Here's a totally different idea: lets assume that the true-false questions are on a related topic. We can give partial credit if wrong answers are consistent wi

Here's a totally different idea: lets assume that the true-false questions are on a related topic. We can give partial credit if wrong answers are consistent with each other: that is, if there is some (simple) model of the topic we're asking about that is close to the correct model and produces those particular wrong results. Intuitively, if there are a bunch of questions about the same "feature" and you get them all wrong, all those mistakes stem from the same misunderstanding. I guess in a well-written test where questions are conceptually spaced out this is not as much of an issue... So to give partial credit, we try to find a simple model consistent with the T/F answers and award credit based on how wrong the model is. In particular, this would catch the problem where you have a single misunderstanding that cascades into a whole bunch of wrong answers even if you actually understood the rest of the system fine. That's one of the main uses for partial credit in longhand answers, isn't it? How would we do this systematically? Well, we can't, really. But there are places where we could. I worked with a professor who did research in program synthesis, and I remember he had an interesting idea for education: when a student submits an incorrect program in, say, Scheme, we could try to synthesize an interpreter that would make the program correct and then extract what the students misunderstanding was. (For example: they used dynamic scoping instead of static scoping.) If you seeded your synthesis system with the various kinds of things students actually get wrong, this could be both useful and practical. You can apply the same idea to grading a test about Scheme. Award partial credit if somebody has a consistent mental model that just happens to be wrong. If they got a whole bunch of questions wrong just because they mixed up scoping rules—but understood everything else—partial credit seems fair. I guess this is pretty explicitly rewarding consistency with partial credit, but that also seems fair in a lot of classes like CS. To be clear, I don't actually think this approach is really practical: it's more of a thought experiment on what could be interesting. Even if it was possible, doing it on T/F questions would likely require a lot of questions since each one only provides one bit of input. If you had questions along the lines of "what does this Scheme program produce", you could get away with significantly fewer if you were clever about choosing them—but you'd still want some redundancy to be at least a bit robust to the student making typos as well as conceptual mistakes.