Learning Math the Wild, Authentic, and Rebellious Way

Learning Math

Ouroboros by Michael Maier, image from Wikimedia Commons

My son found this article called “Lockhart’s Lament” online (available here) and raved about it, saying “Mom, you have to read this. It’s just like what you are always saying.” It’s true – I loved it, and I want to help spread Lockhart’s message far and wide. The great thing is that Paul Lockhart is actually a research mathematician and K-12 teacher, so he has way more credibility than this one little homeschool mom.

His message is this: The standard textbook-driven curriculum that passes for mathematics instruction in our schools is not mathematics at all. What our kids are being taught is only the dried up imitation of math. He uses the analogies of a paint-by-numbers vs. actual painting, and learning to read musical notation without ever playing music.

He says, “In fact, 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.” (p.2)

Why do we do this to kids? Lockhart believes that most math teachers and curriculum providers have the best of intentions, but they don’t even realize what true mathematics can be. It should be about solving real problems, not the phony exercises in a textbook with the demonstrated solution right next to it, but real thought provoking problems/puzzles with no given answers. True mathematics is more of an art form, he says. It should be fascinating, not repetitive regurgitation. The people who best understand true mathematics are mathematicians, not teachers. Ideally we would have mathematicians who happen to be very good teachers too, because not every expert is good at teaching.

Lockhart isn’t saying that kids shouldn’t learn the basic computational skills needed for everyday life, but that those sorts of skills can be taught without all the worksheets. His big criticism is that we mistakenly fixate on getting kids through the dullest possible presentation of Algebra, Geometry and other higher mathematics while simultaneously squelching any hope of inspiring students to delve deeper. He scoffs at the common argument given that students should learn Algebra and Geometry because it develops critical thinking. He would rather see kids doing their own thinking than regurgitating theorems and postulates for a test.

Tests. I think a big reason for our emphasis on equations and formulas is the effort to standardize curriculum and measure results. The type of math education Lockhart describes in his article would be very difficult to administer in large classrooms, and equally difficult to assess. And we all know how much school administrators like to assess.

I faced this problem with my youngest child. When we moved from Connecticut to Hawaii, I knew that she would have to take the mandatory state test for 4th graders and I didn’t think she would know enough of the material unless I started her on a textbook. It really bothered me, because up until then we had just been playing games, using lots of manipulatives, exploring patterns, reading books like “One Hundred Hungry Ants,” and doing art related projects like a life-sized chalk drawing of a blue whale in our cul-de-sac. She didn’t decide that she hated math until faced with a workbook. It didn’t matter which brand I tried, she hated all of them (although there’s a few new ones I wish I could have tried 8 years ago). I think it would have made all the difference if I could have stuck with my convictions and waited a couple of years to introduce some of these things, but the mandatory test forced my hand. Even then, there were things on the test we had never covered, like stem-and-leaf-plots, which made her feel like she wasn’t good at math.

I was SO frustrated! And worried too. Even though my instincts told me that it was OK to wait until she was older, I didn’t have enough experience or confidence to know it would be OK. My oldest son waited until he was twelve before picking up a textbook again, and at the time I still didn’t know how that strategy would work out. But now I know. He learned everything he needed to pull down a good score on the SAT, which is all he really cared about because he wanted to get into college. But this all is exactly the sort of thing Lockhart is lamenting. We should not be treating mathematics like a ladder that must be climbed from basic addition to calculus. We should be approaching it the way the Ancient Greeks did, as something fascinating to be discovered.

He writes: “Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself.” (p. 5)

My middle son (the one who found this article) happens to love math. He dutifully worked through all his textbooks, but he always preferred the non-textbook activities we did. And he very often came up with his own ways of solving problems before he learned the traditional method. He even taught himself how to solve probability problems before he realized that anyone else had done it too. I never instigated any of this. It was just him, thinking and wondering. And now that he has taken chemistry and physics classes in college, the only thing that bothers him is having to show his work. He solves problems his own way (and he is usually always right), and hates to be slowed down by showing a bunch of steps he doesn’t even use.

My only quibble with “Lockhart’s Lament” is that he really leaves us hanging. He makes a very convincing case for overhauling our math curriculum in favor of something more wild and authentic, but since I suspect very few of us homeschooling parents are mathematicians, how are we supposed to recognize wild and authentic mathematical thinking? And just what are we supposed to do about it? I’m going to dedicate all my posts for the month of March to this question. I’ll show you the cool stuff I have found and used over the years (which I think Lockhart would approve of) and scour the math teaching universe for the most innovative ways to buck the current system.

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