If one manages to graduate from high school without the rudiments of algebra, geometry and trigonometry, there are certain relatively high-paying careers probably off-limits for life – such as careers in architecture, chemistry, computer programming, engineering, medicine and certain technical fields. For example, one might meet all of the physical requirements to be a fighter pilot, but he's grounded if he doesn't have enough math to understand physics, aerodynamics and navigation. Mathematical ability helps provide the disciplined structure that helps people to think, speak and write more clearly. In general, mathematics is an excellent foundation and prerequisite for study in all areas of science and engineering. So where do U.S. youngsters stand in math?

Drs. Eric Hanushek and Paul Peterson, senior fellows at the Hoover Institution, looked at the performance of our youngsters compared with their counterparts in other nations, in their Newsweek article, "Why Can't American Students Compete?" (Aug. 28, 2011), reprinted under the title "Math Matters" in the Hoover Digest (2012). In the latest international tests administered by the Organisation for Economic Co-operation and Development, only 32 percent of U.S. students ranked proficient in math – coming in between Portugal and Italy but far behind South Korea, Finland, Canada and the Netherlands. U.S. students couldn't hold a finger to the 75 percent of Shanghai students who tested proficient.

What about our brightest? It turns out that only 7 percent of U.S. students perform at the advanced level in math. Forty-five percent of the students in Shanghai are advanced in math, compared with 20 percent in South Korea and Switzerland and 15 percent of students in Japan, Belgium, Finland, the Netherlands, New Zealand and Canada.

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Hanushek and Peterson find one bright spot among our young people. That's Asian-American students, 52 percent of whom perform at the proficient level or higher. Among white students, only 42 percent perform math at a proficient level. The math performance of black and Hispanic students is a disaster, with only 11 and 15 percent, respectively, performing math at the proficient level or higher.

The National Center for Education Statistics revealed some of the results of American innumeracy. Among advanced degrees in engineering awarded at U.S. universities during the 2007-08 academic year, 28 percent went to whites; 2 percent went to blacks; 2 percent went to Hispanics; and 61 percent went to foreigners. Of the advanced degrees in mathematics, 40 percent went to whites; 2 percent went to blacks; 5 percent went to Hispanics; and 50 percent went to foreigners. For advanced degrees in education, 65 percent went to whites; 17 percent went to blacks; 5 percent went to Hispanics; and 8 percent went to foreigners. The pattern is apparent. The more rigorous a subject area the higher the percentage of foreigners – and the lower the percentage of Americans – earning advanced degrees. In subject areas such as education, which have little or no rigor, Americans are likelier – and foreigners are less likely – to earn advanced degrees.

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In a New York Times article – "Do We Need Foreign Technology Workers?" (April 8, 2009) – Dr. Vivek Wadhwa of the Pratt School of Engineering at Duke University said "that 47 percent of all U.S. science and engineering workers with doctorates are immigrants as were 67 percent of the additions to the U.S. science and engineering work force between 1995 to 2006. And roughly 60 percent of engineering Ph.D. students and 40 percent of master's students are foreign nationals."

American mathematic proficiency levels leave a lot to be desired if we're to maintain competitiveness. For blacks and Hispanics, it's a tragedy with little prospect for change, but the solution is not rocket science. During my tenure as a member of Temple University's faculty in the 1970s, I tutored black students in math. When they complained that math was too difficult, I told them that if they spent as much time practicing math as they did practicing jump shots, they'd be just as good at math as they were at basketball. The same message of hard work and discipline applies to all students, but someone must demand it.