Teaching Math to the Talented

Which countries—and states—are producing high-achieving students?

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Winter 2011 / Vol. 11, No. 1

Podcast: Paul Peterson and Eric Hanushek discuss the study.
Video: Paul Peterson and Marty West discuss the study.
An unabridged version of this article is available here.
An interactive map providing specific information for each state is available here.

In Vancouver last winter, the United States proved its competitive spirit by winning more medals—gold, silver, and bronze—at the Winter Olympic Games than any other country, although the German member of our research team insists on pointing out that Canada and Germany both won more gold medals than the United States. But if there is some dispute about which Olympic medals to count, there is no question about American math performance: the United States does not deserve even a paper medal.

Maintaining our productivity as a nation depends importantly on developing a highly qualified cadre of scientists, engineers, entrepreneurs, and other professionals. To realize that objective requires a system of schooling that produces students with advanced math and science skills. To see how well schools in the United States do at producing high-achieving math students, we compared the percentage of U.S. students in the high-school graduating Class of 2009 with advanced skills in mathematics to percentages of similarly high achievers in other countries.

Unfortunately, we found that the percentage of students in the U.S. Class of 2009 who were highly accomplished in math is well below that of most countries with which the United States generally compares itself. No fewer than 30 of the 56 other countries that participated in the Program for International Student Assessment (PISA) math test, including most of the world’s industrialized nations, had a larger percentage of students who scored at the international equivalent of the advanced level on our own National Assessment of Educational Progress (NAEP) tests. Moreover, while the percentage of students scoring at the advanced level on NAEP varies considerably among the 50 states, not even the best state does well in international comparison. A 2005 report from the National Academy of Sciences, Rising Above the Gathering Storm, succinctly put the issue into perspective: “Although many people assume that the United States will always be a world leader in science and technology, this may not continue to be the case inasmuch as great minds and ideas exist throughout the world.”

The Demand for High Achievers

The gap between the burgeoning business demand for a highly accomplished workforce and a lagging education system has steadily widened. Even as the United States was struggling with a near 10 percent unemployment rate in the summer of 2010, businesses complained that they could not find workers with needed skills. New York Times writer Motoko Rich explained, “The problem…is a mismatch between the kind of skilled workers needed and the ranks of the unemployed.”

Skill shortages have severe consequences for a nation’s overall productivity. Two of the authors of this report have shown elsewhere that countries with students who perform at higher levels in math and science show larger rates of increase in economic productivity than do otherwise similar countries with lower-performing students (see “Education and Economic Growth,” research, Spring 2008).

Public discourse has tended to focus on the need to address low achievement, particularly among disadvantaged students. Both federal funding and the accountability elements of No Child Left Behind (NCLB) have stressed the importance of bringing every student up to a minimum level of proficiency. As great as this need may be, there is no less need to lift more students, no matter their socioeconomic background, to high levels of educational accomplishment. In 2006, the Science, Technology, Engineering, and Mathematics (STEM) Education Coalition was formed to “raise awareness in Congress, the Administration, and other organizations about the critical role that STEM education plays in enabling the U.S. to remain the economic and technological leader of the global marketplace for the 21st Century.” In the words of a National Academy of Sciences report that jump-started the coalition’s formation, the nation needs to “increase” its “talent pool by improving K–12 science and mathematics education.”

A Focus on Math

We give special attention to math performance because math appears to be the subject in which accomplishment in secondary school is particularly significant for both an individual’s and a country’s economic well-being. Existing research, though not conclusive, indicates that math skills better predict future earnings and other economic outcomes than other skills learned in high school. The American Diploma Project estimates that “in 62 percent of American jobs over the next 10 years, entry-level workers will need to be proficient in algebra, geometry, data interpretation, probability and statistics.”

There is also a technical reason for focusing our analysis on math. This subject is particularly well suited to rigorous comparisons across countries and cultures. There is a fairly clear international consensus on the math concepts and techniques that need to be mastered and on the order in which those concepts should be introduced into the curriculum. The knowledge to be learned remains the same regardless of the dominant language spoken in a culture.

Data and Methodology

Our analysis relies on test-score information from NAEP and PISA. NAEP, the National Assessment of Educational Progress, is often called the nation’s report card. It is a large, nationally representative assessment of student performance in public and private schools in mathematics, reading, and science that has been administered periodically since the early 1970s to U.S. students in 4th grade and 8th grade, and at the age of 17. PISA, the Program for International Student Assessment, is an internationally standardized assessment of student performance in mathematics, science, and reading established by the Organisation for Economic Co-operation and Development (OECD). It was administered in 2000, 2003, and 2006 to representative samples of 15-year-olds in all 30 OECD countries (which include the most developed countries of the world) as well as in many others.

We focus on performance of the international equivalent of the U.S. high-school graduating Class of 2009 at the time when this population was in the equivalent of U.S. grades 8 and 9. NAEP was administered to U.S. 8th graders in 2005, while PISA 2006 was given one year later to students at the age of 15, the year at which most American students are in 9th grade.

