Teaching is about understanding what the student needs. Sometimes a nudge in the right direction is all the student needs to come to the right conclusion. It is best to try to give the student just enough so that they figure things out on their own. However, a teacher needs to be able to tell when the student is not going to make the connection. This could be because the solution is counter-intuitive, or because the student has misunderstood or forgotten a fundamental. In either case, it is important to work from the ground up and make sure the student understands the problem at a fundamental level. Regardless of how much work it takes to come to the solution, it is important that in the end the student is able to voice the solution in their own words.