[cmath] Another prominent OP Ed on math in Vancouver Sun appears today

[Nassif Ghoussoub]

It's time to take a new approach to math

When many otherwise successful students need to hire tutors for a  
subject, something is wrong

BY STEPHEN HUME, VANCOUVER SUNAPRIL 6, 2009 3:02 AM

Everybody seems to be weighing into the great mathematics discussion,  
so permit me my two-bits worth.

For the most part, it's not about the math, or the kids -- it's about  
our collective obsession with treating miscalculations as failures  
rather than embracing them as the true learning opportunity that every  
error should become.

In science, business, sports, the arts, it's always the mistakes that  
teach us the most. Knowledge and skill advance by trial and error. I  
sense that getting it wrong is an essential part of learning.  
Sometimes, it takes many wrong answers to discover a way to the right  
one.

Yet when we teach math, we obsess slavishly about wrong answers. In  
the classroom, on examinations, for entrance to university, true  
success means getting all the answers precisely right. Failure means  
having wrong answers exceed some arbitrarily predetermined threshold.

It's not necessarily even about wrong answers. I know kids who have  
been marked down for having arrived at the right answer but by some  
unorthodox method instead of what's prescribed. In other words,  
thinking laterally and outside the box is wrong, too.

Provincial and national statistics demonstrate convincingly that kids  
like and enjoy math in the elementary grades. It's only as they  
progress through high school that interest wanes and many come to  
fear, loathe and detest math.

So we have a system which takes students who enjoy math and then, in a  
few short years, grinds the pleasure and sense of creative play out of  
most of them. But the kids' responses are not innate; they come from  
somewhere else. If it's not from them, it must be from the system and  
its propensity to humiliate and marginalize.

I empathize. As a kid, I, too, went through the agonies of trudging to  
the blackboard to get my long division wrong. Was public shame an  
incentive to improve? Not at 13. I developed an elephant-sized case of  
math anxiety. I fled math at the first opportunity; took the minimum  
required to matriculate; did the minimum amount of work to scrape  
through with the minimum grade that permitted me to go on; joined my  
classmates in self-fulfilling ridicule of what we feared; never took  
another math course and, in university, avoided courses with math  
components.

So I was shocked when, holding down a management job responsible for  
budgets in the tens of millions, the standard psychological evaluation  
required of senior executives reported that my math aptitude was on  
the high end of the bell curve rather than the low.

Recently, I watched my daughter go through the same process in high  
school. Let me say that this is not a young woman who shies from  
challenge. At university she takes on difficult subjects she's never  
before studied and does well at them.

In Grade 7, she'd ranked near the top of the national math test she'd  
taken for fun; by high school she'd walked out of her math class never  
to return, preferring to complete her university entrance requirements  
by correspondence -- and I watched in astonishment as her grades  
suddenly shot up by 25 per cent when she was left to work on problems  
by herself.

When I interrupted an animated discussion with her mother over some  
fine points of Latin syntax to ask her what had happened, this is the  
gist of what she said:

If math is ultimately the language of relationships, we never seem to  
get beyond the grammar and basic punctuation in the classroom. We  
reward students with innate aptitudes and marginalize those without at  
a time when adolescents are most self-conscious and their self-esteem  
is most vulnerable to a sense of public humiliation.

Imagine teaching English literature, she said, by requiring students  
to memorize the Oxford Unabridged Dictionary, grading them only on  
their ability to correctly spell the words they are required to  
memorize and on whether they can parse the sentences. Imagine teaching  
Romeo and Juliet by counting Shakespeare's use of bilabial fricatives  
and ignoring the big themes of passion, pride, love, jealousy and  
betrayal with which teenage readers most identify.

Some time ago, writing a short piece I'd been asked to contribute to  
the Victoria-based magazine Island Parent on the subject of math  
anxiety, I called a dozen friends and acquaintances who either have  
teenagers now in high school or whose kids have just passed out of the  
system.

I had one question: Did your kids require the help of an outside tutor  
to get through the final few years of math in high school? Every  
parent I called said yes, they had, indeed, felt compelled to hire a  
tutor to help otherwise academically proficient teenagers get through  
math. The response was corroborated by a 2007 report from the Canadian  
Council on Learning, which found that about 30 per cent of Canadian  
parents had hired tutors to assist their kids with math. Those  
students averaged B or higher in their general academic performance.

According to a 2004 report from the B.C. College of Teachers, almost  
half of secondary school math classes were being taught by teachers  
without a background in mathematics. It seems that even the teaching  
profession is affected by the compounding uninterest that afflicts the  
subject.

Perhaps, however, there are significant lessons to be learned from the  
fact that somewhere near a third of our brightest high school students  
need outside help in math.

The first lesson is that once they begin studying the subject one-on- 
one outside the classroom, most math students do well enough to meet  
post-secondary requirements. The second is that the system as it now  
exists unfairly penalizes students whose families can't afford to hire  
a tutor.

The mantra of technologically advanced society is math skills. If  
that's the case, why do we persist in an educational model that  
doesn't appear to work?

Should we be completely reinventing the classroom environment when it  
comes to math?

Should we be training, hiring and providing financial incentives to  
more teachers while moving to much smaller math classes where there's  
a sense of collegiality and one-on-one instruction is genuinely  
possible?

Should we be teaching math in shorter periods but teaching it every  
day and in a gaming atmosphere?

Should we be looking at greater use of online resources where kids can  
progress at their own rate without constant comparison to those who  
are more advanced in their skills?

I don't pretend to know the answers here, but I do know that one  
classic definition of stupidity is to keep repeating the same mistake.

shume at islandnet.com

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