### Because they don't do the work, that's why

In which the New York Times goes into considerable length to ask a question for which the answer is staring them right in the face:

The new mathof 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. (They did not understand that each hash mark represented two degrees rather than one, leading many students to mistake 46 degrees for 43 degrees.) On the same multiple-choice test, three-quarters of fourth graders could not translate a simple word problem about a girl who sold 15 cups of lemonade on Saturday and twice as many on Sunday into the expression “15 + (2×15).” Even in Massachusetts, one of the country’s highest-performing states, math students are more than two years behind their counterparts in Shanghai.

Adulthood does not alleviate our quantitative deficiency. A 2012 study comparing 16-to-65-year-olds in 20 countries found that Americans rank in the bottom five in numeracy. On a scale of 1 to 5, 29 percent of them scored at Level 1 or below, meaning they could do basic arithmetic but not computations requiring two or more steps. One study that examined medical prescriptions gone awry found that 17 percent of errors were caused by math mistakes on the part of doctors or pharmacists. A survey found that three-quarters of doctors inaccurately estimated the rates of death and major complications associated with common medical procedures, even in their own specialty areas.

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.

But our innumeracy isn’t inevitable. In the 1970s and the 1980s, cognitive scientists studied a population known as the unschooled, people with little or no formal education. Observing workers at a Baltimore dairy factory in the ‘80s, the psychologist Sylvia Scribner noted that even basic tasks required an extensive amount of math. For instance, many of the workers charged with loading quarts and gallons of milk into crates had no more than a sixth-grade education. But they were able to do math, in order to assemble their loads efficiently, that was “equivalent to shifting between different base systems of numbers.” Throughout these mental calculations, errors were “virtually nonexistent.” And yet when these workers were out sick and the dairy’s better-educated office workers filled in for them, productivity declined.

The unschooled may have been more capable of complex math than people who were specifically taught it, but in the context of school, they were stymied by math they already knew. Studies of children in Brazil, who helped support their families by roaming the streets selling roasted peanuts and coconuts, showed that the children routinely solved complex problems in their heads to calculate a bill or make change. When cognitive scientists presented the children with the very same problem, however, this time with pen and paper, they stumbled. A 12-year-old boy who accurately computed the price of four coconuts at 35 cruzeiros each was later given the problem on paper. Incorrectly using the multiplication method he was taught in school, he came up with the wrong answer. Similarly, when Scribner gave her dairy workers tests using the language of math class, their scores averaged around 64 percent. The cognitive-science research suggested a startling cause of Americans’ innumeracy: school.

The article goes on (and on, and on,

*and bloody on*) in this vein, asking why it is that Asian and other nations consistently outperform Americans in high-school and college mathematics. Not*once*does the NYT's author stop to ask exactly why Asian methods of teaching maths succeed where American ones don't.
As might be expected, I have something of a personal perspective on this. Until the 9th grade, I was trained in the American system of learning mathematics. I swung from really stinking at maths in the 6th grade- I was at best a C student in the subject- to being really, really good at it in the 8th grade.

Then I moved to Australia and started learning mathematics the way the Brits, and thereafter the Aussies, taught it. My word, what a shock. I went from being one of the best maths students in the class, to one of the

*absolute worst*.
What happened? Did the teaching methods change? Well, yes. The American method emphasised the

The Australian approach was to teach a systematic method for solving problems, and then expect the students to drill, and drill, and drill some more, until they figured out the system and applied it. Don't know the Order of Operations? DRILL IN IT UNTIL YOUR EYES BLEED!!!

*process*of solving the problem, but never actually developed a formal*method*for doing so. The American method didn't care that you didn't understand something as basic and important as the Order of Operations- all that mattered was that you*tried*to solve the problem! Good doggie! Eat biscuit! Good boy! The American method was all about*feeeeeeeelings,*which ultimately is why it was*useless*. When it comes to a language as beautiful, complex, and yet ordered as mathematics,*feeeeeelings*don't cut it.The Australian approach was to teach a systematic method for solving problems, and then expect the students to drill, and drill, and drill some more, until they figured out the system and applied it. Don't know the Order of Operations? DRILL IN IT UNTIL YOUR EYES BLEED!!!

