As a physics professor, I have certain pet peeves. For example, I cringe when someone says that “gravity” is 9.8 m/s^{2} when they mean the *acceleration due to* gravity. I’m annoyed if someone says that an object “weighs” 7 kg. And I stifle a laugh if someone says that a roller coaster is exciting because it goes so “fast”—humans can only detect acceleration, not speed, which is why we don’t notice that we’re traveling something like 67,000 mph *right now* in our orbit around the sun.

But my biggest pet peeve may be students *doing algebra with numbers*.

Fellow physics professors will know exactly what I’m talking about, but for the uninitiated, here’s an example:

**If you drop an object from a height of 20 m, how long will it take to hit the ground?**

A student knows that a kinematics equation is needed, hits upon the correct one, *Δy* = *v _{i}*

*Δt*+ (1/2) a

*Δt*

^{2}, and then correctly identifies

*Δy*= –20 m,

*a*= –9.8 m/s

^{2}, and

*v*= 0. So far, so good. They’ve studied their physics, right? What happens next is sheer madness:

_{i}Sigh.

Over and over again I tell students, “don’t plug numbers in until the end.” But students *love* plugging in numbers. They feel they’re actually getting closer to the answer if they’re manipulating numbers. On some level, they still feel uncomfortable with letters—as if manipulating letters isn’t really “math”.

How does this problem look in my answer key? Like this:

You can *now* plug in values if you like…and get *Δt* = √[2(-20)/-9.8] = 2.02 s.

Which of these approaches is more beautiful, more powerful? The approach you pick indicates whether you “get” algebra or not**. If you do algebra with numbers, the answer you get is very narrow and very specific, even if you do it correctly**. That hypothetical student could have gotten 2 seconds as an answer, and I would have given them full credit. But their answer would have been ugly.

The second approach is beautiful, because it is completely general and applicable to multiple situations. I try to tell students “Look! You found the time to fall a certain distance. You now know the answer no matter what the height is, and even no matter what planet you’re on, since *g* doesn’t have to be 9.8 m/s^{2}.” This is usually followed by a blank open-mouthed stare, much like Kristen Stewart in a Twilight movie.

There is a more practical reason to avoid doing algebra with numbers. It’s simply that **when you do algebra with numbers, other people cannot follow your work as easily**. And then, if you make a mistake, it’s harder for someone else to spot. Quick: what algebra error did the student make above? It takes a while to find the mistake.

My ultimate point is that students need experience seeing the power of algebra. It’s all well and good that algebra classes stress real-world applications—else, why teach algebra in the first place? But real-world doesn’t only mean *with numbers*. *E=mc ^{2}* is certainly a real-world application of algebra, and it’s a lot more elegant than saying that 378,000,000,000,000 Joules is released when a teaspoon of sugar with mass 4.2 grams is converted to pure energy, given that the speed of light is 300,000,000 m/s. The hard part, for us physics professors, is to help this spoonful of algebra go down.

on November 30, 2012 at 12:30 PM |dad71I remember my physics professor in college complaining about the math department, He would say ” Don’t the math people teach you anything useful”

Nothing ever changes,

on November 30, 2012 at 1:52 PM |drakodocOh great….now I have the following song stuck in my head:

“Just a 378 trillion Joules helps the medicine go down….”