When Feynman was a boy he'd always relate the math problem to a real world puzzle. With trig problems, he might imagine being given a riddle involving a flag post and rope and calculating distance. One got the sense that he was, in effect, using math to prepare himself to solve future, real-life riddles. Or rather, math was giving him the tools to (correctly) answer questions he otherwise could not have answered - and Feynman's great preoccupation was his obsession with solving puzzles of all kinds, and he would enthusiastically (perhaps greedily?) grab at all the tools he could. (Physics leans heavily on trig almost constantly, so a total mastery of it would be quite handy for a budding young physicist).
It's also interesting to me that he was, at an early age, concerned with the usability of math, and was unafraid to create his own notation that was more comfortable for him (he liked the square root symbol and created analogs for sin(), cos(), etc.)
Frankly, I think this is a fantastic way to approach learning. After all, it feels good to solve puzzles; if you solve enough of them, the way they fall together, the way they relate to each other (sometimes in unexpected ways) become useful insights in themselves. With a large, solid core of puzzle mastery, you might even be able to turn your attention to the more difficult puzzles of "how to teach". (Of course, the greatest thing you can teach is the love of solving puzzles!)
I can't hold back anymore: what a foolish teacher! To get emotional over kids asking if their answers are right! In general, the yearning to be correct in one's calculations (and ordering cards is a calculation) is a good instinct, not to be beaten out of them.
It's also interesting to me that he was, at an early age, concerned with the usability of math, and was unafraid to create his own notation that was more comfortable for him (he liked the square root symbol and created analogs for sin(), cos(), etc.)
Frankly, I think this is a fantastic way to approach learning. After all, it feels good to solve puzzles; if you solve enough of them, the way they fall together, the way they relate to each other (sometimes in unexpected ways) become useful insights in themselves. With a large, solid core of puzzle mastery, you might even be able to turn your attention to the more difficult puzzles of "how to teach". (Of course, the greatest thing you can teach is the love of solving puzzles!)
I can't hold back anymore: what a foolish teacher! To get emotional over kids asking if their answers are right! In general, the yearning to be correct in one's calculations (and ordering cards is a calculation) is a good instinct, not to be beaten out of them.