bcrowell said:
Yes, problem solving certainly needs to be tested on exams. The empirical evidence I referred to above (described in the Mazur book) was from exams that included problem solving.
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This may depend on whether their conceptual understanding is really being probed. The classic observation described in Mazur, which I have reproduced myself many times, is that if you make a scatter plot of students' scores on the FCI/IBCM versus their scores on plug-and-chug problem-solving, you get a triangle filling in one side of the main diagonal, with essentially all students doing better on problem-solving than on the conceptual stuff. But the IBCM does require deep conceptual understanding. It's quite possible that many instructors give points that they claim are for conceptual stuff when in fact the tasks don't really require much conceptual understanding.
I think we are using very different contexts of the phrase 'problem-solving'.
Several of the physics faculty here use various incarnations of peer instruction- think-pair-share, A/B/C/D cards or clickers, etc. I call plug-n-chug problems exactly that- plug-n-chug, and plug-n-chug problems are used in peer instruction because they don't require much time to work out.
What I call problem-solving is more in line with George Pólya. [https://en.wikipedia.org/wiki/How_to_Solve_It] . This approach to learning is very different from plug-n-chug problem solving. 1/2 of my class time is spent working through a 'test-like question' to give students practice with this method.
And every time one of my students says "But I understand the concepts, it's just that I didn't use the right formula. I don't know how to start the problem." I point out (with a few quick questions) that they don't actually understand the concepts. Broadly speaking, my students are great at using Pólya's method in their everyday lives but horrible at using it for anything classroom related.
In fact, I believe the way students think of "understanding the concepts" is very different than instructors thinking "understanding the concepts". In my experience, students believe that if they can solve F = ma when given 2 of the 3 variables, then they 'understand' Newton's second law. They convince themselves they understand what 'Force' is (it's 'F'!). In my experience, many students believe that if they can learn the label of something, then they also understand what is being labeled.
Two examples demonstrate this fallacy: 1) I usually confuse a large fraction of my class simply by writing ma = F instead of F = ma. 2) If I use different symbols, for example I will say "Force equals mass times acceleration" while writing ϑ = ma, students ask me why I didn't use 'F' for Force.
I bet that what you are calling 'conceptual understanding' is close to what I call 'problem solving', or at least that the two concepts are related to each other. One demonstrates conceptual understanding of something by solving a problem involving that concept.