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]]>In Greece, there’s been a rush on the banks. In mathematical circles, there’s panic over a shortage of chalk, but not just any chalk: Hagoromo chalk, from Japan. On Amazon—where a box of 72 pieces of white chalk was recently selling for $79 (formerly about $25), coloured costing $399—the reviews testify: “The Mercedes of chalk.” “This soft chalk is the nectar of the gods.” “It is a well-known fact that, if you write math with this chalk, you do not make any mistakes.” “The best chalk in the world.”

Sadly, Hagoromo Bungu Co. found itself a victim of the rise of the whiteboard and the declining use of blackboards in classrooms. The company, which began production in 1932 and, at its peak, sold 90 million pieces of chalk a year, ceased production at the end of March and is going out of business.

Satyan Devadoss, a mathematics professor at Williams College in Williamstown, Mass., seems to be serving as ambassador of the angst, and reigning expert on Hagoromo’s magical properties. “There are a couple of things that are important. One is the thickness of the chalk,” he says. “It is much thicker in diameter, so it has a heft to it.” His favourite thing about Hagoromo, however, is its firmness and, at once, its give. “The firmness helps you be aggressive in your drawing, or in your writing, which is actually important. A lot of times, when I push just a little bit hard on chalk, the chalk breaks and crumbles.” Not Hagoromo. “The second thing is, when you start writing, it melts like butter. It’s just gorgeous. It gives way to smooth writing.”

Mathematician John Mighton, a member at the Fields Institute for Research in Mathematical Sciences in Toronto, was caught unaware of the chalk panic. “I’m afraid I don’t know anything about chalk,” he said, “except that I occasionally get it all over my clothes.” He wouldn’t, if he used Hagoromo. Each piece of Hagoromo has a wax coating, reducing dust and preventing chapped fingers.

At Stanford, mathematicians are mourning Hagoromo’s demise as “a tragedy for mathematics.” One professor has reportedly hoarded a stock of chalk to last him 15 years.

“This is related to something that is far more important,” says Devadoss, getting philosophical, “which is how much we as humans truly value the physical, but don’t realize it.” Mathematics is mostly a purely intellectual pursuit, dealing in abstractions. But, Devadoss reckons, corporeal things, such as smell and taste and touch, do matter.

Devadoss extolls the essence of chalk, as opposed to, say, whiteboard markers. “I don’t know why any human would prefer a marker,” he says—and indeed, for many, the whiteboard is heresy; they hate the smell of the markers, hate the ink all over their fingers. “Every whiteboard works with every marker. Blackboards and chalk are wholly different beasts,” says Devadoss. “Each has its own personality, its own rhythm, and, when you find two made for each other, it is a piece of heaven on Earth. I find whiteboards to be artificial and plasticky in nature, impeding the flow of thoughts and ideas.”

One way to tell whether chalk is any good, he explains, is to take a couple of pieces and roll them back and forth in your hand. “You will hear the [pieces] hitting each other. The deeper the sound, the better the chalk. A lot of chalk almost tingles like crystal. I immediately throw the chalk away. It’s awful. With that chalk, when you write on the board, you actually can’t erase it; the marks stay, and it’s really hard to get off. It’s disgusting.” The deeper the sound, the richer the chalk. “It’s the umami of chalk,” he ventures. “It resonates.”

At the Perimeter Institute for Theoretical Physics in Waterloo, Ont., the house chalk is Crayola for white, Dixon for coloured. “I enjoy using good chalk,” says resident physicist Lee Smolin, who has a strong preference for slate over whiteboards. “It’s obvious and disappointing when bad chalk is offered. But I never heard of this particular chalk.”

“Apparently, Hagoromo chalk is not widely used by physicists,” says Eamon O’Flynn, Perimeter’s external relations specialist. “The ones who had heard of it suggested it was more of a math thing.” And those who hadn’t? “They are intrigued,” he says, “and a few have joined the rush to buy some while it lasts.”

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]]>TORONTO — Don’t get math teachers started on best teaching practices.

The discussions are emotional, heated and they don’t agree on much — except that Canadian kids are falling behind their peers in other countries, and there’s no clear solution.

There are generally two camps: those in favour of the old-school method to lecture kids with a “drill-and-kill” format that preaches practice, and another, ever-growing group that believes a more creative approach is needed to engage students.

At a recent event in Toronto, dozens of teachers waited in line to take selfies with math-teaching celebrity Dan Meyer, delaying his keynote talk at the Ontario Association for Mathematics Education conference. He is part of the new-school camp.

His approach is simple, Meyer says on the phone from California, where he’s a math education researcher at Stanford University.

He presents a problem at the start of class, and lets the students try to figure it out. Hopefully, he says, the students will struggle.

“That initial moment of struggle prepares them for what they’ll learn later,” he says.

Meyer cites several studies that back up his ideas, including one from Manu Kapur, a professor at Nanyang Technological University in Singapore. Kapur’s study shows students who are given a problem to solve on their own — before instruction from a teacher — outperform students who are given the traditional lecturing style.

The technique is in the early stages of implementation across Ontario, according to Sheena Agius, a math coach who helps teachers with the new method in the Dufferin-Peel Catholic District School Board.

Just like all other boards in Ontario, it is moving away from rote learning to try to get students to understand math at a deeper, more conceptual level.

“Just because we’re doing it, doesn’t mean we’re doing it well yet,” she says. “But it’s a learning process for teachers and that will come.”

Meyer has many acolytes, such as Paul Alves, president of the Ontario Association for Mathematics Education and a high school math teacher at Fletcher’s Meadow Secondary School in Brampton, Ont., northwest of Toronto.

“Teachers are really engaged by the way (Meyer) teaches math because when they try it they see the same thing _ the excitement students have to do the math — and it changes the classroom. It invigorates it and energizes it, which wasn’t the case before,” Alves says.

That engagement is priceless, Alves says.

He says a teacher at another school dove headfirst into the new-school method for his Grade 9 applied math class. The class, he says, jumped from 40 per cent on the provincial tests using the old method to 70 per cent after implementing the new one.

Yet both Meyer and Alves say they aren’t advocating abandoning the classic “chalk-and-talk” style.

“At some point I need to know that kids can factor a quadratic equation, and sometimes you have to practise that skill to get good at it,” Alves says.

On the other side of the dividing line, old-school math teachers are just as vociferous.

Anna Stokke, a math professor at the University of Winnipeg, is a staunch defender of lecturing and practice.

She recently published a report with the C.D. Howe Institute that showed Canadian students’ math performance in international exams declined between 2003 and 2012.

Stokke blames the decline on the style promoted by Meyer, which she dubs “discovery-based learning.”

“A direct method is a more effective way to teach,” she says.

“So guys like Dan Meyer will say, ‘We’re going to spend the next week building a birdhouse and you’ll need to use measurements to figure out dimensions,’ and the kids will learn about area and volume and all that. Then a week goes by and what have you learned? How to build a birdhouse.”

Meyer fires back, calling Stokke’s research simplistic.

“The best teaching is some shade of grey, where before the teacher talks about what to do, the teacher gives students some reason to care and some background on how to care,” he says.

“None of this suggests teachers shouldn’t explain or lecture.”

Stokke does offer Meyer and his disciples an olive branch in her report, saying 20 per cent of math teaching time can be used for these “alternative methods.”

“I’m trying to be objective and I don’t want to tell teachers they can’t use a particular method at all, but I want to be clear on which methods have been shown to work and which haven’t.”

Having said all that, Stokke admits that her research can’t conclusively pinpoint discovery-based learning as the reason for Canada’s faltering math scores.

Her research reinforces an assessment by the Organization for Economic Co-operation and Development in 2012, where 65 countries took part in the Program of International Student Assessment that examined math skills of 15-year-olds. Canada fell in those scores as well.

Her report found every province declined in math scores except for Quebec.

Annie Savard, a math education professor at McGill University, said her research indicates the difference may be rooted in training.

In Quebec, students go to teachers’ college for four years, as opposed to a one-year program that follows a bachelor’s degree in the rest of the country. Ontario is set to move to two years in the fall.

Cathy Bruce, a math education professor at Trent University, is tired of the so-called “math wars.”

“It takes away from figuring out what is happening to Canadian students. The solution is likely somewhere in the middle.”

