case study”. The first stage of the research consists of preparing hypothetical learning trajectories matching the objectives in the curriculum by covering all the objectives in algebra. All activities in HLT were appropriate to the use of representations during teaching. In the second stage, the teaching experiment was conducted with two teachers under the supervision of one of the experts. In the third stage, teachers implemented teaching activities based on HLT in their classrooms. Videos taken during teaching and at professional development meetings with teachers are the main data sources of the present research. Results reveal that teachers use students' thoughts to direct them to use representation, they allow students to create their own forms of representation, and they guide students to establish translations between representations through organizing students' emerging thoughts about representations.

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