2023 78 SBE

The Nature of Pre-Calculus Students' Mathematics and Art Cognitions in Making and Testing Conjectures about the Fibonacci Spiral and the Great Wave off Kanagawa

By: Tuto Lopez Gonzalez

Department: Mathematics

Faculty Advisor: Dr. Shandy Hauk

This study investigates the nature of pre-calculus students' mathematics and art cognitions in making and testing conjectures about the Fibonacci spiral and the Edo period print, The Great Wave of Kanagawa. Additionally, this work examines the potential of using a framework to explore the development of mathematics cognition, the Pirie-Kieren (P-K) framework, for modeling the development of artistic understanding, including attention to embodied responses. Task-based interviews and background surveys were conducted with four pairs of pre-calculus students. Qualitative inductive analysis revealed how the P-K framework is useful in unpacking the math-rich and diagram/visual-rich aspects of cognition by pre-calculus students. The implications of the research include designing new curricula and conducting related research on how to combine art and mathematics. Future work may involve the application of machine learning algorithms to the data collected from task-based interviews, to gain deeper insights into the complex relationships between mathematics and art cognition.