Modeling “How to See” in Static Equilibrium Situations

From facility with problem-solving to crash and burn…

So, recently this semester I’ve been thinking about “modeling skills” versus “modeling problem-solving”. Last week, after modeling how to calculate torque and giving students practice, students very successfully navigated multiple problems where they had to calculate net torque and moment of inertia to predict angular acceleration. Students did quite well without any formal modeling of how to solve those kinds of problems.

But this was not the case with static equilibrium problems yesterday. Lots of students had no clue what to do or how to get started. It was pulling teeth to get them to draw extended free-body diagrams they had so readily done last week. It was pulling teeth to then use their diagrams to sum the torques.  On the surface, you would think that the angular dynamics problems would be harder for students… there’s more involved (torques, moment of inertia, Newton’s 2nd law for rotation, even angular kinematics). But the static equilibrium problems were way harder for students. So why?

Seeing Static Situations as Hypothetical Turning Situations

A big struggle I now see them having is “seeing” these problems as torque. See, I think it’s fairly obvious to students when there’s a balance beam (or actual pivot) that there are effects at trying to turn. Some forces on one side want to turn it one way; other forces on the other side try to do the opposite. In that sense, students natural see it in a way that’s “torque-like”. But that’s not necessarily the case for static situations with no obvious pivot. So the question really is what sort of contexts cue the idea “force as a turner”, which ones don’t, and how can we help students to see “force as a turner” in less obvious cases.

So, my hypothesis is that’s this was the skill I needed to model. “Like OK here’s a situation” My job is model how can I “see” that situation as efforts to turn and efforts to prevent turning. Next time, I would model how to see a situation in terms of turning- and how to communicate how I am seeing these efforts by identifying an “hypothetical pivot”… and identifying how each of the forces either tries to turn or prevents turning.

I would then give students scenarios (without numbers) to practice the same skill—- show how you came up with a way of seeing the scenario in term of turning. What I like about this is also it’s makes the diagram about communicating “how you are seeing it” rather than “a step to problem solving”. What I also like about this is that my modeling is about “how to see” not “how to do”.

If my hunch is correct (that this is the missing skill students needed modeling and practice), then doing this would position students to have had more traction in getting started with the static equilibrium problems.

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