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2013 July 4

Caballero on teaching physics with computation

Yesterday, Danny Caballero left a comment on my blog with pointers to three preprints of papers he’s been a co-author on:

I couldn’t agree more with the overall sentiment in this post. Computing is important for all students of science and for science teachers. However, as you say, I do think my dissertation work has been misconstrued a bit in this post. So, let me clarify.

The inventory you mention measures a small slice of mechanics taught in introductory physics. It’s been an important slice, but maybe now it’s time to think beyond it. What are students learning above and beyond this assessment? In M&I, they are learning about modeling, computing, and connecting the two. My work shows that the present implementation of M&I doesn’t produce great gains on this assessment, that students make mistakes in their code, and that they are less inclined towards computing after instruction.

So what? We are getting to teach students how science is done and they are using computing to investigate models. Now, this implementation is not the most polished one, which means we have a good way to go. But, that’s OK, because we are not going to fix all these issues overnight. We have been working on them for the last two years in various contexts. But, we need to figure out how to teach science and computing together. And we need to figure out how to do it well.

So, I’ll point you to a few other publications on computing in physics that I’ve written. Two concern high school, and another deals with physics majors. The high school work shows we can implement ideas from my dissertation work at the high school level (as others are doing). Moreover, we find that students who know physics and computing ideas can make good models of systems and are not memorizing lines of code. In my dissertation work, we didn’t do any qualitative work like student interviews, but it’s clear that doing so is necessary. The work with physics majors is one of the first forays into integrating computing in upper-division physics. We show that a new model for implementation can positively affect student attitudes.

High School:


This morning I read his three papers.  They all describe prototype courses that use computational modeling to teach physics, with some analysis of the outcomes.  They are not controlled experiments, but prototyping proof-of-principle projects (as are most educational research “experiments”).  This is not a criticism of the papers—one generally has to do a lot of prototyping before arriving at a method that is robust and repeatable enough to be worth the difficulty and expense of controlled experiments.  Engineers see the need for prototyping, but too many people in other fields think that things have to work perfectly the first time or be discarded forever.

These papers bracket the previous work Danny did that studied computational modeling for first-year calculus-based physics.  The two high-school papers are about a 9th grade physics class that uses the Modeling Instruction approach to teaching physics, to which was added computational modeling using VPython.  The “upper-division” paper discusses adding computational modeling to a 2nd-year classical mechanics course for physics majors, following a traditional 1st-year calculus-based physics course.

I was a little unclear on the level of the 9th-grade course.  In one place he refers to it as “conceptual physics”, but in other parts of the description it sounds more like an algebra-based high school physics course (covering the mechanics half of AP Physics B), a step-up from conceptual physics.

From his description, it seemed fairly straightforward to add a computational component to the Modeling Instruction approach, and it helped students see that all the different “models” taught in that approach are really special cases of the same underlying general model.  They used Vpython with a couple of additional packages (PhysKit and PhysUtil) to make creating graphs and motion diagrams easier for beginning programmers.  The additional packages allow lines like

    graph.plot(t, cart.pos.x)

in the inner loop, simplifying the usual VPython interface a bit.

It sounds like the students were finishing the course with a mix of students who knew what they were doing and those who still hadn’t quite grasped the physics or hadn’t quite got the programming.  He did try analyzing some of the student work to see whether students were having difficulty with the physics or VPython for making the simulations, but I found the results hard to interpret—raw numbers don’t mean much to me, because I don’t have a good prior expectation of what 9th graders at a private high school should be able to do.  I’m curious whether difficulties with programming correlated with difficulties in understanding the physics, and whether grading the computational homework gave insight into the misconceptions the students had about the physics.

One of the strong points of the computational approach is that it allowed the students to model phenomena usually beyond the scope of 9th-grade physics (like a soccer ball with linear drag forces).  I found this to be the case for calculus-based physics also, where we modeled pendulums without the small-angle approximation (problem 4.P.89 in Matter and Interactions) and the magnetic field lines of a helical solenoid.

Some of his observations are unsurprising: “Students find debugging their programs difficult; that is, they have trouble determining whether they have made a coding error or a physics error and how to deal with that issue. ”  He also noticed that some students found installing the software difficult—I believe that the VPython developers have been working on that problem, though it is not yet at the level where all 9th graders will find it easy.

Personally, I’d like to see the physics simulations for high school students use computations with units throughout—this would help them catch a lot of their physics errors earlier.  I see this lack of units as one of the biggest flaws in VPython as an instructional tool for physics.  I’ve blogged about this before in Physics with Units, and I’ve done some VPython programming using Unum.  Unfortunately, the Vpython plotting and animation code does not play nicely with Unum, and having to strip out the units before plotting or drawing negates most of the advantages of keeping units around. I realize that for professional physics simulations, units are always implicit (in comments and variable names) rather than explicit, because that makes more efficient use of the computer, but for instructional purposes explicit units would be worth the inefficiency.

The 2nd-year classical mechanics course used Mathematica to solve ordinary differential equations (ODEs), and provided only minimal instruction in Mathematica.  The main improvement to the course from my perspective was the addition of a final project that allowed students to study an open-ended physics question of their own choice using computational modeling.  This improvement was discarded in subsequent offerings, because it required too much instructor time. Caballero wrote, “For junior and research-focused faculty, the computational project is a significant investment of their time and energy given the large enrollment in CM 1. Developing authentic, scientific experiences for students that can be sustained with little faculty input is challenging.”

This is a theme that I see repeatedly in course design in all disciplines and at most universities: the really good parts of prototype courses take a lot of instructor time and get discarded.  I think that the goal “sustained with little faculty input” is a wrong goal, but it is one shared by many faculty and administrators, who think that teaching is a burden that should be given as little effort as they can get away with. I’ve decided, rather deliberately, not to design my courses that way, but to design them around high faculty involvement.  I believe that the value of a University education depends on high-contact courses, and I’m willing to resist the MOOCification of the university at least in my own courses.  This does take a lot of my time, and I’ve given up on writing grant proposals to make the time—not a choice that most junior faculty could afford to make, given that promotion these days is based more on how much money is brought in than on the quality of teaching or research.

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