As an undergrad at Carnegie Mellon in the 80s, I was explicitly taught to do all of these things in one of the first-year programming courses. And it has served

As an undergrad at Carnegie Mellon in the 80s, I was explicitly taught to do all of these things in one of the first-year programming courses. And it has served me very well since then. I especially remember how learning the equivalence of recursion and induction immediately eliminated the “frustrated trial and error” approach for making recursive algorithms that work.