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.

The Problem:

We were solving some simple static equilibrium problems today. The first problem involved a 2m board (60 kg) spanning across two scales that supported the board on each end.  A 70-kg person stands on the board 1.5 m from the left scale. The question was, “How much does each scale read?”

Student Solution:

The standard way to solve this problem would be to sum the forces and torques to zero, but here is how a student today approached the problem:

The board weighs 600N. If the person wasn’t on the board, each scale would have hold 300N of force, because it’s symmetric. When the person (weighing 700N) stands on the board, more of his weight will go on the right side, because he is closer to that side. More to the point, the person is 3/4th of the way down the board, so the right board will have to hold 3/4 of his weight (525 N). This leaves 175 N of his weight on the left scale. Taken together, the board’s weight and man’s weight, the left scale will read 475N and the right scale will read 825N.

My Instructional Move (real time decision vs post-hoc decision)

When I came around to talk with this student, what I did was spend some time making sense of what he did, but then I (regrettably) just basically told him that what he did gave the right answer, and encouraged him to approach the problem the using the more standard approach. In hindsight, I would have liked to have encourage him to assume that his numbers are correct, and to use those numbers to see if in fact the Forces and Torques sum to zero. If those numbers work out to balance both the forces and the torques, than the approach is sound; if not, it’s back to the drawing board. Instead, I encouraged him to start the problem again assuming he didn’t know the answer and see if he got the same answer using a different method. At the end of the day, I should have said, “Check to make sure your answer satisfies the conditions for static equilibrium”. This values his approach, while keeping our idea on the core physics ideas he needed to practice.

General Thoughts on “Starting from Basic Principles”:

The more and more I do this, I become less and less opposed to “guess and check” strategies in physics. This student wasn’t guessing, but the idea is the same. “Hey you have a hunch about how much of the weight gets distributed?” Cool, run with it, prove to me that it satisfies the the conditions for static equilibrium. Oh, you have a strategy that you think might work more generally, even better. Prove to me it works in all cases.”

I think this runs counter to the prevailing attitude that students should start problems from basic physics principles… We want students to start the problem by writing, “Fnet = 0” and “Tnet = 0″… or at least state that idea in words. While I agree the endpoint of learning needs to look something like that (seeing fundamental physics principles and using them to guide process), I’m definitely not convinced its a good starting point. For one, in my experience students don’t see why summing the torques will magically tell them about how the forces get distributed. Forcing them down that path is awkward, because it’s kind of “trust me, it’ll work out. It’s a good strategy. Let’s trust the physics”. But if the students have some guess (or strategies) for figuring out how the forces might distribute, that’s awesome, and I can press them to prove their solutions satisfies basic physics principles.