SENSING AND MAKING SENSE OF DEFORMATIONS: EMBODIED PATHWAYS TO ADVANCED MATHEMATICAL THINKING AND EARLY TEACHER IDENTITY

This study examines how undergraduate mathematics students developed advanced mathematical thinking and early teacher identity through embodied exploration of topological deformations. Students progressed through pre-rigorous, rigorous, and post-rigorous phases while designing teaching resources. Analysis through noticing and agency frameworks reveals how pedagogical awareness emerges when abstract mathematics is approached through embodied, multi-modal pathways. Findings show that mathematical noticing becomes pedagogical noticing when students exercise design agency, offering new perspectives on addressing Klein's second discontinuity through epistemological rather than content-based connections.