# Sex and Mathematics

After decades of efforts to encourage women to pursue math and science, the most enduring accomplishment may be the continuing downhill trend in the academic performance of boys. The *Boston Globe* reported that a male high school student is suing his school for alleged discrimination against boys. Through summer programs in science for girls, affirmative action hiring by university science departments, consciousness—raising programs for parents designed to educate them on how to create a fairer school environment for their daughters, plenty of time, attention and money has been lavished on female achievement.

In spite of the vast efforts to rescue the nation's girls from an epidemic of low self—esteem, it is boys who continue to surpass girls in almost every measure of dysfunction, from suicide and juvenile delinquency, to substance abuse and academic failure. In my son's high school graduation class, only three of the top nineteen students were boys and only twenty of the top ninety—five. But such a failure of boys to compete effectively with girls would not have been predicted from the list of 32 National Merit Scholarship semi—finalists, of which fully half were boys.

Four years earlier at his middle school graduation, more than 70% of the honor role students were girls. This did not prevent the school from requiring seven weeks of workshops on gender issues in the students' seventh grade homeroom classes to show how girls were short changed by a pervasive gender bias that supposedly hindered their progress in schools. Nor did it stop the school from distributing a pamphlet to a group of parents written by researchers alleging extensive gender bias in the teaching of mathematics to middle school students. And definitely nowhere mentioned was the extensive debunking of this gender bias movement which dominates American education in Christina Hoff Sommers' book *The War Against Boys*.

There is one area in academics in which males continue to outperform females, and that is at the most elite levels of achievement in mathematics. A year has passed since Lawrence Summers, the outgoing President of Harvard University, set off a firestorm of by speculating that gender differences in cognitive skills were among possible reasons for the dearth of women in the sciences at elite institutions such as Harvard.

One of those attending the conference, Nancy Hopkins, was so upset by his remarks that she almost fainted. No stranger to complaints about anti—female bias in the sciences, Dr. Hopkins had previously attained fame for feathering her academic nest by alleging gender victimization at the hands of her employer, the Massachusetts Institute of Technology. Though the remarks of Summers were made off the record and though he had said it was not the most likely reason for the paucity of women in the hard sciences at Harvard, the recriminations that followed led to faculty censure and a vast commitment of resources to alleviate the disproportionate numbers.

A study on the relative numbers of males and females at the top end in mathematics looks at gender statistics for elite performers in mathematics, where almost no women are represented among mathematicians in the National Academy of Science, winners of the Field's medal (roughly the equivalent of a Nobel prize in mathematics that is awarded every four years) and the Putnam Competition that is a mathematical competition for college students. The author points out that membership in any of these elite groups is so small that we are talking about people who are almost five standard deviations above the mean for mathematical ability or achievement. By implication, membership in the science departments of the top ten research university math departments represents people who are similarly several standard deviations above the mean. So what we are looking at is not gender difference in mean but in standard deviation.

Another interesting place to look for gender statistics relating to high level performance in mathematics is in the published results of the extensive mathematical competitions organized by the Mathematical Association of America. The American Mathematics Competitions are a series of math contests for high school students culminating in selecting a United States team for the International Math Olympiad. The participants are chosen from the top mathematics students at high schools throughout the country. If you open the above link you will find a line of tabs that are links to the different contests.

The AMC 12 A and B is a test with 25 multiple—choice questions. There are five answers and you get full credit of six points for a correct answer, two points for a blank and no credit for a wrong answer. The highest possible score on this test is 150. A score of 100 entitles the contestant to take the next exam, the AIME.

The AIME is an exam with 15 questions that are much more difficult than the AMC 12 questions. Each answer is a number between 0 and 999 so guessing is virtually impossible. Each correct answer is worth 10 points and there is no penalty for guessing.

This year a combined score of about 233 from the AMC 12 and the AIME qualified the student for the USAMO contest, which is the tryout for the United States IMO team (International Math Olympiad), About 250 qualified to take the USAMO. Clicking on the USAMO tab and selecting from the menu on the left side of the screen, you can find the list of qualifiers for the USAMO test.