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]]>By Jordan Ellenberg

There’s little objectively sexy about math. With its flummoxing sine curves and its formulae written as if in ancient cuneiform, the subject has driven countless people to such frivolous pursuits as writing and journalism. Even the stand-up comedian Louis C.K. recently took to Twitter to rail at the way public schools were dryly meting the subject out: “My kids used to love math,” he wrote. “Now it makes them cry.” But Jordan Ellenberg, a professor at the University of Wisconsin, has positioned himself as math’s Malcolm Gladwell with this crystalline, eminently digestible book. (It doesn’t hurt that the drawings therein are charmingly amateurish, as if scribbled on a napkin during animated repartee over cocktails.)

“Mathematics is the extension of common sense by other means,” Ellenberg writes by way of opening thesis, and the book becomes a wide-ranging treatise in how math is about the choices we make, and how it relates to our political and cultural lives. In one breathtaking, arcing riff, for instance, he begins by asking a simple question—should you play the lottery?—and then passes through debates over the existence of God, the Pentagon Papers, train tracks, Winston Churchill and satellite error codes, before settling back to the suddenly profane-feeling question of whether or not Powerball is a worthwhile venture. Context, not calculus, is his cathexis.

But what of its titular promise that with math, you will never be wrong? Well, this is less an instruction book on opening one’s mind to infallible logic, and more a guide to picking the right kind. But even this he illustrates with aplomb, noting that Francis Galton–a pioneer of so many major statistical theories–also just so happened to have inspired the Nazis by founding the field of eugenics.

The biggest takeaway of the book, then, isn’t that math is always right—but that good math is in the choosing of the right kind of math. Math isn’t one and one making two, it’s in the whys and wherefores of that. “Wrongness is like original sin,” Ellenberg writes. “We are born to it and it remains always with us, and constant vigilance is necessary if we mean to restrict its sphere of influence over our actions.”

Books like *Freakonomics* or Gladwell’s *Outliers* became phenomena not simply by articulating tough conceits in accessible ways, but through tours-de-force of intellectual breadth that made the reader feel smart for coming along for the ride, like a crossword you happen to know all the answers to. Through its asides and cameos—a pinch of Pynchon, a nip of Nader—Ellenberg makes math’s curvy graphs start to look a little more attractive.

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]]>When the Organisation for Economic Co-operation and Development released its international student achievement rankings in December showing Canada had slipped to 13th place in math, it prompted much hand-wringing about the dire need for more math in our public schools. Former deputy prime minister John Manley said the results, which show that the math scores of Canadian 15-year-olds have dropped 14 points in the past decade, were “on the scale of a national emergency.” In Windsor, Ont., a local school superintendent called for “math, math and more math.”

Judging by the steady downhill slide in Canadian math scores, it’s natural to assume that our schools might be suffering from a lack of math. But a closer reading of the OECD’s Programme for International Student Assessment shows just the opposite: since 2003, the amount of time Canadian high school students report spending in math class has risen to more than five hours a week, a jump of 90 minutes.

According to the OECD, Canadian students now spend more time in math class than any country in the Western world. At 75 minutes on average, Canadian class periods are also the longest in the world. The result is that Canadian students now spend significantly more time in math class than their counterparts in countries that outperform them at math. Our students spend twice as much time in math class as students in Finland, a country that slightly outranks Canada on math scores, and significantly more time than other top-performing countries such as the Netherlands and Japan.

The Canadian school year has traditionally been compared to that of other countries, but over the past several years Canadian schools have added to the already long hours students spend in the classroom. Some have begun experimenting with year-round schedules in hopes of preventing students from losing skills over the summer break, while others have extended the school day. Last year, Saskatchewan mandated a 950-hour school year in hopes of boosting student achievement in a province that scores below the Canadian average in math. The change required some school boards to add as many as 50 hours to the school year. New Brunswick lengthened its school day by 30 minutes a decade ago in hopes of improving its academic performance, and in recent years some school districts ended “potato break,” a two-week break that allowed students to work during the fall potato harvest. As a result, the province now has the longest school year in the country, at more than 1,000 hours for high school students, according to Statistics Canada. Yet its students scored below average among Canadian provinces on the most recent international math tests.

The push for more time in school is expensive, and the evidence from global comparisons that longer classes can boost student performance is weak, says Andreas Schleicher, the OECD’s deputy director for education. “You can improve your results by adding more time,” he says. “But you can make a quantum leap by actually focusing more on quality, and that’s clearly what we see from international comparisons.”

Similar debates abound in Asia, he adds, where Japanese students perform as well as their Korean peers at math despite a drastically shorter school day. In high-scoring countries like Finland and the Netherlands, Schleicher says the focus is on getting the best teachers into the worst schools, and on highly individualized academic support for students. Finnish high schools typically have just four 45-minute classes a day, with 15 minute breaks. Teachers typically get two hours of professional development time each day. “Having ‘too little’ instructional time is a problem that I never imagined having,” Tim Walker, an American teacher who moved to Finland, wrote on his blog when he discovered he was expected to teach his Grade-5 students seven subjects in an 11-hour school week, an amount equivalent to just two school days in the North American education system.

Supporters of longer school days argue that more time in school means more opportunities to learn and lowers the risk that students from poor backgrounds, who don’t have access to private after-school lessons, will fall behind their wealthier peers. In the U.S., President Barack Obama has warned that a shorter school year is harming American students. States such as New York and Tennessee recently added 300 hours to the school year in an attempt to improve student achievement. Last year, U.K. Education Secretary Michael Gove pledged to cut summer holidays and extend the school day to 4:30 p.m. in order to emulate the success of top-performing Asian countries, where students often spend long hours in after-school and weekend classes.

In a report published last year that was widely cited by supporters of a longer school day, University of Chicago economists studied the school environment and test results of 47,000 students in 72 countries and found spending more time in class did in fact boost student test scores slightly. But buried in the coverage of the study was that the only students who seemed to benefit from more classroom time were those who went to schools that were safe and well-disciplined. In problem schools, more time in class made no difference to student performance, and very long classes appeared to make things worse.

“If the school isn’t good, if the curriculum isn’t good, if the teacher is not effective, if the kids aren’t well-behaved and focused on learning, then the benefit you’re going to get from additional class time is probably very, very small,” says study co-author Steven Rivkin. “You’re much better off spending your efforts on trying to get a better curriculum, improving the quality of instruction of the teachers and doing things to improve the focus and richness of the classroom environment.”

Not surprisingly, critics of the Canadian school system often point out that more time spent in class is only useful when it’s actually spent learning the right material. One frequent critique is that widespread changes to provincial math curricula over the past decade have strayed too far from teaching essential math formulas, encouraging elementary students to draw pictures of math problems rather than learn fundamental concepts like multiplication or long division. “We have a situation where we’re not focusing on the basics, we’re focusing on everything else,” says Michael Zwaagstra, a Manitoba high school teacher and research fellow with the Frontier Centre for Public Policy. “The issue is not how much time you spend in school, the issue is how efficiently you’re using it.”

Under the new curriculum, introduced about eight years ago, more class time is taken up learning fewer concepts. On top of that has been the move toward a “spiral curriculum,” in which the same concepts are taught repeatedly over multiple grades. The idea is to reinforce fundamental concepts year after year, but critics say in reality the changes mean teachers often end up passing students who are struggling to understand the concepts, because they’ll learn them again in the next grade. “The teachers might start teaching multiplication in Grade 3, but if 50 or 60 per cent of the class doesn’t get it, they say, ‘Who cares?’ because they’re going to see it again next year,” says Anna Stokke, a University of Winnipeg math professor who has become a vocal education critic after researching the math lessons her two daughters were learning in school. The OECD’s Schleicher disagrees that new “inquiry-based” math curricula adopted by many Canadian provinces over the past decade are to blame for the country’s sliding math scores. Such programs are part of a broader global education movement focused on getting students to understand the concepts behind math rather than simply memorizing specific formulas, he says.

More concerning to Schleicher are changes to high school curricula in many countries, including Canada, which allow struggling students to enrol in a “consumer math” stream. Such financial literacy courses, which teach students how to do their taxes or read a mortgage, became popular a decade ago as provinces were looking to lower high school drop-out rates. Allowing students to earn math credits while learning how to budget for groceries seemed a promising way to keep them in school and studying math all the way through Grade 12. But when OECD officials tested students on their math and financial literacy skills, it found that those who had studied academic math tended to also score well on financial literacy, while those who had only taken consumer math courses scored well on financial literacy but still struggled with basic math skills. “They didn’t understand the underlying concepts like probability and risk,” Schleicher says. “That’s really what math is about. So getting people to focus on those concepts makes people capable of applying them in a real-world context.”

