Emma Teitel: ‘I am a 23-year-old woman who can’t do math’

By Emma Teitel - Friday, January 11, 2013 at 9:47 AM - 0 Comments

Call me a ‘word person’: Old-time, hard-core math drills and testing are still revered

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. Continue…

Tarnished Silver: Assessing the new king of stats

By Colby Cosh - Sunday, November 4, 2012 at 4:19 AM - 0 Comments

The whole world is suddenly talking about election pundit Nate Silver, and as a longtime heckler of Silver I find myself at a bit of a loss. These days, Silver is saying all the right things about statistical methodology and epistemological humility; he has written what looks like a very solid popular book about statistical forecasting; he has copped to being somewhat uncomfortable with his status as an all-seeing political guru, which tends to defuse efforts to make a nickname like “Mr. Overrated” stick; and he has, by challenging a blowhard to a cash bet, also damaged one of my major criticisms of his probabilistic presidential-election forecasts. That last move even earned Silver some prissy, ill-founded criticism from the public editor of the New York Times, which could hardly be better calculated to make me appreciate the man more.

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. Continue…

Xs of evil: America’s algebra crisis

By Colby Cosh - Monday, July 30, 2012 at 12:17 AM - 0 Comments

The New York Times ran a deeply contrarian editorial Saturday about math education in the United States. In it, political scientist Andrew Hacker argues that the youth of America is being crucified on a cross of higher math.

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. Continue…

How many journalists can you fit into one square metre?

By Claire Ward - Tuesday, July 12, 2011 at 4:12 PM - 2 Comments

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

Statistical sour grapes

By Colby Cosh - Tuesday, December 28, 2010 at 11:57 AM - 68 Comments

When the U of T Cities Centre announced a couple weeks ago that middle-class neighbourhoods are disappearing in Toronto, the Globe and Mail latched onto the study and squeezed it for all it was worth. Or, rather, what little it is worth and then some. The Globe used the study to craft a news article with a horror-movie lede, to order up a nostalgic Margaret Wente column, and to conduct a live online chat debating the issues raised. In the chat a user named “Paul” brought up a technical question for the study’s lead author, David Hulchanski:

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.

Don't mind me; I'm on a math bender

By Colby Cosh - Monday, April 19, 2010 at 3:11 AM - 19 Comments

As the paid-up holder of a Mainstream Media club card, can I warn the sportswriters away from making too much of the statistical fluke of all eight first-round NHL playoff series starting out tied through two games? The warning will arrive too late for some, but others may yet be saved.

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 2⁸, 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…

Olympic aftermath, The man with the ‘golden arm’ and did Tea Partiers scald David Frum?

By macleans.ca - Friday, April 2, 2010 at 9:00 AM - 24 Comments

Olympic aftermath 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.

The man with the ‘golden arm’ 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.

Did Tea Partiers scald David Frum? 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.

Toronto girl wins a logomachy 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.

Invasion of the body scanners 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.

Earth Hour was the cat’s meow 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.

You’re offside, Mr. Rogge 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.”

Math is its own reward 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.”

School’s tree policy is barking mad 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.”

A former press baron takes on the Globe 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.

This diva’s not for dissing 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.

‘Purple Rain’ man bleeds red ink 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.

A hard day’s night, says the nanny 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.