Maybe you can show him some ways he can check his work without giving him the answers, like checking dimensions/units, orders of magnitude, substituting the answer back into the equation it is supposed to be a solution of, etc. These self-checking methods are absolutely vital in the “real world” but aren’t emphasized much in textbooks or lectures (at least not the lectures I went to!)
Simply telling him whether his answers are right will help him get a good grade but will not help him learn. It’s also unfair to the other students, because you can’t check everyone’s work ahead of time without making the final grade pointless.
In other words, you’re not going to give him right-or-wrong on the whole assignment, because as you correctly note that isn’t fair to the rest of the students. However, he may legitimately be asking for help. So tell him to pick two problems, any two problems, and you’ll tell him whatever he wants to know about them (short of providing the answer cold).
In other words, you’re doing exactly what you do for the other students, but you’re using a semantic shift to describe it differently and thus make it seem like you’re compromising and giving him part of what he wants.
That way, you’ll find out what he really wants. Sort of like the bum who asks for change because he’s hungry, and if you give him a sandwich he asks for the change anyway, because he really wants to buy a forty. If the student takes and appreciates your offer at face value, he’s on the up-and-up. If he resists, then he’s trying to cut corners and get the benefit of unfair treatment.
With the students I work with (adults taking continuing education in their profession) I will look at a few answers and try to pick one with a correct answer and one with a wrong answer and then ask the student to justify why they answered that way.
Quite often when talking the thought process out they will realize their mistake on the wrong answer. By giving them a right answer to ponder, they learn there is no free lunch.
I am not as concerned as to how many the student gets right as much as I am concerned as to how they think.
After reviewing the two answers I will ask them if there are any other specific questions.
Give the students a break and post the correct answers to all the problems outside your door. Just the answers, though and not the solution. In that way any sufficiently motivated student can come by at any time and check their work if they so desire. It is open to all who want to take advantage of it.
Homework should be the students’ opportunity to make mistakes. That is the time for them to best learn, and you learn best when you make a mistake and know you made a mistake.
For the better students, this can only encourage them to work the problems early and hand in quality homework. For other students, chances are any marginal grade benefit they get from higher homework grades will shake out during exam time.
