NYT: Why Do Americans Stink At Math?

Today the frustrating descent from good intentions to tears is playing out once again, as states across the country carry out the latest wave of math reforms: the Common Core. A new set of academic standards developed to replace states’ individually designed learning goals, the Common Core math standards are like earlier math reforms, only further refined and more ambitious. Whereas previous movements found teachers haphazardly, through organizations like Takahashi’s beloved N.C.T.M. math-teacher group, the Common Core has a broader reach. A group of governors and education chiefs from 48 states initiated the writing of the standards, for both math and language arts, in 2009. The same year, the Obama administration encouraged the idea, making the adoption of rigorous “common standards” a criterion for receiving a portion of the more than $4 billion in Race to the Top grants. Forty-three states have adopted the standards.

The opportunity to change the way math is taught, as N.C.T.M. declared in its endorsement of the Common Core standards, is “unprecedented.” And yet, once again, the reforms have arrived without any good system for helping teachers learn to teach them. Responding to a recent survey by Education Week, teachers said they had typically spent fewer than four days in Common Core training, and that included training for the language-arts standards as well as the 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).”

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.