Getting students to solve problems effectively

I just gave the second midterm in my P132 course covering physical/wave optics and electrostatics with a few questions on the previous material of quantum mechanics and geometric optics. One of the comments I often see when I ask students to reflect on their preparation is along the lines of, “I did all the extra practice problems but still did poorly on the exam.” When I ask these students one-on-one about their study habits, it seems that often,  while they do try every problem, their procedure when they get stuck is inefficient.

What do students do when they get stuck on a problem? From informal conversations, it seems that many of them look at the answer and then, if anything, try to work backwards. If you ask them, “Why did you get stuck?” a common response in my experience is “I forgot equation X.”

Clearly, this is not a response that digs to where I think most physics teachers want students to go; such responses are indicative of students thinking about physics as a list of equations as opposed to a set of ideas. Further prodding of students, “Why did you ‘forget’ that equation? What idea are you missing?” can be met with stares.

I have tried in the past to get students to think about why they get stuck or why they get problems wrong as part of my in-class activities with not quite the results for which I would hope. First, I have learned that the instructor must provide some scaffolding: students do not know how to even begin approaching this process on their own. Of course, feedback is also important. How to achieve such feedback in a class of two sections of 250 each? I have tried having students write on scraps of paper their “keys” to the problem and then reviewing a few, but I am not sure how well this is working. Also, I find that many students are parroting back tips I have said with, I suspect, little understanding.