Professor Hung-hsi Wu of the University of California Berkeley writes many interesting articles about mathematics education reform in the United States.

http://math.berkeley.edu/~wu/

In one of Professor Wu's recent lectures,

http://math.berkeley.edu/~wu/Lisbon2010_4.pdf

he points out a problem of fraction addition from the federal National Assessment of Educational Progress (NAEP) survey project (the same "Nation's Report Card" mentioned in the article submitted here). On page 39 of his presentation handout (numbered in the .PDF of his lecture notes as page 38), he shows the fraction addition problem

12/13 + 7/8

for which eighth grade students were not even required to give a numerically exact answer, but only an estimate of the correct answer to the nearest natural number from five answer choices, which were

(a) 1

(b) 19

(c) 21

(d) I don't know

(e) 2

The statistics from the federal test revealed that for their best estimate of the sum of 12/13 + 7/8,

7 percent of eighth-graders chose answer choice a, that is 1;

28 percent of eighth-graders chose answer choice b, that is 19;

27 percent of eighth-graders chose answer choice c, that is 21;

14 percent of eighth-graders chose answer choice d, that is "I don't know";

while

24 percent of eighth-graders chose answer choice e, that is 2 (the best estimate of the sum).

I wrote an email to Richard Rusczyk about Professor Wu's document, and he later commented to me that if only 24 percent of eighth graders in the United States can find the best answer for that question from that list of choices, that's suggestive that 76 percent of American young people have no hope of having any career that demands mathematical competency.

Some countries set much higher standards of mathematics competency for young learners. My wife is from one, Taiwan, and I know various first-generation immigrants to the United States from other countries where primary mathematics instruction is much better than in the United States. Chapter 1: "International Student Achievement in Mathematics" from the TIMSS 2007 study of mathematics achievement in many different countries includes, in Exhibit 1.1 (pages 34 and 35)

http://pirls.bc.edu/timss2007/PDF/T07_M_IR_Chapter1.pdf

a chart of mathematics achievement levels in various countries. Although the United States is above the international average score among the countries surveyed, as we would expect from the level of economic development in the United States, the United States is well below the top country listed, which is Singapore. An average United States student is at the bottom quartile level for Singapore, or from another point of view, a top quartile student in the United States is only at the level of an average student in Singapore. That is despite the fact that most students in Singapore in my generation attended school in a foreign language (English, which was not a language they spoke at home) so that there is no more than one generation in Singapore that can even be relied on to carry on a conversation at home in the sole language of school instruction there.

The United States is making some painfully slow gains, as the article reports, but it has a long way to go to provide "world-class" education to all pupils, even though my local school district is one of many that claims to be providing "world class" education.