In 2005, NAEP tested representative samples of 8th-grade public and private school students in each of the 50 states in math, science, and reading. For each state, NAEP 2005 calculates the percentage of students who meet a set of achievement standards: a “basic” level, a “proficient” level, and an “advanced” level of achievement. The focus of this report is the top performers, the percentage of students NAEP found at the advanced level of achievement (subsequently referred to as “advanced”).

Only 6.04 percent of the students in the United States in 8th grade in 2005 scored at the advanced level in math on the NAEP. Some critics feel that the standard set by the NAEP governing board is excessively stringent. However, the 2007 Trends in International Math and Science Study (TIMSS 2007), another international test that has been administered to students throughout the world, appears to have set a standard very similar to NAEP 2005, as only 6 percent of U.S. 8th graders scored at the advanced level on that test as well.

We use the NAEP 2005 advanced standard to compare U.S. performance with that in other countries. Because U.S. students took both NAEP 2005 and PISA 2006, it is possible to find the score on PISA that is tantamount to scoring at the advanced level on NAEP, i.e., the score that will yield the same percentage of students as the percentage of U. S. students who scored at the advanced level on the NAEP.

A score on PISA 2006 of 617.1 points is equivalent to the lowest score attained by anyone in the top 6.04 percent of U.S. students in the Class of 2009. (The PISA assessment has an average score of 500 among OECD students and a standard deviation of 100.) It is assumed that both NAEP and PISA tests randomly select questions from a common universe of mathematics knowledge. Given that assumption, it may be further assumed that students who scored similarly on the two exams will have similar math knowledge, i.e., students who scored 617.1 points or better on the PISA test would have been identified at the advanced level had they taken the NAEP math test. Inasmuch as a score of 617.1 points is more than one standard deviation above the average student score on the PISA, it is clear that a group of highly accomplished students has been isolated. (For more methodological details, see sidebar.)

We start with the national share of 8th-grade U.S. public and private school students (most of whom are 14 years of age) who reach the advanced level in math on NAEP 2005: 6.04 percent. These students are assumed to be part of the cohort of 15-year-olds who participated in PISA 2006 one year later. Thus, using the PISA 2006 microdata, we can calculate the PISA math test score at which the 93.96th percentile (100.00 – 6.04) of the U.S. student population performs. All PISA calculations use the PISA sampling weights to yield nationally representative estimates. The PISA scaling methodology returns student performance estimates through a range of five plausible values, which are random draws from the estimated probability distribution for a student’s underlying performance. We perform our analysis separately for each of the five plausible values provided by PISA 2006. We then average these results. Based on these calculations, we estimate the PISA score at which the 93.96th percentile of the U.S. student population performs to be 617.1 PISA points.

Next, we calculate from the PISA microdata the share of students reaching this cutoff point for each country participating in the PISA 2006 test. This provides an estimate of the share of students in each PISA country who reach the equivalent of the advanced level in 8th-grade math on NAEP 2005. The share of students who reach the advanced level in 8th-grade math in each U.S. state is taken from NAEP 2005. For information on the statistical significance of differences among jurisdictions, see the unabridged version of this study, available here.

Because representative samples of student performance on NAEP 2005 are available for each state, it is possible to compare the percentages of students in the Class of 2009 who were at the advanced level for each state to the percentage of equally skilled students in countries from around the globe.

In short, linking the scores of the Class of 2009 on NAEP 2005 and PISA 2006 provides us with the opportunity to assess from an international vantage point how well the country as well as individual states in the United States are doing at lifting students to high levels of accomplishment.

U. S. Math Performance in World Perspective

We begin with an overall assessment of the relative percentages of young adults in the United States and other countries who have reached a very high level of mathematics achievement. It is frequently noted that the United States has a very heterogeneous population, with large numbers of immigrants. Such a diverse population, with students coming to school with varying preparation, may handicap U.S. performance relative to that of other countries. For this reason, we also examine two U.S. subgroups conventionally thought to have better preparation for school—white students and students from families where at least one parent is reported to have received a college degree—and compare the percentages of high-achieving students among them to the (total) populations abroad.

Overall results. The percentage of students in the U.S. Class of 2009 who were highly accomplished is well below that of most countries with which the United States generally compares itself. While just 6 percent of U.S. students earned at least 617.1 points on the PISA 2006 exam, 28 percent of Taiwanese students did. (See Figure 1 for these results as well as for the international rank of each U.S. state.)

Click to enlarge

It is not only Taiwan that did much, much better than the United States. At least 20 percent of students in Hong Kong, Korea, and Finland were similarly highly accomplished. Twelve other countries had more than twice the percentage of advanced students as the United States: in order of math excellence, they are Switzerland, Belgium, the Netherlands, Liechtenstein, New Zealand, the Czech Republic, Japan, Canada, Macao-China, Australia, Germany, and Austria.

The remaining countries that educate a greater proportion of their students to a high level are Slovenia, Denmark, Iceland, France, Estonia, Sweden, the United Kingdom, the Slovak Republic, Luxembourg, Hungary, Poland, Norway, Ireland and Lithuania.