While policies aimed at keeping students in math class for longer, such as easier courses and longer school days, are popular with policy-makers and the public, they also mean cash-strapped governments aren’t able to put their limited resources into changes that have actually proven to increase student performance, such as investing in teacher professional development, more effective curricula, more individualized support for students and safer and more orderly schools, he says. Ultimately, pouring resources into making sure Canadian students are spending hours each week in math class might seem like a good idea, but if it’s not actually making them better at math then it becomes a waste of money—and a waste of time.

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]]>One measure considered was the Programme for International Student Assessment’s standardized exam. StatsCan observed that only 23% of Canadian 15-year-old girls who scored in the top three of six categories on the math section of the recent PISA test ended up taking STEM compared to 46% of boys in the top three. Among top performing females, 48% chose social sciences.

Another measure they looked at was high school grades. Among students with marks in the 80% to 89% range, 52% of boys chose a STEM program in university compared to only 22% of girls who were just as highly graded. Among girls who had 90% or above in high school, only 41% chose STEM compared to 61% of boys with marks in that range. The pattern held true for low marks too.

Lack of self-confidence among females doesn’t explain the difference, according to StatsCan: “Among university-bound students who considered their mathematics skills as “excellent”, 66% of males chose a STEM program compared with 47% of females. Among those who considered their mathematical abilities as “good”, 36% of males and 15% of females chose a STEM program.”

StatsCan points out that women were especially likely to avoid engineering, where they made up only 23% of graduates in 2011, and mathematics and computer science, where they made up 30% of graduates. That means many females are missing out on two fields with some of the best job prospects. According to the Ontario Graduate Survey, 2010 computer science graduates had average salaries of $63,044 two years after graduation, up $5,050 over three years earlier. Engineering graduates averaged $61,884, up $2,032. Meanwhile, the average salary for new social sciences graduates—more than two-thirds of whom are women—was $42,585, a drop of $798.

Click to see how employment rates and average salaries are changing for new graduates

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]]>Learning is tricky. On Tuesday the Organisation for Economic Co-operation and Development (OECD) released a global report on adult skills based on surveys of 166,000 people in 23 countries.

The results showed that Canada scores below the average of those countries in numeracy, or mathematical skill.

The first sentence of the *Sun* newspapers’ story that afternoon said, “Canadians are at or above average when it comes to math, reading and problem-solving, a new global study has found.” Well, no it didn’t, not when it comes to math. But perhaps it’s too much to hope a mere Canadian could read statistics more accurately.

The OECD’s survey, the Programme for the International Assessment of Adult Competencies (PIAAC), is the first of its kind. National authorities in every country administered tests to at least 5,000 people aged 16 to 65. So the PIAAC doesn’t measure how kids are doing in school, it measures how well people are doing later in life with the knowledge and skills they accumulated in school and after.

It’s an overstatement to say that in the modern world, knowledge is everything. Oil, armies and the not-yet-entirely-squandered inheritance from past glories still counts for a lot. The U.K., Germany and the U.S. score below the average of PIAAC countries on literacy, but they still carry clout. But if you compare the countries at the bottom of that list (Italy, Spain, France and Ireland) to the countries at the top (Japan, Finland, Netherlands and Australia), it seems likely that the top of the list can look forward to a brighter 10 or 15 years than the ones pulling up the rear.

A well-educated population is more adaptable, more resilient in the face of challenge, and maybe even wiser. Japanese participants with only a high school education scored at the same level as university graduates from Italy. That’s a solid advantage. In France, where the value of a good education is constantly trumpeted, the consistently lousy results posted in this and other surveys feels like a betrayal of a national ideal. France scored 21st in number skills, 22nd in literacy. “Dunce cap for French adults,” the headline in *Le Figaro* said.

But at least younger French adults outperform their elders; in Britain and the United States, there’s no such improvement from generation to generation, and former advantages are in danger of being lost.

The picture for Canada is less worrisome. But in important ways, it’s not much to write home about. Canada ranked at the OECD average in literacy and comfortably ahead in computer skills, but it ranked below the average in math. And Canadian women consistently scored lower than Canadian men on math.

Statistics Canada surveyed large samples in every province and territory, and among immigrant and off-reserve Aboriginal populations, to get a clear look at regional and demographic variations within Canada. More prosperous provinces generally posted better results. On literacy, Alberta and Ontario scored above the OECD average, ranking just behind Sweden and Norway. New Brunswick and Newfoundland and Labrador scored below average, down near Poland and Ireland. Remote Nunavut was, on every measure, by far the lowest-performing Canadian jurisdiction, well below any European country.

But Nunavut aside, the differences between Canadian regions are smaller than the differences within populations. Canadian adults aren’t all average. They tend to extremes. More Canadians scored at both the highest levels and the lowest levels on literacy than in most other participating countries.

How is it that Canadians manage both to lag badly in some cases, and to beat the world in others? The answer seems to lie in the Canadian school, which emerges from this report as an unusually powerful mechanism for correcting for sociological differences. It’s actually truer in Canada than in many other countries that the longer you stayed in school, the better you performed on this international test.

Here are two heartening examples.

Aboriginal participants living off-reserve did score lower, on average, than non-Aboriginal populations. But in one of the survey’s most striking results, Aboriginal participants who completed a given level of formal education scored as high as non-Aboriginal participants with the same education.

Then there’s the gap between participants with highly educated parents and those with less-educated parents. In some countries, if neither of your parents finished high school you will probably score a lot worse on the literacy test than someone who had at least one parent finish university. Those countries include Germany and the United States. But that gap is one-third smaller in Canada, which means parents’ education is much less likely to seal the next generation’s fate here.

Taken together, these results suggest Canadian schools are a strong force for equalizing opportunity, but that they could still stand to pick up their game. In an interview, Alberta Education Minister Jeff Johnson recognized as much.

Johnson is the chair of the Council of Ministers of Education of Canada, which administered the PIAAC survey in Canada with help from Statistics Canada. He was, understandably, eager to look on the bright side: “I was personally very encouraged to see how well we’ve done on problem-solving in a digital environment,” which is the fancy term PIAAC uses for computer literacy. He also noted that Canada has one of the smallest gaps between the scores of immigrant and native-born test-takers.

But he did recognize Canada’s shaky performance on math, as well as the persistent gender gap on the same subject. “Numeracy has been a topic of conversation around the table among ministers for a while,” he said. One possible remedy: specialized teachers who, unlike some of their generalist colleagues, will actually be comfortable with math and can share their fluency with students. As for the gender gap, “We need to make sure girls are inspired and excited by how they’re taught science and math,” Johnson said.

Easier said than done, perhaps, especially in an environment of coast-to-coast budget restraint. Together, health and education costs comprise a majority of every province’s budget, Johnson said. “If you need to find cuts, it doesn’t take a rocket scientist to figure out where it’s going to come from.” But he noted that internationally there’s not much correlation between the cost of an education system and the results it produces. That’s reassuring, if true, because even with limited resources, Canada’s education system needs to post better results. Pretty good won’t always be good enough.

On the web: For more Paul Wells, visit his blog at macleans.ca/inklesswells

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]]>The number is 2 multiplied by itself 57,885,161 times, less one, reads…

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]]>The number is 2 multiplied by itself 57,885,161 times, less one, reads a press release issued by researchers. And, for anyone who needs a high school math refresher, this new prime number can be divided by only one and itself.

The discovery was part of a project called the Great Internet Mersenne Prime Search, in which volunteers use their personal computers to look through prime candidates, with anyone who discovers one eligible for a cash prize.

To read the entire prime number, you’d have to download 22.5MBs, explains CNET. Want to try? The link is here.

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]]>The post Waldorf closes, the Mad Minute & Carleton discrimination appeared first on Macleans.ca.

]]>1. The Waldorf, a two-year old arts venue in Vancouver’s east end, has been sold to developers. Artists are, unsurprisingly, enraged. Grimes was among those who played the tiki-themed multi-room venue. Her Tweet on Thursday captures the reaction to the closure: “wow vancouver is so f*d if they shut down the waldorf. f*k this city. you’ve destroyed nearly every piece of culture that you had.” Rhys Edwards, wrote this in a piece for The Ubyssey’s blog: “The Waldorf is one more victim in the amorphous onslaught of gentrification in a city that simply does not prioritize cultural activities that do not promote economic development.” Without the Waldorf, she says, Vancouver will be less weird.

2. Emma Teitel says she can’t do simple math and she’s blaming the pressure to perform, which in her case took the form of the “Mad Minute,” an exercise where students race against a clock to do as much arithmetic as possible. This created a fear of math and caused her to give up. She points out that Finnish students, who don’t face much pressure from teachers, perform best in the world.

