Teaching Computational Physics

Starting in September, I will be teaching first year undergraduate students computational physics. Well, that’s the plan, at least.

Mark Guzdial has posted a sobering series of blog posts that highlight how difficult achieving that plan is going to be. Mark’s blog posts summarize PhD research performed by Georgia Tech graduate Danny Caballero.

We experimented with a computational component in this course last year as one aspect of a series of major reforms. Our goal was to provide a small taste of how computer programming can be used in physics problem solving because this idea is emphasized in their textbook. However, we didn’t want to get distracted from our main goal: teaching physics. We provided the students with working vPython programs and problems that could be solved by making minor and obvious changes to certain lines of code, or changes to initial conditions, for example. We collected feedback from the students that indicated that no one was satisfied with this treatment: most students were not interested in programming and were frustrated at being forced to work with code they didn’t understand while the students who did have an interest in programming were frustrated at the lame, unchallenging activities they were presented with.

This year, we have decided to make a commitment to teaching programming, giving more challenging tasks that will satisfy the students who are interested in learning programming, while providing proper instruction in programming ideas so that (hopefully) no one feels the code they are working with is mysterious or scary.

In the first blog post, Mark explains why our students are less likely to learn the physics content of the course. Basically, by spending time on teaching programming, we have less time to spend on the physics, and the physics naturally suffers.

Of course, the main goal of the course is the teach physics, but it is a mistake to think that should be the only goal. It is especially a mistake to think that the point of the course is to achieve high student performance on the Force Concept Inventory. This course is an enriched physics course where most of the students are expected to go on to major in physics where they will take many more physics courses. This is very different from most first year physics courses which, for most students, are the last time in their lives they will receive any physics instruction. In these courses, it is reasonable to be concerned that your students have not become Newtonian thinkers. But a student who majors in physics will have Newtonian ideas reinforced over and over for several years, and so there is perhaps less pressure to ensure they are thinking Newtonianly at the end of their first course.

What is important for these student, in the context of their entire degree, is that they become well trained in all three pillars of physical reasoning: theory, experiment, and numerical computation. In my own undergraduate experience, I spent many hours each week developing myself as a theorist, and many hours each week in the lab developing myself as an experimenter throughout the entire duration of my degree. Numerical computation was relegated to a single course in a single semester taught by the math department without any explanation for how numerical analysis might be used by physicists. So, we would like to fix this problem and instill students with the idea that being able to solve problems by programming a computer is as important to your training as a physicist as being able to analytically solve problems, or make careful experimental measurements. Like analytical problem solving, or experimental methods, numerical techniques should be introduced early and reinforced throughout the entire duration of the degree program.

So, it is good to teach numerics to first year students, even if it temporarily sets back their education in physics concepts like Newtonian mechanics. The important thing is finding the right balance, and using the time you spend well.

The third blog post in the series, has even more troubling news for us. Caballero developed an instrument to assess the student’s attitudes toward computational modelling. This instrument is a series of questions which probe various aspects of attitudes, and the student answers are compared with answers given by experts at computational modeling. So, it produces a measure of how “expert-like” the students have become over the course of instruction. But, the results from this instrument are negative.

In particular, students after instruction had less personal interest in computational modeling, agreed less with the importance of sense-making (the third bullet above), and agreed more with the importance of rote memorization (last bullet above).

These results remind me of how students attitudes toward physics and science often shift to becoming less expert-like after most physics courses. Learning is shaped like a U, with an initial decline in performance as knowledge is getting restructured.

If some negative progress early on is a normal part of learning computational physics, perhaps we shouldn’t be too concerned, given that this isn’t the only course they will take. After all, the grand plan is to keep developing each student’s ability at computational physics regularly over the course of 4 years. So, if the bottom of the U occurs after the first semester, there is still plenty of time to spend on getting the students to climb up the slope of the other side of the U over the next three years of computational physics instruction. By the end of that, they should be more expert-like than when they started school, even if they experience a dip somewhere in the middle…at least according the the U-shaped learning idea. If most of the students in a course will never do another physics course, leaving them at the bottom of the U is probably a bad idea. But, with students who are majors, the final state of the student brain is what it looks like at the end of the entire degree, not at the end of the first semester of instruction.

Unfortunately, it may be a long time before we can really start thinking about the efficacy of entire degree programs in a truly evidence-based way. What PhD student is going to want to research a whole 4-year degree for their thesis project?! For the moment it is very frustrating that in trying to move forward, you have actually taken a step backward and have to look for excuses that make you feel good about knowingly taking that step backward.

Now, I’m going to take a close look at the types of errors made by the students Caballero worked with and figure out how they might inform our computational physics instruction. I’ll post more as the brilliant insights come to me.

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