What appropriately challenging cheat-proof calculus assignment could you give to a classroom of 100 undergrads?
As soon as those questions leave the classroom, they will be passed around in group chats. That’s why exams remain relevant. If a student averages 95% on their assignments, but shows up to the exam and can’t solve ∫sin x dx like they had supposedly done a hundred times on their own, then they’re probably cheating.
We don’t even have math assignments anymore. All we do is write an exam at the end of the semester, and the people who didn’t learn will just not pass.
The math exam which I wrote was also very demanding and had a very tight time limit. There wasn’t any time to compare results with a group chat or use tools like wolfram alpha. Either you knew how to solve the exercises or you didn’t and failed.
If you are teaching something you're probably teaching it for >10 years. If every year you create 20 multi-part questions ("We have a factory producing boxes, what's the optimal size of box for X when Y"). You can then distribute a random question to every student in a similar bin of grade distribution. If a group of people are cheating they'll likely be in the same grade bin so this makes sure each cheater doesn't see the questions everyone else does.
You repeat this process every year for 10 years and now you have 200 questions. The next professor comes in and does the same but now also has 200 questions + answer guides.
With some basic programming you could make it automatically change the numbers (to "friendly" numbers that break up into round numbers) and have an infinite pool of challenging quiz, midterm, and final questions. If everyone gets different questions they cannot cheat by sharing answers. Only by sharing approach.
For one of my physics classes, it was like 10% HW, 10% class participation quizzes, 30% lab, 50% exams. The HW was optional (and your exam scores would replace your HW scores if you so chose) but the HW pretty closely followed the exam. The class participation quiz points were fully awarded as long as you showed up every day to lecture. The labs weren't skippable or cheatable because everyone had different measurements and you had to document every step of the way. The exams were personalized 1-10 such that you'd never be sitting next to anyone who had your same exam (and the questions were never recycled). Two pages of notes allowed on every exam.
Apart from some high-tech cheating, I'd say it was a reasonably cheat-proof class. I don't know how applicable that model is to calculus though.
Sounds like a proof of work system is needed. Let’s say every answer included a something unique to the test taker, time, place and question. These values would be inserted early in the computational process, like maybe as a coefficient to sin, such that the process is easy to grade but difficult to cheat since the values of each downstream step are unique.
As soon as those questions leave the classroom, they will be passed around in group chats. That’s why exams remain relevant. If a student averages 95% on their assignments, but shows up to the exam and can’t solve ∫sin x dx like they had supposedly done a hundred times on their own, then they’re probably cheating.