Lie-to-children

I admit, the first time I saw this phrase in print, I was a little put off. Lie-to-children? That sounds like the kind of thing that gets you a lot of extra time in purgatory.

Then I learned more about it and decided that perhaps it wasn't so bad after all. Well, maybe. It still could be bad.

I should explain all that. The first thing I thought when I saw the phrase "Lie-to-children" was that people were talking about the kind of thing that you tell kids because it's convenient, even if in the long run it doesn't help them at all. That's not what it actually is.

What lie-to-children refers to is the type of simplification that happens when you are teaching someone (anyone, it turns out: doesn't have to be a child) about physics, or math, or chess, or any field of human endeavour with a deep and complicated body of knowledge. The idea is that throwing the full force of, say, quantum electrodynamics at a beginner will only turn them off the field all together, so you teach them simplified forms (in this case, simplified electricity and magnetism) that you know aren't entirely correct. Since it wouldn't really be good teaching practice to emphasis their incorrectness at each turn, you're sort of lying. Hence, lie-to-children.

In this sense the concept has some merit. I've come to realize, though, that there's two different types of simplification. One is a type that, while simplified, gives students the right intuition about how the more complicated process works. The other type does the opposite: it is a subject simplified in such a way that students either don't make any progress towards understanding the fuller ideas.

Here's an example of the good type. In high school and early undergraduate physics, we teach students a theory of friction. In this theory, friction forces depend on the materials rubbing past each other (eg rubber on concrete or skin on carpet) and the force pushing them together (gravity in most cases)--and the dependence of friction on the force pushing the two objects together is linear (double the one force, double the other). There's no dependence on the size or shape of the contact area, or any other factors.

Clearly this can't be the complete theory of friction. If it was, then all cars with the same material in their tires would have the same stopping distance, and sports cars wouldn't need fat tires or good suspension for good handling--skinny tires would work just as well. But it works as a lie-to-children because it lets students figure out things like force, energy, and work in ways that serve them well as they move on to more complete forces. (As an aside, the wikipedia article about friction is terrible. Please don't read it unless you want to be seriously confused and misled).

An example of the bad type of lie-to-children is how we teach uncertainty estimates. The most common way of introducing students to measurement uncertainty in high-school and first year labs is to tell them to look at the four or five data points we've told them to collect, and subtract the largest from the smallest to get a range of uncertainty.

Why is this so terrible? For starters, it gives students the idea that a range of uncertainty on a reported value means that the true value cannot possibly be outside of that range. That's an unfortunate idea, though one that even professional scientists sometimes seem to have. It's not the worst of it, though. The worst part of calculating uncertainty this way is that the uncertainty goes up the more measurements you take. Taking more measurements gives you a higher chance of having a particularly large or particularly small one, which makes an uncertainty based on max minus min get larger. This is bad; we want students to get an intuitive feel for uncertainty as a measure of the confidence in a set of data, then we give them a way of calculating it that implies that the more data you have, the less confident you are in it.

I'm not going to go into how I think uncertainty should be introduced in high school. All I want to do here is point out that we need to shift the question from "how can we simplify this body of knowledge?" to "does this simplified version build students' (or readers', depending on context) intuition in the right direction?" If we can do that, the lie-to-children will be a little less of a lie.