This post is primarily of interest for college faculty.
There have been a wealth of good discussions at this conference about how to work on making changes to upper-division or middle-division college courses. We’ve made so many great changes at the introductory level, so what are the issues facing our physics majors at the upper division? Dr. Manogue had several thoughts based on her many years teaching a radically transformed program at Oregon State called Paradigms. Here are some of them, below.
In junior E&M, the idea of having a vector at every point in space (which is the basic idea of a vector field) is quite new to students, and they struggle with it. One way to deal with this is to represent vector fields in multiple ways (like using color to represent the 3rd dimension).
Chunking & Cognitive Overload
I thought this was the most valuable idea mentioned in these discussions. Our working memory has only about 7 “slots” to put information in while we’re actively learning or thiking about that information. That’s why phone numbers are 7 digits long. We can increase the amount of information we can stick in our working memory by grouping ideas together in some way. For instance, which sequence of numbers is easier to memorize, 9749-6589 or 2001-1945? The second two are both easily-recalled years, whereas the first two are random sets of numbers. We can use chunking to help students process more information by using sets of knowledge they already have in order to teach a topic. For example, in E&M, you can build an understanding of potential, use their current understanding of forces, and then put those “chunks” together. In addition, just being aware of cognitive overload as you’re teaching these difficult topics is important. There are many concepts that we are already facile with, but students are thinking about them a bit more slowly. For instance, if you’re lecturing about the B field of a current carrying wire and use the term “theta-hat” and continue talking… if your students are still stuck on “theta-hat” they’re going to miss the rest of your brilliant explanation.
Mathematics and physics
There is a real mismatch between how the math department teaches math and how the physics department teaches math. One thing we can do in physics is to emphasize geometry and use a variety of ways of showing the math (like graphs, words, and pictures). We can also emphasize that math is about symbols and physics is about things. We need to separate our symbolic knowledge from the physics represented by that knowledge. That distinction is often not clear to students, who see the math in a symbolic for that looks very different when they leave math courses and enter physics courses.
In addition, the struggle to understand the mathematics at this level can cause a cognitive overload that makes it difficult for students to attend to the actual physics behind the math.
Chandrelekeh Singh (from Penn State) also gave a talk on some similar concepts. She added the following
Functional (conceptual) understanding
What we want students to be able to do, Dr. SIngh argues, is to be able to apply the concepts they learn to new situations In other words, if they learn about the general theory of conductors, they should then be able to do a problem in the real world that applies that knowledge. But this is very difficult for students to do. She found that graduate students had great math skills, but often lacked what she calls “functional understanding” — they had difficulty in answering conceptual questions. She thinks this is due to poor training at the undergraduate level.
Many of the concepts at this level are very abstract, and as instructors we need to help guide students in making the connection from the concrete situation to the abstract formalism (“scaffold” in ed speak). As instructors, we have much more experience with these abstract concepts an they seem quite obvious to us. We have an intuition about these abstractions which makes it difficult for us to empathize with students struggle. For example, she’s noticed that students continue to be uncomfortable with polar coordinates, and will often transfer a problem to cartesian coordinates even when it’s easier to do in polar.
The way the educational system is currently structured, those students who thrive in a system where you learn by lecture, not learning deep concepts and able to perform calculations without understanding are rewarded (through admission to graduate school). We, as instructors, make that system. If we want to reward a different type of student understanding, the onus is on us.