Last week I got more angry at one of my classes than I have been all year. And it was over a question that gets asked at some point in every math class: “When am I ever going to use this?” Every teacher who has been in the classroom more than ten minutes has an array of answers to this question, and normally I can shrug it off with one of my precomposed responses; but there were two things about this specific question during this specific topic in this specific class on this specific day really got to me.
- The class was honors algebra 2 – a class with mostly freshmen and sophomores designed to get students through BC (or sometimes MV) calculus before leaving high school. These students are usually self-motivated, intrinsically passionate about mathematics and many are working towards careers in the STEM fields.
- The topic I was presenting was word problems involving systems of two linear equations – a skill students are expected to have mastered coming in to class on day 1.
In their defense, the problem they had was one of the most contrived, psuedocontextual questions out of any textbook.
John is collecting stamps. He can buy cheap stamps for 70 cents or expensive stamps for $1.30. He buys 15 stamps all together and spends a total of $13.80. How many of each stamp did John buy?
Yeah – I know, it’s a stupid question to begin with; but remember, I’m not trying to hook these kids on math – I’m just (what I thought was) reviewing a fairly straightforward skill. My first reaction to their complaints was to ask why I had to teach them something they were supposed to already know coming in to my class, but knowing the futility of such a comment, I quickly squelched that retort. Instead I took a new approach to the old question. It went something like this:
You’re right. You’re never going to have to answer a silly question about different priced stamps. So instead of that question perhaps I should pull data from the Keplar Space Telescope and ask you to determine whether or not a planet that is 100 light years away might be habitable. But then again, you are freshmen and sophomores in high school and not post doctoral students studying astrophysics, so you wouldn’t know where to begin on such a question. So I could create a problem about determining whether or not Core-Shell Nanodiamond Geometrics could be used to design a safer and sturdier helmet, but then I remembered you’re not post doctoral students studying mechanical engineering and have no idea what Core-Shell Nanodiamond Geometrics even is.
So I here is a stupid problem about collecting stamps, which I only give you because 1) you know what stamps are, and 2) it gets specifically at the skill of solving systems of two linear equations. When are you going to use this problem? Never. When are you going to use this skill? I can’t answer that since I don’t know your future. Of course I can tell you many places it is used, but in reality it’s just a single footnote in the fields of math and science. Is it an essential, stand-alone skill? Probably not. But it’s a lot like writing the letter “e.” It’s pretty useless on its own, but an instrumental part of understanding the vast landscape of mathematics. And as the great physicist, Richard Feynman, once put it, “to those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … if you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.”
So here’s a stupid, made up, problem about stamps. Because it gets at just one of the millions of underlying skills in the world of mathematics. Here is one small puzzle piece to one of the most amazing things I have ever witnessed – the thing that made me decided to spend my career trying to show you what I see in mathematics. So I am going to ask you to do this stupid problem about stamps today and hope that one day you know enough math to see the true beauty of the mathematics we study.
Is this the answer I will use any time someone asks that age old question? Most certainly not. But for this group of students at this particular time, it really seemed to get their attention. They were certainly more focused that day than they have been in the past.