Lockhart's Lament

 So far, out of all the articles I've read, I really resonated with Lockhart's article the most and there are many points I agree with. 

There was one particular statement that I both agree and disagree with: (p.5)

"By removing the creative process and leaving only the results of that process, you virtually guarantee that no one will have any real engagement with the subject."

I've always thought the monotonous lecture-y type lessons weren't that interesting and I wholeheartedly agree that being told a particular strategy/formula to solve problems simply becomes purely memorization/"plug-and-chug" without truly knowing what it is they're doing. I like logic puzzles, not because I can get the answer (I don't always get it!) but because of the journey to get to the answer --- it makes me wrack my brain to try different ways to approach the problem, be creative, and if I do get the answer, there's so much more satisfaction to it because I know it's my own hard work that led to it, not a ready-made algorithm given at the start to solve the problem for me. The same idea can be applied to mathematics. 

However, at the same time, I don't think there will be absolutely no engagement with the subject if a method/formula is given to solving a problem. What is stopping a student from working backwards or trying to explore for themselves how that formula/method is produced? Is that not a form of engagement and critical thinking with the subject? 

I can see resemblances between Lockhart's insistence on exploring the processes behind mathematics and Skemp's argument about relational maths (the "why") being very similar. However, what I found interesting was that Lockhart preferred a more unique type of relational math where students came up with their own reasonings compared to Skemp's teaching students relational maths which Lockhart was actually against (rigid proofs or so he called them) (see High School Geometry: Instrument of the Devil from Lockhart's Lament).