The 30-country list includes virtually all the advanced industrialized nations of the world. The only OECD countries producing a smaller percentage of advanced math students than the United States are Portugal, Greece, Turkey, and Mexico. The performance levels of students in Spain and Italy are statistically indistinguishable from those of students in the United States, as are those of students in Latvia, which has subsequently joined the OECD.

State-level performance. The percentage of students scoring at the advanced level varies among the 50 states. Massachusetts, with over 11 percent of its students at the advanced level, does better than any other state, but its performance trails that of 14 countries. Its students’ achievement level is similar to that of Germany and France. Minnesota, with more than 10 percent of its students at the advanced level, ranks second among the 50 states, but it trails 16 countries and performs at the level attained by Slovenia and Denmark. New York and Texas each have a percentage of students scoring at the advanced level that is roughly comparable to the United States as a whole, Lithuania, and the Russian Federation.

Just 4.5 percent of the students in the Silicon Valley state of California are performing at a high level, a percentage roughly comparable to that of Portugal. The lowest-ranking states—West Virginia, New Mexico, and Mississippi—have a smaller percentage of the highest-performing students than Serbia or Uruguay, although they do edge out Romania, Brazil, and Kyrgyzstan.

In short, the percentages of high-achieving students in the United States—and in most of its individual states—are shockingly below those of many of the world’s leading industrialized nations. Results for many states are at a level equal to those of third-world countries. (Click the image below for an interactive map providing specific information for each state.)

Click to find specific information for each state

White students. The overall news is sobering. Some might try to comfort themselves by saying the problem is limited to large numbers of students from immigrant families, or to African American students and others who have suffered from discrimination. For example, the statement by the STEM Coalition that we “encourage more of our best and brightest students, especially those from underrepresented or disadvantaged groups, to study in STEM fields” suggests that the challenges are concentrated in nonwhite segments of the U.S. population.

Without denying that the paucity of high-achieving students within minority populations is a serious issue, let us consider the performance of white students for whom the case of discrimination cannot easily be made. Twenty-four countries have a larger percentage of highly accomplished students than the 8 percent achieving at that level among the U.S. white student population in the Class of 2009. Looking at just white students places the U.S. at a level equivalent to what all students are achieving in the United Kingdom, Hungary, and Poland. Seven percent of California’s white students are advanced, roughly the percentage for all Lithuanian students.

Children of parents with college degrees. Another possibility is that schools help students reach levels of high accomplishment if parents are providing the necessary support. To explore this possibility, we assumed that students who reported that at least one parent had graduated from college were likely to be given the kind of support that is needed for many to reach high levels of achievement. Approximately 45 percent of all U.S. students reported that at least one parent had a college degree.

The portion of students in the Class of 2009 with a college-graduate parent who are performing at the advanced level is 10.3 percent. When compared to all students in the other PISA countries, this advantaged segment of the U.S. population was outranked by students in 16 other countries. Nine percent of Illinois students with a college-educated parent scored at the advanced level, a percentage comparable to all students in France and the United Kingdom. The percentage of highly accomplished students from college-educated families in Rhode Island is just short of 6 percent, the same percentage for all students in Spain, Italy, and Latvia.

The Previous Rosy Gloss

Many casual observers may be surprised by our findings, as two previous, highly publicized studies have suggested that—even though improvement was possible—the U.S. was doing all right. This was the picture from two reports issued by Gary Phillips of the American Institutes for Research, who compared the average performance in math of 8th-grade students in each of the 50 states with the average scores of 8th-grade students in other countries. These comparisons used methods that are similar to ours to relate 2007 NAEP performance for U.S. students to both TIMSS 2003 and TIMSS 2007. His findings are more favorable to the United States than those shown by our analyses. While our study using the PISA data shows U.S. student performance in math to be below 30 other countries, Phillips found the average U.S. student to be performing better than all but 14 other countries in his 2007 report and all but 8 countries in his 2009 report. (Oddly, the 2007 report takes a much more buoyant perspective than the 2009 report, though the data suggest otherwise.) Phillips also finds that individual states do much better vis-à-vis other countries than we report.

Why do two studies that seem to be employing generally similar methodologies produce such strikingly different results?

The answer to that puzzle is actually quite simple and has little to do with the fact that Phillips compares average student performance while our study focuses on advanced students: many OECD countries, including those that had a high percentage of high-achieving students, participated in PISA 2006 (upon which our analysis is based) but did not participate in either TIMSS 2003 or TIMSS 2007, the two surveys included in the Phillips studies. In fact, 19 countries that outscored the U.S. on the PISA 2006 test did not participate in TIMSS 2003, and 22 higher-scoring countries did not participate in TIMSS 2007. As a report by the U.S. National Center for Education Statistics has explained, “Differences in the set of countries that participate in an assessment can affect how well the United States appears to do internationally when results are released.”

Put starkly, if one drops from a survey countries such as Canada, Denmark, Finland, France, Germany, and New Zealand, and includes instead such countries as Botswana, Ghana, Iran, and Lebanon, the average international performance will drop, and the United States will look better relative to the countries with which it is being compared.

