After teaching a course I try to make some notes on how it went, to help my memory the next time I teach it. But in general there is no reason those notes can’t be more widely shared, in case they are useful to someone else. So here are my thoughts on teaching Western Physics & Astronomy’s graduate course Astronomy 9610 “Fundamentals of Astrophysics” in fall 2014.
This course is aimed at beginning Astronomy graduate students. The idea is to provide some background in astronomy for students who may not have had it as undergrads. Even students with astronomy background are now required to take it as we’ve found that it’s helpful preparation for our PhD comprehensive exam. The goals of the course are to:
- familiarize students with astronomical jargon and modes of research
- give students experience with applying physics to astrophysics
- develop students’ problem-solving skills
Of course there is a course outline and detailed list of specific learning objectives. (Later edit: my colleagues Aaron Sigut and Els Peeters both contributed to both of these.) These are aligned with our expectations for the PhD comprehensive exam. Typically the course has about 10 students, about half to two-thirds with some astronomy background. While our students all have physics backgrounds, we don’t require the Physics GRE, so we can’t quantify their preparation that way.
For the last several years I have co-taught this course with someone else: the other person taught the first half, which covers stars, the interstellar medium and radiative transfer, then I took over and did the Milky Way, galaxies, and cosmology. This works out well from an expertise perspective, but does mean that the general tone of the course is pretty much set by the time the second person takes over. I haven’t found this to be a problem – my colleagues are awesome – but it is certainly something to keep in mind.
“What textbook should we use?” is often a big question when planning a course. We looked at a number of them when this course was started in 2011:
- Advanced Astrophysics, N. Duric
- Astrophysics in a Nutshell, D. Maoz
- Astrophysics for Physicists, A.R. Choudhuri
and eventually decided on “Astrophysics for Physicists” because it included most of the topics we wanted to cover at more-or-less the right level. It’s also a manageable size, which was important because the exams and quizzes in this course were open-book until 2014. [Note to self: students may have an e-copy of the book, in which case one needs to define the internet-usage policy during exams!] The idea of an open-book exam policy was that we wanted to focus on understanding rather than memorization, but we dropped it as we still found that students spent too much time looking things up.
In 2014 we switched over to using An Introduction to Modern Astrophysics by Carroll & Ostlie, largely because that was the new specified reference for the PhD comprehensive exam. The exam reference had been Zeilik & Gregory’s “Astronomy & Astrophysics” but that was getting rather out of date. Although Carroll & Ostlie is an undergraduate-level textbook and this can be problematic (in particular we found the worked examples to be overly low-level for our students), it does use a wide range of physics, which we thought was important.
A feature of this course is that we require students to submit weekly Reading Memos, on the material that’s the subject of the next week’s classes. These are graded for completion, not for content, and while some students found them annoying, others found it useful to be forced, er, encouraged, to keep up with the reading. We collected these on Fridays each week and I used them to plan the next week’s classes around the most common sources of confusion. In the future I would change a couple of things: (1) collect the reading memos earlier in the week so that I didn’t have to do weekend prep and (2) instruct students to focus on the learning objectives while reading, so that they knew what the most important parts of the reading were.
My in-class time was spent mostly using the board to explain material that students found difficult or to do example problems. I wanted the students to be active participants in class, by asking questions or participating in discussion, but this didn’t always work well. Possibly the time of day was too early for some students. I did have occasional success posing small problems, having them work in groups, and then explain the solution to the rest of the class. I tried not to just lecture with slides (although I did use some slides to show graphs and illustrate concepts) but it was too easy to slip into lecture mode and I still need to figure out how to better encourage participation.
Formative assessment in the course consisted of problem sets and in-class quizzes: n=4-6 of each over the term, with only the best n-1 counting toward the course grade. We changed n a bit from year to year, mostly downward to reduce the workload on both the students and ourselves. The problem set questions were intended to be challenging; given several weeks to work on them the students tended to do well. The quizzes didn’t go as well: it was challenging to come up with problems which tested understanding but were solvable in short periods of time. I tried not to reuse problems from year to year (we did make some previous quizzes available to students) but of course the issue with making up new ones is that there’s never enough time to thoroughly check them in advance. I made extensive use of other textbooks’ problems as inspiration for creating new ones.
Summative assessment in the course was a three-hour final exam which covered all of the course topics. We constructed these with a “do n-1 out of n questions” structure to give the students some choice of topics. As with the quizzes, running out of time was a problem for some students. I don’t know that there is a solution here: you don’t really want the exam to be a test of speed, but if you allow too much time it becomes a test of endurance instead. In most years we found a much wider range of student performance on the exam and quizzes than on the problem sets.
So is this course achieving its goals? Student evaluations have generally been quite positive, but I don’t know how useful they are. We have a small number of students who know that they will likely interact with the instructors over the course of their grad program, so they may be reluctant to say what they really think. One data point is that, since we started the course, no one who has done well in it has subsequently failed our program’s PhD comprehensive exam. (Students who do poorly in the course typically don’t go on to the PhD.) I would still like the instructor’s role in the course to be more “guide on the side” than “sage on the stage” but perhaps this is unrealistic in a course meant for students just out of undergrad.
Appendix: I mused on Twitter about making the course materials available for others to use, and got a positive response, so I’ll do that once I figure out the least painful method. In the meantime, Universe in Problems is one place that covers some of the course material at the graduate level.