Tiny babies can count before they can walk or talk. Hold up one toy, then two toys, then three and, scientists say, even a newborn will know the difference between more and less.
Chimpanzees keep track of their bananas, border collies can tell when sheep are missing and lionesses will do a rough tally of how many intruders have entered their patch of savannah before deciding whether to flee or attack.
Numbers, it seems, are hard-wired in all of our heads.
So what is it about higher math that freaks us humans so?
Why is it that harmless, colourless words like “functions” and “trig” can transport even bright, successful, self-confident adults back to the sweaty misery of a high school classroom where the blackboard is aswirl with incomprehensible logarithms and the teacher speaks a foreign jibberish they have no desire to learn.
Can so many of us really be genetically incapable of absorbing mathematical formulae?
Or is math phobia a head game, where anxiety becomes a self-fulfilling prophecy, as the fears and shortcomings of one generation of pi-challenged students are passed down to the next, not in the womb but in the classroom?
Today, mathematics plays an ever bigger role in our ability to keep pace with a digitized, computerized, knowledge-powered planet. At the same time, educators and parents are mulling the conundrum of why Johnny and Jacqueline can’t add, multiply and divide. Is the solution a curriculum overhaul or better teachers? Does the answer lie in fewer calculators or supplying every school age child with an electric keyboard or a 12-string guitar?
“The really good question is why are so many people afraid of math,” says Bill Byers, a mathematics professor who retired from Concordia University last January. “It is my experience that mathematics causes more anxiety than any other subject.”
“It’s like any kind of trauma. If you are traumatized by something, you withdraw from it. And then when it comes to choosing a career, well, let’s see, if I want to choose something in the health sciences, I have to have a DEC in science and to get that I have to pass these math courses. But I’m frightened about mathematics. So I can’t become a nurse, and I veer away from that kind of profession. But that’s a tragedy.”
So common is the phenomenon that dozens of books have been written about math anxiety. In a lovely ironic twist of the knife, there’s even a computational table called MARS – short for Mathematical Anxiety Rating Scale – to measure the depths of a student’s trigophobia.
Byers, the author of of How Mathematicians Think: Using Ambiguity, Contradiction and Paradox to Create Mathematics, argues math anxiety often has more to do with inept teaching and bad experiences in grade school than from innate inabilities to understand math concepts.
And while very few people are like the genius janitor Matt Damon played in Good Will Hunting, Byers is convinced most of us have a much greater capacity to understand complex math ideas than we know.
I just do not believe that people are so neatly divided into the math stupids and the math smarts. That’s a cop out.
“Numbers are one of the most basic things that make us human. … We all have a certain affinity for numbers. I am really upset with people who say of a seven-year-old, ‘Oh, he’s just missing a math gene.’ Or that some people are good at it and some people are bad at it. I think that’s an unfortunate way to look at it. Everyone has some ability to appreciate mathematics.”
Not only ability, but need.
“As a professor who teaches students in science, I can’t tell you how important math is, both in developing their proficiency with numbers and in honing their logical skills,” said Virginia Penhune, a psychology professor at Concordia University.
Over the last decade, neuroscientists like Elizabeth Spelke, Stanislas Dehaene and Michael O’Boyle have focused much of their research on the apparently intrinsic capacity of all humans to keep track of numbers and grasp concepts of spatial distances.
In 1999, Dehaene of Service Hospitalier Fréderic Joliot and Spelke of Massachusetts Institute of Technology showed how different parts of the brain were used to do different kinds of math. Their study suggested such basic arithmetic as learning to add and multiply uses the same parts of the brain that are used for verbal memory tasks. A different part of the brain was put to work when subjects were asked to estimate which of two answers might be correct. Being able to approximate the right answer – tapping into what Dehaene and Spelke referred to as “a numbers sense” – was seen as a better gauge of a person’s ability to think a problem through and make spatial connections than memorizing multiplication tables.
Another aspect of their 1999 study may have particular pertinence for Quebecers because it looked at the arithmetical skills of bilingual people. Their research showed that bilingual people were more likely to get the right answer quickly when they were tested in the language in which they had studied math, even if it was not their first language.
More recently, Spelke, now at Harvard, has explored possible links between music training and improved math scores. In a study prepared last spring for a symposium on the brain, learning and the arts, Spelke showed how students with intensive music training outperformed students with little or no music training in a range of geometric tests. The experiment, which controlled for differences in IQ, academic performance and social and economic factors, appears to shore up theories that intensive music training, with its built-in tonal spaces, might prove useful in helping students better understand geometrical concepts.
Making a connection between math and music is as old as the Pythagoreans, a cult of ancient Greek vegetarian mathematicians who believed math was the basis of everything and noted harmony in the ratios of musical time.
“If you think about mathematics as certain kinds of patterns, music is patterns of sound,” said Byers. “And music is mathematical, it’s the science of sound.”
Penhune, whose research explores the brain’s plasticity when we learn motor skills or practise music, said to date the case for a link between music and math skills isn’t that strong. Taking music lessons is certainly good for developing general skills, like learning to practise and focus on a task, in addition to the more obvious musical elements, like remembering auditory information, concentration and planning. But Penhune’s not yet convinced that music training in itself will improve anyone’s ability to do math. “Real music training is like school. There’s the social interaction and it is rich and rewarding, but it is very much about learning. But I’m not sure that’s all that different from acquiring another intellectual-type skill, such as joining the chess club.”
