This is harder for professors to do, and maybe fails in intro courses, but generally is quite effective.
Although most homeworks and exams aren't nearly that cool IME, they're virtually all about synthesis and fundamental understanding rather than rote memorization. This "first principles" approach to most everything is one of my favorite things about Caltech.
Sagan told Thorne he was writing a science fiction novel, needed FTL travel, and asked Thorne if he could suggest something that would be reasonable. Thorne agreed to look into it.
After the conference, Thorne spent a while working on it and came up with a wormhole approach and worked out the physics of it.
In addition to giving it to Sagan, Thorne also put it on the Ph 236 (General Relativity) final exam. He didn't tell the students on the exam that it might imply FTL travel. He just set up the conditions and had them work out the physics. Most of his students succeeded in that, but he was a little disappointed that none of them happened to notice that it implied FTL travel.
(I got the above from an unpublished book Thorne was working on in the early '80s. It was a collection of biographies of and interviews with physicists, astronomers, cosmologists, etc., written and conducted by Thorne. He had the draft chapters and the raw interview transcripts in a world readable directory on the physic's departments VAX, where they were widely read by the rest of us with accounts on that machine).
Else you might as well call the degree "rote" because that's what you measure.
> maybe fails in intro courses
If someone cheats their way through intro courses they are up for a bad surprise since the upper level courses assumes a mastery of the intro classes!
I'd still point out that the system is not robust against: - Working in groups. (Bad if tests are supposed to assess individual performance.) - Asking outsiders for help.
Also, your downplaying of "rote" learning feels misguided, no matter how advanced/abstract/high-level the domain in question is. Cue the Bruce Lee quote about 10,000 kicks..
We are so used to exams being about doing stuff that literally nobody in real life would ever even consider.
However, I'd assume that doing either during a test would be against the honor code.
Students hate carrying dead weight so to speak. Sure they might be tempted to swap favors (A helps B for a certain subject and the reverse is true for an other one). If the exam is properly constructed you might be able to detect plagiarism however.
Rote is absolutely necessary for a well rounded education, but I really feel the need to overcorrect in the opposite direction because testing for rote is the lazy approach. Over time a lot of testing has the tendency to shift to simply measuring rote.
The real problem is people paying others to take exams, or simply copying answers from others. I work as an independent tutor, and I get contacted far too much by people looking to have me take their exams for them.