You’ve Never Really Taken a Math Course…

Critics of the classical and Christian model sometimes wield the universal certainty of mathematics like a trump card.  “Two plus two is four for everyone, always, period.”  Even Christians will commonly use this as a defense for putting their kids in a school that eschews their family’s values or biblical truths, with a sort of what-difference-does-it-make kind of attitude.  Well, let’s examine this a bit more closely for a moment. One thing that really troubled me the first time I heard it was that I had probably never gotten beyond the grammar stage of mathematics.  In a very helpful series of talks on classical and Christian education by Mitch Stokes, Senior Fellow of Philosophy at New Saint Andrews College, he poked some holes in my thinking about the discipline of mathematics.  In a message dramatically-entitled, “Mathematics: How We’ve Missed the Whole Point,” he piqued my interest with the following:
“What if I told you you’ve never really taken a math course?  You’ve never really studied math, even if you’ve done many, many problems…? Math is a lot more than you thought it was.”
He went on to explain himself by suggesting that the following is true for almost all of us (I know it’s true for me):
  1. We don’t know where math in its current form came from.  We don’t know the history or the philosophies that undergird it or how much of a religion it has been in itself to so many cultures of the past…cultures on whose shoulders we stand when we punch a problem into our smart phone calculators.
  2. We have learned little more than a series of recipes and formulas that – when properly followed – will produce the correct answer the same way, every time…even if we can’t actually tell you why the answer is correct.
I can’t really argue against this.  Until recently, I had never learned anything about the significant role mathematics has played in the way Western minds have made sense of the universe.  I’ve been too preoccupied memorizing the quadratic formula.  Isn’t that more immediate? Urgent, even? What’s more, I still have no idea how the quadratic formula actually works…or where it came from…because I’ve never gotten beyond the grammar of mathematics. That’s right.  I took college calculus, but the best I could tell you now is that certain formulas can help you determine the area from one point to another under a parabola.  Big whoop. Sure, I use plenty of basic algebraic and geometric principles around the house, but even that puts me in pretty rare company. No matter how sophisticated the formulas I’ve memorized, they still comprise only the grammar of math.  That’s not to say that my six-year-old should know geometric formulas since that’s grammar stuff and she’s in grammar school; remember that the “grammar” of a subject refers to the basic or even factual information, as distinguished from the logic or rhetoric of the subject.  And the grammar/elementary educational level heavily emphasizes providing grammar students with the grammar of the disciplines.  But I digress. Given the way we teach mathematics, it’s little surprise that students so often hate math.  Stokes suggests that we entertain what it would look like if we tried to pull such a stunt in history classes:
“I’m going to put up some dates on the board and I’m going to attach names and events to it.  And that’s all I’m going to do. And what I want you to do on the exam is put them in order. Okay?  That’s it.  And we’re just going to do this for twelve years.  And then you’re going to go to college, and we’re going to do more.  List more dates, events, and people.  And then [you’re] going to go to graduate school.  And then you’re going to do that again, and again.  And that’s all you’re ever going to do.  You’re going to have this humongous timeline.  And that’s all we’ll talk about in history.
“Now, do you think that would end up making you hate history after awhile?”
But here is his point: that is exactly what we’ve done in math.  We’ve given formulas and recipes with little background or analysis, and we wonder why students so often despise it.  The reality is that if we haven’t gotten beyond the grammar in our own classes, we’ve never actually taken a math class. Neither is it surprising when there’s little student buy-in in math classes.  I have a hard time imagining Aristotle asking Plato, “Yeah, but when will I ever use this stuff when I get out of here?”  Mathematics, properly taught and understood provides a way to make better physical sense of a universe that God has, in fact, created in mathematical order.  Perhaps the question that our students sometimes ask is more intuitive than we previously thought.  Perhaps the best answer is not, “because it’s your job to learn this, and you’re learning how to discipline your mind,” etc.  Perhaps it should be, “Because I’m teaching you how to better understand God’s creation. And mathematics is only an example.  The truth of the matter is that being true to a particular discipline, and getting past the grammar of that discipline means spending time examining primary sources and asking lots of how and whyquestions…and even equipping our kids to answer those questions intelligently and persuasively, which we will be our aim at Evangel Classical School.