I think what you are doing is great! Good luck going forward!
I also don't think humans are less human just because machines started making mistakes similar to human ones.
But I do see this similarity as a reminder that machines are becoming more human in an accelerating way.
Isn't there a probabilistic nature to ChatGPT replies? So even if a student finds a response that gives a correct proof, that doesn't mean it'll work every time. Or am I wrong here?
I've asked students to share their full dialog, both prompts and replies, so the whole class gets to see; and I'll invite one or two to talk through their attempts. This is all just a trick to make students engage with "how do you you spot bugs in a proof?", hopefully more than they would from just reading CLRS! Often, students engage well when they're hearing the material from other students.
Edit: I was not in any way rude nor saying anything incorrect.
If you want to see how to do what I’m talking about, here’s an almost finished article describing the above:
https://github.com/williamcotton/empirical-philosophy/blob/m...
I asked ChatGPT to add element to a relation R={(1,2),(1,3),(1,4),(6,1)} so that the relation becomes transitive. The program was not able to do so. When I gave some hints to solve this problem ChatGPT began some steps and in those steps the program was claiming that some element that weren't in R were in R. Trying hard to give some more hints, for example asking to check each line of its output, the same error were made. Even I simplified the problem asking just for element r(x,y,z) such that (x,y) in R, (y,z) in R and not (x,z) in R and add those elements until there are no more r(x,y,z). The program made the same error in the intermediate steps not being able to detect what elements were or were not in R. So ChatGPT is like a toy not solve even very basic logic problem. Sorry for being hash with ChatGPT, but it should be considered just like a language model and not used for something more.
I'd be so honored to be one of these proofs. "Your wrongness is an elegant balance of instructive error and subtle misunderstanding. Can I save it for posterity? (c-)"
After we go through Breadth First Search, there's a practical assignment where students are asked to modify the algorithm to return _all_ shortest paths. Then I ask ChatGPT for its solution, and students try to spot its mistakes.
Later, after going through the proof of correctness of Dijkstra's algorithm, I ask ChatGPT for a proof of correctness of its all-shortest-paths algorithm, and again students try to spot what's wrong in the proof. I want students to learn to tell the difference between a bullshit proof and a real proof; in the past I've given them bullshit proofs from real students in exams, but ChatGPT makes the point more nicely.
Finally, students are asked to figure out prompts that will make ChatGPT give a correct algorithm and proof. I haven't managed this myself! I'm looking forwards to seeing what students manage.
Here's a link to lecture notes, including the ChatGPT dialog: https://www.cl.cam.ac.uk/teaching/2223/Algorithm2/alg2-full....