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<p>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 <i>VIBE framework</i>, a student-centered approach, structured around four pedagogical pillars: Visual, Inquiry-based, Braided (collaborative), and Embedded (contextualized) learning. Rooted in constructivist theory, VIBE supports cognitive development, spatial reasoning, and mathematical engagement across diverse learners. We present a sequence of low-threshold, high-ceiling activities designed to develop core topological concepts while fostering creativity and exploration. Through qualitative heatmaps, clustering visualizations, and classroom snapshots, we demonstrate how knot theory can be transformed into a powerful medium for inquiry and interdisciplinary connection. We believe that the VIBE framework provides a structured yet adaptable approach that supports the integration of deep, meaningful mathematical experiences into secondary education.</p>

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The VIBE framework for student centered teaching of knot theory in secondary mathematics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月23日

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  • Ioannis Diamantis

摘要

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 VIBE framework, a student-centered approach, structured around four pedagogical pillars: Visual, Inquiry-based, Braided (collaborative), and Embedded (contextualized) learning. Rooted in constructivist theory, VIBE supports cognitive development, spatial reasoning, and mathematical engagement across diverse learners. We present a sequence of low-threshold, high-ceiling activities designed to develop core topological concepts while fostering creativity and exploration. Through qualitative heatmaps, clustering visualizations, and classroom snapshots, we demonstrate how knot theory can be transformed into a powerful medium for inquiry and interdisciplinary connection. We believe that the VIBE framework provides a structured yet adaptable approach that supports the integration of deep, meaningful mathematical experiences into secondary education.