Response to Lockhart (2002)

Lockhart's (2002) view on teaching math is extreme and lacks specific guidance on implementing his approach (which may be intentional), yet I find some of his points compelling, particularly his critique of the rigid curriculum and its limited relevance to students' daily lives. I have pondered over the questions, "do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited?" On one hand, there is societal pressure to make math relevant, popularized by lists of "things you wish you'd learned in math class." We aim to equip students with skills for adulthood and for their future, five to ten years beyond high school. However, the real-world connections we make, even if practical, often lack the meaningfulness needed for lasting retention. While developing an intuition for compound interest is essential, memorizing formulas like A = P(1+r/n)^(nt) is not as valuable – I actually had to look it up myself. This raises the question: how do we teach and assess in ways that prioritize skills and intuition over content and formulas?

When it comes to geometry, Lockhart argues that "The art of proof has been replaced by a rigid step-by-step pattern of uninspired formal deductions" (2002), but I disagree. Like Simplicio, the interviewer in his dialogue, I grew to love math through the rigor and satisfaction that geometric proofs offer. The structured, step-by-step approach helped me develop precision in notation, language, and logical reasoning. It even fostered perspective-taking; I often imagine myself as a proof-reader (pun-intended), or an outsider reading my proofs, ensuring they are clear and logical without relying on my own context. In this sense, the structure of proofs has given me valuable skills in logical organization. Furthermore, the shared language of notations and terms is crucial for knowledge transfer and collaboration, even across different cultures and languages.

Skemp (1976) would align with Lockhart's view that relational understanding in math fosters intrinsic motivation. When students grasp mathematical relationships, they are driven by curiosity and an organic enthusiasm for the beauty of math. They see patterns and connections and are motivated to seek answers independently. In this scenario, the teacher becomes more of a guide rather than the sole point of access of mathematical knowledge.