The top 12 scorers on the USAMO become candidates for the IMO team that trains in Nebraska for three weeks, and from which 6 are chosen for the final team.

For all the contest tabs (AMC 12, USAMO, etc,) if you click and then select archives you will find extensive statistics for the results of the contests for this year and also previous years. Among the statistics are gender statistics that are quite revealing. At the start of the contest, roughly equal numbers of males and females are invited by their respective schools to take the AMC tests.

The 100 score qualifying line changes this demographic considerably and a high percentage of the AIME qualifiers are male. Of the 250 or so USAMO qualifiers, a very high percentage are male, as can be ascertained from the statistics or from looking up the individual names which are listed by states. If you look over the last few years at the top 24 performers on the USAMO you will find very few girls names. This year was one of the few years in which a girl qualified for the United States IMO team.

The tests are completely fair. With the exception of the USAMO and IMO, they are graded by computer so there is no room for subjectivity. In virtually all the schools that take these tests seriously there are math teams where girls are encouraged to participate. The results are what they are. I offer no explanation as to why the top performers are predominantly male.

We live in a competitive world. In the long run we had better start rewarding academic talent if we hope to continue to compete with the rest of the world.

It is incumbent on our society to take a hard look at what we are doing in our schools. In the face of extensive documentation of massive underperformance by boys as measured by potential vs. achievement, and the continued demonstration of stiff competition from overseas as evidenced in international mathematics competitions, the performance of boys in mathematics should be a source of pride.

Yet because of a prevailing ideology of male oppression, the achievements of males at the most elite levels of mathematical competition are seen as the victimization of females. We see the success of men as a failure to encourage women. And so rather than focusing on producing the best possible mathematicians regardless of gender, we focus on making sure that men do not outperform women.

At a time when boys are falling behind girls on almost any measure of either achievement or dysfunction, more money will be poured into programs designed solely for women. This will be the future legacy of Larry Summers' failed effort to raise legitimate questions about sex and achievment.

*Jonathan Cohen teaches mathematics at DePaul University.*

After decades of efforts to encourage women to pursue math and science, the most enduring accomplishment may be the continuing downhill trend in the academic performance of boys. The *Boston Globe* reported that a male high school student is suing his school for alleged discrimination against boys. Through summer programs in science for girls, affirmative action hiring by university science departments, consciousness—raising programs for parents designed to educate them on how to create a fairer school environment for their daughters, plenty of time, attention and money has been lavished on female achievement.

In spite of the vast efforts to rescue the nation's girls from an epidemic of low self—esteem, it is boys who continue to surpass girls in almost every measure of dysfunction, from suicide and juvenile delinquency, to substance abuse and academic failure. In my son's high school graduation class, only three of the top nineteen students were boys and only twenty of the top ninety—five. But such a failure of boys to compete effectively with girls would not have been predicted from the list of 32 National Merit Scholarship semi—finalists, of which fully half were boys.

Four years earlier at his middle school graduation, more than 70% of the honor role students were girls. This did not prevent the school from requiring seven weeks of workshops on gender issues in the students' seventh grade homeroom classes to show how girls were short changed by a pervasive gender bias that supposedly hindered their progress in schools. Nor did it stop the school from distributing a pamphlet to a group of parents written by researchers alleging extensive gender bias in the teaching of mathematics to middle school students. And definitely nowhere mentioned was the extensive debunking of this gender bias movement which dominates American education in Christina Hoff Sommers' book *The War Against Boys*.

There is one area in academics in which males continue to outperform females, and that is at the most elite levels of achievement in mathematics. A year has passed since Lawrence Summers, the outgoing President of Harvard University, set off a firestorm of by speculating that gender differences in cognitive skills were among possible reasons for the dearth of women in the sciences at elite institutions such as Harvard.

One of those attending the conference, Nancy Hopkins, was so upset by his remarks that she almost fainted. No stranger to complaints about anti—female bias in the sciences, Dr. Hopkins had previously attained fame for feathering her academic nest by alleging gender victimization at the hands of her employer, the Massachusetts Institute of Technology. Though the remarks of Summers were made off the record and though he had said it was not the most likely reason for the paucity of women in the hard sciences at Harvard, the recriminations that followed led to faculty censure and a vast commitment of resources to alleviate the disproportionate numbers.