Did NCLB shift the focus away from the best and the brightest?

Some attribute the comparatively small percentages of students performing at the advanced level to the focus of the 2002 federal accountability statute, No Child Left Behind, on the educational needs of very low performing students. That law mandates that every student be brought up to the level a state deems proficient, a standard that most states set well below NAEP’s proficient standard, to say nothing of the advanced level that is the focus of this report.

In order to comply with the federal law, some assert, schools are concentrating all available resources on the educationally deprived, leaving advanced students to fend for themselves. If so, then we should see a decline in the percentage of students performing at NAEP’s advanced level subsequent to the passage of the 2002 federal law. In mathematics, however, the opposite has happened. The percentage performing at the advanced level was only 3.7 percent in 1996 and 4.7 percent in the year 2000. But the percentage performing at an advanced level climbed steadily to the 7.9 percent attained in 2009.

Perhaps NCLB’s passage in 2002 dampened the prior rate of growth in the achievement of high-performing students. To ascertain whether that was the case, we compared the rate of change in the NAEP math scores of the top 10 percent of all 8th graders between 1990 and 2003 (before NCLB was fully implemented) with the rate of change after NCLB had become effective law. Between 1990 and 2003, the scores of students at the 90th percentile rose from 307 to 321, an increment of 14 points, or a growth rate of 1.0 points a year. Between 2003 and 2009, the shift upward for the 90th percentile was another 8 points, or a change of 1.3 points a year. Our results are confirmed by a more detailed study of NCLB’s impact on high-performing students conducted by economists Brian Jacob and Thomas Dee.

In short, the incapacity of American schools to bring students up to the highest level of accomplishment in mathematics is much more deepseated than anything induced by recent federal legislation.


The economic and technological demand for a talented, well-educated, highly skilled population has never been greater. Not only must everyday workers have a set of technical skills surpassing those needed in the past, but a cadre of highly talented professionals trained to the highest level of accomplishment is needed to foster innovation and growth. In the words of President Barack Obama, “Whether it’s improving our health or harnessing clean energy, protecting our security or succeeding in the global economy, our future depends on reaffirming America’s role as the world’s engine of scientific discovery and technological innovation. And that leadership tomorrow depends on how we educate our students today, especially in math, science, technology, and engineering.”

Unfortunately, the United States trails other industrialized countries in bringing a large proportion of its students up to the highest levels of accomplishment. This is not a story of some states doing well but being dragged down by states that perform poorly. Nor is it a story of immigrant or disadvantaged or minority students hiding the strong performance of better-prepared students. Comparatively small percentages of white students are high achievers. Only a small proportion of the children of our college-educated population is equipped to compete with students in a majority of OECD countries.

Major policy initiatives within the United States have in recent years focused on the educational needs of low-performing students. Such efforts deserve commendation, but they can leave the impression that there is no similar need to enhance the education of those students the STEM coalition has called “the best and brightest.” Yet, with rapidly advancing technologies in an increasingly integrated world economy, no one doubts the extraordinary importance of highly accomplished professionals.

Admittedly, the United States could simply ignore the needs of its own young people and continue to import highly skilled scientists and engineers who were prepared by better-performing schools abroad. But even such a heartless, irresponsible strategy relies on both the nature of immigration policies and the absence of better opportunities abroad, two things on which we might not want the future to depend. It seems much more prudent to encourage the most capable of our own people to reach high levels of academic accomplishment.

Eric A. Hanushek is senior fellow at the Hoover Institution of Stanford University. Paul E. Peterson is the director of Harvard’s Program on Education Policy and Governance and senior fellow at the Hoover Institution. Ludger Woessmann is professor of economics at the University of Munich.

Comment on this article
  • Mahkno says:

    Ok fine… American students don’t get as many high scores in ‘advanced math’. What is ‘advanced math’? The typical math progression in schools is Algebra-Geometry-Trig-AlgebraII-PreCalc-Calculus. So…. is ‘advanced math’ Algebra II? Calculus? Differential Equations? Could someone (NBC or you) put the numbers into something that the rest of us can work with. When broadcast on NBC the numbers mean little if you don’t qualify them.

  • Gary says:

    There are three web-enabled math programs offered by http://ilearn.com. ThinkFast covers numerical fluency and can be used at multiple grade levels. iPass covers the curriculum from first through eighth grades. It can identify gaps in mastery with middle school students and direct a customized learning sequence for each student. Classof1 is designed for math remediation at the college level but is also useful for high school students. There is ample testimony on the website that these programs move underperforming students to mastery in math. It’s a powerful alternative to the one-size-fits-all classroom experience. I’m taking these programs into the home market so parents and students have an alternative to ineffective teachers and inadequate textbooks.

  • Al says:

    I’m kind of surprised by the poor white scores because in countries like Germany the immigrants do drag the average way down. A lot of whites in the U.S. do mimic black behavior though (watch the audience at an MTV music awards show) so maybe that is a factor.


