Lockhart’s Lament

I agree with the emphasis on the importance of real understanding: Just as Lockhart emphasizes the beauty and art of true mathematical understanding. Many educators emphasize the need for deep understanding in every subject. Teaching for memorization or simply to pass exams misses the essence of true learning.  

Both articles emphasize the importance of real understanding. While Lockhart focuses on the art and beauty of mathematics, Skemp discusses the difference between instrumental and relational understanding.

Edited: Lockhart emphasizes that mathematics is an art form and should be treated as such. He argues that true understanding in mathematics comes not from rote memorization but from engaging with and enjoying the subject. This aligns with my previous agreement on the importance of real understanding in education. From my personal experience, I never understood the meaning behind Pythagorean Theorem when I was in high school. What my math teacher told me is to memorize the formula and learn how to apply it for questions. There is no engagement in this content. And I really appreciate that now teachers are more focus on teaching the meaning behind the math contents. 

While Lockhart is highly critical of the way mathematics is taught in schools, seeing it as destructive and overly rigid, I would like to say that some structure and guidance are necessary for learning. Introducing foundational concepts in a structured way can provide a framework upon which students can build their understanding. I do agree that creativity is crucial but in my opinion, it can be fostered within a structured environment.