The VIBE Framework: A Student-Centered Approach to Teaching Knot Theory in Secondary Mathematics
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916814935556096 |
|---|---|
| author | Diamantis, Ioannis |
| author_facet | Diamantis, Ioannis |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22886 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The VIBE Framework: A Student-Centered Approach to Teaching Knot Theory in Secondary Mathematics Diamantis, Ioannis History and Overview 97D40, 97D60, 97D99, 97G99, 00A35 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 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. |
| title | The VIBE Framework: A Student-Centered Approach to Teaching Knot Theory in Secondary Mathematics |
| topic | History and Overview 97D40, 97D60, 97D99, 97G99, 00A35 |
| url | https://arxiv.org/abs/2506.22886 |