    International comparisons

    Students with an immigrant background sometimes struggle to keep up

    The third to have been conducted since 2000, the latest PISA-E study polled 57,000 15-year-olds in 1,500 schools across the country and concentrated on testing knowledge in natural sciences, mathematics and literacy.

    Saxony came out top in every discipline in the 2006 study.

    But put in an international context, Germany’s results are decidedly mid-range. In terms of literacy skills, only three other German states along with Saxony — Rhineland-Palatinate, Thuringia and Bavaria — placed above international average, but they still lag far behind the top performers in Korea and Finland.

    In the natural sciences, however, Saxony occupies second place behind Finland.

    While Saxony is outperforming Bavaria for the first time, other outcomes of the report confirmed trends apparent in the first ever PISA-E survey published in 2000, which triggered what Germans dubbed “PISA shock” when the OECD results revealed that Germany’s education system was a chronic underachiever.

    German students tested for the 2000 report ranked in the lower half of those surveyed in the 32 leading industrial nations, well behind Britain, Japan, South Korea and much of continental Europe.

    Why Saxony does so well

    The results have continually shown a clear link in Germany between social background and educational success. The latest report reveals that that this correlation is most apparent in Bavaria.

    “This is shameful,” Marianne Demmer from the GEW education union told the Munich-based daily Sueddeutsche Zeitung, pointing out that middle class children were still much more likely to attend high school than children from poor homes or immigrant families.

    “The main challenge faced by politicians is to help these young people,” she said.

    Experts, meanwhile, attribute Saxony’s success to precisely this phenomenon. Compared to western German states, its schools contain fewer “risk” students, such as immigrants. Moreover, its shrinking population means there are fewer pupils per class.

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  • Tom Shillock says:

    Should we be concerned because of what poor ‘advanced math’ performance portends for the American economy, or for what it says about intellectual development and the quality of public Education per se? The claim that better advanced math performance will reduce unemployment and make America more productive and that this will help the economy is false.

    In the late 1980s and early 1990s when there was worry that America might be short about 850,000 scientists and engineers, business, academia and government decided that it was cheaper to import them than to encourage American students to become scientists and engineers. So Americans flocked to law, business and medicine where they could make more money sooner in less intellectually demanding ways.

    Between 1990 and the end of the last decade the global labor force doubled (see ‘Labor Market Imbalances’ by Richard Freeman). As a result, offshoring of work and “virtual immigration” (as a recent Dallas Fed economic letter termed it) increased. The pace is expected to increase (See ‘Offshoring: the next industrial revolution?’ and subsequent papers by Alan Blinder). This has primarily to do with the cost of labor, labor arbitrage, not the math and science skills of Americans versus foreigners. Even if Americans were the best in all levels of math it would not change what is fundamentally an economic matter. High tech executives use the poor showings on math and science tests to excuse offshoring and virtual immigration.

    As far as American productivity is concerned, the government counts productivity (output per worker per unit of time) in terms of the value of the product as finally assembled in the U.S. If, as in manufacturing, increasing amounts of work is done offshore but the final assembly remains in America then the American workers look more productive, and of course fewer of them may be needed, which also improves the equation.

    Tom Shillock
    M2 Consulting

  • Walter Skipwith McMann says:

    More troubling than the scores is the fact that the Washington Post did not print this article. I am becoming convinced that the omission stems from the fact that the Post’s mother company sells much of the garbage now touted by the educationists as being the way to improve scores. Eisenhour warned us years ago of of the military-industrial complex. Just as foreboding is the educational-industrial complex.

  • Diana says:

    Is a definition of “advanced math” provided anywhere? Others have asked for clarification, but I haven’t found a response.

  • Julie says:

    I wonder if the trend away from handing back tests (teachers show them to the students and then take them back the same day) has anything to do with the problem identified in this report. How are students supposed to learn from their mistakes and advance to higher levels in math, if they can’t review their mistakes and learn from them?

  • [...] In a study drawing on Program for International School Assessment (PISA) results and linking closely to the National Assessment of Educational Progress(NAEP), researchers found that the math achievement of 8th and 9th graders in the United States lags far behind that of their peers in 30 other countries. Even when researchers looked at white U.S. students with at least one parent with a college degree, only 10.3 percent of U.S. 8th and 9th graders score at an accomplished level in math on the PISA—compared to 28 percent in Taiwan and at least 20 percent in Hong Kong, South Korea, and Finland. [...]

  • Jim says:

    In response to the comments asking “What is meant by ‘advanced math’?”, I would point readers to the third paragraph in the ‘Data and Methodology’ section of the article:

    “In 2005, NAEP tested representative samples of 8th-grade public and private school students in each of the 50 states in math, science, and reading. For each state, NAEP 2005 calculates the percentage of students who meet a set of achievement standards: a “basic” level, a “proficient” level, and an “advanced” level of achievement. The focus of this report is the top performers, the percentage of students NAEP found at the advanced level of achievement (subsequently referred to as “advanced”).”

    The authors are not comparing students who take advanced math classes in school, but those students who actually performed at an advanced level on the NAEP, as defined by that test.

