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”?