I was working in the math tutoring center and a student in a math ed class wanted help with creating a magic square given the center element and eight other numbers some of them negative. The peer tutor and I proceeded to help her solve the problem. At best, given my state of knowledge, the solution method is sophisticated guess and check. Afterwards I started to wonder why she was given the problem. I checked her text and found the problem in a section on the addition and subtraction of negative numbers. The intention of the assignment as I see it now was to get the student to spend some time adding positive and negative numbers. By helping the student solve the problem we subverted its intention.
So, when not to help a student with their homework? Answer: Most of the time. For most math homework is not about product but about process. When will a student get good at reading technical questions, recalling lecture material, finding information in texts, recognizing dead ends, finding errors in their work and all the other problem solving skills if not on the homework. How much learning happens if a student is taught “if you see a problem like this, here is what you do.” If students learn this way, a small change in the wording of a problem can throw them off. I’ve seen it happen. There is a line here somewhere. We have stepped over it. Too much mathematics teaching is about steps to working problems and not enough is about concepts and applications.
Note: I alluded to this before with to respect to group work in this post.