    At least that’s the way I read it.

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  • Alex Smith says:

    The NAEP is not an accurate portrayal of US students’ ability. Students do NOT take the test seriously partly because they are not allowed even to see their OWN score. Students in the highest scoring countries have been taught to conform and do their best at all times no matter what. In the US, students think for themselves and ask, “Does this test count for anything that matters to me?” Since the answer is “No!” when it comes to the NAEP, most students blow it off.

  • AprilS says:

    It is time for our country to get away from focusing on teaching to the test and minimum standards and instead showing children how fun it is to learn. When kids enjoy learning, they succeed in education because they want to be in class, listening to the teacher. It’s amazing the difference in success between a teacher who loves math and teaching and one who teaches the textbook because that is their job. We need to stop underestimating kids. They have the capability to learn if we make it interesting and valuable to them.

    Thank you for sharing this scary trend. It should be a wake up call for all of us. In fact, it inspired me to write a blog post in response:

  • [...] more languages enhances mental flexibility and cognitive skills. Additionally, the United States is behind many industrialized countries when it comes to math education: Only 6.04 percent of the students in [...]

  • Ali Burrow says:

    How much of Massachusetts high math scores can be attributed to the numerous private middle and high schools in the state?

  • Laura Maaradji says:

    With 22 plus years in middle school science I have seen my share of brilliant math students waiting patiently for their peers to catch up. We have no system or strategy to support gifted and talented math/science students partly due to standards based education and the confinement of an age/grade system. Two anecdotals to make my point. My daughter was involved in an accelerated math program in 5th grade, she was able to sit through almost 5 years of mathematics before she learned something new in math, as a sophomore. My nephew, as a first grader, explained mathematically exponential growth to my brother. This youngster is now in the 4 grade and has learned to do his work, do not show off by knowing all the answers and do not correct the teacher, even if they are wrong.

  • [...]  “Teaching Math to the Talented” by Eric Hanushek, Paul Peterson, and Ludger Woessmann in Education Next, Winter 2011 (Vol. 11, #1, p. 10-18)  http://educationnext.org/teaching-math-to-the-talented [...]

  • mtepper@skahalb.org says:

    Here’s the actual article I told you about!

  • Laura says:

    We need to stop waiting and educate these kids.

  • David Cordeiro says:

    There is at least a partial solution to this problem in the diverse and vibrant math circles that are emerging around the country. The Metroplex Math Circle is an excellent example (http://www.metroplexmathcircle.org) but MSRI maintains a list of all math circles in the country at http://www.mathcircles.org

  • jonathan aguillon says:

    we have no silicon valley and no processor no computers no semicon company exist w/o these people i mean genius in math… did u know that most of the executives in blue chip company are doctor in math and in physics.. silicon valley were flooded by mathematicians and physicians then..that’s why ………we have hi tech gadget now…..

  • Barry Garelick says:

    The article states “Major policy initiatives within the United States have in recent years focused on the educational needs of low-performing students. Such efforts deserve commendation, but they can leave the impression that there is no similar need to enhance the education of those students the STEM coalition has called “the best and brightest.” ”

    True, but only in part. The article does not mention that education of low-performing students may in fact be hindered by poor instruction and substandard curricula and texts and the latest edu-trends such as inquiry based and student-centered learning.

    The article’s concluding statements are interesting in light of what we’ve said in the past. The article states: “The economic and technological demand for a talented, well-educated, highly skilled population has never been greater. Not only must everyday workers have a set of technical skills surpassing those needed in the past, but a cadre of highly talented professionals trained to the highest level of accomplishment is needed to foster innovation and growth.”

    Similar sentiments have been expressed in previous eras. Notably, this is from the preface of the teacher’s edition of Grade 6 “Growth in Arithmetic” by Clark, Junge and Moser (1957):

    “It is imperative that schools challenge able pupils to discover, to invent, to prize originality and resourcefulness in thinking. The future of a technological culture and the security of our way of life demand high-level education of our superior youth.”

  • [...] with other states, but not as well when compared with other countries. In EducationNext’s winter publication, Stanford economist Eric Hanushek and two colleagues tell us that only 6% of American 8th [...]

  • [...] consequences — which this blog is largely about. Yesterday’s blog also contained a link to another report, which compares each state’s 8th grade advanced math scores to scores of [...]

  • AsianRock says:

    The article failed again (like many other similar reports) to recognize the math achievements of Asian American students even those from immigrant families.

    It would be interesting to see the Asian American student performance alone compared to the other countries.

