My school system spends the first 7 years teaching that "math" is arithmetic with some vague hinting at algebra, and the next 3 teaching that "math" is matching

My school system spends the first 7 years teaching that "math" is arithmetic with some vague hinting at algebra, and the next 3 teaching that "math" is matching the problem to one of maybe 30 types, remembering the "correct" algorithm, and executing it on paper. It's not until Physics and AP Chemistry (first accessible junior year) that anyone tells you what calculus is, much less lets you glimpse the incredible beauty of what it can reveal about nature. When Precalculus started to introduce derivatives, I had the same thought as binarymax: you could have told me that years ago. When we first started working with slop and x^2 in 6th grade, it occurred to me that a curve's slope must be an equation instead of a nmuber, but the school system wasn't going to develop that thought for 6 years. I definitely agree with teaching math inside science. That's where a lot of it was invented, anyway, and it's a lot easier to stay motivated when you can what the skills you're working towards will let you accomplish.