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”?

Posted in Learning & Teaching, Modeling Instruction, Pedagogy | 3 Comments

MI-U “models” for physics 2

So after yesterday’s workshop on MI-U (Modeling Instruction, University level), I’m brainstorming possible “models” at the heart of a typical calc-based Physics II course, which I just happen to be teaching this fall. Here’s what comes to mind for models and their component sub-models…

In optics:

  • ray model of light, which includes (as component models or sub-models):
    • model of the human eye and perception of “images”
    • Snell’s Law model of refraction
    • law (model) of reflection
  • wave model of light, which includes (as component models or sub-models):
    • model of traveling waves
    • model of standing waves
    • model of polarization

In electricity & magnetism:

  • Coulomb model of electric forces, which includes (as component models or sub-models):
    • atom/electron/conductor/insulator model of charge buildup & transfer
    • Coulomb’s model of electric forces
  • electric field model (is Gauss’ Law a separate “model”, or just a tool accompanying the electric field model?)
  • magnetic force model(s)
  • magnetic field model
  • Faraday model of electromagnetic induction

In circuits:

  • DC current model of electric circuits, which includes (as component models or sub-models):
    • “charge escalator” battery model
    • Ohm’s Law model of current flow through materials
    • Watt’s Law model of power dissipation
    • series & parallel circuits “models” (??)
  • AC current model of electric circuits, which includes (in addition to the DC model’s components):
    • capacitor model
    • inductor model

Am I making this too complicated?

Posted in Learning & Teaching, Modeling Instruction, Physics Education Research | 3 Comments

AAPT: modeling workshop with Eric Brewe

Recently, in various papers, grant proposals, and the like that I’ve been drafting, I’ve found myself writing something along the lines of “These are several qualities that we ought to be incorporating into our physics instruction, but aren’t… um, except for ISLE and Modeling Instruction, which are taking big steps in those directions.” I decided that if I have to keep saying that, perhaps I ought to learn more about them, and maybe even incorporate (elements of?) one or both into my own teaching.

So, here I am at the AAPT meeting in Philly, having attended this afternoon a four-hour workshop on Modeling Physics for University Physics conducted by Eric Brewe of FIU and his current/former graduate students Jared Durden and Vashti Sawtelle. (Frustratingly, the ISLE workshop conflicted with it.) It was a high-energy affair, devoted entirely to group activities (casting us attendees in the role of students in a Modeling Physics course), and the four hours flew by quickly. At least for me; Eric admitted that he was a bit wiped out after arriving at 2:00 AM this morning, and then running two workshops today. Adrenaline is amazing stuff.

I won’t try to summarize here the Modeling Instruction for University (MI-U) approach to instruction; if you’re interested, go read about it on FIU’s page about it. Instead, I’ll dump a few of my thoughts and reactions as a way of processing my experiences, in no particular order.

