Our Bad Math Scores--Posner's Comment

The Program for Individual Student Achievement (PISA), the source of Becker's statistics, does triennial international comparative studies of 15-year-olds' educational achievements. The latest results to be reported are those of the 2003 survey. The United States came out in the middle of the European pack in reading literacy, but in math proficiency we were below the European average, as well as below several Asian countries in the sample. There are three questions to ask about these results: (1) Are they meaningful, in the sense of providing an accurate picture of relative math proficiency? (2) If so, are there economic or other real-world consequences? (3) If there are, what if anything should be done to increase our rank score? (1) The answer to the first question appears to be "yes," partly because of consistency with other studies. There is a good article on this issue by Paul E. Peterson, available on the Web, called "Ticket to Nowhere." See also an article by Mariann Lemke and colleagues in a recent issue of the Educational Statistics Quarterly, also available on the Web. Math skills appear to be deteriorating in the United States as well asto be inferior to the average of the 40 countries in the PISA sample; and this is true even if blacks and Hispanics, who on average do poorly (especially blacks) on these tests, are excluded from this comparison, although such exclusion does increase our international rank somewhat (but a proper comparison would require similar exclusions from some other countries in the sample). I agree with Becker that it would be interesting to see what difference it would make if college rather than high school students were tested. But I would not expect much difference, because little emphasis is placed nowadays on math in American colleges. (2) But so what? Here I agree with Becker; perhaps I am even more emphatic than he, that better education in mathematics would not have substantial effects on social and economic welfare. Very few jobs nowadays require even simple math skills ("deskilling" is the story of modernity); almost all computation is automated. Even fewer jobs require advanced math skills--and kids cannot acquire those skills by education; they are innate. What would be socially and even economically useful would be to instruct high school students in the rudiments of statistical theory. That would help them learn to think straight about a range of public policy issues, as well as to avoid certain recurrent mistakes in everyday life. People are terrible at handling probabilities. For example, most people, including otherwise quite intelligent and well educated people, don't understand that randomness is not regular alternation--that a typical random pattern is 1000110110001, not 101010101010. And this mistake leads them, for example, to give undue weight to the recent performance of a mutual fund (e.g., 1101). But whether to teach statistical theory in high school is an issue of educational policy rather than a matter of raising the scores on math tests. It would also be helpful to the United States, mainly from a public policy standpoint, if more of our people were scientifically literate; and it would help them to be so if they knew some math, because modern science is heavily mathematical. In my book Catastrophe: Risk and Return (2004), I examined the issue of scientific literacy briefly, pointing out that only a third of American adults (adults, not 15-year-olds) know what a molecule is, that 39 percent believe that astrology is scientific, that 46 percent deny that human beings evolved from earlier animal species, and that almost 50 percent do not know that it takes a year for the earth to revolve around the sun (many do not know that the earth revolves around the sun). These are amazing statistics, and yet, according to the materials I consulted, the scientific literacy of the U.S. population actually exceeds that of the European Union, Japan, and Canada. In the age of the computer and the Internet, school education probably has rather limited effect on job performance, marital stability, happiness, or other measures of welfare, except perhaps for elite people--but they attend elite educational institutions and probably get a better education than is available in any other country; our best colleges and universities are the envy of the world. And because of compulsory schooling, a very bright child almost always will be spotted even if he or she comes from a poor or educationally deprived home, and will be shunted onto the elite track. So I do not think that the low quality of public education matters a great deal from an overall social standpoint, except that our public schools seem needlessly costly, and also unresponsive to the special needs of very poor students. These are reasons why I strongly support school voucher programs. (3) If this is wrong and our poor international standing in math proficiency is hurting the United States, the solution is to teach more math and less of something else. It should not be to drill the kids in the 2003 PISA math test so that they can do better on the next one. It is always possible to improve scores on standardized tests by orienting instruction to the tests, by tutoring, or, if worse comes to worst, by withholding the test from the weakest students!

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