Modeling Terminology


In teaching modeling physics, there is some terminology that is used that I have found confusing.

For instance, we (modeling teachers and authors of “Teacher’s Notes” in the modeling materials) talk about the paradigms. The paradigm is a real thing that serves as a familiar example or exemplar of a concept. So, it’s pretty clear to say, when something moves with constant velocity, that it moves like the paradigm, the blinky buggy. As long as I explain what paradigm means, and repeat it a few times throughout the year, students seem pretty comfortable with this.

The problem arises with the term model. The modeling materials tend to talk about the “Constant Velocity Model”, a “math model” (an equation), a “graphical model” (a graph of the motion). Following this terminology, I suppose you could even say something about a verbal model (a description) and a pictorial model (a motion map).

I have always found all of these many models a bit confusing.

Last year, I decided to settle on a different terminology. There is the paradigm, the conceptual model for the paradigm, and the representations of the paradigm (mathematical, graphical, verbal, and pictorial). So, instead of saying equation or math model, I would refer to “mathematical representation.” Or instead of graph or graphical model, I say “graphical representation.” These are representations of the conceptual model.

So far, so good. Before, students seemed confused by talking about the Constant Velocity Model, the math model for constant velocity, and the graphical model for constant velocity. When I say representation, they haven’t hesitated, acted confused, or asked what I mean. And some have used the term themselves. I don’t remember many using the terms math model or graphical model so early in the year.

Perhaps old hat to everybody else, but it pleased me to figure this out.


About marcreif

I live and teach high school physics in the town I was born in, Fayetteville, Arkansas. My professional interests include modeling instruction and Advanced Placement courses. I also work as a College Board Workshop Consultant, which means I lead Pre-AP and AP Science Teacher workshops. Lately I've also been leading a fair amount of student review sessions for the National Math and Science Initiative. I have a website for students ( and another for AP Summer Institute participants ( I tweet infrequently (@marcreif).
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