A student I started working with said he can factor trinomials and he understands the process for the first time in his life. (He is a high school graduate, with some college under his belt.) He was OK factoring some of the form x^2 + bx + c, but now he grasps those as well as those of the form ax^2 + bx + c. In all his years at school, from all the teachers he had, he never learned how to factor. I’m the only one to give him a comprehensive presentation of it.
I like that compliment, that last sentence. It shows some intelligence on his part: he knows, in some sense, that I gave him an integrated, hierarchical presentation, not merely some rule of thumb out of context of most everything else he knows. I taught him as the ancient Greeks would, not the ancient Egyptians.