Simple Math

It's legendary in the Sudbury literature: the five-month math class. As Sudbury Valley co-founder Daniel Greenberg reports in the above article, it took twenty weeks—a mere twenty contact hours—for a group of twelve kids ages 9 to 12 to cover all six years of elementary-school math.

A miracle? Hardly.

Greenberg's friend Alan White, a longtime elementary school math specialist, wasn't surprised. "Everyone knows," he said, "that the subject matter itself isn't that hard. What's hard...is beating it into the heads of youngsters who hate every step. The only chance we have is to hammer away at the stuff bit by bit every day for years. Even then it does not work...Give me a kid who wants to learn the stuff—well, twenty hours or so makes sense."

This squares with my experience as well. I once taught math to three students who consistently showed up on time. One day, however, I waited and waited...but they never appeared. A bit puzzled, I wandered back to the main room, only to find these students hard at work on their own. They'd gotten too busy and distracted working on math to think about math class.

Another time, a student asked me out of the blue—not in class, just in the course of a normal day—what I knew about counting in base 2 (a.k.a. binary numbers, the basis for digital computers). A spontaneous quasi-class ensued, as she and I looked things up, using a chalkboard to piece together the mysteries, treating it like a puzzle or a grand game: When do you add another digit? When is a 1 replaced with a 0? and so forth.

The way math is taught tells us much about how an educational system works...or why it doesn't. Some of the most powerful arguments on this theme are made in a piece popularly known as "Lockhart's Lament." Paul Lockhart teaches at Saint Ann's School in Brooklyn. Written in 2002, "A Mathematician's Lament"  is a scathing critique of math education that has circulated widely, despite having never been published. The remainder of this post offers an overview of this unusually insightful and frank work.

There is surely no more reliable way to kill enthusiasm and interest in a subject than to make it a mandatory part of the school curriculum. Include it as a major component of standardized testing and you virtually guarantee that the education establishment will suck the life out of it.

Lockhart opens with nightmare scenarios of music education reduced to teaching notation, and art education that's mostly worksheets, memorization, and paint-by-numbers. Beyond being absurd, this approach spells death for creativity.

If I had to design a mechanism for the express purpose of destroying a child's natural curiosity and love of pattern-making, I couldn't possibly do as good a job as is currently being done—I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

To Lockhart, mathematics is "the purest of the arts...the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration." Mathematics touches on the very core of human meaning-making: patterns, imagination, and creativity. Yet in schools it is replaced by the sterile doppelganger of decontextualized facts and regurgitated formulas.

Students learn that mathematics is not something you do, but something that is done to you. Emphasis is placed on sitting still, filling out worksheets, and following directions...The main problem with school mathematics is that there are no problems...[only] "exercises." "Here is a type of problem. Here is how to solve it. Yes it will be on the test. Do exercises 1-35 odd for homework." What a sad way to learn mathematics: to be a trained chimpanzee.

Beyond decrying what schools have done to mathematics, Lockhart also delves into what teaching truly means. Rather than training students to perform, teaching is to him a matter of being authentic, making connections, and manifesting the delights of discovery.

Teaching is not about information. It's about having an honest intellectual relationship with your students...You will never be a real teacher if you are unwilling to be a real person. Teaching means openness and honesty, an ability to share excitement, and a love of learning. Without these, all the education degrees in the world won't help you, and with them they are completely unnecessary.

Before I close, here are a few more of Lockhart's gems:

We learn things because they interest us now, not because they might be useful later. But this is exactly what we are asking children to do with math...Of course it can be done, but I think it ultimately does more harm than good. Much better to wait until their own natural curiosity about numbers kicks in.

Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.

How can schools guarantee that their students will all have the same basic knowledge? How will we accurately measure their relative worth? They can't, and we won't. Just like in real life.

The good news is that the frustrations of misguided education are more than matched by the delights of authentic learning. Whatever your take on math education or Sudbury schooling, all our schools—indeed, our culture in general—could benefit from a massive infusion of this kind of passion for common sense and reason.