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?
There has to be evidence of their process for me to accept it as evidence of understanding/ability. I have made it clear to them that this is necessary. Their job is to convince me that they know what they’re doing. (But… I’m teaching HS Mathematics). So … I’d mark it wrong/incomplete. I’m also working on student understanding of consequences of their actions, so wouldn’t give them another opportunity on that exam. They would need to improve things on the next exam.
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.
I found the equivalent of high school maths in my country to be similarly intuitive and trivial. The kids who think that the maths they’re being taught is obvious will just memorise what the examiners want to see and regurgitate it even if they feel like it’s teaching shapes to a baby. If you are “gifted” and truly do understand it then it shouldn’t be hard to just overexplain (which is what most exam boards are looking for)
Yeah, I figured that out in high school too. I think it just irks me that different students are being graded on a different standard, subjectively speaking. The neurotypicals are being judged on their ability to learn, while the gifted kids are being judged on their ability to explain. Maybe the gifted kids wanna learn too. They’re all told their whole lives the point of school is to learn, and then they’re met with disappointing reality. We expect gifted kids to grow up so fast, and having to explain the material back to the teacher to prove they know it doesn’t help. I wish they got to spend a little longer just being kids.