## Got equations? In my calculus-based physics class, equations don’t come first.

At the beginning of the second three-hour class period of this semester’s studio physics course, I told my students that we wouldn’t be using any equations for the next week.

Just to be clear, I am not teaching a general education physics course for liberal arts majors. Instead, I’m teaching a second semester calculus-based physics course largely populated by students majoring in engineering and the physical sciences. In a few short weeks, I’m going to write on the document camera the equation relating field and potential (in this case, electric field and electric potential) which – as practitioners and aficionados know – involves multivariable calculus with partial derivatives and all that nasty stuff.

But for now, we are starting with what should always come first, which is understanding how things work without the mathematical crutches that equations often become for novice learners of physics.

I start the second semester course with the unit on DC (direct current) circuits from Lillian McDermott’s Physics by Inquiry. The idea is both to improve student learning about circuits and electric current and to ease the transition into the relatively abstract subject of electrostatics by giving students a hands-on introduction to electric potential.

Does it work? My students learn twice as much about DC circuits as students in traditional classes do. So that’s a win. But does the inquiry-driven circuit unit succeed in easing the transition into electrostatics? It hasn’t been obvious during the last half dozen years or so that I’ve been leading off the second semester with McDermott that it does. So this semester, science education doctoral student Mark Akubo is leading an observational study of how a group of students handles the transition from circuits to electrostatics. The methodology is similar to that of a study in my fall 2017 class about how students learned about mechanical energy that led to instructional improvements that we implemented this past fall.

As we have been working through the early stages of this course (and the study) this month, I’ve been thinking about a conversation I had with an engineering professor recently who told me that implementing a studio instructional model for physics isn’t worth the trouble because the only thing students are supposed to learn in a college physics class is how to manipulate equations. I was caught so completely off-guard by the comment that it took me a few moments to regain my composure, and the response I should have given – that a physics course should provide students with a strong understanding of the laws of nature that the best innovators have – eluded me until I had left the engineering building.

If that misbegotten belief about what is (and should be) taught in college and high school physics classes is widespread, then it is a wound that the community of physics educators has inflicted on itself by not fully embracing teaching strategies based on the research on how students learn best.

Do I hate equations? Heck, no! In fact, this semester I’ll be implementing a scheme that was suggested by some of the students and TA’s I’ve had this year in which instead of just providing a cheat sheet of equations for the final exam at the end of the semester we progressively build an equation sheet during the semester by adding each week the equations used in that week’s lessons. But two weeks into the semester, we haven’t started this project yet because we haven’t used any equations yet. That will change quickly in the next few weeks.

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