This post is mostly directed towards college teachers.
I just went to a session with Brad Ambrose from Grand Valley State University (in Michigan). Along with Michael Wittman from U. Maine, he’s developed tutorials for teaching college-level mechanics. All his materials can be downloaded at http://perlnet.umaine.edu/imt/index.html.
Tutorials are a small-group method for teaching material so that students wrestle with the concepts in an individual way, engaged with the questions and figuring it out for themselves, instead of being lectured. Students must be intellectually active in order to learn material, and it’s been shown that when students advanced topics (such as upper level mechanics or E&M) they don’t actually reflect on the basic ideas that underlie these topics. Many faculty believe that the advanced understanding of a topic will cement a better understanding of the basics, but it’s not clear that that’s true. So, the tutorials focus on the conceptual understanding and reasoning behind a topic, and making a connection between the math and the physics. His tutorials replace one or two lecture periods (out of 3 50-minute lectures per week).
His tutorials consist of a pretest, the tutorial, and then related homework. The one that we did asked a pre-test question involving equipotential lines and which direction a charged particle would move when placed at different points along those lines and the relative force on the different particles. Many students answer the question in terms of the *magnitude* of the potential at a particular point, instead of the *rate of change* of the potential at that point — in fact, only 10% of them get the question (magnitude and direction of the force) correct. The tutorial set up an analogy using contour maps and which direction a boulder would move when placed at different points on that contour map, and then asking questions about force and potential energy. By the end, students can articulate the relationship between force and potential. Note that when I taught junior E&M, I saw that many students did indeed struggle with these relationships, between Force, potential, potential energy, and work.
I think that these tutorials or other group methods can be very valuable for junior-level physics majors. Many of the skills we wish these students to get by the end of their junior year are not made explicit (like checking units, etc). We expect them to pick up many of the tools of physicist by osmosis by doing hard problems, and faculty indicate that they don’t want to “coddle” them by telling them specifically what they should do (such as setting up a clear analogy about introductory topics, as in this tutorial, or even just telling them to check the units in their answer). However, we observe that many students aren’t making the connections that faculty wish them to, and so we argue that making those connections more explicit is an important part of these courses. Corinne Manogue at OSU argues that these courses aren’t really upper-division — they’re middle-division. These courses are a bridge between the freshmen/sophomore level courses and the more sophisticated upper-level courses. Currently as these courses are taught, there isn’t much of a bridge, students are asked to jump quite abruptly from freshmen-level to advanced skillsets.