I spend quite a bit of my time helping high school students understand physics and mathematics concepts, so I’ve also spent some time wondering how I can better help them understand things. It’s a tough challenge, because I’ve never been like other people in terms of understanding — I’ve always been such a voracious reader that I can use my prior knowledge to make sense out of things.

I do not, however, see many other people doing the same.

What I tend to see instead is students memorizing *how to do* problems. For example, I was recently helping teach students about enthalpy. There’s a major equation involved:

$latex Q = mcDelta T$

which basically states that the energy you put in to an object changes its temperature in proportion to the objects mass and its specific heat. Mathematically it’s a very simple expression to use. Your typical physics problem might say “How much energy does it take to heat a 2kg lump of steel 10 degrees Celsius?”, in which case you look up the specific heat of steel and then plug the numbers right into the equation.

But then the teacher throws a curveball. Now you’re given the mass of the object and told that it was heated by ten degrees over ten minutes, with 200J of energy put in every minute. What’s the object’s specific heat?

The method to do this, of course, is to figure out the total energy put in (10 * 200 = 2,000J), plug in the numbers, and solve for specific heat. But I have literally watched students approach this problem and give up with no idea of what to do.

I may not be able to see into their minds, but the problem I see is this: rather than learning the concepts and forming a mental model of how something works, students are learning (and are being taught) *how to do* certain problems. If a problem is outside the scope of what they’ve been taught, it’s considered impossible — even when it actually could be solved with their current knowledge. When a teacher tries to make students think outside the box, she’s accused of testing students on “stuff she never taught us.”

Is this really a good way of approaching learning? I don’t think so. One could argue that high-school physics will never be useful later in life; the key is that it will never be useful in the sense that most students will never have to figure out the specific heat of a lump of steel ever again. But this approach to learning denies students the other benefit of an education: a better understanding of how the world works. When you actually understand how energy and temperature relate (rather than knowing how to find one when given the other), you are better equipped to meet life’s smaller challenges and better understand the environment around you. You might not be doing algebra in your head 24/7, but at least you’re benefited with a sort of physics intuition.

I concur