Recent efforts to teach thinking could be unproductive without a theory of what needs to be taught and why. Analysis of where thinking goes wrong suggests that emphasis is needed on 'actively open-minded thinking', including the effort to search for reasons why an initial conclusion might be wrong, and on reflection about rules of inference, such as heuristics used for making decisions and judgments. Such instruction has two functions. First, it helps students to think on their own. Second, it helps them to understand the nature of expert knowledge, and, more generally, the nature of academic disciplines. The second function, largely neglected in discussions of thinking instruction, can serve as the basis for thinking instruction in the disciplines. Students should learn how knowledge is obtained through actively open-minded thinking. Such learning will also teach students to recognise false claims to systematic knowledge.