The Minefields of Math
by Stephen Hume
The desks were sturdy, well-worn affairs, their patina of ancient varnish removed by generations of grubby fingers which had nevertheless smoothed the underlying surface to a dark, glossy finish of its own.
Solid wood tops flipped up on hinges to expose the pencil cases, ill-used workbooks and geometry kits inside. On mine, just above the groove for holding pencils, a former occupant—no doubt as bored as I was—had carved his name and the date. Memory plays tricks after half a century but I recall it was “Will, 1906.”
The frames were grimy cast iron. They rested on clawed feet that looked suspiciously similar to those on our high-sided enamel bathtub at home with its chipped enamel and white-handled faucet.
The desks’ feet were screwed to a pair of long two-by-fours. Arranged in parallel rows, the desks made the classroom look like a mass start for a bobsleigh race that wasn’t going anywhere soon.
In the top right corner of each desk was a glass inkwell. Into it we dipped the straight pens we used to practice the rolling, swooping loops and curls of 19th Century penmanship from the age of Charles Dickens.
What I remember most from that classroom 50 years ago is my paralysing fear of long division. Not for me the experiment with “new math” that would later bedevil my little brothers, not sets and subsets, not binomial equations or x and y axes, not Euclid’s theorems, axioms and proofs, just the simple cursed process of long division.
Looking back into that dim past, I know where the fear arose and how it was amplified until my anxiety over getting the divisions wrong inflated to fill the room.
Not that I was without blame in this. I’d been telling my mother my homework was done so that I could escape to the outdoors where a life more real than numbers beckoned. Unfortunately, the farther I got behind in my homework, the more impenetrable the long division problems became.
My intimidation was amplified by one teacher’s attempt to discipline an unruly classroom with the clock ticking oh, so slowly toward recess.
I don’t blame the teacher. He liked his classroom quiet and his students diligent. We’d been noisy. He told us to do our long division.
The teacher wore shoes with crepe rubber soles. When he patrolled the long bobsleighs of pupils, he’d come up behind in absolute silence, look over your shoulder and if—as was the lamentable case with me—you were drawing a jet plane because you didn’t quite grasp the concept of long division or why it was necessary, down would come his ruler on your desk with an almighty THWACK!
I levitated. The humiliation of trudging to the blackboard to demonstrate my woeful ignorance with the very problem I’d been evading, to the delight of my classmates, followed. Then, I thought them a treacherous lot. Now I recognize that their levity was simply an expression of relief that another had been chosen and that they had been spared, for the moment, a similarly ignominious fate.
Still, that ruler and the trip to the blackboard left me with an anxiety about my ability to do math that would plague me through the rest of my school years and almost prevented me from attending university.
Imagine my shock when a mid-career corporate aptitude test showed that my native mathematical and reasoning skills were actually strong.
And all along I thought it was me, just as tens of thousands of other kids sitting in classrooms this fall—and their beleaguered parents—have been led to believe that it is they who are failing math rather than that somehow math and the way we teach it seems to be failing them.
Now I don’t intend a criticism of teachers here. For the most part, I think teachers do a commendable job given the resources they get and the demands from parents and politicians who pander to parents. I’m more concerned about the institutional culture we’ve collectively created around math as a discipline and within which students, teachers and parents must now operate.
Preparing to write this article on the issue of math anxiety, I conducted a completely unscientific straw poll. 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?
In every case, the parents I called said yes, they had, indeed, felt compelled to hire a tutor to help their otherwise academically proficient teenager get through the minefields of math. Why? They did it for the same reason we did for our own child—because everyone understands that math is required for entrance to post secondary educational institutions or to move on in many of the technical trades.
There’s no doubt that mastering math is essential for much of the work that maintains and advances our technologically rich society. Whether science-based bio-tech or tracking medical imaging records, running trans-global corporate communications networks, managing a small business, planning government finances or simply keeping the family books in order, math skills from basic to advanced are required everywhere.
So why do we persistently do such an abysmal job of teaching math?
We continually fail to engage too many kids with a subject that is essential to their own futures and, by extension, to the economic health and well-being of our tech-driven society. We teach kids to fear math, even to loathe it, when we should be instilling in them a sense of its beauty and importance as a truly universal language that unlocks doors to shared global understanding in ways that politics, religion and poetry can’t.
Provincial and national statistics show convincingly that while Canada’s kids like and enjoy math in the elementary grades, their enthusiasm dwindles at an alarming rate the farther they progress through middle school and high school.
Somehow, we take generations of kids who like math, systematically grind their enjoyment out of them, then make the kids feel that they are the problem. Well, let me argue that the kids are not the problem.
The evidence of our failure in this crucial field is everywhere. There are the laments from business and industry regarding the dearth of science and engineering graduates from universities and technical institutes. There’s the wholesale abandoning of math by students as soon as it ceases to be a required subject. There is the difficulty in recruiting, training and keeping adequate numbers of math teachers.