3. Leslie Armstrong, editor in chief of York University’s Excalibur student newspaper, questions how newspapers like the Toronto Star and Toronto Sun cover crime in the north of the city where York is located. “When a 22-year old man is stabbed to death outside Randy’s Sports Bar and Restaurant on Keele just south of Steeles, it can’t be without mention of York University, even though the bar is a good 20-minute walk from the outskirts of the Keele campus,” she writes. “I would understand if the crime occurred in the housing district, home to many York students,” she adds. She wonders whether York is truly less safe than downtown campuses like Ryerson University or the University of Toronto, or if the media is simply less likely to link crimes to those campuses. I think she may have a point. In other news, 46 lockers were broken into at York during December.

4. Carleton University Students’ Association will tweak its “Discrimination on Campus Policy” after a motion passed that said “CUSA should not arbitrarily ban but instead should work to condemn all groups that commit hate crimes.” That seems like a good move toward encouraging healthier debate on campus. While I’m sure few people would object to the parts of previous policy that banned specific groups like the Ku Klux Klan, they also had banned Carleton Lifeline, an anti-abortion group that, while controversial, has relatively wide support. CUSA’s Vanessa Ebuka told The Charlatan student newspaper that the motion came after the Justice Centre for Constitutional Freedoms, an Alberta-based think-tank, gave Carleton University an “F” grade on their policies. “Simply put, it was problematic to have a discrimination policy that was discriminatory, divisive, and didn’t uphold universal human rights to all.” It’s hard to argue with that!

5. Student newspapers from coast-to-coast are covering the Idle No More movement and many have run supportive opinion pieces ahead of this crucial weekend. In case you haven’t been paying close attention, here’s a rough guide to the movement so far. In case you’ve been paying *too much* attention, check out comedian Scott Feschuk’s lighter take on this very serious affair.

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]]>The post Emma Teitel: ‘I am a 23-year-old woman who can’t do math’ appeared first on Macleans.ca.

]]>Tori Spelling’s resolution for 2013 is to get back into her skinny jeans. Wyclef Jean’s is to never again remain silent in the face of violence because it’s “a scar on the world’s cheek.” Mine might be more ambitious than both: I am going to learn how to add. In my life, this is anything but a trivial endeavour. I happen to be innumerate—which means I do not, and cannot, do simple math. In fact, I avoid it at all costs. Literally. I’d rather pay the whole dinner bill than try to calculate the tip.

There are many people like me, some of whom may be reading this column: otherwise seemingly well-adjusted members of society who hand the cashier a $20 bill for a coffee when they have exact change, or never bother to count the change when the cashier hands it back because they doubt they’d be able to determine if there was an error. And besides, it would take so long that everyone in line behind them would probably leave the store. (For innumerates, the fear of attempting math is compounded by the fear they’ll hold up the line indefinitely if they do attempt it.)

One recent American study found that for math-phobic people, the anticipation of numerical computation actually triggers a brain reflex commonly associated with pain. According to a recent report in Britain’s Independent, “the number of [British] adults who have numeracy skills no better than those expected of an 11-year-old has shot up from 15 million to 17 million—49 per cent of the adult population—in the last eight years.” That’s a lot of pain, and a lot of self-defeating, ironic surrender. The last time I took math was in the 10th grade. It was a remedial class called personal finance, where the only reason anyone touched a calculator was to steal the batteries.

But the black humour hides the true trauma and stigma of math phobia. For some reason, illiteracy is considered a legitimate deficit, while innumeracy is seen as a punchline condition, the kind of gap girls develop because they can’t be bothered to be logical. Not only is this nonsense, it obscures the thing that for me was the root of math phobia: the idea that the best way to teach someone something that has concrete right and wrong answers is to make a “game” of it. My first (and fatal) brush with this theory came in the second grade during a drill called “Mad Minute”—also a pre-First World War phrase used, fittingly, by British riflemen to describe the attempt to hit a 12-inch target 15 times in 60 seconds. It was a class-wide competition in mathematical speed and ability. Every student got a sheet of paper with a series of problems on it. The object was to answer as many problems as you could in one minute: one deafeningly silent and scary minute, monitored by a stopwatch on the teacher’s desk. I cheated every single time, because I was so anxious, I could barely think—so I’d look over Marley’s shoulder (thank you, Marley, wherever you are) and write down her subtraction answers. Marley was smart. I got by. But Marley was more than smart; she enjoyed Mad Minute. Not me. Why?

There’s a common misconception, from academia to action movies, that stress breeds success; that you’ll be a better problem-solver if you know an asteroid is heading straight for Earth or, in my case, you only have one minute to prove that you don’t suck at long division. The problem is, however, that when you do suck at long division, pressure doesn’t help your performance. It hinders it, to a point of near paralysis. Yet the Mad Minute approach to math, old-time, hard-core drills and testing, is still very much revered. According to a 2009 academic evaluation of 15-year-old students called the Programme for International Student Assessment, Canada ranks 10th worldwide in math, and many people assume the countries that outrank us—China is one—do so because they use the traditional, high-intensity drill method. People forget, though, that in some cases, these countries remove “unessential” programming from school curriculae, like sports and theatre, in order to focus entirely on academics—math, in particular. They also gloss over the fact that Finland, a country that also outranks us in math, doesn’t put its students through standardized tests until they hit high school, and is significantly lighter on homework.

Myself, I pretty much decided, from the day of my first Mad Minute onward, that I was a word person, not a math person, and word people just aren’t good at math. But I decided I was a “word person,” not so much because I loved to read and write, but because, in English and history class, I didn’t feel pressure to perform. There were no one-minute intelligence contests in English class. There were only open-ended questions, sometimes with more than one right answer. I could play the game of sentences and stories, but no one taught me how to navigate the game with sums and remainders. Which is how I stand before you today, a 23-year-old woman who finds herself determined to learn how to count her change before the store closes.

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]]>The post Tarnished Silver: Assessing the new king of stats appeared first on Macleans.ca.

]]>The situation is that many of Nate Silver’s attackers don’t really know what the hell they are talking about. Unfortunately, this gives them something in common with many of Nate Silver’s defenders, who greet any objection to his standing or methods with cries of “Are you against SCIENCE? Are you against MAAATH?” If science and math are things you do appreciate and favour, I would ask you to resist the temptation to embody them in some particular person. Silver has had more than enough embarrassing faceplants in his life as an analyst that this should be obvious.

But, then, the defence proffered by the Silverbacks is generally a bit circular: if you challenge Silver’s method they shout about his record, and if you challenge his record they fall back on “Science is always provisional! It proceeds by guesswork and trial-and-error!” The result is that it doesn’t matter how far or how often wrong Silver has actually been—or whether he adds any meaningful information to the public stockpile when he does get things right. He can’t possibly lose any argument, because his heart appears to be in the right place and he talks a good game.

Both those things count. Silver is a terrific advocate for statistical literacy. But it is curious how often he seems to have failed upward almost inadvertently. Even this magazine’s coverage of Silver mentions the means by which he first gained public notice: his ostensibly successful background as a forecaster for the Baseball Prospectus website and publishing house.

Silver built a system for projecting future player performance called PECOTA—a glutinous mass of Excel formulas that claimed to offer the best possible guess as to how, say, Adam Dunn will hit next year. PECOTA, whose contents were proprietary and secret and which was a major selling point for BPro, quickly became an industry standard for bettors and fantasy-baseball players because of its claimed empirical basis. Unlike other projection systems, it would specifically compare Adam Dunn (and every other player) to similar players in the past who had been at the same age and had roughly the same statistical profile.

For most players in most years, Silver’s PECOTA worked pretty well. But the world of baseball research, like the world of political psephology, does have its cranky internet termites. They pointed out that PECOTA seemed to blunder when presented with unique players who lack historical comparators, particularly singles-hitting Japanese weirdo Ichiro Suzuki. More importantly, PECOTA produced reasonable predictions, but they were only marginally better than those generated by extremely simple models anyone could build. The baseball analyst known as “Tom Tango” (a mystery man I once profiled for *Maclean’s*, if you can call it a profile) created a baseline for projection systems that he named the “Marcels” after the monkey on the TV show *Friends*—the idea being that you must beat the Marcels, year-in and year-out, to prove you actually know more than a monkey. PECOTA didn’t offer much of an upgrade on the Marcels—sometimes none at all.

