I was a curve-breaker to the downside, I became convinced since that math is exclusively about plug-and-chug formulas, and that each course would fling these at

I was a curve-breaker to the downside, I became convinced since that math is exclusively about plug-and-chug formulas, and that each course would fling these at you. Now I better understand that it's a story about problem solving. I think organizing the course around the complexity of the differential model under inspection is a bad principle. The course should be organized around broadest-applicability solution methods to narrowest. Something like early numerical-methods. This might help lift the veil.