I taught a college pre-calc course for a short time. We had "show your work" exams, so I got to see how students solved problems. I think that many of them had been taught "test taking skills" in high school, including a method of finding answers to math problems by guess-and-try or process of elimination. Basically, their teachers had hacked the standardized testing process. (Probably including the AP exam).<p>Honestly, college math wasn't much better. Rather than confronting them with critical thought, we simply replaced the old hack with a new one:<p>1. Recognize the "form" of the problem, corresponding to a section in the textbook.<p>2. Plug the parameters of the problem into an equation solvable by the method of that section.<p>3. Apply the method and write the answer.<p>When I realized this, I told my students about it.<p>There was a chapter on maxima and minima. But the only function they had learned was the quadratic, so all optimization problems boiled down to arranging things into a quadratic. The text had them graphing each quadratic. I decided it would be more interesting for the kids to see how we make our own formulas, so we derived one for the optimum of a quadratic function, and memorized it.<p>Now is this math or not? Well, I think there's a place in math that involves classifying the forms of expressions and equations, sort of like taxonomy in biology. But it shouldn't be the only thing.