Why Are Americans So Bad at Math?

The New York Times has a noteworthy piece on why math education is so poor in the United States. Borrowing examples from how math is taught in Japan, the article outlines how different initiatives to reform math education in America have failed (and why they are likely to continue to fail). Worth the read.

It wasn’t the first time that Americans had dreamed up a better way to teach math and then failed to implement it. The same pattern played out in the 1960s, when schools gripped by a post-Sputnik inferiority complex unveiled an ambitious “new math,” only to find, a few years later, that nothing actually changed. In fact, efforts to introduce a better way of teaching math stretch back to the 1800s. The story is the same every time: a big, excited push, followed by mass confusion and then a return to conventional practices.

The new math of the ‘60s, the new new math of the ‘80s and today’s Common Core math all stem from the idea that the traditional way of teaching math simply does not work. As a nation, we suffer from an ailment that John Allen Paulos, a Temple University math professor and an author, calls innumeracy — the mathematical equivalent of not being able to read. On national tests, nearly two-thirds of fourth graders and eighth graders are not proficient in math. More than half of fourth graders taking the 2013 National Assessment of Educational Progress could not accurately read the temperature on a neatly drawn thermometer.

I hadn’t heard of this parable/story before, but it is quite the embarrassment:

One of the most vivid arithmetic failings displayed by Americans occurred in the early 1980s, when the A&W restaurant chain released a new hamburger to rival the McDonald’s Quarter Pounder. With a third-pound of beef, the A&W burger had more meat than the Quarter Pounder; in taste tests, customers preferred A&W’s burger. And it was less expensive. A lavish A&W television and radio marketing campaign cited these benefits. Yet instead of leaping at the great value, customers snubbed it.

Only when the company held customer focus groups did it become clear why. The Third Pounder presented the American public with a test in fractions. And we failed. Misunderstanding the value of one-third, customers believed they were being overcharged. Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald’s. The “4” in “¼,” larger than the “3” in “⅓,” led them astray.

Maybe we need to develop more system-wide efforts to showcase teaching styles to observers, like they do in Japan:

In Japan, teachers had always depended on jugyokenkyu, which translates literally as “lesson study,” a set of practices that Japanese teachers use to hone their craft. A teacher first plans lessons, then teaches in front of an audience of students and other teachers along with at least one university observer. Then the observers talk with the teacher about what has just taken place. Each public lesson poses a hypothesis, a new idea about how to help children learn. And each discussion offers a chance to determine whether it worked. Without jugyokenkyu, it was no wonder the American teachers’ work fell short of the model set by their best thinkers.

What else matters? That teachers embrace new teaching styles, and persevere:

Most policies aimed at improving teaching conceive of the job not as a craft that needs to be taught but as a natural-born talent that teachers either decide to muster or don’t possess. Instead of acknowledging that changes like the new math are something teachers must learn over time, we mandate them as “standards” that teachers are expected to simply “adopt.” We shouldn’t be surprised, then, that their students don’t improve.

Here, too, the Japanese experience is telling. The teachers I met in Tokyo had changed not just their ideas about math; they also changed their whole conception of what it means to be a teacher. “The term ‘teaching’ came to mean something totally different to me,” a teacher named Hideto Hirayama told me through a translator. It was more sophisticated, more challenging — and more rewarding. “The moment that a child changes, the moment that he understands something, is amazing, and this transition happens right before your eyes,” he said. “It seems like my heart stops every day.”

Worth reading in entirety here.

On Business and Design Considerations of 1st Class Airplane Seating

David Owen, writing in The New Yorker, in a cleverly titled article “Game of Thrones,” describes the business and design considerations of seats in modern-day airplanes. While the economy seating is fairly routine (cramped), there is a lot of creativity involved in how 1st class and business seating is designed and built:

Airplane interiors are even more tightly regulated. Nearly every element undergoes a safety-enhancing process called “delethalization”: seats have to withstand an impact equal to sixteen times the force of gravity, and to remain in place when they do, so that they don’t block exit routes or crush anyone, and they can’t burst into flames or release toxic gases when they get hot. Doing something as simple as slightly increasing the thickness of the padding in a seat cushion can necessitate a new round of testing and certification, because a more resilient seat could make a passenger bounce farther after an impact, increasing the risk of injury caused by turbulence or a hard landing. Delethalizing some premium-class seats—in which a passenger’s head and torso have a lot of room to accelerate before being stopped by something solid—requires the addition of a feature that many passengers don’t even realize is there: an air bag concealed in the seat belt.

