I'm not spending a lot on this story or comments, only skimmed yours too (sorry) but I notice that you object to an emphasis on rote learning.
although it's nice to have history and background the truth is that the math that's most useful to us is pure rote - things like the multiplication table, adding and subtracting numbers.
when people go into a subject, like 3d game design, and 'wish they paid more attention in (that part of) math' they don't wish they had a finer appreciation for the background: they wish they would just know the formulas when they need them so they don't have to stop and think.
it's like logical arithmetic. if it's second nature to you you can refactor or's and and's and xor's and not's into and out of parentheses in code faster. who cares about the finer stuff behind it.
I am not saying this as someone who has a great deal of rote in me. But the part that I do have has served me well. I bet if I had been forced to memorize a 100*100 multiplication table and addition, and subtraction table (10,000 members each) and did my multiplication, division, addition, and subtraction, two digits at a time instead of how I do them (like everyone else) it would have served me quite well in life.
not saying that that's a good use of the precious little time kids have between 6 and 14, but just saying that rote is extremely useful for a lot of key things. set-theoretical logic, probably not so much.
although it's nice to have history and background the truth is that the math that's most useful to us is pure rote - things like the multiplication table, adding and subtracting numbers.
when people go into a subject, like 3d game design, and 'wish they paid more attention in (that part of) math' they don't wish they had a finer appreciation for the background: they wish they would just know the formulas when they need them so they don't have to stop and think.
it's like logical arithmetic. if it's second nature to you you can refactor or's and and's and xor's and not's into and out of parentheses in code faster. who cares about the finer stuff behind it.
I am not saying this as someone who has a great deal of rote in me. But the part that I do have has served me well. I bet if I had been forced to memorize a 100*100 multiplication table and addition, and subtraction table (10,000 members each) and did my multiplication, division, addition, and subtraction, two digits at a time instead of how I do them (like everyone else) it would have served me quite well in life.
not saying that that's a good use of the precious little time kids have between 6 and 14, but just saying that rote is extremely useful for a lot of key things. set-theoretical logic, probably not so much.