What’s in a model?

I’m trying to incorporate some of the ideas and practices of Modeling Instruction, especially Eric Brewe’s University Modeling Instruction (MI-U), into my teaching this semester. I can’t do full-on MI-U, since (a) I don’t have six hours per week of contact time in a studio classroom, and (b) I don’t have time to wrap my head around the MI/MI-U curriculum before classes start on (gulp!) Monday. However, I also can’t go back to business as usual now that I’ve got the Modeling bug (and the ISLE bug, too) planted in my brain. I’m not sure if Modeling (and/or ISLE?) is the holy grail of teaching, but it’s definitely a step in the right direction compared to almost all other physics pedagogies out there.

One facet of MI that I’m trying to adopt is organizing the course content around a relatively small set of “models” that students will (be led to) develop, understand, and become facile “deploying” in order to explain phenomena and analyze physical scenarios. That leads to the thorny question of “What, precisely, should count as a distinct ‘Model’?” Let’s take Physics II as an example. It’s pretty clear to me that the “ray model of light” (what MI calls the “particle model”) is a bona fide Model. It’s less clear to me whether to identify the polarized wave model of light, the wave model of sound, and the wave model of transverse and/or longitudinal mechanical waves as distinct Models, or lump them together into one “wave Model.” At the moment I’m leaning towards having one “traveling wave model” that includes light, sound, mechanical waves, polarization, and both longitudinal and transverse variants, in order to emphasize the unity of mathematics and representations; and a separate “standing wave model” of vibratory phenomena that is related to it, but framed as its own Model. Why? Because practically, I find that as a physicist, I seem to have a generic picture of “traveling waves” that I pull out for all of those phenomena, and another of standing waves. Each has its own typical representations, diagrams, common mathematical manipulations, etc. And isn’t that what Modeling is really getting at?

Similarly, I’m entertaining merging electric charges, two-body electric forces, two-body electric potential energy, mass, two-body gravitational forces, and two-body gravitational potential energy into one Model of “electric and gravitational charges and forces.” Although electricity and gravity could be two models, their mathematical and conceptual similarities beg for unification. I will likely, however, separate out a Model of “electric and gravitational fields,” including the vector fields and their corresponding scalar potential fields, since the two-body force perspective and the fields-cause-forces perspective are really two different ways of conceptualizing those interactions.

Are AC and DC circuits two separate Models, or one? I’m leaning towards separating them, though the AC circuits model is really an extension of the DC model. And each includes many little sub-Models: the Drude model of current flow, a “charge escalator” model of batteries, the Ohm’s Law model of linear resistors, models for capacitors and inductors, etc.

Clearly, Models are in general composed of sub-models, are connected to other Models, and can be unified into yet more encompassing Models. (I do so enjoy scale-free, fractal self-similarity.) Given that, it seems that how to parse a course’s content into Models must be made on pedagogical grounds, not philosophical ones. At the moment, I’m entertaining a list of ten Models for Physics II, hoping that’s few enough to keep the course from seeming like a wilderness of disjoint bits and pieces—one of the primary objectives of Modeling Instruction.

What do you think? If you’re a Modeler, how do you think about the boundaries of “Models”?

About Ian

Physics professor... science education researcher and evangelist... foodie and occasionally-ambitious cook... avid traveler... outdoorsy type (hiking, camping, whitewater kayaking, teaching wilderness survival skills to high school students, etc.)... amateur photographer... computer programmer and amateur web designer... and WAAY too busy!
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3 Responses to What’s in a model?

  1. Theron Cross (@torquedu) says:

    I like the approach. I’m heading into my first year teaching MI, and it already bothers me that constant velocity and accelerated motion are treated as separate models. Isn’t constant velocity just a special case of the more general kinematics model? The obvious problem is that we’re trying to get the ideas across to people with very naive notions. Lumping too many ideas into a single model could backfire by no longer being specific enough for students to use. The ultimate question has to be: will this better enable someone new to physics to understand and predict the behavior of a system? Which misconceptions will students likely have if you unify gravitational and electric forces into a single model? Which will they likely have if you treat them separately? Could you get the same benefit by having them find the similarities and differences between the two models?

    Please keep writing about it. I’d love to hear what you learn.

    • Kelly O'Shea says:

      In a way, the Constant Velocity Particle Model gets rebuilt when you start looking at the Constant Acceleration Particle Model. It’s a special case, to be sure. Balanced Forces are also a special case of Unbalanced Forces. And Projectile Motion and Central Force are also special cases of Unbalanced Forces.

      The cool thing is that it makes sense to build them as separate models from the perspective of encountering and constructing these ideas for the first time. But then it also makes sense to collapse some of them from the perspective of understanding it and having used it for a while. And students get to experience both perspectives during the year. At some point in the spring, I like to ask them: If we were going to play Model Survivor, which Model would you vote off the island? So far, every class has voted off Projectile Motion. (I think Constant Velocity would be their next choice.) They totally get that it isn’t anything new, once they’ve used it a bit.

      Anyway, I guess my thinking here is that you have to look at both perspectives when you’re thinking about what’s going to make sense for students. If you look at it too much from the expert side, the chunks might get too big for a novice. Of course, on the novice side, the chunks might not always get glommed together correctly, and every problem seems totally different from the last (let alone big ideas), so there needs to be some guidance and direction about how to do the chunking (hence the guided inquiry part of MI). I think I might have stopped making sense there, so I’ll stop now.

  2. Josh Gates says:

    +1 with everything above about keeping them a little more separate than an expert would for the benefit of students, the ability to unify a bit more later, etc.

    Another pro, in my mind, for initial separation – forcing ‘the choice’. For most of the year, I set up motion as a choice between constant v and constant a (with a possible third choice of non-constant a), forces as a choice between balanced an unbalanced, momentum and energy as a choice between conserved (for a given system) or having transfer in or out of the system. While you can explain all of those pairs under a single model (and we eventually do), making the process of choosing a model explicit is one of the best things that you can do to get across the idea of science as a modeling activity. OK, I’m going to try to make this prediction. The real system’s super-complex, so I need to make some approximations, simplifications, and choices. Without having to consciously choose how to model it, it’s just back to procedures (“oh – everything something hits something, I need to follow these steps” ickiness).

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