Is counter example a valid form of counterexample?

In student writing about math, I see the term "counter example" instead of "counterexample" too often. Does anyone have good ideas about why people think "counterexample" is two words? When I see the term "counter example" I think of something you’d find in a home furnishings store.

I don’t see people misspell the terms like counterpart or counterintuitive by making them two words.