“When am I ever going to use this?” (a new response to an old question)

Bored math students often ask, “When am I ever going to use this stuff?” Even math students who are not bored often articulate the same question, albeit in a more polite phrasing, such as “Can you give us an example of an application of the theoretical math we’ve been learning?” The question deserves a respectful answer.

I discussed this issue two years ago, but I have a slightly different point of view now. Here’s what I said then:

I know, I’ve written about this topic before, but it bears further consideration. Too often I hear the question, “When will I ever use this stuff?” This is a common question in Weston, and surely elsewhere as well.

Sometimes the question comes from a bored student who is really asking a deeper question, something like, “I don’t like this, I don’t understand this, why should I have to learn it?” In that case it’s hard to know whether to answer the explicit question or the implicit question.

But sometimes the question comes from an otherwise engaged student who actually wants an answer. And it’s hard to give a satisfactory answer. There are at least two reasons for this — probably more. First of all, no high-school student really knows what he or she is going to be doing in life. It’s important to keep the doors open, in case the unanticipated economics course in college or statistical analysis in a job turns out to require something from a high-school math course. But that’s pretty vague and abstract, and of course it isn’t a very satisfactory answer for most students, even though it’s a true answer.

The other reason why the question is hard to answer is that the hidden but more important curriculum in high school has nothing to do with the specifics of logarithms, cosines, etc. When a student takes Algebra II or Precalculus or whatever, the important things that s/he is learning have to do with problem solving, approaches to mathematics, and learning itself. Sure, you might never see logs again (although the odds are that you actually will); but the analytic techniques and reasoning methods that you learn will stand you in good stead.

The only trouble is that most Weston students don’t want to hear this, or it doesn’t make sense to them. They want to know how they are going to use the precise content in the job that they imagine that they will have, even though the probability is that they will be doing something else entirely. How do we give them an answer that they will consider satisfactory?

I finally have an answer that I can believe in. I still believe everything I wrote two years ago, but I hadn’t figured out the answer to my concluding question. Maybe I still don’t have one, but I truly like what the Math Curmudgeon has to say on the matter. Even though I often disagree with the Curmudgeon (whose real name I don’t even know), I have taken to heart his words on this matter. He says the right things in his speech to his students (complete with a fractal tree). Here’s the first half; read the rest of it yourself:

“When are We EVER going to have to use this?”

“Beats me,” I usually answer. “You can’t even tell me definitively what you’ll be doing next month, forget about four years from now. How can I definitively say when or whether you’ll use THIS? All I can say is that it is useful in certain situations (the word problems in this section are limited versions of the same problems some people face daily), useful as mathematical development for later work (which may be a prerequisite for the course or job you really wanted) or is mental development to expand your brain beyond the limited understanding and very limited world-view you currently have. I’m not being critical here — you really have no experience at life. How could you possibly know the utility of everything you’re learning?

“You have millions of possibilities ahead of you, thousands of doors along this hallway you call life. Writing ability will unlock many of them, artistic ability others, mathematical ability many more. Some may require that you speak English well — certainly 95% of the jobs in this country do. Some will require a little of everything. Each of these doors is along a different stretch of hallway, sort of like that fractal tree over to the right. Each educational decision you make takes you down one branch or another, closing off some possibilities and making others available. To switch from one branch of the tree to another may require a little backtracking to pick up things that you could be learning now. I have no idea which doors will interest you so I have to lay a very broad groundwork and push you in directions you may not immediately see any need for. You have to trust that, over the course of many years and many students, I have a good sense of what you might need and of what you may find interesting after we’re done.

“How do I know this? I talk to my students after they graduate. They tell me what they found useful or pointless. I get all kinds of stories about topics that we covered here that directly applied to something they were working on, stories about being the only one who really understood something the professor was trying to say. There aren’t many complaints that we spent too much time on a topic they never saw again.

“If there is ever a commonality in the comments of returning graduates, it’s this: ‘I never imagined that THAT would be useful. I was surprised when it showed up. So was the professor — he was grateful SOMEONE knew about it.’”

Categories: Teaching & Learning