Of course, there will always be people whose synapses fire on all cylinders when they do math in ways that wouldn’t happen for the rest of us, no matter how much we practise.
Albert Einstein is said to have been a fairly average math student. Yet his brain was remarkable for larger than normal parietal lobes, regions on the right and left side of the brain that are important for mathematical thinking and visual imagery.
In one 2005 study, published in Cognitive Brain Research, Michael O’Boyle’s team at the University of Melbourne used functional magnetic resonance imaging to examine two sets of teenage boys while they set to work on a difficult math problem that involved mental rotation tasks. One group of boys had average math skills while the others were considered gifted, scoring in the top percentile in standardized math tests. In both groups, the scan showed several areas of the brain lighting up while the boys tackled the exercise. But in the case of the gifted students, the activity was more intense on both sides of the brain and additional sectors were also put to work – including the prefrontal cortex, the brain’s decision-making centre, and an information processing system known as the anterior cingulate that is thought to be particular to math whizzes. O’Boyle said the research showed “that not only is there a quantitative difference in which gifted brains are more active and have additional processing resources, but some regions of their brain are selectively and uniquely engaged.”
Wayne Sossin is obviously a smart guy. A neuroscientist at the Montreal Neurological Institute and Hospital, he recently published a study that examined how synapses in our brains change when we form memories depending on whether we learn material over time or in short intervals.
And Sossin says he was pretty good at math in school. “I wasn’t intimidated by it, I was good at semantic math, logic problems. It was when it got to a higher level, where it involved some kind of intuitive knowledge, that I said, ‘Whoa, what is this?’ ” He can’t help comparing his experiences with those of his late father-in-law, who was a very strong mathematician. “For him, it was intuitive, a way of perceiving the world,” said Sossin.
“For people who do mathematics, creative mathematicians, it’s almost like an art form, a kind of creativity, like art is,” said Byers.
“People used to talk about left brain and right brain. The left brain had language and logic. It was kind of linear. And the right brain was more your artistic side, for spatial intuition and things like that. But in my opinion, math requires both sides of the brain.
“If you are teaching a kind of low kind of mathematics, then of course it will help people become logical and develop logical skills. If you are teaching geometry, you are developing geometric and spatial skills. And if you are teaching mathematics creatively, you are teaching how to integrate these different aspects of your intelligence, so you need everything.
“I personally think that mathematics requires imagination and creativity. Even at relatively elementary levels, students can explore mathematical situations and learn to identify patterns and then, if you want, you can argue whether that is a real pattern.
“So logic comes in after the exploration, later on when the child is a little bit older. … Kids naturally are interested in numbers and play with numbers and you can make up games with numbers and that’s all ways of having people explore a kind of mathematical universe.”
A neuropsychologist at University College London, Brian Butterworth is the author of The Mathematical Brain and What Counts: How Every Brain is Hardwired for Math.
Like Byers, he believes everyone is born with the capacity to do basic arithmetic “whether they are Cambridge graduates or tribesmen in … the New Guinea highlands.” He suggests those who begin to stumble as math gets more complicated often do so because of “earlier failures to understand.“
Which brings us back in a neat mathematical arc to the reason so many people find math so daunting – misunderstandings, compounded by mediocre teaching.
Nick Fiori, a specialist in teacher learning and mathematics education at Yale University, cites a handful of ways in which math teachers could do a better job of streamlining lessons, making the material more relevant and giving students time to solve their own mistakes.
“Most of my mathematician friends and I are only able to solve about two problems a year – if we’re lucky!” Fiori wrote in the Phi Delta Kappan journal. “Outside of mathematics, does anyone you know ever get 40 things done in a day? … Let’s cool it with the daily deluge of exercises and reconsider the quality of problems that can be completed at a rate of 40 per night.”
Byers, who is in his early 60s, says it wasn’t all that long ago that the common view was that men were good at math and women were not. “Those were social myths. They were not true,” he said, recalling a conversation he had with a former colleague, an eminent molecular biologist who had studied at Harvard. “She said, ‘Oh, I was never good at math.’ And I laughed at her. I said, ‘You have a PhD, you’re a brilliant scientist and you’re telling me you weren’t smart enough to learn calculus. It’s ridiculous. Someone indoctrinated you with the idea that you were not smart in that way.”
Now consider the fact that the vast majority of elementary school teachers are women, many of them raised before the math enlightenment.
“In Quebec for example, people who teach mathematics do not have to have studied mathematics (in university), much less have been good at mathematics or loved mathematics,” said Byers. “So what happens when you get this perpetuation of anxiety, where anxiety is passed down from teacher to students because no one is really comfortable with it?
“The teachers who teach math should be trained in the teaching of math. If it turns out that the people teaching math hated math as students, then you are only adding to the problem.”
Given the monumental role that math and computational skills play in the way our society functions, Byers is baffled when people simply resign themselves to the notion that they or their children just aren’t up to the task.
“If you have a baby, would you say, ‘Well, we’ll have to see when she gets to be two years old whether she will be able to speak or not?’ She’s a human baby, she’ll be able to speak. I feel the same about math. She’s a human baby, she should be able to do some math.”
“Every intelligent person can do math. So if they don’t do math, we have to look for the reason for that elsewhere.“
BE YOUR CHILD’S FIRST MATH TEACHER! – Teach Your Child to Count to 10 – Early Learning Method
Source: The Gazette (Montreal) – http://tinyurl.com/ylg2rhk