PECOTA came under added scrutiny in 2009, when it offered an outrageously high forecast—one that was derided immediately, even as people waited in fear and curiosity to see if it would pan out—for Baltimore Orioles rookie catcher Matt Wieters. Wieters did have a decent first year, but he has not, as PECOTA implied he would, rolled over the American League like the Kwantung Army sweeping Manchuria. By the time of the Wieters Affair, Silver had departed Baseball Prospectus for psephological godhood, ultimately leaving his proprietary model behind in the hands of a friendly skeptic, Colin Wyers, who was hired by BPro. In a series of 2010 posts by Wyers and others called “Reintroducing PECOTA”—though it could reasonably have been entitled “Why We Have To Bulldoze This Pigsty And Rebuild It From Scratch”—one can read between the lines. Or, hell, just read the lines.

Behind the scenes, the PECOTA process has always been like Von Hayes: large, complex, and full of creaky interactions and pinch points… The numbers crunching for PECOTA ended up taking weeks upon weeks every year, making for a frustrating delay for both authors of the

Baseball Prospectusannual and fantasy baseball players nationwide. Bottlenecks where an individual was working furiously on one part of the process while everyone else was stuck waiting for them were not uncommon. To make matters worse, we were dealing with multiple sets of numbers.…Like a Bizarro-world subway system where texting while drunk is mandatory for on-duty drivers, there were many possible points of derailment, and diagnosing problems across a set of busy people in different time zones often took longer than it should have. But we plowed along with the system with few changes despite its obvious drawbacks; Nate knew the ins and outs of it, in the end it produced results, and rebuilding the thing sensibly would be a huge undertaking. We knew that we weren’t adequately prepared in the event that Nate got hit by a bus, but such is the plight of the small partnership.

…As the season progressed, we had some of our top men—not in the

Raiders of the Lost Arkmeaning of the term—look at the spreadsheet to see how we could wring the intellectual property out of it and chuck what was left. But in addition to the copious lack of documentation, the measurables from the latest version of the spreadsheet I’ve got include nice round numbers like 26 worksheets, 532 variables, and a 103 MB file size. The file takes two and a half minutes to open on this computer, a fairly modern laptop. The file takes 30 seconds tocloseon this computer. …We’ve continued to push out PECOTA updates throughout the 2010 season, but we haven’t been happy with their presentation or documentation, and it’s become clear to everyone that it’s time to fix the problem once and for all.

For the record, the Wieters Bug turned out to be a problem highly specific to Wieters; in Silver’s “copiously undocumented” rat’s nest of a model, there was a blip in the coefficients for the two different minor leagues in which Wieters had played in 2008, and BPro did not have time to ransack the spreadsheets looking for the possible error. The Ichiro Problem, by contrast, is intractable by ordinary statistical means; there are just a few players who are so unusual that a forecaster is as well off, or better off, falling back on intuition and first-principles reasoning. (Unless, that is, he has better data. Today’s PECOTA is able to break batting average into finer-grained statistical components in the hope of detecting Ichiros more perceptively.)

If the history of Silver’s PECOTA is new to you, and you’re shocked by brutal phrases like “wring the intellectual property out of it and chuck what was left”, you should now have the sense to look slightly askance at the New PECOTA, i.e., Silver’s presidential-election model. When it comes to prestige, it stands about where PECOTA was in 2006. Like PECOTA, it has a plethora of vulnerable moving parts. Like PECOTA, it is proprietary and irreproducible. That last feature makes it unwise to use Silver’s model as a straw stand-in for “science”, as if the model had been fully specified in a peer-reviewed journal.

Silver has said a lot about the model’s theoretical underpinnings, and what he has said is all ostensibly convincing. The polling numbers he uses as inputs are available for scrutiny, if (but only if) you’re on his list of pollsters. The weights he assigns to various polling firms, and the generating model for those weights, are public. But that still leaves most of the model somewhat obscure, and without a long series of tests—i.e., U.S. elections—we don’t really know that Nate is not pulling the numbers out of the mathematical equivalent of a goat’s bum.

Unfortunately, the most useful practical tests must necessarily come by means of structurally unusual presidential elections. The one scheduled for Tuesday won’t tell us much, since Silver gives both major-party candidates a reasonable chance of victory and there is no Ross Perot-type third-party gunslinger or other foreseeable anomaly to put desirable stress on his model. Silver defended his probabilistic estimate of the horserace this week by pointing out that other estimates, some based on simpler models and some based on betting markets, largely agree with his.

This is true, and it leaves us with only the question of what information Silver’s model may actually be adding to the field of alternatives. The answer could conceivably be “Less than none”, if his model (or his style of model-building) is inherently prone to getting the easy calls right and blowing up completely in the face of more difficult ones. (Taraji P. Henson Alert!) It is worth pointing out that a couple of statisticians have given us a potential presidential equivalent of the Marcels—a super-simple model that nailed the electoral vote the last two times (and that actually is fully specified).

It is also worth pointing out that Silver built a forecasting model for the 2010 UK election, which did turn out to be structurally unusual because of the strong Lib Dem/Nick Clegg performance. Silver got into squabbles with British analysts whose models were too simple for his liking, and the whole affair was an exemplar of what Silver’s biggest fans imagine his role to be: the empiricist hard man, crashing in on the pseophological old boys’ club and delivering two-fisted blasts of rugged science. It did not go well in the end, as his site’s liveblog of the returns records:

10:00 PM (BST). BBC exit poll predicts Conservatives 307, Labour 255, LibDems 59.

10:01 PM (BST). That would actually be a DROP for Lib Dems from the last election.

10:02 PM (BST). BBC nerd says: “The exit polls are based on uniform behavior”, a.k.a. uniform swing. So we haven’t really learned anything about whether uniform swing is the right approach; it’s baked into the projection.

10:07 PM (BST). We would obviously project a more favorable result than just 307 seats for Conservatives on those numbers. Calculating now.

10:11 PM (BST). If the exit polls are right but the seat projections are based on uniform swing, we would show a Conservative majority on those numbers.

10:13 PM (BST). Here is what our model would project… [Cons 341, Lab 219, Lib Dem 62]

The final result? Conservatives 306, Labour 258, Liberal Democrats 57. The BBC’s projection from exit polls, using simple uniform-swing assumptions to forecast the outcome of a very wrinkly three-sided race, was so accurate as to be almost suspicious. And how was Silver’s performance *after being basically given the national vote shares for the parties*? Perhaps it’s best to draw the veil of charity over that.

Which, in fact, seems to be what has happened. Lucky thing for Silver’s reputation!—but then, he has always been lucky.

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]]>The post Xs of evil: America’s algebra crisis appeared first on Macleans.ca.

]]>A typical American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.

My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. …There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong—unsupported by research or evidence, or based on wishful logic. (I’m not talking about quantitative skills, critical for informed citizenship and personal finance, but a very different ballgame.)

Hacker argues that the math used in the typical American workplace—even a technical, highly quantitative workplace—does not much resemble math as it is taught in the American classroom. Engineers, doctors, and bankers rarely use algebra as such. What we probably should be doing, Hacker thinks, is to foster mathematical intuition amongst students who can’t master higher levels of abstraction.

Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call “citizen statistics.” This would not be a backdoor version of algebra, as in the Advanced Placement syllabus. Nor would it focus on equations used by scholars when they write for one another. Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives.

It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted—and include discussion about which items should be included and what weights they should be given.

I’ve had some Canadians point out Hacker’s editorial to me in the spirit of “This guy’s crazy, right?” But his remarks have to be understood in an American context. There has been a strong push in the U.S. for pretty high universal national standards in mathematics, standards which have seen many states run afoul of what’s called “Algebra II” in curriculum circles.

American high school graduates are taking harder math and science classes, according to a recent report by the National Center for Education Statistics.

In September, Tom Luce, former CEO of the National Math and Science Initiative, said that the United States needs a “STEM-literate population” that starts by “convinc[ing] the entire country that every child must conquer Algebra II.” America has made steady progress toward that goal—in 1982, just 40 percent of high school graduates took Algebra II; in 2009, more than 75 percent did.

Keeping those figures in mind, here’s a short sample from an Algebra II exam: I note with some alarm that it features a question about complex numbers, which I don’t think I ever learned in the classroom despite having fought through Alberta’s Math 31 high-school course and a year of university calculus and statistics. This is pretty esoteric stuff to be expecting “every child” in a large, diverse country to conquer. (I think only physicists would ever actually use complex numbers at work, though I know electrical engineers are expected to master them as part of their theoretical education.) Insofar as Hacker is just pointing that out, his op-ed falls into the category of “man identifies patent, unaddressed insanity swirling around him” rather than “man quarrels with high educational expectations.”

