If you want to know how a student will confront a real problem, you need to create a context where they won't try to outsmart whoever wrote the question.

It's entirely possible to solve a math problem using psychology instead of math, because math problems are made by people. We've all done a horrifying amount of schoolwork, and thus have a pretty good data set in our head from which to extrapolate.

Suppose I tell you that an algebra textbook question includes the numbers 32, 4 and 64 in the problem text. What's the answer? I'd bet most of us would guess 2 or 4.