This bit about how expensive video-back video screens is fascinating:

In economy, the tight spacing of the seats makes air bags mostly unnecessary. But seat-back video screens and the hard frames that surround them pose a safety challenge, partly because of the potential for injuries caused by head strikes, and partly because the computers and the electrical systems that serve them have to be both fireproof and fully isolated from the plane’s—so that crossed wires in somebody’s seat don’t allow a ten-year-old playing a video game to suddenly take control of the cockpit. Largely as a result, in-flight entertainment systems are almost unbelievably expensive. The rule of thumb, I was told, is “a thousand dollars an inch”—meaning that the small screen in the back of each economy seat can cost an airline ten thousand dollars, plus a few thousand for its handheld controller.


The article mentions but doesn’t link to the TheDesignAir’s Top 10 International Business Classes of 2014 (it’s well worth a look).

The Male Deficit Model and Friendships

Do men suck at friendships? Or, at least, are they worse at being friends than their female counterparts? Research suggests the answer is yes. This Men’s Journal article provides an excellent overview:

The Male Deficit Model is based on 30 years of research into friendship and relationships — from Mayta Caldwell’s and Letitia Peplau’s 1982 UCLA study, which found that male friendships are far less intimate than female friendships, to a 2007 study at the College of the Holy Cross in Worcester, Massachusetts, which reported greater interpersonal competition and lower friendship satisfaction among men. A just-completed report from California State University Humboldt, meanwhile, holds that the closer men adhere to traditional male gender roles, like self-reliance and a reluctance to spill their guts, the worse their friendships fare. “Since most men don’t let themselves think or feel about friendship, this immense collective and personal disappointment is usually concealed, sloughed over, shrugged away,” writes the psychologist Stuart Miller in his opus, Men and Friendship. “The older we get, the more we accept our essential friendlessness.”

What’s the key to healthy aging? Good diet and exercise, right? Well, perhaps another factor outweighs them all:

That’s because nearly all research into healthy aging has found that the key to a long, happy life is not diet or exercise but strong social connections – that is, friendships. Loneliness accelerates age-related declines in cognition and motor function, while a single good friend has been shown to make as much as a 10-year difference in overall life expectancy. A huge meta-study performed in part at Brigham Young University, which reviewed 148 studies with a combined 308,849 subject participants, found that loneliness is just as harmful to health as not exercising, smoking 15 cigarettes a day, and alcoholism, and fully twice as bad as being obese. Still more startling is a 2010 study published in the Journal of Clinical Oncology that looked at 2,230 cancer patients in China. Social well-being, including friendship, turned out to be the number one predictor of survival.

Some of this stems from the fact that isolated people tend to exercise less, eat poorly, and drink too much. But some researchers believe that loneliness has a negative health impact all on its own. In numerous studies over the past 30 years, John T. Cacioppo, a professor of psychology at the University of Chicago and the pioneer of the biological study of loneliness, has found that lonely people have chronically elevated levels of the stress and fear hormones cortisol and epinephrine. In a 2007 paper published in Genome Biology, Cacioppo even demonstrated a correlation between loneliness and the activity of certain genes associated with systemic inflammation, elevating risk for viral invasion and cardiovascular disease.

And yet the capacity of men to combat loneliness – and improve their health – by building strong friendships seems to be steadily eroding. Cambridge, Massachusetts, professors Jacqueline Olds and Richard S. Schwartz, writing in The Lonely American: Drifting Apart in the Twenty-First Century, point to a current tendency among adults to build stronger, more intimate marriages at the expense of almost all other social connections. In a study of contemporary childcare arrangements, Olds and Schwartz found a deep sense of loneliness among many parents, especially men. “Almost every father we spoke with explained that he had lost contact with most of his male friends,” they write. And lest you believe family is company enough, the 2005 Australian Longitudinal Study of Aging showed that family relationships have almost no impact on longevity. Friendships, by contrast, boosted life span as much as 22 percent.

