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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