It took me two long and painful years to figure that out. I had to spend

*hours*of self-study, doing all of the homework problem sets, and then all of the problems that*weren't*in the homework assignments. I was never tutored by anyone other than my parents, but eventually, through sheer bloody-minded hard work, I got my scores up.
I got to be so good at it, in fact, that by the time I moved to Singapore and finished high school, I was one of the best students in maths in one of the best high schools in the

Today, I hold two degrees in mathematics from two of the best universities in the world.

Today my job requires the ability to think through complex problems, think outside the box, and figure out how to make broken things work again with the least amount of pain and resistance possible. It's not easy, but it is a

*world*.Today, I hold two degrees in mathematics from two of the best universities in the world.

Today my job requires the ability to think through complex problems, think outside the box, and figure out how to make broken things work again with the least amount of pain and resistance possible. It's not easy, but it is a

*lot*of fun.
And all of this happened because I

*put in the work*. That's all there is to it.
That is the difference between American students- who by and large

*do not*put in the work- and Asian students, who put in the work whether they like it or not.
Think I'm exaggerating? In my first-year undergraduate economics courses, we would start applying differential calculus to utility functions constrained by income, and shifts in aggregate supply and demand. I was a

*first-year*doing this stuff, and I was tutoring*third-year*American transfer students from some of America's best liberal arts and private colleges, who were shell-shocked to discover that they were expected to know how to differentiate functions in an*introductory*economics course.
There are valid criticisms of the drillwork mentality of Asian methods of teaching. When it comes to maths, though, that's the only method that works. Case in point: when I was about 8, my mum locked me in my room and told me that she wouldn't let me out until I could recite my multiplication tables up to the 12s.

In America, she'd have been arrested for child cruelty.

In Asia, her approach is normal.

It is also a big part of the reason why I am still pretty darn good at quantitative problem solving. (Certain mildly embarrassing slip-ups aside.) Hell, I work in a job that

In Asia, her approach is normal.

It is also a big part of the reason why I am still pretty darn good at quantitative problem solving. (Certain mildly embarrassing slip-ups aside.) Hell, I work in a job that

*requires*that I know how to pick apart complex technical problems and then put together solutions. I didn't get that way by being some kind of intuitive*wunderkind*- I'm not. I got there through dint of sheer hard work.Hell, even the article seems to admit as much, albeit in a very half-arsed manner, by pointing out that street urchins in Third World countries who constantly have to do mental arithmetic are really, really good at it, but fall apart the moment someone tries to teach them a problem-solving approach similar to the way Americans are taught. The reason is simple: those kids have to do the same thing, over and over and over again, and so get to be

*really good*at the processes of mental arithmetic. They

*do the work*.

This is the fundamental lesson that Americans seem to have forgotten in this day and age. No matter

*what*field you want to pursue,**success comes from work**. There is simply no other way to get good at something. If you want to get good, you have to put in the work.
It is tiresome. It is frustrating. It is irritating. It can really hurt if you're not careful. It is also the only way.

And as long as Americans continue to seek the easy way out, to look for the magic bullet that will cure all of their ills without having to sweat and sacrifice and work for it, they will never again reach their full potential as human beings and as a nation.

Great post and spot on. Americans are becoming even fatter, lazier, and stupider (is that a word? As an American, I don't know.) And the entire US education system is based not on learning or working, but on how you are feeling. Ugh!

ReplyDeleteI think we paid more attention to boosting a students self esteem than laying the sound foundation the learning of math. As a teacher it is getting harder and almost impossible to teach to any discernible standard without having the parents and the school administrators intervening to passing the students. The worst culprits are the "Math Education" PhD's who are continually tweaking an system they broke without really addressing the real cause of the problems that prevent students from the learning math. I am old school and I learned math at a time when the British system was very rigorous and also when a lots of people in academia knew about "British Applied Mathematics". Sadly, it is not true anymore. The British system also seen marked deterioration of standards. At least in Eastern Europe and Asia math is being still taught to a intellectually challenging level. The Singaporean GCE-(A/L) where they use the "Singapore Math" is very good. I know so, because I had the opportunity of perusing past exam papers online and the students are sure being challenged. The All India IIT entrance exams which comprises of math,chemistry and physics exams are the toughest I have seen thus far. The math and physics questions of the IIT entrance exam are of level of junior and senior level of a US college/univeristy!!!

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