Why, though, do they think of a function as a machine for doing something? Because we tell them so. Before starting any standard CS curriculum (ignoring, for

Why, though, do they think of a function as a machine for doing something? Because we tell them so. Before starting any standard CS curriculum (ignoring, for a moment, self-taught hackers), the only place a student should have heard about "functions" is in math class---where they are definitions. They get to intro Java and we tell them "no, no, that's not a function, this is a function, look, it's got variables and for loops and increments and a bunch of returns all through it, this is the real stuff, remember it!" We un-teach them about recursion, and later, when we try to re-teach it to them, we have to undo all of our previous work. In the past, there was considerable merit to un-learning the inefficient definition-style functions and learning to think closer to the machine. Today, I think there's a lot more to be gained by sticking with the math-style function-as-a-definition, because we have efficient abstractions to deal with it, but of course, this is one of the friendliest forums for that sort of philosophy. FWIW, I propose that all of academia make a distinction between pure, recursive, definition-style "functions", and imperative, stateful "methods". Probably won't catch on :-/