  • Bayard Lyons says:

    The authors have made a compelling argument. They have convincingly argued that we are sorely lagging in the percentage of students with advanced math skills. As a father of a second grader I am concerned about the math education my daughter is receiving when I read articles like this and when I hear how frustrated friends who have recently moved from Germany, India and Russia complain loudly about the low expectations for math achievement set in U.S. schools. Both my wife and I did well in math and were science majors in college. Math success was directly related to our academic success and I know that at least some of the math comes in handy in our daily lives. We would hate to forsake our daughter a high quality math education that we consider to be a key part to being a well rounded person. However, this article does not address how math success relates to other areas of her success or vice versa. Will raising a nation of mathematicians or engineers, as some countries do, continue to keep us as a nation at the top? Should we be thinking about math education in a vacuum as this article suggests or instead should we consider it in relation to other areas of academic performance? Should we perceive math to be an important complement to education in other areas – science, music, philosophy, history, literature, sports? Are Steve Jobs and Bill Gates great mathematicians do the excel in multiple ways? The article does not address how much math ability we need to be a successful nation? When I say how much I mean how many people performing at a advanced level and what level of math does the average person need to acquire? How are we deciding how much is enough? This article needs to be placed into a context against our achievements as a nation in other areas. Unfortunately, too often educational policy is driven by reports that while very thoughtful about one area of educational planning set in motion educational planning for raising math test scores at the expense of all the ways that our children and our nation need to grow. Finally, this article does not address how in this age where things have become more global our industries’ current heavy reliance on foreign born and educated engineers is unsustainable. Maybe one of the many reasons for our success as a nation over the years has been to create a environment in which innovators in science and math can thrive? A prudent national education strategy might include strengthening education in general as well as continuing to create a welcome place for world’s best and brightest.

  • Jen says:

    I am a counselor at a middle school, and recently had an SEOP (planning) meeting with a student from India. His father was upset that his son had to take geography, history, art, language arts, and other non-science or math classes – he said that in their country, those are optional, and students take nothing but science and math. So, to be like those other countries, will we have to sacrifice other areas of learning? How committed are we to educating the whole person?
    I do agree that there is a lack of opportunity for advanced students, and too much focus on catching up the low-achieving (thanks to NCLB)… but at the same time, how much do we REALLY want to be like those other countries?

  • edlharris says:

    “AsianRock says:
    12/10/2010 at 6:07 pm
    The article failed again (like many other similar reports) to recognize the math achievements of Asian American students even those from immigrant families.

    It would be interesting to see the Asian American student performance alone compared to the other countries.”

    Well, there isn’t a breakdown of math based upon racial/ethnic groups, but there is for reading:

    When you look at the document on PISA supplied by the Department of Ed,
    you see that in reading literacy, Asian-Americans scored best in the world. (541)
    White Americans came in 4th (525)
    US Overall 500
    Hispanic Americans 466
    African Americans 441.

  • [...] income level, or even the work by leading education scholars Paul Peterson and Eric Hanushek on the nation’s low math performance compared to the rest of the world. Let’s not even mention Education Trust’s recent [...]

  • The following was submitted as a letter to the editor:

    As the former president of the Fairfax County Association for the Gifted and a parent of three children who attended Thomas Jefferson (TJ) High School for Science and Technology in Alexandria, Virginia, I was thrilled to see the study that looked more closely at how well the U.S. is (not) doing at teaching math to gifted students. Normally, research studies focus on scores for No Child Left Behind assessments, rather than on how much or little academically gifted students are learning.

    I’m not sure that your prescription to cure this problem will work that well, though, especially for elementary and middle-school students. At least in areas where there is a critical mass of highly and exceptionally gifted math students, a better solution may be to group them together in a magnet school with unusually rigorous classes that go above and beyond the normal “honors” or “advanced” curriculum. That’s basically what TJ does for 9th- through 12th-grade students, and it works well.

    Children, no matter how gifted, often have difficulty with online courses. Some students lack the discipline to do what’s required on a timely and consistent basis. Some students are not technically savvy enough to figure out what they are supposed to be doing. For example, they may have difficulty understanding how to access and turn in assignments.

    Further, making rigorous online courses available does not mean that gifted students will be allowed to take them for credit. At least in the Fairfax County Public Schools (FCPS), students generally are not allowed to earn credit for rigorous online math courses offered by organizations such as the Johns Hopkins University’s Center for Talented Youth (CTY), Stanford’s Education Program for Gifted Youth (EPGY), or the Art of Problem Solving. Instead, gifted students are required to take online courses developed by FCPS employees for an academically heterogeneous mix of students.

    In some areas of the United States, the logistics of having a magnet school for the highly gifted may be so daunting that online math courses are the best option. In more densely populated areas, however, I believe there is a better alternative. Just restructure gifted programs so that there are enough highly and exceptionally gifted students in one school building, and provide those students with appropriately challenging classes.

    Louise Epstein
    McLean, Virginia

  • Alfred Peschel says:

    The fact that Asian-Americans demonstrated the highest score in literacy achievement says a lot. When analyzed I strongly suspect similar accomplishment in mathematics.

    Literacy in mathematics requires learning definitions, understanding and connecting the meaning of concepts, capturing through repetition such understanding into long term memory, reinforcing procedural skills through spaced, cumulative practice and repeated use of these concepts in applications to different situations. We think learning mathematics requires sustained motivation to achieve, master coaching and persistent after-class practice. Clearly more is involved than just attending school classes.

