What to do with students coming to office hours asking to check their homework? As a teaching assistant (TA), how to handle the situation where a student comes to office hours asking to check their homework? I.e. the student hands in their solution to the homework and ask the TA to check for any mistake. Assume homeworks are worth somewhere between 20% and 50% of the grade.

If country-specific, I am interested in the United States. If field specific, I am interested in computer science, linguistics, neuroscience and maths.
Answering from the point of view of a physical scientist, and in keeping with my personal take on what kinds of help are appropriate or inappropriate.

(I haven't been a TA for a long time, but I teach at an all-undergrad department so I have to be my own TA.)



These are great teachable moments if you have the time (and it can take a lot of time).

You don't check their homework, you ask them to explain their solutions to you.

But there is a catch: you don't let them get away with "I used this formula, and I solved for [variable]"; instead, make them explain their logic and the conceptual basis of their work step by step. When they are stuck or are proceeding incorrectly, you probe their understanding of the problem in a Socratic style.

The kind of questions you might ask include:


Conceptual basis


What physical principles apply to this problem?
Are their any hidden assumptions here? If so, what are they?
What statements in the problem or facts about the world brought you to select that particular approach? And why did you use that expression of the principle in mathematical form?
How well do the explicit assumptions in the problem match the real world (i.e. is this a PhysicsLand (tm) cartoon or a somewhat realistic treatment)?
Are these results reasonable for the real world? If so, why? If not how do you expect the world to differ and what neglected effects would make the answer more realistic?

Math basis (where they'll want to spend all their time at first)


Why is is that the right value for that variable?
Why is that substitution allowed in this case?
What does it mean that there are two solution to that equation? Which one do you use and why? Is the other one meaningful as well?
Does this situation actually meet the preconditions used in deriving the result you want to use?
Can this problem be stated as a special case of one we're already done? Why or why not?

Problem solving basis


What is the goal here? (You'd be surprised how often they lose sight of that.)
What can you learn from what we've been given? (If you don't know how to proceed just try shotgunning it; forward version.)
What list of thing would get you in position to find the answer? (If you don't know how to proceed just try shotgunning it; backward version.)
Do we already know the correct solution to a simpler version of the problem? Does that hint at a way to proceed here?



Most students will find those questions very difficult at first, but as they become more adept at handling the questions they should see their homework and exam scores improve markedly.

If they have the patience they will solve the problem for themselves right there in your office.

Though this is very time consuming most students will not be regulars. Some will simply become frustrated at what they see as your unwillingness to "help" and look elsewhere; and others will get better at the discipline: as the term progresses they'll bring you fewer problems and ask more perceptive questions about them.



In addition to wanting to talk about formulas first, they are going to want to talk about values ("and then I plugged in the 18 from the problem..."). Don't let them do that either. Make they say what quantity it was ("and then inserted the given initial velocity ...").

Beginners are all about numbers and formulas, but learning the discipline is about principles first, problem solving process second, and particular results last.



Philosophical note: As I see it the purpose of homework is to facilitate learning. I wouldn't even grade it except that there is no other way to insure that they will do it. That's why it doesn't bother me that they are getting a lot of support doing the homework for my class: when they come to me I get to make it a learning experience for them. 
(The first time they come in they may think they are going to get one for free, but they're in for some skull sweat.)

Admittedly, I get to decide that for my own class and when you are a TA, you may have to abide by the professor's opinion about how much and how directly you should help with assignments.