Lockhart's Lament

I agree with Lockhart that removing the history, process, and human struggle in mathematics makes teaching math meaningless. Lockhart describes how the beauty of doing math can be transmitted by exploring “mankind’s struggle with the problem of measuring curves… Eudoxus and Archimedes and the method of exhaustion… [and] the transcendence of pi” (Lockhart, 2002, p. 9). By incorporating the history and process of discovering in mathematics, we help students to see math in context.  I have learned the importance of “teaching from context” in several of my other classes, often under the lens of cognitive justice. By incorporating context into mathematics education, we show students how and why discoveries are made and can incorporate other ways of knowing without musuemifying them. The process of incorporating history also addresses the culture surrounding mathematics. Many students I have had were quick to say “I’m bad at math” or “I’m not a math person”. However, showing students historical struggles with math, even among great mathematicians, could help them see that struggles in math are normal and worth it.

I disagree with Lockhart when he describes that conveying math as a “set of rules” (Lockhart, 2002, p. 11) removes the excitement from mathematics. Both my partner and I went to the same high school, learned math from an instrumental approach, and both loved math enough to pursue it in university. We were both drawn to the organization, rigour, and feeling of achievement when we used what we learned to solve challenging problems. Although we both struggled later when math became more proof-based and arguably artistic, what kept us from quitting mathematics altogether was our foundation of passion and appreciation of challenge. I also disagree with the idea of completely teaching mathematics “as art for art’s sake” (Lockhart, 2002, p. 11). On one hand, I also have physics as a teachable, so I appreciate how mathematics is used in science. From another perspective, I know many people who find the creative process of art frustrating and not useful. Many people have similar feelings about mathematics without it being taught as an art, so I am not convinced that teaching mathematics entirely as an art would be an improvement. That said, I see the value for getting different students engaged in mathematics and showing my students different perspectives of mathematics. I also struggled immensely with proof-based courses in university, so perhaps it would have been beneficial for me to learn math from an artistic perspective.

Lockhart and Skemp argue that promoting instrumental understanding, which is the current emphasis in school, is not enough to understand mathematics. I found it interesting that both Lockhart and Skemp use nearly the exact same analogy of music to demonstrate why instrumental teaching is so damaging. I think in Lockhart’s case it is a more effective analogy, because it is clear how teaching music as a purely instrumental subject removes its artistic value, which is key to Lockhart’s arguments about how mathematics should be taught. However, Lockhart’s article was published over 25 years after Skemp’s article was, so I wonder if Lockhart heard the music analogy from Skemp and recycled it.