Grounded in the disciplinary-responsive teaching framing, this study examined facilitator–students’ interactions with Pick’s theorem activity in ninth-grade high school mathematics students during an after-school program. We noted how facilitators addressed students’ conceptual challenges in algebraic reasoning, equation manipulation, and proof construction, promoting students’ algebraic thinking and proof competence. Utilizing the observational data, we depicted five instances where facilitators applied adaptive scaffolding to alternative solution methods, establishing equation equivalence, and theorem formalization in the semi-structured Pick’s theorem activity. The results suggested that responsive pedagogy supports students in moving from empirical pattern recognition to deductive proof, in our study, leading to the development of Pick’s formula from observed patterns, making the Pick’s theorem statement, and proving it. Such studies focused on responsive pedagogy provide insights into inquiry-based enrichment activities and teacher professional growth in high school mathematics, highlighting how facilitator responsiveness can bridge student mathematical intuition with formal mathematical rigor.
Rajan et al. (Tue,) studied this question.
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