Checking for understanding

In this chapter, I argue that "checking for understanding" is impossible all we can ever do is check for misunderstandings. By using examples relating to Pythagoras' Theorem, I argue that correct answers are open to many interpretations, but incorrect answers (so long as the questions are well designed) can give really precise, valuable information about students' misunderstandings. We can never conclude that a student has perfect understanding of something, but we can devise ever-trickier tasks that will find the weaknesses in their understanding, and, once we have found them, that's where learning can begin.