I think one of the key points comes at the very end: teaching algorithms becomes rote learning _if the teacher does not understand the underlying mathematics in depth_.

I wonder how many of the teachers who advocate for "visual" learning instead of algorithms are doing so because otherwise they'd have to admit they couldn't explain why the algorithm works themselves?

Math was always really tough for me. My mother professed a "math block" and didn't deal in numbers. My father knew everything but kept the numbers to himself. I do suppose he helped some on my elementary math problems. There was no shortage of calculators, slide rules, and other gadgets lying around our home.

I sometimes surprised people by telling them that as a computer hobbyist/IT professional, I needed to know very little about math. As a programmer it was true. Internet engineering can rely highly on crunching small numbers in terms of addresses, ports and other things, so you get the binary and hex conversions.

But by high school, I was questioning the goals of learning advanced math. I was railroaded into calculus and beyond by college, and my teachers weren't great at giving me real-life scenarios where I'd be using this in my career or daily life, so I sort of checked out. I typically confuse numbers and forget them easily (unless it's the first girl I phoned in high school) and it worked out that I never needed calculus or trig in my career or daily life, ever at all.

Returning to community college recently, I found reductions in math requirements for the IT degrees, and lots of help. There was a supportive tutoring center where they could walk me through anything. I took online classes where I could basically brute-force every quiz for 100%. And if I was inclined to cheat, there were calculus solver websites that could do everything where my HP calculator fell short.

I suppose if I were a city planner, or a farmer-businessman, or going for some MBA to run companies, I'd be interested in calculating volumes of things or predicting financial outcomes, but I'm not and I won't, so these days I'm just amusing myself with finding prime numbers, and factoring the other ones.

I think this is an important realisation and it brought to mind John Von Neumann, who said to Felix Smith: "Young man, in mathematics you don't understand things. You just get used to them."

I think I have sabotaged by own education in maths (to a degree) by wanting to "understand" the "why" of something rather than just get used to it, practice and get fluent. The understanding can wait and might not even be important.