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Tangible connections within the mathematical horizon: Exploring the Dihedral Calculator
Ami Mamolo1, Parker Glynn-Adey2
1Ontario Tech University, Oshawa , Canada.
Learners explored dihedral symmetries using a tangible geometric model, enhancing their understanding of abstract algebra concepts. This hands-on approach supports the development of interconnected mathematical knowledge for educators.
Area of Science:
- Mathematics Education
- Abstract Algebra
- Geometry
Background:
- The study is situated within the historical context of Felix Klein's Erlangen Program.
- It connects to current research in spatial visual reasoning and teacher knowledge.
Purpose of the Study:
- To investigate the use of tangible geometric models in teaching group theory.
- To explore how these models foster structural and interconnected understanding in learners.
Main Methods:
- A group theory activity involving learners exploring dihedral symmetries.
- Utilizing a tangible geometric model for conceptualization.
Main Results:
- Tangible geometric models offer significant opportunities for learning abstract algebra.
- Learners developed a structural and interconnected understanding of mathematical concepts.
Conclusions:
- Tangible models are effective tools for teaching abstract algebra concepts like dihedral symmetries.
- This approach supports the development of 'knowledge at the mathematical horizon' for teachers.
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