  • I’ve been wondering how MI-U differs from other strongly inquiry-based approaches like ISLE. Eric’s answer: Since learning science (genuinely) means learning to play the modeling game, all approaches that teach science well are really teaching the same thing, more or less. What distinguishes MI-U is that it puts an explicit focus on the core models and the modeling process, whereas approaches like ISLE do it more implicitly. (He admitted that ISLE has a more comprehensive view of experimentalism, which MI-U can learn from. His colleague at FIU, the always-incisive David Brookes, teaches with ISLE. What a department!)
  • MI-U organizes content around basic “models” rather than “topics” or “principles” or etc. I suspect this has two benefits with respect to framing students’ thinking about phyit makes clear the distinction between the model and the thing modeled, and it ties the object of learning (the model) directly to the action (“modeling”). Neither “topic” nor “principle” have verb counterparts.
  • “Discourse management” strategies are an essential component of the MI-U approach, which is one of the reasons it’s disseminated through workshops rather than published curricular materials. I’d venture to suggest that the biggest differences between MI-U and other inquiry approaches such as ISLE lie in its classroom interaction modalities and in how learning is framed, and not so much in the specifics of the learning activities and content. (Though I could be wrong, having little familiarity with the actual details of either ISLE or MI-U curricula.)
  • MI-U is very much not a “discovery learning” approach, but instead is a “guided inquiry” approach. A critical component of the method is having the instructor(s) “seed” key ideas to various groups, ideally with the faintest of guiding questions or other nudges. In fact, a significant component of the written instructor support materials indicate the ideas to be seeded during each activity, with suggestions for ways to do so.
  • FIU teaches six sections of MI-U intro physics, capped at 30 students each. Enrollment is by lottery (getting something like 400 applicants). The rest take non-MI-U sections. Each MI-U section meets for three two-hour classes per week, in a mixed lab/discussion setting. And this is going to be a potential deal-breaker for many of us who might aspire to implementing MI-U: I currently teach my university’s one and only intro physics section, which had 60 students for Physics I. I supervise the two lab sections, but have undergraduate TAs (LAs) to do the actual teaching of those. Splitting that into two 30-student sections (barely manageable by one lone instructor, according to Brewe et al.) that meet six hours per week would quadruple my contact time for that course. Definitely. Not. Sustainable. (Even assuming I could get the schedule time and appropriate classroom.)
  • I don’t think Eric or anyone else knows yet how one might apply the MI-U approach to higher-level physics courses, which are typically more theory-driven, more mathematical, less accessible to student intuition, and less directly connected to observable phenomena. FIU uses it for Physics II, including electromagnetism, though that curriculum is not yet ready for distribution. I’m interested to see how they handle non-intuitive topics like magnetic fields.
  • Each class keeps a common “consensus board” (perhaps a big, central flip-chart) to serve as a record of things the class as a whole agrees upon that they’ve learned, or something like that. I’m a bit fuzzy on exactly what this board is and how it works, but I think we were told that it acts as a record of what students are responsible for knowing. This is one tool for giving the students ownership of their learning. This piece could be critical, and I need to understand it better.
  • I like the way that scientific behaviors and norms are developed both explicitly and implicitly. For example, the instructor(s) develop an expectation for students to compare their whiteboards to other groups’ boards during whole-class “board meetings”, challenging other groups as necessary — which sounds a lot like peer review to me.
  • I very much like the idea of using open-ended “Tell me everything you can about this situation” modeling/analysis challenges rather than traditional highly-specified physics “problems” for homework and exams. I think I should be able to build more of this into my teaching, even if I can’t work the entire MI-U approach in (right away, anyway).

That’s enough processing for now.

Posted in Learning & Teaching, Pedagogy | 2 Comments

Stephanie’s latest podcast

the PER User's Guide logoOver on the PER User’s Guide, the always-dynamic Stephanie Chasteen has posted a new podcast in her series Learning About Teaching Physics. This one’s entitled Preparing Students to Learn from Lecture: Creating a “Time for Telling”. The idea of a “time for telling” — that students can learn effectively from exposition (“lecture”), but only when the ground has been appropriately prepared for the seed to take root (motivation, context, grounding, connections) — is at the heart of my principle of “question-driven instruction”, as I bloviated about in my paper Technology-enhanced formative assessment: A research-based pedagogy for teaching science with classroom response technology.

This whole idea of making Physics Education Research results more accessible to in-the-trenches teachers is fantastic. Go, Steph! And a salute to Sam McKagan, the creator/editor of the PER User’s Guide, as well. (Disclosure: I’m on the PER User’s Guide Editorial Board. Because I believe in it.)

Posted in Educational Research, Learning & Teaching, Pedagogy, Physics Education Research, problem/project-based learning | 1 Comment

how to use a paper towel

I love finding new, presumably better ways to think about things we’ve been taking for granted. Here’s a brief (4.5 min), entertaining TED talk that teaches us a better way to dry our hands with paper towels:

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