[patta54]

My high school calculus teacher was really great at this. He didn't just teach a bunch of transformations to memorize. That was part of it, naturally, as you aren't going to use the definition of limits and the FToC in all your problem solutions. He actually made us construct volumes from pieces of poster board, measure the segments and calculate the Riemann sum. When we did function analysis, he didn't allow us to use the Cartesian plane at first. We had to show visually how a function deformed the one-dimensional real line. How x^2 squished values between -1 and 1 toward 0 and stretched the other values toward +infinity.

It gave me a good "visual" grasp of the concepts and made most of my higher math classes much easier.

I do agree diff eq instruction sucks. I got an A in that class and didn't understand a thing. "This equation has this form; this is the canned solution."