In this section, Prof. Aram Harrow shares his approach for helping students move forward when they become stuck during problem solving.
Usually students get stuck on a problem because they possess a brittle understanding of the technique involved in solving it. They know how to apply the technique in one context, but they don’t understand the larger framework in which it’s embedded. When I can get students to explain why they’re solving a problem in a particular way, I expose misunderstandings they have about the bigger concepts involved in the problem, and this helps me support them strategically.
Assuming the problem set isn’t due the next day and I have ample time to support a student stuck on a problem, I take a Socratic approach to help the student explain how he or she is thinking about the problem. I ask the student why he or she is approaching the problem in a particular way, what he or she knows about different approaches for solving the problem, and why the student thinks one approach might be more or less productive than another. This dialogue seems to helps students move forward with solving the problem.
I also look at students’ calculations, and point out simplifications they might not have seen. I think sometimes students learn a certain way of doing something, and they might do it 100 times and never realize that they could have been doing it differently the whole time. They could get the answer either way, but if they do it the simpler way, their solutions might be less prone to errors. Although pointing out simplifications might not help students get “un-stuck,” when solving problems, it is an important part of supporting their overall problem-solving endeavors.