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.

This isn't really a heuristic, but I hate "functions are formulas". For most students it takes 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

\begin{gather} f(n) = \{\text{1 if $n \bmod 2 = 0$ $\lor$ $-1$ otherwise}\} \end{gather}

as a function until you write it as $f(n) = (-1)^n$