Read the rest here.

Valeria Lukyanova, Real-Life Barbie

This is a creepy piece in GQ Magazine on Valeria Lukyanova, who looks like a real-life Barbie. Here’s a photo of her:


The future Barbie was born nowhere near Malibu. Valeria hails from Tiraspol, a gloomy city in Europe’s poorest country, Moldova. Valeria remembers both her Siberian-born grandfather and her father as very strict and began to rebel at the usual age of 13. Stage one involved dyeing her hair, which is naturally a low-key shade of brown. Valeria went for the goth look first—about the farthest you could get from Barbie. She wore all-black clothes to accentuate her very white skin. Kids at school began to tease her.Look, a witch! At 15, traumatized by the name-calling, she doubled down: bracelets with sharp two-inch spikes, artificial fangs. She was dismissed from a school choir for standing bolt upright when the singers were instructed to sway; in different circumstances, this budding nonconformism could have brought her straight into Pussy Riot.

Instead, she began modeling, small-time stuff, and learned to apply makeup and hair dye in increasingly theatrical ways. Valeria was less interested in attracting men than in repelling them: “A dude would try to talk to me on the street and I’d be like—” she switches to a raspy basso—” ‘Oh, honey, aren’t I glad I had that operation.’ ” Another time, a guy tried grabbing her by the hand and she semi-accidentally cut him with her bracelet spike.

Proceed to read the whole thing with caution.

On the Brief History of the SAT Exam

From this excellent piece about a mother who decided to take the SATs (and naturally, decided to write a book about it: The Perfect Score Project: Uncovering the Secrets of the SAT), we learn about the history of the SAT exam:

The SATs were administered for the first time on June 23, 1926. Intelligence testing was a new but rapidly expanding enterprise; during the First World War, the United States Army had given I.Q. tests to nearly two million soldiers to determine who was officer material. (Walter Lippmann dismissed these tests as “quackery in a field where quacks breed like rabbits.”) The SAT’s inventor, a Princeton professor named Carl Campbell Brigham, had worked on the Army’s I.Q. test, and the civilian exam he came up with was a first cousin to the military’s. It contained some questions on math and some on identifying shapes. Mostly, though, it focussed on vocabulary. Brigham intended the test to be administered to students who had already been admitted to college, for the purposes of guidance and counselling. Later, he argued that it was foolish to believe, as he once had, that the test measured “native intelligence.” Rather, he wrote, scores were an index of a person’s “schooling, family background, familiarity with English, and everything else.”

By this point, though, the test had already been adopted for a new purpose. In 1933, James Bryant Conant, a chemist, became the president of Harvard. Conant, the product of a middle-class family, was dismayed by what he saw as the clubbiness of the school’s student body and set out to attract fresh talent. In particular, he wanted to recruit bright young men from public schools in the Midwest, few of whom traditionally applied to Harvard. Conant’s plan was to offer scholarships to ten such students each year. To select them, he decided to employ the SAT. As Nicholas Lemann observes in his book “The Big Test” (1999), this was one of those small decisions “from which great consequences later flow.” Not long after Harvard started using the SAT, Princeton, Columbia, and Yale followed suit. More and more colleges adopted the test until, by the mid-nineteen-fifties, half a million kids a year were taking it.

In the early decades of the test, scores were revealed only to schools, not to students. This made it difficult to assess the claim made by the College Board, the exam’s administrator, that studying for the SATs would serve no purpose. Still, a brash young high-school tutor named Stanley Kaplan concluded, based on the feedback he was getting from his pupils, that the claim was a crock. Kaplan began offering SAT prep classes out of his Brooklyn basement. Accusations that he was a fraud and a “snake oil salesman” failed to deter his clientele; the students just kept on coming. In the nineteen-seventies, Kaplan expanded his operations into cities like Philadelphia, Los Angeles, Chicago, and Miami; this is when the Federal Trade Commission decided to investigate his claims. The commission found that Kaplan was right: tutoring did boost scores, if not by as much as his testing service advertised. The College Board implicitly conceded the point in 1994, when it changed the meaning of the SAT’s central “A”; instead of “aptitude” it came to stand for “assessment.” Then the board took the even more radical step of erasing the meaning of the name altogether. Today, the letters “SAT” stand for nothing more (or less) than the SATs. As the Lord put it to Moses, “I am that I am.”

