[noduerme]

Doesn't this all go back to, sort of, "teach a man to fish"?

I never passed a math class after my second try at pre-calculus. Before that I never even had to look at a book. Looking back I think it was a failure for me to ask the right questions or a failure of the teachers to help me visualize how to work out the systems starting from basic principles. I couldn't solve anything without starting from scratch. Still can't. I get paid ludicrously well for making a marketable skill out of that form of reasoning, so I can't think it's either a mental flaw or laziness that prohibited me from grokking calculus in 12th grade. Somewhere in there was a failure to provide the reality handle that mapped to something I could reinvent if necessary.

[edit] fwiw I think I've reinvented trigonometry at least six times when I needed to for games. I never remember how it worked the last time.

[bawolff]

Keep in mind lots of high school math teachers are just bad at their job when it comes to calculus.

I do recall when first taking calc they briefly mentioned delta-epsilion proofs and limits but really hand waved past it, which i guess would be hard if you want everything on solid foundations.

[Loic]

8th Grade or so in Germany, my son got a tricky system of linear equations to solve. I showed him how to solve it in Python and also explained him how to quickly go back to fractional notation instead of floats (0.133333... = 2/15).

As the teacher looked at the results, he said I should receive a Nobel for my work. As my son told me that, I had a very long sigh...

[noduerme]

Hah. That's quite funny.

I don't think you deserve a Nobel, but I do think that teaching your son to solve lots of different problems with algorithmic recursion is going to help him much more in life than memorizing the way to solve one problem on a math test.

I don't think I ever understood math except where it was logical, within the bounds of what I could deduce. But when I learned to write recursive algorithms, that capacity for deduction expanded exponentially.

[bawolff]

I'm not really sure what the difference is, at least at the high school level between writing algorithms and doing math.

(Eventually math switchs much more to be about proving things [inb4 someone yells howard-curry], but that is more mid-undergrad degree.)

[coldtea]

So, what made those who did managed to grok it, grok it? Given that they had the same teachers and material?

[noduerme]

I frankly don't know. I went to a "gifted school" as a 1st grader that required you to pass an IQ test to get in and have >150 on their chart. This was in the early 1980s. At least half the kids were what we'd now call "on the spectrum". A couple of them were already performing at college level in math by the time they were 11. One of them went straight to UCLA when he was 13. I was programming in HyperCard at the time and could simply not fucking grok the math that the kid at the desk next to me was just absolutely smashing. I was inherently intelligent and I was raised with the best possible chance of getting to that level of competence and ability, but I ended up being an art school dropout who programmed a bitcoin casino and still can't deal with multivariable math unless I write a block of logic for it. I have no idea how or why that kid (Eric Kim was his name) was so much more brilliant than me. We were in the same exact math class with a really great teacher who also happened to teach the afterschool "programming club" in the Mac SE lab, in HyperTalk.

One kid just groks the math. One kid groks the fun(){} ...in a perfect world, those brains should just complement each other, I guess.

[lopis]

Different mental starting points and a healthy dose of randomness and luck. To me, learning maths always felt like playing puzzle games. The more you play different games, the more you get used to the "secrets" behind the puzzles and the easier your brain makes successful connections. But when you're learning calculus, you barely have time to make those connections. Give the same starting point and same experiences, brains will make different connections and learn things a little different.

[matwood]

I have a similar story as noduerme, but for me it was interest and laziness. I got by in all my pre-college math just by listening in class. But, if I couldn't connect it to something I found fun (like taking apart and putting back together my NES for the 100th time, or playing some sport), I just didn't do anything beyond the minimum. Then college came around, and I got an F in my first math course. I retook the course and found a teacher who connected most topics to gambling and/or business and I was hooked. I managed to take that teacher for almost all the math I needed for my CS degree :)