Capturing conceptual development through the embodied-based experience in infinite sets comparison

Designing pedagogical experience to serve as groundwork on which to build an understanding of abstract concepts is a challenging mission for educators. Much research has found that embodied activities could facilitate conceptual metaphor for students to understand such concepts. This study has captured the trajectory of reasoning occurred during the embodied-based experience designed for the infinity concept. The participants, 42 secondary students who had never been exposed to the formal concept of infinity, passed through a designed series of making-sense tasks, so called the Embodied-Based Activity of Infinite Sets Comparison (EBIC). The EBIC intervention was conducted in 2 phases; (i) careful observation of 2 voluntary students, and (ii) integration for 40-classroom practice. The first phase was to examine the students' conceptual development through their utterances, actions and inscriptions. Open-ended questions were used to capture the students' insights and reasoning in the second phase. The qualitative data was collected and mined to associate pairability and Cantor's metaphor. The finding showed the reasoning trajectory of some participants and the shift from improper reasoning to 1-1 correspondence pairing of countably infinite sets. This mathematical thinking shift was a consequence of conceptual embodiment, outlining the analysis of the embodied-based experience to develop abstract reasoning.