Showing how to be wrong

After writing the previous blog post (Finding errors by asking how your answer is wrong) and rereading one I wrote three years ago (Who tells you if you're correct?), I got to thinking about how students are supposed to learn how to check if they are right.

It occurred to me that, at least at university, we almost always show students how to be right, but almost never show them how to be wrong. We give them highly polished examples in lectures that proceed smoothly from the original information to the final answer, and then we move on. We very very rarely check our answers to see if they are correct, and even if we do check them, they are correct.

So the students never see any examples of how to deal with the situation where they are wrong. Is it any wonder, then, that they don't know to find and fix their own errors?

If we're going to give them examples in front of the class, I think we could spend a bit more time showing them how to check their work, and at least sometimes we should actually find errors that need fixing and fix them. Then they might actually see some strategies they can learn, rather than simply being lost when they're wrong.