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Comment by PaulHoule | Hacker News Reader

See https://en.wikipedia.org/wiki/The_Two_Cultures

When I was homeschooling my son I got him between 2-3 grades above grade level at math. He was so good at mental arithmetic that I had to improve my skills to keep up with him. On the other hand I was not able to get him to do algebra at all and he did not master it in high school although he did OK with geometry.

From my viewpoint it was really puzzling, almost like he had some kind of psychological resistance or mental block to the whole idea of algebra.

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This is not uncommon. My education was in math and, although there are also polyvalent people, I'd say quite a few of my comrades were either mainly Analysis or mainly Algebra people. In a sense, Algebra is similar to high-level languages and OOP, thinking of structure and how things articulate because of their nature, Analysis is like closer to the metal programming, how does this thing behave locally, controlling approximations and such. I believe programmers are equally split along this axis, are they not?

This split does exist, and I often refer others to https://josephg.com/blog/3-tribes/

There's a 3rd type of programmer, besides the first two you mentioned.

Not sure which one I am in. It really depends on the project and who I am working with, I’m kind of a chameleon and sometimes I change to fit in with my organization and other times I change to be what the other people around me aren’t.

When I was 12, I'd been BASIC programming for two years, and of course I used variables constantly (variably?) yet I didn't understand this simple crucial fact about algebra, which is that the letters are variables. I had a bright yellow pocket book titled "Calculus" and I used to carry it around in the hope that people would notice, but I couldn't understand page 1. I was into substitution cyphers and I devised a few, and I read about numerology, and at one point came up with the theory that the letters in algebra stand for numbers based on their position in the alphabet. Despite being steeped in all these instances of symbols standing for other things - and maybe even using x and y as variables in my programs - I just didn't imagine that algebra might be doing the same thing. It had a sort of stony, inscrutable face, permanently mysterious.

My wife teaches Algebra 1 and this is something she’s encountered with a few of her students. They’ve been able to get by more or less by using what we refer to as “advanced arithmetic” e.g. figuring out the variable in an equation by inspection rather than solving the equation. But of course that only gets you so far, and she’s worried they’ll bomb Algebra 2 next year. But no matter what she does they just can’t/won’t learn algebra.

You mean like numerical analysis, where you stick values in until one works, and call that the answer?

Basically. The questions were easy enough that they were doing it in their heads. She figured it out when she made them show their work, and their "work" turned out to be just plugging the right number into the equation.

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