Sept 25 - Lockhart's Lament

 

The article "A Mathematician's Lament" by Paul Lockhart is a very powerful read in my opinion. I found myself agreeing with him that there is such beauty in mathematics much like music or art. It is unfortunate that this beauty is stripped away by the school systems and what remains is a depressing gray classroom where formulas are memorized. I like the analogy that Lockhart uses to argue that math teachers must know and be able to recognize its beauty in order to 'teach' it and share the appreciation of mathematics with their students. I resonate with Lockhart's point that students need autonomy and freedom to figure out their own solutions and proofs and I wonder how much of students' perspectives of math will change if we stopped focusing so much on the correct notation and rather give more weight to notion, as G.H. Hardy said. I think that notation is the very last think we should be teaching our kids after they figure out a math idea for and by themselves. In my experience, students are the most confused when they have to learn set notation and interval notation, for example. Perhaps taking this approach towards 'doing' mathematics in classrooms would encourage Relational Understating that Richard Skemp talks about in his article.

In this article, Paul Lockhart focuses majorly on appreciating the beauty of math and 'doing' it rather than teaching it. In my opinion, Lockhart fails to take into consideration the people that do not necessarily want to appreciate art. Building on his art class analogy, I am one of the (probably few) people that do not enjoy making art. I have given it my best and despite all my efforts, I simply do not have a knack for art and this is okay. Similarly, there are people that do not want to do math and that is completely fine. For them, Lockhart's proposed approach might be even more frustrating. Fr this reason, I believe that Skemp's Instrumental Understanding is also just as important. Hence, I do not agree with Lockhart that his 'new' artistic approach will solve the problem. It might improve the condition of math classrooms a little, but we need to consider all the implications it will have.