Response to Lockhart: A Mathematician’s Lament

 

It was interesting to read Lockhart’s Lament in the context of the work on our art project right now. I found some interesting parallels. I agree with Lockhart’s suggestion that seeing math as an art form could be a way to spark interest in students.  His idea of teaching math through art resonates with me, especially in how creativity can transform the way students engage with math. The art project has demonstrated how visual or artistic approaches can draw students in, making math concepts more relatable and stimulating. As Mark said last night, “This image tickles my brain.” Over the past week, I’ve developed new feelings about the connection between art and math, realizing how much I enjoy interacting with both concepts myself. I’ve also been considering how I could incorporate music into the study of mathematics, as it appears that many have written about this connection. These approaches could be a powerful tool to make math more engaging and enjoyable for students who may not naturally connect with the subject.

However, I also think Lockhart’s perspective may be a bit idealistic when it comes to the role of structure in learning. While teaching through creative exploration is exciting, some students need more structure to thrive in math. A balance between creativity and structured learning is essential because not all students are naturally inclined toward artistic or exploratory approaches. This is where I think Lockhart’s vision isn’t entirely on point. He seems to underplay the necessity of structure, which, for many students, provides a foundation for building understanding and confidence in the subject.

Additionally, I found Lockhart’s criticism of teachers’ mathematical understanding to be exaggerated. He suggests that many teachers don’t deeply understand math, which he believes negatively impacts students. While it’s true that some teachers may struggle with engaging students, I think teacher understanding is likely normally distributed. Many excellent teachers can impart math to various types of students, and I’m sure some may lack the necessary depth. However, the idea that most teachers fail to inspire interest seems overstated. Many teachers are more than capable of generating student engagement with the right tools and support.

Comparing Lockhart and Skemp, both authors believe that the ultimate goal of teaching math should be to inspire student engagement, and they both see the teacher as central to this process. Lockhart argues that a mechanical approach to teaching math, focusing on memorization and rote learning, damages students’ ability to appreciate the subject's beauty. This aligns with Skemp’s distinction between relational and instrumental understanding. Both authors agree that a relational approach, where students understand why mathematical concepts work, not just how to use them, is crucial for fostering long-term engagement. Lockhart’s emphasis on creativity in learning math as an art form accompanies Skemp’s idea of relational understanding, as both highlight the need for deeper, more meaningful learning experiences in math education.