Math has a special, awkward place in education. It is no wonder that it stirs passions and raises fears, for it is pure concentrated abstraction, and everybody senses on some level that how far you can go in math (speaking as someone who got the equivalent of a B in first-year calc) is a very precise, cruel measure of one’s cognitive separation from the cleverer beasts. America is pushing Algebra II because, of all high-school courses, it is “the leading predictor of college and work success”. But you don’t need Riemann curvature tensors to understand the logical flaw in the proposition “If Algebra II predicts success, making everyone pass Algebra II will make everyone successful.” Understanding the square root of minus one is no use to most of us, in itself; yet it is true that those who can be taught to understand it will, over time and as a group, earn and accomplish much more than those who don’t. This is true of any reasonably abstract concept, which is why there is always confusion over the actual value of learning to read a musical score or figure out a left fielder’s on-base percentage.

Andrew Hacker’s “algebra problem” is an interesting symbol of how rampant egalitarianism is in the American academy. Primordial America possessed an intellectual counterweight to the Jeffersonian faith in education; the minor Founding Father Fisher Ames is said to have responded to the notion that “All men are created equal” with the retort “…but differ greatly in the sequel”. Today’s American right, however, takes the tactical ground that no child must be “left behind”—that all can be educated for a STEM future, just as any goose can make foie gras in his liver if he is stuffed full enough. This happened because American public education became compromised by the teacher trust and its slovenly “easier-for-us” ideology: it became too tempting to whack the education industry over the head with standardized testing and with the excellent results of other countries’ education systems, as President Bush 2.0 did. It is probably not really realistic to expect the U.S. to compete in mass mathematics education with a small, homogenous Nordic country like Finland—but what American will admit to that? We built the Bomb and went to the Moon, man! (One supposes it would be unkind to note that the “we” in that sentence denotes, respectively, “a bunch of Europeans who fled the Nazis” and “a bunch of Nazis who fled the Russians”.)

Even Hacker, whose essential complaint seems to be that 25% would be a much better estimate of the number of American children capable of mastering Algebra II than 100%, won’t put it in such a direct, offensive way. But it doesn’t help that he conflates “algebra as taught in American schools” with algebra as such. Algebra is, above all, a single step up in abstraction. It’s a step that most children can take: once you give them the core idea of performing operations on “x” rather than on a particular number, the royal road is open.

And that much—the whole notion of a variable—is something ordinary people do require, if they hope to have the instincts, training, and mental safeguards Hacker agrees that they need. How the hell are you going to teach even the crudest statistics or concepts of probability to a student who doesn’t get what a variable is? How could an ordinary Cartesian graph be comprehensible? How, indeed, would one teach the difference between arithmetic and geometric growth—and hence the power of compound interest?

I suppose you do it, though Hacker specifically denies it, by sneaking the abstraction in through the back door: you give eleventy real-life examples of compound interest at work, until the student eventually realizes that the principle’s the same no matter what the actual principal and the particular interest rate are. He learns to identify a “variable” without being intimidated up front by *x*s and *y*s. There might be some merit in such an approach, for it is in fact the symbology that seems to frighten the math-averse. In this article about the rigours of Algebra II, a person claiming to be an accountant says “Most people I know who are lower income couldn’t solve 2x = 14 if their life depended on it.” And maybe he’s right. Yet there can’t literally be many people who couldn’t stumble into an answer to “Two times what is fourteen?” if it were presented that way and they were given a few minutes to wrestle with it.

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]]>The post Where do Canada’s math geniuses go? appeared first on Macleans.ca.

]]>It’s one of the most prestigious—and lucrative—in the world. The winning team gets $25,000. The winning individual gets a scholarship to Harvard.

Naturally, teams from Harvard, MIT, and Caltech have won the most titles (55, 40 and 30).

But there are two Canadian schools whose students consistently do well too. The University of Toronto and The University of Waterloo each have 18 team titles and top five placements (Queen’s is next in Canada, with three). Waterloo’s wins are particularly impressive, considering the Putnam competition predates its birth in 1957 by a few decades. But those aren’t the only two Canadian schools to do well recently.

Here’s how our schools stacked up over the past five years.

**Teams in the top 10
** University of Toronto —4

University of Waterloo—4

University of British Columbia—2

**Top scoring individuals (winners and honorable mentions)
**University of Waterloo—13

University of Toronto —8

University of British Columbia—6

University of Alberta—1

McGill University—1

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]]>The post Students are fleeing STEM degrees appeared first on Macleans.ca.

]]>Today, the *New York Times* suggested that President Obama’s goal of training 10,000 more engineers per year, plus 100,000 more STEM (Science, Technology, Engineering and Math) teachers annually is unlikely to be reached.

For decades, the U.S. has been trying to up its output of STEM students. But the percentage of all students earning Bachelor of Engineering degrees has actually fallen from nearly 10 per cent of the total in the mid-1980s to 5.4 per cent in 2009-10. Computer engineering hit peaks of 4.3 per cent of the totals in 1984 and 2004, but has fallen again to 2.4 per cent in 2009-10. It’s a similar story in other STEM fields too, like biology. As more people are educated, it seems fewer are choosing STEM.

And what’s especially interesting is a couple of studies cited in the article that show the problem isn’t lack of interest in STEM programs, but lack of persistance in science, math and engineering after students start university. Twice as many students leave STEM degrees, either by dropping out or switching to other majors, than are leaving arts or education degrees. One major cause of the flight from STEM is simply that high marks are harder to achieve—fear of failure scares students away.

But whatever the reason, shortage of STEM graduates is a problem in Canada too. That’s why deans of graduate engineering schools have redoubled their efforts to recruit to engineering programs. It’s also why Seymour Schulich’s new $60,000 scholarships are for STEM students only.

But there are good reasons for students to persist through calculus and chemistry. Maybe more would if they realized that all of the Top 10 most lucrative bachelor’s degrees are in STEM.

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]]>“We’ve kind of been watching a train wreck,” University of Winnipeg math Prof. Anna Stokke told the *Winnipeg Free Press* last week. She’s talking about the fact that many education students aren’t getting the math they need in university and are therefore less likely to be able to teach elementary school students the subject, perpetuating bad math skills at a time when more jobs require them.

Most people aren’t aware that a student can get into a faculty of education with only Grade 12 consumer math, Stokke said. “I wouldn’t even call it a math course — it’s a life-skills course.”

That’s why she is circulating a petition demanding higher standards for education students. So far, 224 people, including professors, parents, students and teachers have signed the petition.

“Currently, many students enter education faculties in the universities in Manitoba with the least demanding of the Grade 12 mathematics courses,” reads the petition. “University math professors have found that students with this minimum requirement often have *alarmingly weak mathematics skills* and *high levels of math anxiety*…. It has also been documented that math anxiety in a classroom teacher may transfer to his or her students.”

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]]>The post How many journalists can you fit into one square metre? appeared first on Macleans.ca.

]]>**Don’t forget to read the article that inspired the experiment about inflated attendance numbers at Pride parade in Toronto**

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]]>The post Statistical sour grapes appeared first on Macleans.ca.

]]>I note that the maps drive off AVERAGE income. Do we know what they would look like if they drove off MEDIAN income? The published maps tell us that there is a growing class of people with super-high incomes. I think maps based on the median would be more informative about the middle class.

Let’s raise a glass to Paul. Even if you don’t understand why his point is important, you can see in the chat that Hulchanski’s answer is unsatisfactory: he says both that his team didn’t have median-income numbers going back far enough to make them the focus of the study *and* that he’s confident it wouldn’t make any difference. I think a criminal lawyer would call this “presenting an alibi and a justification at the same time.”

Hulchanski’s study found that the proportion of middle-income neighbourhoods in Toronto was 66% in 1970; it is now just 29%. Low-income neighbourhoods made up 19% of the city in 1970; that figure’s now 53%. Paul’s problem is that these types of neighbourhoods are defined relative to the mean individual income for the whole city ($88,400 in 2005). A middle-income neighbourhood is one whose residents are within 20% of the mean either way, while a low-income neighbourhood is 20%-40% below it. But a mean or average, unlike a median (i.e., the income that half the city makes more than and half makes less than), is sensitive to scale changes in individual outliers at the top of the distribution.

We can see the problem if we perform a thought experiment and imagine another city; we’ll call it Otnorot. In 1970, Otnorot had an unusual economic structure: it was divided into 100 equal-sized neighbourhoods numbered 1 to 100, each with an average real income corresponding (by total coincidence) to its number. In miserable Neighbourhood 1, the residents scrape by on 1 credit per year per person. In Neighbourhood 47, they make 47 credits on average. In Neighbourhood 100, they make 100 credits apiece, the filthy plutocratic bastards.

