How Would You Handle Students Cheating?
I gave my students a take home exam over spring break. (This is normal where I teach) One of the questions was particulary difficult. It came down to a factor of three in the solution. That factor inexplicably appeared with no justification on many of their exams. I intend to have the students I suspect of cheating come to my office to solve the problem on the board. What would you do?
How do you deal with students who say “my gut says it works this way. This is an easy problem, the answer is obvious. I don’t know how to explain it to you any more simply”?
I mean, it takes 162 pages to formally prove that 1+1=2, but we got by just fine before we wrote down that proof. We just knew the answer, we couldn’t explain how. If a student is gifted, a high school level problem could be as simple to them as 1+1 is to most people. They might know and not be able to explain how. Now, in a university environment I’d expect them to learn the proof, but that’s not the point of high school maths, is it? The point of high school maths is to know how to solve the problem, not to know why the solution works.
it takes 162 pages to formally prove that 1+1=2
This is ridiculously backwards, Whitehead and Russell’s motivation for writing the PM was to come up with a set of axioms and deductive rules that the entirety of mathematics could be derived from. When they worked out their proof that 1 + 1 = 2, it didn’t tell the world that now 1 + 1 = 2 is now officially a fact, it told the world that the logic and axioms they built were capable of deducing some very simple facts that we’ve already been confident are true. The hope was that maybe if we keep working at this and modifying our rules when need be, we’ll be able to get a set of axioms and inference rules that are sufficient to determine the truth of any mathematical question. A few years later Gödel came along and completely obliterated any hope of a project like that succeeding, and today literally no one thinks of the PM as more than a historical curiosity. (If you actually wanted to prove 1 + 1 = 2 from first principles today, you’d use the Peano axioms for the naturals: S0 + S0 = S(S0 + 0) = SS0, done.) That’s a tangent from the actual topic but I feel compelled to call it out.
Getting back on track, probably 90% of the points I give on exams are for partial credit, because there needs to be distinctions between having no clue, knowing where to start and getting stuck, understanding essentially every meaningful step but then writing 1 + 1 = 3 to wrap up, etc. I’m grading on both their ability to solve problems and their ability to communicate their ideas. Both are equally important.
This is very controversial, but I don’t go out of my way at all to worry about cheating. I don’t want to play policeman and teach with the mindset that my students are potential criminals. Even if I’m 99% sure a student is cheating, if that happens enough times I’ll hit the 1% where I’m giving a student who doesn’t deserve it an undeservedly hard time. I’m not paid anywhere near enough for it to be worth having a more adversarial relationship with my students.
I had a student earlier this month where it looked like he probably snuck out his phone for an exam. I just wrote a note on those problems that I couldn’t follow his work and wasn’t comfortable giving points for work I don’t understand, please walk me through your solutions for the points back. I told him this verbally as well when I handed it back to him. He never took me up on that, but it feels more humanizing than just calling him a cheater. I think OP is getting at something similar, but I think there’s value in not phrasing it in an accusatory way.
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Christian