A study on the relative numbers of males and females at the top end in mathematics looks at gender statistics for elite performers in mathematics, where almost no women are represented among mathematicians in the National Academy of Science, winners of the Field's medal (roughly the equivalent of a Nobel prize in mathematics that is awarded every four years) and the Putnam Competition that is a mathematical competition for college students. The author points out that membership in any of these elite groups is so small that we are talking about people who are almost five standard deviations above the mean for mathematical ability or achievement. By implication, membership in the science departments of the top ten research university math departments represents people who are similarly several standard deviations above the mean. So what we are looking at is not gender difference in mean but in standard deviation.

Another interesting place to look for gender statistics relating to high level performance in mathematics is in the published results of the extensive mathematical competitions organized by the Mathematical Association of America. The American Mathematics Competitions are a series of math contests for high school students culminating in selecting a United States team for the International Math Olympiad. The participants are chosen from the top mathematics students at high schools throughout the country. If you open the above link you will find a line of tabs that are links to the different contests.

The AMC 12 A and B is a test with 25 multiple—choice questions. There are five answers and you get full credit of six points for a correct answer, two points for a blank and no credit for a wrong answer. The highest possible score on this test is 150. A score of 100 entitles the contestant to take the next exam, the AIME.

The AIME is an exam with 15 questions that are much more difficult than the AMC 12 questions. Each answer is a number between 0 and 999 so guessing is virtually impossible. Each correct answer is worth 10 points and there is no penalty for guessing.

This year a combined score of about 233 from the AMC 12 and the AIME qualified the student for the USAMO contest, which is the tryout for the United States IMO team (International Math Olympiad), About 250 qualified to take the USAMO. Clicking on the USAMO tab and selecting from the menu on the left side of the screen, you can find the list of qualifiers for the USAMO test.

The top 12 scorers on the USAMO become candidates for the IMO team that trains in Nebraska for three weeks, and from which 6 are chosen for the final team.

For all the contest tabs (AMC 12, USAMO, etc,) if you click and then select archives you will find extensive statistics for the results of the contests for this year and also previous years. Among the statistics are gender statistics that are quite revealing. At the start of the contest, roughly equal numbers of males and females are invited by their respective schools to take the AMC tests.

The 100 score qualifying line changes this demographic considerably and a high percentage of the AIME qualifiers are male. Of the 250 or so USAMO qualifiers, a very high percentage are male, as can be ascertained from the statistics or from looking up the individual names which are listed by states. If you look over the last few years at the top 24 performers on the USAMO you will find very few girls names. This year was one of the few years in which a girl qualified for the United States IMO team.

The tests are completely fair. With the exception of the USAMO and IMO, they are graded by computer so there is no room for subjectivity. In virtually all the schools that take these tests seriously there are math teams where girls are encouraged to participate. The results are what they are. I offer no explanation as to why the top performers are predominantly male.

We live in a competitive world. In the long run we had better start rewarding academic talent if we hope to continue to compete with the rest of the world.

It is incumbent on our society to take a hard look at what we are doing in our schools. In the face of extensive documentation of massive underperformance by boys as measured by potential vs. achievement, and the continued demonstration of stiff competition from overseas as evidenced in international mathematics competitions, the performance of boys in mathematics should be a source of pride.

Yet because of a prevailing ideology of male oppression, the achievements of males at the most elite levels of mathematical competition are seen as the victimization of females. We see the success of men as a failure to encourage women. And so rather than focusing on producing the best possible mathematicians regardless of gender, we focus on making sure that men do not outperform women.

At a time when boys are falling behind girls on almost any measure of either achievement or dysfunction, more money will be poured into programs designed solely for women. This will be the future legacy of Larry Summers' failed effort to raise legitimate questions about sex and achievment.

*Jonathan Cohen teaches mathematics at DePaul University.*