Abstract / Synopsis
This essay is aimed at a wide audience: anyone who has engaged in learning or teaching math. It provides a unique perspective drawn from a mathematician’s interests in working with K-12 teachers, familiarity with artificial intelligence (AI), and amateur pursuits of learning to play an instrument and of learning a difficult sport. While I delve into these topics, no special background is needed in the slightest. In particular, I draw lessons from some failures in AI that reflect on why the conventional procedural approach to teaching and learning math fails many students. I also provide insight into how we learn and how competency and proficiency are best achieved in any field. I also discuss some very common misconceptions about learning math. Drawing on music and sports, I show why these misconceptions are so flawed, though firmly believed by many. More so, I characterize learning math as similar to learning a performance art in order to provide an alternative view to teaching and learning math even to those who are well schooled in the best pedagogical practices. I hope that this will strengthen their understanding of their teaching methods and provide them with additional insights possibly for use in discussions with others less convinced of their methods.
Recommended Citation
James Diederich, "An Essay on Teaching and Learning Mathematics: Through the Lens of Artificial Intelligence, Music, and Sports," Journal of Humanistic Mathematics, Volume 16 Issue 2 (July 2026), pages 387-407. . Available at: https://scholarship.claremont.edu/jhm/vol16/iss2/21
