The practicality of wonder

The math that comprises most of the curricula we mandate for young people is not only an insult to the nature of mathematics, it’s undermining our intention that young people learn what they need to learn to get by and thrive in the world.  Again from Antoine de Saint-Exupéry: “If you want to build a ship, don’t drum up people to collect wood, and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea.”

I was reminded of Paul Lockhart’s Mathematician’s Lament the other day when I overheard a disagreement about why it’s important to teach/learn math.

When kids ask the age-old question “Why do I have to learn this, I’m never going to use it,” the answer tends to vary a bit depending on the kind of math they’re asking about.  If they’re talking about fractions and decimals they’re likely to get an answer like “You’ll need it for everyday life.”  If they ask the same question about algebra there’s likely a delay and then an answer that goes something like this: “It… uh… improves your thinking skills!  Yes; that’s it.  Your thinking skills!”

This is the kind of thing we say when the truth is we’re not sure why we make them learn something but we know it’s required for college.  (Lockhart points out that the “thinking skills” answer is particularly absurd given how little a person’s thinking skills are improved by being told how to do things, which is what most math education looks like.) The truth is, algebra is still included in college preparatory curriculum not because we think it’ll be useful or improve thinking skills but because we trust and are extremely attached to our traditions.  We decided at one point that to be educated one needed to know a particular set of things in the areas of the humanities and natural sciences (and to have learned them in a particular order).  We haven’t revisited our curricular traditions lately.

Most of the math we teach in school and in traditional curricula is about arithmetic, not about math.  It’s about calculating and marching through steps, not about thinking and musing and considering and solving.  It shortchanges the young people to whom it comes easily, who get to the end of the sequence and can do lots of it but have minimal context or appreciation for what they’re doing.  Those who don’t take to it easily find themselves cut off at the knees, long before they even have a chance to be shortchanged.  There’s no invitation into math, no reason to bother to investigate, to find out whether or not it’s something that might be of use or interest.  Math is not dull by nature.  We just make it seem dull, and that forces us to force kids to do it just because we say so, just because they have to.  It’s lose-lose, with frustration all around.

Lockhart’s book is a case for teaching mathematics for its own sake, for the art and wonder of it.  The fact that math has practical consequences is not, he writes, a good reason for reducing it to its practical applications. And there are some teachers and programs who do share with students the beauty and intrigue of math, but that teaching is often only available to those who have already mastered the less beautiful and interesting parts.  It’s available to the very ones who already felt welcome and comfortable in the world of math.  Why not let everyone get an early glimpse of what’s really possible?

Lockhart’s advice may seem foolish in such trying economic times.  We’re busy doing things like increasing the amount of time young people spend on academic work, not in the interest of uncovering complexities and art but in the interest of competition. We’re concerned with kids winning jobs at a time when jobs are scarce. There are too few slots in freshman classes, too few jobs for graduates. We think we don’t have time for wonder. We can’t afford it.

But maybe, instead, we actually can’t afford not to turn our attention to wonder. Maybe because there are so few slots and jobs it’s more important than ever to have a wider perspective on what you learn and know.  It’s more important than ever to have more than a cursory grasp of the material covered in the course of your education.  It’s more important than ever to be flexible in your thinking, to understand the nuances of things, not just the facts that sit on the surface.  It’s more important than ever to feel connected to and inspired by what you’re learning.  And that’s something we can’t expect to facilitate by dulling things down. When we remove the natural appeal of any subject, we make it more difficult to convince young people to pursue its mastery with the kind of vigor it takes to distinguish one’s self.

Reviving the wonder of mathematics that compelled the ancients to study it for fun may in fact offer the access to depth of understanding and distinction that we actually want for kids.  It’s not likely to turn every one of them into a passionate mathematician, but that’s OK; we don’t need that anyway.  What we need is to make room for each of them to explore it, to use it for what they need it for, to recognize it as more than a chore.