What would the Prof. Hulchanski of imaginary Otnorot report back to us about the economic structure of his city? The average income of the neighbourhoods (and the people in them) is, as the young Carl Friedrich Gauss could tell us instantly, the sum of the numbers 1 to 100 divided by 100: 50½ credits. Neighbourhoods 41 to 60, or 20 in all, are “middle-income” neighbourhoods within 20% of that mean. The “low-income” neighbourhoods are numbers 31 to 40; there are 10 low-income neighbourhoods.

By 2005, the vast majority of Otnorotians are living just as they and their forefathers always did. In Neighbourhoods 1-99, real incomes have not changed at all, nor have the relative population sizes changed. Neighbourhood 1 still earns 1 real credit per person, which buys exactly what it did in 1970. Neighbourhood 99 still earns 99. Only in Neighbourhood 100 has there been a change. Perhaps the residents held shares in the wildly successful Otnorotian version of Trivial Pursuit; perhaps they put their heads together and invented smell-o-vision. For whatever reason, they have gone from wealthy to superwealthy (at nobody else’s particular expense, or at least nobody’s in Otnorot), and they now earn a fantastic 8,000 credits per citizen every year.

For most Otnorotians, life hasn’t changed. The presence of the one new hyperrich neighbourhood would certainly have social effects, probably a mix of good and bad; you could, for example, almost certainly expect the Royal Otnorot Museum to acquire a hideous new glass mega-extrusion. But you wouldn’t say that the Otnorotian middle class had disappeared.

And yet—Shock! Concern!—that is exactly what Otnorot’s version of Prof. Hulchanski finds, unwisely using average incomes as his baseline. The overall average income for Otnorot is now a whopping 129½ credits a year, so no group at all outside lucky Neighbourhood 100 reaches the lower middle-income cutoff (103.6). The lower bound for a “low-income” neighbourhood, however, is now 77.7 credits. Where we once had just 10 low-income neighbourhoods out of 100, now everybody from 78 to 99 is defined as low-income, so we have 22.

It so happens that in Otnorot, lukewarm social science performed at public expense and promoted by newspaper editors is punished by means too horrendous to translate into English. Things are done differently in the real Toronto, a mercifully liberal-minded place. But the processes that so confused our alterna-Hulchanski are surely, in an oversimplified way, the same processes that have confused the real scholar. Observers of inequality have observed a genuine, dramatic numerical increase in it over the past two or three decades; one only need have been looking at business-magazine “rich lists” for a while to see that billionaires, all but unknown in the early 1980s, are now as common as seagulls.

There are real social and political dangers from this, to the degree that we allow economic power to translate into social and political power. But it does not mean that the “middle class” has really disappeared or dwindled. It only means that the logarithmic scale of possible incomes has stretched out at the top in a new Gilded Age, a realm of pervasively low marginal taxes and new deregulated industries.

Toronto might really, in some sense, have become bifurcated more arrestingly between rich and poor. But the Cities Centre’s measurement procedure cannot prove that this has really happened. Would it be a good thing for social conditions in Toronto if the Bridle Path were annihilated by a meteor? If that happened, Prof. Hulchanski (and the *Globe*) would probably be able to report several “low-income” neighbourhoods magically re-entering the “middle class”.

Respectable social science of this sort will ordinarily work with medians or with log-income (as the UN Human Development Index does), or it will approach inequality questions with the aid of the Gini coefficient—a metric totally absent from the Hulchanski study. No doubt Prof. Hulchanski would give the same sour-grapes defence he gave to our friend Paul: don’t have the numbers, don’t need the numbers. But there’s a further question. Why should we necessarily be concerned with *between-neighbourhood* inequality at all? The Cities Centre would use the same “average income” figure to describe and classify both Neighbourhood X, where everybody makes a healthy $100,000 a year, and Neighbourhood Y, where half the residents make $200,000 and half make nothing, bartering and stealing for their living. Funny sort of egalitarianism, if you ask me.

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]]>As a landmark of NHL parity, the large number of 1-1 results in 2010 is not going to prove very useful. Imagine that game outcomes are statistically independent of each other and that the better team has a *p* chance of winning each individual game in the home team’s rink. If that’s the case, then the chance of a given series standing level after two games is 2(*p*)(1-*p*).

The 1-1 tie is always, for realistic values of *p*, the most common outcome. In a world of perfect parity—all teams are equal, no home-ice advantage, *p* = 0.5—half the series will be tied 1-1 after two games. And because the chance of the better team going up 2-0 is counterbalanced by a decreased chance of the other team going up 2-0, the overall chance of a tied series doesn’t drop off very fast as you depart from the parity condition, *p* = 0.5. For *p* = 0.6, about 48% of the series are still tied 1-1 after two games. (The better team is ahead in 36%, or 0.6²; the worse team is up 2-0 in 16%, about 0.4².)

But you can see that having eight series tied 1-1 will be incredibly rare even in the world of perfect parity. The probability of that happening in a given year will be the total product of the chances of a 1-1 tie in each of the series. Given an average overall value of *p*, the odds of all eight series starting out equal works out to, at most, (2(*p*)(1-*p*))^{8}—a pretty small number, demonstrating the great flukiness of the “eight ties” outcome. Even in the perfect-parity world the expected frequency works out to 1 time in every 2^{8}, or 256, years. In the real world, the right average figure for *p* is probably around .54, giving us an “eight ties” year about 1 time in 269. In a fairly extreme non-parity world where the 1-4 seeds had an average 60-40 edge—that is to say, *p* = 0.6—the “eight ties” outcome would happen once every 355 years.

In other words, using this fluke as any kind of sign, indicator, or test for parity is about like insisting on reading a book only by the light of Halley’s Comet. You’d better have a comfortable chair. And plenty of kids, so they and their progeny can continue the observations (over several millennia) after you die in it…

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]]>Olympic ice dance champions Tessa Virtue and Scott Moir ended their storybook season in Turin by winning their first World Championship last week. Virtue, 20, and Moir, 22, whose fiery on-ice chemistry does not extend to a romantic relationship away from the rink, say they’ve yet to decide if they’ll compete next year. In another graceful move, John Furlong, the head of the Vancouver Olympic Organizing Committee, travelled to the mountain village of Bakuriani, Georgia, to attend the memorial service for Nodar Kumaritashvili, the 21-year-old luger killed in a training crash on the Whistler track. Furlong said he saw hundreds of condolence letters from Canadians and others when he visited the family. Nodar’s father, David Kumaritashvili, said during the service his son’s death shouldn’t discourage others from practising luge.

James Harrison of Australia received a life-saving blood transfusion as a 14-year-old. Since then, he’s returned the favour in spades. Now, age 74, he’s approaching his 1,000th blood donation. He earned his “golden arm” nickname because his blood contains a rare antibody that can save babies with Rhesus disease, a deadly form of anemia. His blood was used to develop a vaccine called Anti-D. Health officials estimate that Harrison has saved some two million babies from death or brain damage.

The fallout continues after Toronto-born conservative commentator David Frum was shoved last week from his right-wing perch at the American Enterprise Institute (AEI) think tank in Washington. The firing came after the one-time speech writer for George W. Bush blogged that the Republicans blew the health care debate with hysterical rhetoric and a refusal to negotiate compromises with the Democrats. “We followed the most radical voices in the party and the movement and they led us to abject and irreversible defeat,” wrote Frum, who blames Fox News, Rush Limbaugh and the likes of the hard-right Tea Party faction for marginalizing the party. Frum says pressure from donors forced the AEI to end their seven-year association—a charge denied by the institute.

L-o-g-o-m-a-c-h-y (a dispute about words) is just one of the puzzlers 11-year-old Laura Newcombe had to spell to win the Canwest Canspell National Spelling Bee for the second year in a row. Laura credits her knowledge of Greek and Latin root languages with helping her win the $15,000 education award. She and 11-year-old Scott Xiao of Burnaby, B.C., bested 250,000 students to make the finals in Ottawa. The two duelled for nine rounds before Scott stumbled on “normancy” while Laura correctly spelled “lidar”—a radar-like system that uses laser light.

A female security officer at London’s Heathrow Airport has proven privacy experts right: the controversial full-body scanners that “see” through clothing to look for weapons are open to abuse. Jo Margetson, 29, says a male colleague took her picture as she walked through one of the machines. She says John Laker leered at her and made lewd comments about her body. “I’m totally traumatized,” Margetson told Britain’s Sun. She is considering a lawsuit. Laker was given a harassment warning, and may face further discipline.

