<p>Going back to a good point raised by Pizzagirl in post #408 (and with a promise to catch up on the intervening discussion later): What about students whose high school background and approach puts them in a situation where introductory calc-based physics is hard, even with a lot of work? (Also, with apologies for the continued physics focus).</p>
<p>People in the STEM university community do wrestle with this issue, though probably not as much as we should. About 20 years ago, there was a book by Sheila Tobias, called “They’re Not Dumb, They’re Different: Stalking the Second Tier,” about ways to encourage students to continue in science if they weren’t near the top of their introductory classes.</p>
<p>We need lateral thinkers in science. We need people who can look at a problem scenario and not have the same set of thoughts about it that everyone else has. Therefore, we would really benefit from different thinkers. At the same time, we really need to build their capabilities, so that they can actually put their different approaches into use.</p>
<p>How to accomplish this? I have worked on a few possibilities over time. The first is to try to make the implicit assumptions explicit. There are a lot of cases where a problem in my field seems hard, because a student has not noticed some feature that other students quasi-automatically bring to bear on the problem. It might be a standard mathematical approximation, a physical principle, or something totally different. It might be a question of how the problem is worded. It is hard for a faculty member to predict this sort of thing–especially at first–but with some experience, one can pick up patterns and try to re-word questions for clarity.</p>
<p>Another approach that I use is based on the premise that lateral thinkers may need more time to solve problems on tests, because they think of multiple approaches, instead of quickly adopting one and powering through to a solution. When I am teaching undergrads, I try to get my classes scheduled for a room that is unoccupied during the next class period. Then I write exams that are intended as hour exams. The first students normally leave after about 45 minutes. Since the room is unoccupied during the change of classes and also the next class period, I can permit students to stay and work for a total of about 140 minutes–which some of them will take. (If the students have a class scheduled right after mine, we work out an alternative exam time arrangement.)</p>
<p>One of my colleagues mentioned talking with a student who had come to office hours for help with a quantum mechanics course. As they were talking, he showed how to fill in the gaps between successive equations in the text by doing a short derivation. The student remarked, “You are allowed to do that?!” So problems can come from a direction that looks like “out of the blue” to a lot of faculty.</p>
<p>On the thread about the new NY state common core exams, I mentioned that with tests of that type, it is often very illuminating to see what students were actually thinking if they picked the wrong answer. I never give multiple choice exams, but I do try to have students articulate their thinking or approach, even if it seems to be going nowhere.</p>
<p>At the root of it all, though, there is a lot of hard work that goes into understanding physics. I think that understanding has to be achieved by each person, personally. No teacher, no matter how good, can confer understanding from the outside. The teacher can set things up so that as many students as possible acquire understanding, but it is really non-transferable.</p>
<p>Having been in a discussion with PG about how “hard” various types of work are, I am not looking for a reprise of that. Other things are hard, too.</p>