Sixth-Grade Students’ Mathematical Abstraction Processes in a Teaching Experiment Designed Based on Hypothetical Learning Trajectory

Abstract

This study explored the mathematical abstraction processes of three sixth-grade students who were selected as the focus group in a classroom teaching experiment that was designed based on a hypothetical learning trajectory and determined their abstraction mechanisms with respect to volume measurement in rectangular prisms. The study also determined the role of class social and sociomathematical norms in this process. The teaching experiment was conducted over nine weeks in two stages through whole-class discussions with 12 students and discussions with small groups consisting of three students with low, medium or high academic achievement. One of the small groups was selected as the focus group. The results showed that all the three students in the focus group, particularly the low-attaining student, used reflective (based on thinking) abstraction for volume measurement in rectangular prisms. In this process, it was also observed that social norms such as explanation-justification of ideas and solutions, agreement or disagreement and trying to listen to, understand and question each other and sociomathematical norms such as making an acceptable mathematical explanation-justification and making mathematical solutions played a supporting role in the students’ reflective abstraction in addition to their own individual actions.