Barry Penner, B.C.’s ever-earnest environment minister, set the stage for a romantic Earth Hour dinner with his wife, Daris. Electric lights were off in the spirit of the energy-saving event and the house flickered with the glow of candlelight. All went well until their five-year-old cat, Ranger, brushed against a candle. “Suddenly there was a poof of smoke,” and a very “disgruntled” cat, Penner told reporters. Ranger suffered no serious damage. “His hair is a little bit singed and his pride is somewhat affected,” says Penner. The couple opened windows to rid the house of the smell of burnt fur. Using an electric fan, of course, was out of the question.

International Olympic Committee chairman Jacques Rogge better keep his head up and his stick on the ice. His doubts about the future of women’s Olympic hockey raised the ire of former governor general Adrienne Clarkson. Hours before Canada’s gold-medal win in Vancouver, Rogge questioned if women’s hockey can remain an Olympic event if Canada and the U.S. are the only teams in serious contention for the championship. Clarkson, who created the Clarkson Cup championship to foster the women’s game, says the sport needs more time and resources to grow outside North America. She said that, and more, in a letter mailed to Rogge. Rogge didn’t respond to Clarkson’s “shot across the bow,” as she put it, so she wants Canada’s ambassador to Switzerland to hand deliver her missive to IOC headquarters. The future of women’s Olympic hockey can’t be decided in a closed meeting of a committee of the male-dominated IOC, she says. “This cannot be just a one-sided announcement. There has to be dialogue.”

Reclusive Russian mathematician Grigory Perelman has won a US$1-million prize for solving the “Poincaré’s conjecture,” one of seven fabled math problems that have eluded experts for a century. If the conjecture—a complex piece of abstract mathematics dealing with shapes that exist in four or more dimensions—is beyond the comprehension of, well, almost everyone, so is his response to the prize money, offered last week by the Clay Mathematics Institute in Cambridge, Mass. Perelman has so far refused to accept the money, even though the unemployed former researcher at the Steklov Mathematics Institute lives in a tiny apartment with his mother in St. Petersburg. The 43-year-old has also turned down all math-related job offers over the past four years. Leave self-promotion to those who seek it, he told London’s Telegraph. “I do not regard it as a positive thing.”

A woman who rescued a five-year-old boy stranded for 45 minutes in a tree at the Manor School playground in Melksham, U.K., wound up in trouble with school authorities and the local police. Kim Barrett, 38, a part-time cleaner, was chastised for trespassing on school grounds after seeing the boy safely back to class. Head teacher Beverley Martin said health and safety rules prohibit tree rescues. “Our policy when a child climbs a tree is for staff to observe the situation from a distance so the child does not get distracted and fall.” Barrett says no one was watching the boy. “When I took him in they had no idea he was missing.”

Fallen press baron Conrad Black, whose current address is the Coleman Correctional Facility in Florida, lashed out at the Globe and Mail on Saturday for claiming he and his wife, Maclean’s columnist Barbara Amiel, have lost their Palm Beach mansion. The property, assessed at US$32 million, was transferred to Blackfield Holdings, a Connecticut-based investment firm, to settle an $11.6-million mortgage on the property. It is for sale at an undisclosed price. Black used his column in the National Post to “rebut almost all” of the Globe story. He called Blackfield the “technical owner,” but “I retain an interest in the house and full flexibility to sell or reassert that interest.” The U.S. Supreme Court is expected to rule soon on the appeal of his convictions for fraud and obstruction of justice.

Did Justin Bieber, the 16-year-old international pop sensation from Stratford Ont., really insult überdiva Mariah Carey? For a brief time, Britain’s Sun quoted the baby-faced singer as saying Carey is past her best-before date. “I don’t love her new music. It’s not the same,” he allegedly lamented. “It’s like Michael Jordan coming back to the NBA. She is past her best.” Two things suggest the quotes were too juicy to be true: 1) they’ve been hauled off the Sun’s website; 2) Carey hasn’t ripped out his tonsils.

Prince, the musician formerly known as a taxpayer, is listed as a tax delinquent in Carver County, Minn. Officials estimate that Prince R. Nelson and his company, PRN Music, owe US$450,000 to state and other government bodies. He’s also on the hook for the equivalent of US$3 million in damages after a Dublin judge held him liable for cancelling a 2008 concert on short notice. The Purple One lived in Toronto’s tony Bridle Path neighbourhood after marrying Manuela Testolini of Don Mills, Ont., in 2001. He returned to the U.S. when the marriage ended five years later.

Heather Mills, the ex-wife of former Beatle Paul McCartney, is back in a courtroom, and the experience is proving as unflattering as her divorce proceedings. She is being sued by Sara Trumble, a former nanny to the estranged couple’s daughter Beatrice. Trumble claims that Mills was “rude and horrible” to her staff. “I wasn’t the only person who felt that at that time,” she testified. “It’s just that nobody else will stand up.” She said Mills was a generous employer who grew angry and demanding after the marriage breakup. Trumble’s duties included blow-drying Mills’s hair and giving her “nude spray tans,” she said. She was once called in from her maternity leave and ordered to tell a video crew “how wonderful Heather was,” she said. Trumble returned after that leave to find she’d been reassigned to a cleaning job. She is suing for sex discrimination, unfair dismissal and changes to her employment terms. Mills has yet to testify. “I don’t know whether to laugh or cry,” an angry Mills whispered to her lawyer.

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]]>Nearly half of the Canadians polled in a recent Harris-Decima survey said they feel Canada’s educational system does not adequately prepare young people for work in the modern economy.

Albertans are most pessimistic about the system – 52 per cent say they find it inadequate.

Younger Canadians, between the ages of 18-34, are more likely to say it is up to snuff than older respondents.

Nathan Seebaran, a student at Edmonton’s Ross Sheppard High School, says he feels optimistic about the training he’s getting through a registered apprentice program.

He’s studying to become a cabinetmaker and will be doing projects at the University of Alberta as part of his training.

“I was thinking of dropping out of high school because I didn’t really think I needed it, but I’m glad I stayed to do this,” Seebaran said.

Confidence is the hallmark of the so-called “Generation Y,” which is now hitting graduation age, says Harris-Decima vice-president Jeff Walker.

“Part of that self-awareness and self belief of that generation of people is the feeling that they work extremely hard and that the system has been beneficial to them,” said Walker.

When asked to grade different levels of education, Canadians gave high school the lowest marks.

Only 37 per cent felt high school did “very well” or well at preparing young people for the workforce.

Walker said that affected how Canadians see the education system overall.

“What it shows us is that if people perceive that there is even one weak link the system, they really worry that the system isn’t necessarily getting Canada or Canadians to where they need to be.”

The response was more favourable to graduate schools, where 62 per cent thought they were doing well at giving young Canadians the skills and abilities they needed.

Ironically, a recent report by the Science, Technology and Innovation Council noted that high school students are actually performing well in science, math and reading when compared to their peers in other countries.

The report said not enough students are getting science and engineering degrees, or PhDs.

The telephone poll of 1,000 Canadians was conducted between May 21 and May 24. The margin of error was 3.1 percentage points, 19 times out of 20.

*– The Canadian Press*

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]]>Science nerds and humanities classes aren’t supposed to mingle. If a Nerdian ventures into the City of Artsy Classes, we’re exiled from our homeland on pain of death. Or at the very least, our Star Wars action figure sets (all sealed in original mint-condition packages) will be smacked around a little and have a corner viciously folded down. But in direct defiance of the Nerd Code of Honour, I’m finding the class… well… interesting.

The class, “Individuals and Families in a Diverse society,” claims to cultivate “an awareness of and insight into students’ own personal and family development.” It also promised to teach Learning Skills.

Surely I was doomed.

But then something miraculous happened. I didn’t have the gall-bladder bored out of me. When we learned about the traditional transitions that adolescent Canadians face, I didn’t find my mind shutting down into a sanctuary of exponential equations and horizontal asymptotes.

I’ve even gained some invaluable Learning Skills.

No, it doesn’t quite match the thrill of finding a derivative, setting it equal to the slope of a tangent, and then solving a problem in which a point off the curve of a function must be found. But if losing the right to say words like “vertices” and “polynomial” means finally learning what the hell words like, “conceptual framework,” and “occupational attainment” actually mean, then it’s totally worth it.

Unless, of course, it means my Bobba Fett is in any sort of danger.

scott.dobson.mitchell@gmail.com

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