I haven't done it either (and as a grad student, have only ever written portions of exams, never an entire test). However, my general opinion from the students' perspective is that offering hints is an added choice (unrelated to chemistry) that could make the exam in general more stressful. Why spend brain power weighing the odds of needing the hint, when that energy could be spent answering other questions or checking one's work? There's also the potential for humiliation, especially if hints are requested during the exam by raising ones hand (for example). Which starts to get into dicy psychological stuff that I think would detract from the exam. I guess my philosophy is that a well written exam will provide a variety of opportunities for a student to demonstrate their knowledge without the need for hints. If the questions are computational, written alternatives can be incorporated into the exam, like "Using your answer from part A, determine/calculate X... OR, for (n) points less, determine/calculate X using the following value ___." (And, if they used an incorrect answer from part A, they would lose no more points than if they'd taken the given value, etc.) Those are my thoughts. I'll be interested to hear others.

This is an interesting idea.  I'm not sure how one would go about implementing it, though.  I do know some colleagues who will let students re-do certain exam questions.  Usually this has happened when most of the class did poorly on something they *should* have been able to do.  In that case, the professor has let them work on the question as a take home exam and then if they do well, they get some partial credit back on the exam.  Perhaps one might be able to implement something like that where ground rules were discussed before the exam and if the student got really stuck she could elect to do the question at a later time, take home for partial credit.

The only time I've seen this done "in the flesh", as it were, was in my undergrad Quantum course. We had challenging multiple choice questions at the beginning of the exam, with 5 possibilities, and they were worth, say, 3 points. You had the option of picking (e). Options (a) through (d) were plausible (if occasionally humorous) answers, and (e) was always, "I don't know. Give me a point."

The cynics reading this will have noticed that this is mathematically identical to the manner in which the SAT penalizes you for guessing. The psychology is, of course, completely reversed.  It's kind of a relief to pick up a point for being willing to say, "Yeaaaah.....I just dunno."

I tried it on my final exam this year.  Its a long story, but I gave one version of my final as an oral exam, and realized that one question was too hard.  So I wrote up 2 hints, one worth 5 points (25% of the problem) and the other worth 10 (50%).  The first hint was designed to get students over the biggest stumbling block of the problem.  of the 8 or so students who took hint 1, 5-6 of them found it useful.  hint 2 changed the problem dramatically, and the 2-3 students who took hint 2 scored most of the remaining 10 points.  I think it worked well.  I did inform the students at the start of the exam that hint 1 was a hint and hint 2 changed to problem to an easier one, so they sort of knew what they were getting into.

Adam

Taking together Julia and Adam's comments, I wonder whether there are places this might work better and other places it might work worse. Julia mentions a scenario where I can envision it being all bad. Students (maybe even first-year) students are in a room, taking an exam. Asking for a hint is both a disruption and an admission of weakness before one's peers. Neither is really what you want to force students through. In contrast, Adam's scenario is in an oral exam, with students one-on-one with the faculty member, and the whole exam has a give-and-take flavor to it, where "I'd like to buy a vowel" seems perfectly in keeping with the nature of the test. I could see this working well on, for example, a challenging take-home exam, where the students are expected to come in and talk to the prof-you might be able to give "logistical help" (no cost), a "hint" (slight cost), or "a big hint" (moderate cost) on any given problem, without it suffering the problems of forcing students to run up a white flag to get through the Born-Haber cycle in a genchem midterm.