Grading True/False Questions

A student just told me that they had gotten a true-false wrong, but knew the answer. They had marked it "True" and then written in the margin, "It's true, but you made a typo: it should be x/y" (or whatever the math had been— I didn't understand the question well enough to know what she was talking about). So, as instructor what do you do with that?

Mark it correct of course. The correction demonstrates the knowledge we were testing for, and even if they missed the entire point of how True-False is supposed to work, we're ultimately trying to determine their knowledge of course objectives, not their understanding of test-format. So that's just funny, but deserves a mark.

Indeed, I would argue that all True-False should work that way. Good T/F design* includes students explaining why the F options are false. That not only catches the sort of problem above, but ensures that students choosing F aren't just guessing, and that they know the right answer. There may also be more than one way to make a false statement true...that's all okay, as long as it demonstrates the students knowledge (or lack thereof).

T/F Ice freezes at 0 degrees C

That's true; but 'false' and adding "at sea level" is also correct and tells you even more about the student's knowledge. Both answers should get the mark.

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*Okay, that's an oxymoron: almost all T/F are useless and to be avoided, but there are a few special circumstances—memorization of definitions, names, or dates, as if any of that is ever useful—where they can be used successfully.