Problem-Based Learning in Solid State Physics

I taught Solid State Physics for the first time at Berry in Spring 2010. In addition to the main concepts of lattice structure, lattice vibrations and phonons, electronic states and conductivity, and magnetism, I introduced the students to the Linux operating system and programming in the C language. The class went fairly well, and I had planned some improvements to the programming assignments as well as some new interactive worksheets when I taught it again in Spring 2012.

In early January, my wife and I attended a workshop on an instructional technique called Problem-Based Learning (PBL) at the University of Delaware (UD). The idea of PBL is to challenge students with open-ended, real-world problems for which there are no well-defined solution methods. Students can use course material as a valuable starting point, but must strategize, pose relevant questions, and pursue additional information in order to come to a resolution of the problem. One physics example described during the UD workshop requires students to use pictures and evidence from the scene of a car accident to prepare to be an expert witness for a trial. Great idea, right? I decided to include two PBL activities in the Solid State Physics course in Spring 2012, in addition to the other improvements I had planned.

It's challenging to create a good PBL problem! It must be clear and relevant enough to capture students' attention, but contain enough complexity to sustain investigation and discussion. It should extend the course material, should be within students' capabilities with some diligent work, yet should not be easily resolved via a simple Google search. There should be clear criteria to distinguish an effective resolution from an ineffective one, but the problem should not be fully determined, with only one possible resolution (i.e., one "right answer").

The UD PBL group maintains a digital repository of PBL activities, to which one can apply to gain access. The repository includes a number of problems in physics, though currently (as of March 2012) few for upper-level physics courses, and none for Solid-State Physics. During the workshop, I had created a trial PBL problem requiring students to apply an understanding of nucleation theory to devise a research strategy for further improvement of the the treatment of cataracts, which are known to start forming via the nucleation of misfolded crystallin proteins within the eye lens. As observed by other workshop participants, however, this question has been partly resolved in the research literature already, and would require specialized biological knowledge and further experimentation to really make progress on. It is really beyond the background and capabilities of students in an undergraduate Solid-State physics course, and would likely lead only to a literature search and a frustrating experience.

After more thought, I decided that engineering problems (specifically, problems for which no pre-made design algorithms appear in a quick Internet search) might serve as good PBL activities in upper-level physics courses. There is often a lot of theoretical material in upper-level physics courses, and engineering problems to which this material is applicable can be a fun change of pace, as well as help students to realize (discover) the real-world relevance of the material. To accompany a unit on strength of materials in my Solid-State Physics class, I created a problem in which students had to determine if a makeshift bridge was strong enough to support a loaded pickup truck. You can find a link to the actual assignment, including a funny backstory to help stimulate students' interest, at this website.

This was an unfamiliar assignment, so I gave the students a rubric clearly explaining how they would be evaluated: 20% preparation (before class), 50% participation (in-class), and 30% final presentation. During the in-class discussions, I served only as a facilitator, letting the students drive the work to the greatest extent possible. I did think about the problem on my own beforehand. During class discussion, I pointed the students away from a very technical formulation of structural mechanics and toward a more modest formulation of beam mechanics that was practical for the time allotted for the project. I insisted that the students define the most important next steps to take at the end of each class, and that they assign clear responsibilities among their team for work before the next class meeting. This did seem to keep the project focused, and to give me a way to evaluate each students' preparation work outside of class.

How did it go? Although the students did not pull together the final presentation quite as I had hoped, I think that the project was successful and a good use of class time. The students were exposed to the process of defining a challenging problem, making useful simplifying assumptions, and deciding on a mathematical approach simple enough to be tractable but accurate enough to be meaningful. They had to sift through a good deal of material and make decisions as to what was relevant. It was certainly important that I had done serious thinking about the problem beforehand, as this enabled me to be a useful guide during the process. (Note I did not attempt to see the problem through to a resolution beforehand, but did take time to explore several possible approaches and find some good resources.)

I am in the process of creating the second PBL problem for the course, which will concern electrical conductivity in some way. I will stick with the same basic structure for the second problem, and encourage the students to follow through more fully on their final presentation.

AST 121: The Discovery of Galaxies

In Fall 2010 I taught, for the first time, a new astronomy course called "The Discovery of Galaxies." This is a course intended for non-science majors. The course focuses on the historical development of idea about the place of our solar system within the larger universe of stars, galaxies, etc. We begin with the two sphere model of the Ancient Greeks in which the Earth was thought to sit at the center of a spherical surface, while the stars sat on this surface and rotated around the Earth once each day. We discussed ancient theories about the Milky Way and nebulae, then made our way through history examining important arguments as we went. We looked at various methods that were used to estimate the distances to stars, how the Copernican Revolution ultimately led to the conception that the Sun was one of an infinite number of stars in an endless universe, and how the invention of the telescope revealed the nature of the Milky Way and the nebulae.

Much of this first part of the course deals with very speculative attempts to understand the universe and our place in it. The middle section of the course introduces important new techniques that made stellar astronomy much more quantitative and reliable. The advent of photography, spectroscopy, and photometry radically changed the nature of astronomy and put the study of stars and nebulae in the forefront of the field. The creation of well-equipped and well-located new observatories led to tremendous advances, especially in the US.

The final part of the class dealt with the discoveries of the 20th century. These include Shapley's Big Galaxy, Hubble's discovery of Cepheid variables in the Andromeda Nebula (now the Andromeda Galaxy), the discovery of the expansion of the universe, and the eventual triumph of Big Bang cosmology.

Throughout the course the focus is on understanding the arguments used by astronomers to reach conclusions about the nature of the universe and our place within it. In many cases these arguments are faulty, or they were based on bad data, or they include hidden assumptions that turn out to be incorrect. This is part of the way science works - we slowly sift out the errors and try to keep the good stuff. My goal is to bring the excitement of real science to my students while at the same time giving them an honest view of what science is and how it works.

In order to best show my students how scientific theories are evaluated, and how theories and data are used in conjunction to reach conclusions about nature, I have the students spend their class time working through these arguments on their own. They work in small groups to complete worksheets that guide them through important arguments. In many cases they are assisted by working with computer simulations that I have created for this purpose. Anyone interested in my curricular materials can find more here:

Scale of the Universe Page

I have also written my own textbook for this course (the result of a year-long sabbatical), but the book has not yet been published.

I was generally satisfied with how the course went. I have not taught the course twice, and also taught an honors version of the course. Students seem pretty happy with the course, although they find it challenging. The mathematical level seems appropriate for my students (we use logarithms for the stellar magnitude scale, some trig for parallax, a fair bit of basic algebra, etc), but might be a little high for less selective schools (or a bit low if the audience is mostly science majors). I'm very happy with the way I am teaching the course. The activities are, I think, the most effective way for students to learn this material. They have to work through this stuff themselves. Group dynamics aren't always great, but when the groups are working well this teaching method is very effective.

For the future I would like to develop some large scale projects for the course, thus allowing me to move away from relying on exams for evaluating the students. I already have them do extensive essay writing. It makes the class grading-intensive, but I think the students get a lot out of it.

I'm hoping to publish some of the activities in The Physics Teacher in coming years, but anyone interested need not wait for that. Just look at the materials on the web site linked above.