    A student’s learning cycle is driven by: 1) personal family values that either don’t value academic achievement or values that lead to richer prior knowledge coming into a class; 2) curriculums that either spiral to merely expose concepts or short spirals that reinforce learning to mastery; and, 3) either expecting little homework or providing systematic after-class tutoring, re-inforcement and practice of newly acquired skills.

    In the better performing school districts many teachers moonlight to provide after-class tutoring. Many students in Asia enroll in special after-school schools. Kumon is an after-class supplemental program that is particularly popular amongst Asian-Americans. All these programs require sustained student & parent discipline. Are such after-class studies accounted for in these comparisons?

    Does anyone understand what might account for the difference in the Masachusetts and California comparisons? If “proficiency” in math in California is defined as a score of 58% on the standardized test is such a standard useful? Are Taiwan, Hong Kong or Korean students less distracted after class than American or German students? If teachers are held in greater esteem in other cultures does this make a difference?

    The best students will learn what is expected of them if we help them to repeatedly attend more to their mathematics studies. What are we doing culturally to stimulate student mathematical thinking – both in school and after school? Should successful after-class programs be provided by moon-lighting teachers, specially contracted-for or simply privately offered to parents? Is there a significant difference between public schools and private schools?

    Some answers to these questions would be very helpful in understanding these state and international comparisons

  • Chung Yang says:

    As an American of Taiwanese decent, I am frankly surprised to see Taiwan scored on top as I had fully expected to see China, Japan, or Korea. Taiwan has been shifting its educational policy to a more “western-style” education with emphasis on creativity rather than regurgitation of books and texts. Perhaps in the transition they’ve inadvertently hit a happy medium with regards to mathematics? Or perhaps it simply points to the difficulty of providing high quality eduction in nations with large and diverse population?

    The government in Taiwan realized years ago, that their education policy was effective in producing high performing work force. However, it failed to create leaders and entrepreneurs. The shift in policy was to address that very problem. While the score is encouraging, I would argue it was simply a bi-product of the system as the Taiwanese educational officials are judging their own success by an entirely different set of criteria.

  • [...] American students, as reflected in the Program for International Student Assessment (PISA) (see “Teaching Math to the Talented,” features, Winter 2011), will prevent them from accessing good, high-paying jobs. And, as [...]

  • anon says:

    I agree with Asian Rock. The percentage of students of Asian descent in the districts/states/etc would be interesting to see.

    And remember that Asian-Americans are immigrants too for those too quick to deride the benefit of immigrants to their communities!

    The comment about about whites acting like blacks – you need to check your racism at the door.

  • Robert says:

    “anon says:
    09/29/2011 at 4:06 pm
    The comment about about whites acting like blacks – you need to check your racism at the door.”

    I have been very interested in education policy since I was a kid, having gone to one of the worst elementary schools in my city, followed by one of the best high schools in my country.

    I have noticed that whenever people talk about how bad US public schools are, they always blame blacks. The first time I had heard this was when “The Bell Curve” came out.

    I know for a fact that if black children are raised to value education, and if they are given the same opportunities to pursue quality education that whites get, they will perform as well as or better than white children. In my HS graduating class at one of the best schools in the country, I ranked ahead of most of my white classmates. The student with the lowest class rank was white, so every black student did better than him.

    The solutions to the education problem begin well before anyone enters a school building. Large cities need residential desegregation and de-concentration of poverty. Another article on this website said that James Coleman found that black children and white children in the same classroom raises black achievement but does not lower white achievement. But since we live in different neighborhoods, and school assignment is tied to residence, such classrooms hardly exist.

    Urban planning that includes more mixed-income neighborhoods, along with a high-level marketing campaign on the part of large urban school districts, will go a long way in alleviating the educational disparity caused by whites with money moving to the suburbs or sending their children to private school, and leaving black children who are smart but have parents who can’t afford to move or put them in private school stuck in classrooms with children who think being smart is something to look down upon.

  • [...] a recent report, “Teaching Math to the Talented,” published in Education Next, American students were significantly outperformed by 33 countries [...]

  • [...] significant for both an individual’s and a country’s economic well-being.” The study by Eric A. Hanushek, Paul E. Peterson and Ludger Woessmann compared the percentages of high achieving math students in the U.S. and other countries. Check [...]

  • Chuck says:

    It’s disheartening to see an article about math that doesn’t use math to drill down and decompose the gross statistics. Taking into account relevant and tracked characteristics (gender and race), we find that the real #1 state for math is Texas, followed by New Jersey and, then, Massachusetts.
    Check it out. Is there an error in the methodology?

  • John Adams says:

    “The gap between the burgeoning business demand for a highly accomplished workforce and a lagging education system has steadily widened.”

    It’s interesting to observe how, more than 100 years after the Rockefellers and others proposed that the purpose of education should be to train workers for efficient work in factories producing goods for the factory owners, this value is still held as being relevant and primary to school goals, despite a century of profound failure of this philosophy.

  • [...] and educate everyone do it better than the U.S., including Canada, France, Brazil, and Finland. And other research has shown that U.S. kids who have richer families and parents with more education still lag their [...]

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