This isn't really a heuristic, but I hate "functions are formulas."  It takes a lot of students a really long time to think of a function as anything other than an algebraic expression, even though natural algorithmic examples are everywhere.  For example, some students won't think of f(n) = {1 if n is even, -1 if n is odd} as a function until you write it as f(n) = (-1)^n.