Tag Archives: metacognition

Is Physics a language class?

When I teach Physics, I like to focus heavily on the conceptual side, as well as the process of problem solving and how to think about problems in general, rather than just the mechanics of the math. After all, the math we do in Physics is typically a year or more behind what they are actually studying in Math class, so they should be pretty good at it. In other words, I like to get metacognitive about the subject.

Physics is not exactly about the real world. Physics is about studying mathematical representations (models) of reality, in hopes that those representations can be predictive. For the cognoscenti, real science hides in the places where the math does not predict what we see in the real world, but we rarely delve into those places in school. Instead, we focus on how the models do match and predict reality. In any event, we need to translate what we see around us into math in order to manipulate the model, and then translate it back from math to real world.

It is that translation piece that got me thinking about the title of this post. When we do physics, we are really “translating” from the language of the real world top the language of mathematics – a bit like translating a question from German to English, answering the question in English, and then translating it back – the grammar doesn’t always match, so we have to be judicious in how we translate. And when we study languages we learn to recognize the nuances of each, and the differences in how they work to express things. Likewise in Physics, we need to recognize how a mathematical representation is similar to, and how it differs from the real world.  There are of course other ways to represent reality – artistic, linguistic, and so on, as well as other analogies for translation (thinking gene expression here…), but I’m not sure they convey the same sense of how Physics operates.

Here’s the thing – though I have learned other languages, I have never taught other languages, so I don’t really have a sense of the metacognition of that process. I think it’s about time I explored that in order to develop a full toolkit to help my students understand more about the process of doing Physics.

 

How you do math is, well, not how you do math

Math is an important tool in life, but the mechanics of math, the way it is often taught, is not actually the way it is typically applied. Probably because our brains aren’t wired like computers.

Here’s an example – you are the cashier at a grocery store. A customer buys $43.37 worth of groceries, and hands you a $50 dollar bill. What do you give them in change?

In math, you would find the difference, $50 – $43.37 = $6.63, then count the change out as $5, $1, 2 quarters, a dime and three pennies.

A real cashier, however, counts up: from $43.37, three pennies makes .40, a dime and 2 quarters makes $44, then $1 and $5 make $50. They don’t need to know the total change amount is $6.63, because the goal is to hand over change, not count it.

Likewise, when solving division problems we don’t tend to do division in our head, we do multiplication. When asked how many nickels make up 45 cents, we don’t think 45/5 = 9. We think what times 5 = 45? It seems that we are programmed to think forward, and that thinking backwards is really difficult to do, and when we do think backwards, we are actually thinking forward in a series of backward steps (like the lagging strand of DNA, if I may be so nerdy).

I think this is really important to recognize. In an earlier post on my approach to problem solving, I talked about the necessity of working backwards from the answer to ensure you know where you are going, and that experienced problem solvers do this without even thinking about it. So when I teach problem solving, I not only try to model this as explicitly as possible for my students, but I also teach the metacognitive side – to get the students thinking about their own thinking process when problem solving. To expose the man behind the curtain, as it were.

Certainly to be good in science one has to have a handle on evidence-based problem solving, both inductive and deductive. I feel that teaching metacognition is a way to help students develop those skills. It also helps me fathom the workings of the teenage brain.