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Angela
is a good student; she's also lovely to look at - auburn hair that
falls in waves, just so, smooth skin, and bright eyes that smile,
but say something more, a depth, a curiosity, a hunger for life.
She's also forgotten fractions. Now in the scheme of things, she's
way beyond fractions: second year algebra to be exact. And she's
perturbed to discover that she's forgotten how to add them.
I ask Angela to consider what might happen if she were to ask
100 random people on the subway one weekday morning if they would
be kind enough to take a short little quiz on fractions to help
her with, say, a little research project. It's a long commute, and
there are a lot of professionals on the train into work, but I
suspect her responses would include some fear and trembling, some
rude "no's," and possibly one or two death threats,
despite her smiling eyes.
Why do we hate math so much? After all, it's supposed to open
doors, earn us more money, help us in everyday life, right? So
what's wrong? Why would the average person rather clean all the
toilets in a high-rise than ponder a question with fractions or do
a few little factoring problems?
There are many reasons, most of them good, I'm afraid, but few
of them have anything to do with the nature and beauty and essence
of the subject itself. But it wasn't the essence of math that you
learned in the classroom. It is among the greatest ironies of
education that a subject so graceful and elegant, so able to
inspire and bolster confidence, and so useful for living a joyous
and effective life, should be presented in a manner that strips it
of its substance and glory, and leaves students feeling bludgeoned
and inept, convinced they "stink at math", unaware of
its beauty, or their own precious abilities.
And they are there. Most people are convinced they are awful at
math. They're wrong. Mathematics is vast; mathematical strengths
and abilities come in many forms. If our view is so limited that
we present math as a mere collection of techniques, then only
those who can perform these techniques will see themselves as
successes. But we can change our view of mathematics. And through
this, change our students' view of themselves.
Jared is an athletic 14 year-old who's had his share of
troubles. Discarded by his parents, he's known the inside of drug
treatment centers, special schools, and psychiatric hospitals, and
has witnessed shooting, violence, and drug use from an early age.
I was assigned to teach him mathematics, a subject he had little
use for, and could tell me in detail why not. He was bold and
defiant, but when he thought no one was looking, he was also
curious.
We struggled. Patience and consistency were not things Jared
had learned in his short life. He wanted to fly, and the steady,
sure pace of skill acquisition was not to his liking. He and the
small group of students in his class didn't want to learn
fractions; they wanted to learn trigonometry and calculus.
Trigonometry is the mathematics of triangles, particularly
right triangles, and the constant ratios of sides in those
triangles. We can figure out a lot of things with those ratios.
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Now, between you and me, ratios are fractions, but
trigonometric ratios have an aura about them that fractions don't
have.
"I could teach you guys the first month of trig in a few
days," I told them with some truth, and a bit of bravado,
"but you'd have to stop talking long enough to let me."
They let me. And they learned. Not because they are brilliant, or
because I am brilliant, but because they wanted to. They tried on
the image of that competency and liked what they saw and how it
felt. They reasoned, and figured, and grappled with problems and
found their way to solutions, on their own. There was a toughness
to it that they liked, and a sense of mastery they could feel, and
they could see themselves fitting into that world. In Jared's
world before, the big guys had done drugs and guns. Jared can see
a world now where the big guys do trigonometry and calculus.
People hate math because over and over we tell them they're not
good at it. We do this through frequent testing that puts a big
red mark through every "wrong" answer, as if doing math
means getting right answers. We do this by teaching math as a
collection of arcane manipulations that few see the reason for, or
the connections between.
This erodes the confidence and self-concept of our children,
but our current system fails them in an even more fundamental way.
Mathematics requires thinking and reasoning, pulling together
ideas and information, and then problem-solving toward a solution
- without a road map or delineated instructions. This is rather
like what life will ask of them. In mathematics, we have the best
opportunity to praise, nurture and development these tremendously
valuable skills. There are few experiences we can give them in
their childhood years more valuable than that sense of their own
competency and ability to find their own way, using their own
strengths and skills. But we miss the chance.
Consider basketball. To watch Michael Jordan sail through the
air with the greatest of ease and then describe the game as a
sport of dribbling would be absurd. Yet what we have done in
presenting mathematics to students is akin to taking the flight
out of the sport of basketball and leaving only the dribble.
Maneuvering free, soaring up and making a basket must leave the
athlete with a rather good sense of himself, probably better than
he feels after dribbling practice. Few kids have the equivalent
experience in mathematics: maneuvering past obstacles, seeing the
way clear to the goal, soaring up, and making it. Maybe this is
the biggest failing of our system, because a child who
accomplishes this in math - and it is available to all students,
not just the 'whizzes' - knows, deep down, that if he can do that,
he can do anything.
What life asks of us, mathematics prepares us for. We have all
heard that, and we accept it in some vague way, thinking it refers
to measurement or finances or velocity. "The true value of
mathematics lies outside commonplace activity," says Jerry P.
King, author of The Art of Mathematics.
While you cannot change the curriculum, the grading system, or
the teaching approach in your child's mathematics education, there
is much you can do to help. The next time you are about to say,
"I stink at math", or the next time you hear your child
utter similar sentiments, or the next time you see a test score
that seems to reflect such sentiments, take a different view.
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Reconsider what math is. Expand your view of the
subject. Challenge the stereotype that math is only about numbers,
figuring, or manipulations of symbols to get a 'right' answer. Ask
yourself, or your child, what is being sought, and why. Try to
glimpse the bigger picture. Surprisingly, your child's textbook,
in the textual material and in the colorful sidebars, will give a
view of this. And don't neglect your public library. Both the
children's and adult sections have a wonderful selection of books
that go beyond the drudgery to give you a new view of what math is
all about.
Encourage the process of discovery and reasoning. Mathematicians
wonder, and seek to discover. Conclusions are derived logically,
from premises clearly laid out before. This rigor of thinking and
reasoning is an invaluable asset to all of us far beyond math
class. Help your child see the connection between reasoning and
finding the right answer. This will help you and your child see
math as more than a haphazard series of manipulations and
techniques, as you connect thinking to problem solving.
Permit exploration. Don't require a clear path. Accept
the struggle as normal. Let your children know that mathematicians
struggle just as they do. Our frequent testing and assigning
grades to these tests gives students and parents the idea that the
goal is to know the answer or the technique fast, right away,
without errors. But this is not how mathematics is done, nor is it
what math is about. Give your child permission to try a variety of
paths toward a solution. The schools won't stop testing or
grading, but you can de-emphasize their importance, and positively
reinforce your child's wondering, exploration, and struggling.
Praise the journey. Let your child know this is the
process of mathematics, and that he is doing it very well. Because
he is. Most students want to understand, and want to see
themselves as successes in math. Your child will have unique
strengths and aptitudes in this process, but he probably won't see
them as strengths, he'll only see the red letter at the top of the
test. Help him see beyond that. His anxiety will decrease, and his
sense of competency will increase. His view of math will change,
and his view of his place in it. He may actually come to see that
he belongs.
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