A huge problem with math is we end up teaching mathematical vocabulary, not mathematical fluency. It's like high-school language classes: everyone memorizes voc

A huge problem with math is we end up teaching mathematical vocabulary, not mathematical fluency. It's like high-school language classes: everyone memorizes vocab lists, stutters out canned phrases, and forgets it all later. I'd prefer to speak fluently with a 3-year old's vocabulary than artificially with a high-schooler's. Similarly, I'd prefer students leave high school fluent in basic algebra, vs. trying to force-march people through algebra 2, trig, calculus, etc. when it's clear they'll just hate the subject afterwards. (Some students will read ahead, great. The others, since they actually enjoyed math, will pick up the other stuff later). Asking "When will I use this?" reveals that we don't understand a major goal of math education: fluency with powerful mental models, not just factoids you can directly apply.