Indeed, a 2004 report from the B.C. College of Teachers said that almost half of secondary school math classes were being taught by teachers without a background in mathematics.
Most significant, perhaps, is the fact that scientifically-founded studies support the anecdotal evidence I got from my own straw poll.
“The widespread use of private tutors is a new feature of the Canadian educational landscape,” concludes research by the Canadian Council on Learning released in 2007.
It cites other research which shows that the number of companies offering private tutoring as a supplement to public education grew between 200 per cent and 500 per cent in major Canadian cities during the 1990s.
Furthermore, the organization discovered, one out of three Canadian parents has hired a tutor for children in school and “Most tutors are hired to assist with mathematics.”
Even more telling, it found the majority of parents hiring tutors reported their kids’ general academic performances were in the A or B range of grades and that the single greatest predictor for parents hiring a tutor was family income.
So somewhere near a third of our best and brightest students now need help from outside in order to pass math with grades that won’t compromise their ability to move on in the post secondary education and training that government, educators and business repeatedly remind parents is essential for success.
And for those kids whose parents can’t afford to hire a tutor, the system erects a barrier which places them at an unfair disadvantage in the eventual pursuit of post-secondary education precisely at a time when rising costs already make it an increasingly daunting prospect for even moderate incomes.
It’s true that some standardized surveys show that on average Canadian 15-year-olds do reasonably well in science by comparison with other developed countries. Results from tests published late in 2007 rank Canadian kids third in science skills among the 14 countries surveyed.
However, the same results show Canada lost ground in its ranking for mathematics, slipping from second place in 2003 to fourth place in 2006.
More troubling, however, is the fact that Canada’s graduation rate in those science and engineering disciplines which demand math skills is below average for a developed country. What’s happening is that kids are improving their skills by hiring private tutors simply to get through math and science courses but once they get to university, they swiftly abandon that learning for other subjects.
This tells me that while kids clearly have the natural skills to learn math and its science applications, there is something embedded in the culture of education that turns many of students against it and even causes a disproportionate number to fear and loathe it.
What might it be?
One thing that strikes me as a student, teacher and parent of a recent high school student is that if we taught English literature or coached minor soccer the same way we devise and teach the mathematics curriculum, we’d have a similar collapse of enthusiasm there, too. Imagine studying Shakespeare’s plays through endless parsing of his sentences to deconstruct his grammar, counting the verbs and nouns and memorizing lists of characters instead of discussing the great universal themes of pride, passion and betrayal in Romeo and Juliet or Othello.
To some extent, I think, the former is what we do with math and science rather than the latter.
I know, there are basic concepts to be grasped. But for math—and science—we emphasize quantifiable outcomes which require that answers be either right or wrong, rewarding one and punishing the other. Students tell me that when they come up with some novel way of reaching an answer to a math problem they often lose marks because they haven’t used the prescribed method.
In other words, while we trumpet the need for innovative thinking, we actually punish those who think outside the box.
Thus, students are generally subjected to grading systems which punish them for the “wrong” answer when we know that, in the real world, science advances as much when a hypothesis is proved wrong as when it is proved right. In a system of trial and error, it is not wrong to be “wrong” because being wrong is often right.
Mistakes advance scientific knowledge as much as correctness. Somehow, we need to imbue the culture of high school math with this sense that making a mistake isn’t necessarily good or bad in itself and that learning from that mistake is cause for celebration.
Another thing that strikes me is that the success rates that accompany hiring private tutors for math-challenged students suggest that we need to re-think the structure of classroom approaches to math.
It’s obvious from the results that kids respond well to one-on-one tutoring where they don’t respond to the one-size-fits-all structure imposed by the education system. Perhaps our math classes should be much smaller, maybe two or three students to a teacher.
Perhaps we need classes in which very small numbers of students can be grouped according to their grasp of the subject, so that slower learners don’t feel left behind while faster learners are able to challenge themselves with new material. Perhaps we need shorter classes with greater continuity and consistency through the school year. This, of course, would require greater investment in the training and hiring of math specialist teachers and paying the wages that will keep them in classrooms.
What’s happening now is that students, teachers and parents all seem frustrated by a system which isn’t firing on all cylinders.
Government and business talk endlessly about the economic importance of math skills to our technological society, yet they off-load the cost of resolving the problem onto already stressed parents, creating a new sub-class of non-participants in higher education on the basis of family income.
Ultimately, the responsibility for initiating change comes back to parents as citizens. Parents have to insist that the politicians to whom they delegate responsibility for funding the education system rethink priorities.
If what those same politicians say about Canada’s compelling need for math, science and engineering graduates is correct, then we all need to find out why so many kids who start with an irrepressible enthusiasm for math wind up hating it after 12 years of exposure to the way we teach it.
Then, instead of more penny wise and pound foolish tinkering with what doesn’t work for so many, we need some innovative thinking about how to address the math problem.
Stephen Hume is yet another math-challenged parent.