Read the rest here.

Before Laika: the Soviet Space Dogs

This is a very interesting post on Medium about the dogs the Soviets sent into space in the 1950s:

While the US test rocket programme used monkeys, about two thirds of whom died, dogs were chosen by the Soviets for their ability to withstand long periods of inactivity, and were trained extensively before they flew. Only stray female dogs were used because it was thought they’d be better able to cope with the extreme stress of spaceflight, and the bubble-helmeted spacesuits designed for the programme were equipped with a device to collect feces and urine that only worked with females.

Training included standing still for long periods, wearing the spacesuits, being confined in increasingly small boxes for 15-20 days at a time, riding in centrifuges to simulate the high acceleration of launch, and being placed in machines that simulated the vibrations and loud noises of a rocket.

The first pair of dogs to travel to space were Dezik and Tsygan (“Gypsy”), who made it to 110km on 22 July 1951 and were recovered, unharmed by their ordeal, the next day. Dezik returned to space in September 1951 with a dog named Lisa, but neither survived the journey. After Dezik’s death, Tsygan was adopted by Anatoli Blagronravov, a physician who later worked closely with the United States at the height of the Cold War to promote international cooperation on spaceflight.

They were followed by Smelaya (“Brave”), who defied her name by running away the day before her launch was scheduled. She was found the next morning, however, and made a successful flight with Malyshka (“Babe”). Another runaway was Bolik, who successfully escaped a few days before her flight in September 1951. Her replacement was ignomoniously named ZIB — the Russian acronym for “Substitute for Missing Bolik”, and was a street dog found running around the barracks where the tests were being conducted. Despite being untrained for the mission, he made a successful flight and returned to Earth unharmed.

A good piece of trivia from the piece: Laika wasn’t the original name for the most famous of Russian space dogs; it was named Kudryavka (Russian: Кудрявка, meaning Little Curly) before its name was changed.

The Human Element in Quantification

I enjoyed Felix Salmon’s piece in Wired titled “Why Quants Don’t Know Everything.” The premise of the piece is that while what quants do is important, the human element cannot be ignored.

The reason the quants win is that they’re almost always right—at least at first. They find numerical patterns or invent ingenious algorithms that increase profits or solve problems in ways that no amount of subjective experience can match. But what happens after the quants win is not always the data-driven paradise that they and their boosters expected. The more a field is run by a system, the more that system creates incentives for everyone (employees, customers, competitors) to change their behavior in perverse ways—providing more of whatever the system is designed to measure and produce, whether that actually creates any value or not. It’s a problem that can’t be solved until the quants learn a little bit from the old-fashioned ways of thinking they’ve displaced.

Felix discusses the four stages in the rise of the quants: 1) pre-disruption, 2) disruption, 3) overshoot, and 4) synthesis, described below:

It’s increasingly clear that for smart organizations, living by numbers alone simply won’t work. That’s why they arrive at stage four: synthesis—the practice of marrying quantitative insights with old-fashioned subjective experience. Nate Silver himself has written thoughtfully about examples of this in his book, The Signal and the Noise. He cites baseball, which in the post-Moneyball era adopted a “fusion approach” that leans on both statistics and scouting. Silver credits it with delivering the Boston Red Sox’s first World Series title in 86 years. Or consider weather forecasting: The National Weather Service employs meteorologists who, understanding the dynamics of weather systems, can improve forecasts by as much as 25 percent compared with computers alone. A similar synthesis holds in eco­nomic forecasting: Adding human judgment to statistical methods makes results roughly 15 percent more accurate. And it’s even true in chess: While the best computers can now easily beat the best humans, they can in turn be beaten by humans aided by computers.

Very interesting throughout, and highly recommended.