That was an interesting read. I wasn't expecting to actually read 25 pages as a result of a comment here, but the author wrote with enough passion to hold my interest and presented some interesting ideas that I hadn't heard before. Thanks for sharing it and begging me to read it.

I also went a watched a quick video on common core (which used a multiplication example) after reading Lockhart's paper, to try and better understand where I was going wrong, and where you were coming from. Prior to this, my last look at Common Core was many years ago, and fairly brief. It also lacked appropriate context, just the news, so I was entering with a bias (more on that bias later).

I do agree that providing a formula and telling kids to use it 100 times to drill it into their head is probably not a great way to teach. A person can't really extrapolate on ideas when they aren't understood, but rather memorized. It wasn't until after collage that I stumbled across some gifs showing how/why various formulas in geometry are what they are, and I was really upset that those types of things weren't shown in school. All I had was Donald Duck in Mathmagic Land, lol. I find it much easier to remember things if I can conceptualize them and understand why something is the way it is. If I can deduce it myself, to the paper's point, that is even better. That way, even if I forget the formula, I know how to get back to it.

My opinions on any change of the math curriculums have been colored by my own experience 25-ish years ago when my high school introduced Integrated Math, to replace the traditional track. My class was the first one without a choice. At the time we were told the idea behind Integrated Math was that no one needed high level math, so why bother preparing kids for it... which was an idea also touched on in the paper. I was planning on going into engineering and needing high level math, so that program kind of screwed me. To live in the author's perfect world, college would likely need to change as well to not assume knowledge of various things going into college level math programs. I liked math (or at least what I thought was math before reading that paper), and Integrated Math destroyed that for me. It was very unfortunate. A year after I graduated, I received a letter from my high school asking me about the program and what I thought of it after having been out for a year. I wrote a pretty scathing letter in response. The program was abandoned some years later. I tried to jump on the traditional track in college, but I did too well on the placement test, so they wouldn't let me take algebra, but didn't really get the foundation to effectively move forward into calc.

To this day, I still feel like I have a gap due to missing out on the traditional math track in high school, and the ramifications that had on my college and career (not that I'm doing bad, I'm probably better off for it). Hindsight being 20/20, I didn't actually need it, but things do come up from time to time that make me think I missed out. I've attempted, to go back a few times to learn on my own. Without being in school, and the boring nature of most mathematics instruction, I've never gone that far.

I like the ideas presented in the paper about viewing mathematics as art. At the risk of going against every point he was trying to make, are you aware of anything resources that teach mathematics through this lens that I could check out? Some sort of framework to give me problems to try to solve to lead me in the right direction, while also showing how to see math problems in the everyday and the solutions as art, instead of wandering around in the desert for the rest of my life hoping I stumble upon the problems/solutions that took centuries to uncover. Are some of the Common Core resources out there a good place, or is there something in the spirit of Lockhart's paper that is better?