Monday, May 6, 2013

The New Old Math


            Math and I are formidable foes and I have written about our rocky relationship before.  But there’s a new twist to the story of late-- one I think you’ll enjoy.  For those of you who’ve been following along, I’m in graduate school to get a masters degree in teaching elementary education.  I mention it because the class I took this semester was in how to teach young children math with Cognitively Guided Instruction or intuitively—in other words: letting the child solve the problem the way he or she instinctively wants to.  “Intuitively?!” you exclaim.  Yes, you heard right.  The entire gist of the class and the bedrock of the two textbooks we worked from was this: allow kids to arrive at the answer the way in which their brains naturally get them there.  “What!?!” I hear you blathering, “but that’s the opposite of how I learned math as a child!  I spent hours learning logarithms that made no sense and buckled under the weight of wrote memorization drills.  I remember fear, anxiety and being told I was doing it wrong as if it were only yesterday.”  I know, pal.  You and me both.  Calm, down, you’re sweating a little.  Are you okay?
            The idea is that children show up the first day of kindergarten with a robust brain full of informal or intuitive knowledge of mathematics—just ask any four year old what to do with one cookie when his sister is sitting next to him in the back seat of the car.  Break it in half.  That’s intuitive problem solving.  That’s math.  Over the years, addition, subtraction and multiplication become organic extensions of what little kids already know, and they know a lot.  Then, with any luck, your young child will get a teacher who has been taught that creating a positive attitude about math is not only important but germane to her bright future.  No more fear—a lot less shame.
            Imagine a teacher who is actually paying attention to how your child is thinking not just what he’s thinking.  Imagine a classroom where as much time is spent discussing wrong answers to fraction problems as correct answers.  Imagine a pedagogic ethos wherein children are not only taught to learn from their mistakes but actually come to understand mathematical concepts by exploring mistakes, locating the exact spot where her brain jogged left when it should have jogged right, then letting the child enjoy the excitement of an ‘aha!’ moment, where she notices what she did wrong herself.  That’s right, folks, in this math utopia, the teacher doesn’t publically tell her her answer is wrong, the student locates the problem-- perhaps in concert with a peer partner or group-- then fixes it.  Together.  I know.  It sounds crazy to me, too.  But it’s amazing.  And it works. 
            If children learn early math concepts they way that makes most sense to them—by counting on fingers, drawing pictures, talking out loud, or moving legos, pretzels or ‘manipulatives’ around in groups on a desk or rug, they’re more likely to get it.  And if they can help each other and arrive at the answer by reasonable group discourse, (the way adults do in many, many career fields) then maybe the harsh competitiveness of math will be removed long enough for your child to actually feel free to fail and therefore learn.  And don’t worry-- if you think they’ll be counting on their fingers forever, they won’t be.  It’ll take too much time and they’ll become impatient and eventually a classmate will show them how to skip-count by tens or multiply instead of add and they’ll happily jump on that bandwagon.  Who wouldn’t?  It’s our nature to embrace the shortcut-- to evolve and improve. 
            Once the basics are embedded, children are encouraged to see oncoming new math strategies as compatible layers to an involved and fascinating game-- the way they learn the rules for Pokemon trading card duels or professional baseball line-up strategies.  They’re much more likely to remember the algorithms—those slippery rules and strategies-- because they’ll make sense.  If children can approach an algebra problem the way they approach a video game, with curiosity, gumption and the resolve to keep going until they find the gold coins or the trap door or the answer for what x stands for—just imagine!  Imagine not feeling shame when you get the answer wrong, or not comparing yourself to the kid who always seems to know what’s going on when you don’t.  I know, easier said than done.  If only. 
            But it’s going to get better because more and more teachers are going to allow your child’s mind to follow its own path to the answers.  Math will become more like building a snow fort with your friends.  I’ll do it my way and you do it your way and we’ll all meet in the middle.  And if there’s a weak spot, we’ll find it together, and work through to improve it, with persistence and resolve-- as a team of learners.  As a mighty force for mathematics good. 

(Author’s note: Download: “The Kindergarten Files” on iTunes for shining examples of this exciting revolution in learning or read Thomas P. Carpenter et al.’s “Children’s Mathematics: Cognitively Guided Instruction, 1999)

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