The VIBE Framework: A Student-Centered Approach to Teaching Knot Theory in Secondary Mathematics
Knot theory, a visual and intuitive branch of topology, offers a unique opportunity to introduce advanced mathematical thinking in secondary education. Despite its accessibility and cross-disciplinary relevance, it remains largely absent from standard curricula. This paper proposes the {\it VIBE framework}, a student-centered approach, structured around four pedagogical pillars: Visual, Inquiry-based, Braided (collaborative), and Embedded (contextualized) learning. Rooted in constructivist theo…
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