# Some Thoughts on Modeling

Here’s a definition of modeling I’ve offered in a couple of conference sessions:

Describing the world with mathematics, in order to make reasoned predictions and decisions.

That I borrow heavily from Dan Meyer is readily apparent, especially when considering some of the activities I’ve created over the last couple of years (e.g., Charge!, LEGO Prices, Predicting Movie Ticket PricesMocha Modeling).

In each of those activities, students build a model in order to make a prediction, ideally a more precise one than the wild estimate I typically call for at the beginning.

A couple weeks ago, a colleague of mine (Jason Merrill) invited me to expand my definition a bit by considering how modeling often plays out in physics. Rather than a method for making precise predictions, modeling in the physics classroom (or laboratory) may sometimes offer a process for inferring material properties and physical constants.

#### Physics Teachers, Help Me Out

Do Jason’s comments resonate with your experience? If so, can you share any exemplar activities in that inferring properties and constants vein?

#### Math Teachers, What Say You?

How often does your modeling work serve as a means for making predictions? How often does it serve as a means for something else? How would you expand (or revise) the definition of modeling I’ve offered above?

1. So, I’m a physics teacher, and I’ve been thinking about this question a lot over the past few days.

In physics, we do model. We describe the world in terms of mathematics. We make reasoned predictions and decisions.

But this description still doesn’t feel satisfactory. Yes, it’s all true. But it’s missing something.

I think it’s because we don’t start and we don’t stop with the mathematics. We have some toy model, some very oversimplified model, that still works. Chad Orzel does a great job of describing that here -> https://www.forbes.com/sites/chadorzel/2016/10/12/the-surprising-power-of-really-simple-physics/#1612e1197dab

Sometimes, as physicists, we try to get a handle on how, if one measurable property of a situation is changed, how another measurable property will change. We will manipulate our data until we get a straight line and then figure out what that relationship is. (I’m still miffed that Desmos won’t let me linearize the way a physicist would linearize.) That’s when we don’t have a model.

But, along with the mathematical formalism, I often find physicists using some sort of overarching model of the world, often a visual representation. The AMTA (American Modeling Teachers Association) was started by physics teachers thinking about how can we model the world. They focus constantly on drawing a representation of what’s going on in the situation.

When we have a model, we use it. Even if we think it oversimplifies the situation. And then we apply the model, using mathematical reasoning if not mathematical techniques. And we see if it gives a good enough prediction to be an applicable model.