The Big Lie
By Dr. Eugene Maier
A hallway conversation between sessions at a recent National Council of Teachers of Mathematics convention centered on the role of math in everyday life. An engineer-turned-science-writer expressed her surprise at discovering how inconsequential math was in the lives of most writers in the university town in which she lived. From what she observed, they got along just fine without paying any attention to mathematical matters. The conversation drifted elsewhere and at the time I didn't think to ask her why she found this surprising.
All of us, I believe, know people who lead satisfying lives and have little use, if not an aversion, for anything mathematical. Besides my own acquaintances, I can name any number of persons famous enough to be listed in the Biography section of Webster's, who, according to their biographers, fared poorly in school mathematics and had little regard for it: humorist George Ade, novelist Ellen Glasgow, journalist Edgar Guest, publisher Randolph Hearst, playwright William Inge, poet Vachel Lindsay, diplomat Henry Cabot Lodge, historian William Prescott, to name a few.
So why is it we feel surprised when we find a covey of math-avoiders who are perfectly content in their math-less world? The reason I suggest is that it contradicts a message drilled into us in grade school from many different sources--home, society at large and especially school: you must learn mathematics because you'll need it sometime. Messages heard repeatedly in childhood from authority figures become part of one's belief system--lying dormant in one's psyche until some event in adult life brings it to a conscious level. It wasn't until my own children were in school that I became aware of the pervasiveness of that message and how I had never thought, till then, to challenge it.
I remember our youngest, a third-grader at the time, announcing at the dinner table that they were doing something new in math at school, but he couldn't remember its name. I asked him to describe what they were doing. He said something about rubber bands and boards with nails in them and I said, "Geometry?" He said, "Yes, that's it. What's geometry good for?" Not ready to make a case for the value of geometry to a third-grader and knowing art was one of his favorite subjects, I deflected his question with one of my own, "Well, what's art good for?" "Oh, that's fun." he said. "Was what you did today in geometry fun?" I asked. He replied that it was. "That's why you did it," I said. The answer seemed to satisfy him, because he didn't push the matter further.
Only a few days later, while engaged in a chore with my middle-school son, I asked him what he liked about math. His answer was immediate, "I like magic squares. What are they good for?" This time I was a bit quicker on the uptake. "To think about," I said. He said, with apparent satisfaction, "Oh." We are misleading students and stymieing their interests, I decided, when we make future utility the motive for studying math. And so I formulated what, in my own mind, I dubbed The Big Lie of School Mathematics, namely, "You must study this because you'll need it sometime."
No matter what the mathematical topic, if I tell my students--or give them the impression--that it is something they will need to know at some point in their life after school, I'm almost certainly lying to someone in the class. For some topics, like dividing by a fraction, I'm lying to almost everyone in the class. (Some tell me they are doing this when they halve a recipe, but in this case they are not dividing by a fraction--they are dividing by 2.) Furthermore, telling a student they should study mathematics because they'll need it some time provides a reluctant student with a great opportunity to discount your admonition. The scenario goes something like this: You introduce a topic. The student asks, "When am I going to need this?" You say, "When you do such and so." The student says, "I'm never going to do such and so'" You say, "You'll also need it to do this and that." "But I'm never going to do this and that." And so it keeps going, as long as you last. In the end, the student wins--they are never going to do any of those things, so there's no need to study math.
But, most importantly, attempting to motivate the study of math on the basis of some possible future use has a negative impact on those students--and this is most of them--who are quite willing to study math for the satisfaction it gives them at the moment. Telling them The Big Lie is telling them they are studying math for the wrong reason and leads them to question the aptness of their efforts.
As far as my own teaching is concerned, I find it best to be straightforward whenever a student questions when they are going to use the topic at hand. My answer is "Maybe never, but that's not the point." The point of studying mathematics is not to learn the mathematics one will someday need. There is no way of foretelling what that might be--indeed, the mathematics they need may not be invented yet. The point is that, whenever the need or interest to pursue a mathematical topic arises, one is confident and capable of doing that. With that as a goal, the particular mathematics one studies isn't as important as the process of studying mathematics. My hope is that the material covered in a course is appropriate for my students' stage of development, is as interesting to them as it is to me, and builds their mathematical competence and confidence.
Once I adopted this stance and no longer risked lying to my students about the future utility of what we were studying, the classroom atmosphere became much more relaxed. If a question arose about future application, it was out of a genuine curiosity on the part of a student, and it was acceptable to not have an answer to that question. A student might find a topic difficult or dull, but its utility wasn't challenged. And, best of all, it freed me and my students to study mathematics for its own sake.