What's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success (16 page)

The differences that have been found between girls and boys in mathematics and physics classes do not suggest that all girls behave in one way and all boys in another. Indeed, Zohar and Sela found that one-third of the boys they interviewed also expressed strong preferences for a deep, connected understanding. But they, like I, found that girls consistently expressed such preferences in higher numbers and with more intensity. Such gender differences are interesting
, and they may also hold the key to understanding women’s low levels of participation in STEM (science, technology, engineering, and mathematics) subjects
.

The idea that girls and women value a different type of knowing was famously proposed by Carol Gilligan, an internationally acclaimed psychologist and author. In Gilligan’s book
In a Different Voice,
she claimed that women are likely to be “connected thinkers,” preferring to use intuition, creativity, and personal experience when making moral judgments. Men, she proposed, are more likely to be “separate” thinkers, preferring to use logic, rigor, absolute truth, and rationality when making moral decisions.
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Gilligan’s work met a lot of resistance, but it also received support from women who identified with the thinking styles she described. Some years later a group of researchers developed Gilligan’s distinctions further, claiming that
men and women differ in their ways of knowing, more generally. Psychologists Mary Belenky, Blythe Clinchy, Nancy Goldberger, and Jill Tarule,
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proposed stages of knowing, and again claimed that men tended to be separate thinkers and women connected thinkers. The authors did not have a lot of data to support their claims that women and men think differently, and they received considerable opposition, which is understandable given that they were suggesting fundamental distinctions in the way women and men come to
think
and
know.
When I reported my own findings, that girls were particularly disadvantaged by traditional instruction that did not give them access to knowing how and why, I also received resistance. Indeed, some of my colleagues challenged me, saying that it was not possible that girls would have different preferences from boys in such a cognitive domain. But there are many reasons why girls may develop different preferences and a stronger push for understanding, ranging from known brain differences to vastly different socialization processes. For me the question of why girls pursue a depth of understanding in greater numbers than boys do is less important than the question of how we can change mathematics environments so that all students can understand deeply, and so that girls and boys not only can achieve at equal levels but can also pursue STEM subjects in equal numbers.

Classes in which students discuss concepts, giving them access to a deep and connected understanding of math, are good for girls and for boys. Boys may be willing to work in isolation on abstract rules, but such approaches do not give many students, girls or boys, access to the understanding they need. In addition, high-level work in mathematics, science, and engineering is not about isolated, abstract-rule following, but about collaboration and connection making.

There are plenty of boys who value and need connections
and communication and who choose other subjects because mathematics does not offer these, just as there are girls who can happily work in isolation without mathematical connections. If mathematics teaching included opportunities for discussion of concepts, for depth of understanding, and for connecting between mathematical concepts, then it would be more equitable and good for both sexes, and it would give a more accurate depiction of mathematics as it is practiced in high-level courses and professions.

Where Are We Now?

Given the ways in which mathematics is commonly taught and the preferences of many girls for deep understanding and inquiry, it is perhaps surprising that girls do as well as they do in mathematics—and they do perform very well. In 2010, women made up 42 percent of math majors and 41 percent of those taking masters degrees in mathematics and statistics. These numbers do not show equality and are not ones we should be complacent about, but they may show higher proportions of women than many think. Psychologists Janet Hyde, Elizabeth Fennema, and Susan Lamon produced a meta-analysis
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of studies that have investigated gender differences in achievement, combining more than one hundred studies involving three million subjects. Even in 1990, with such a vast database, they found very small differences between girls and boys, with a huge amount of overlap.
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Hyde and her colleagues argued that gender differences were too small to be of any importance and that they have been overplayed in the media, which has helped to create stereotypes that are damaging.

In most examinations in the United States there are also no recorded gender differences in mathematics. The small performance differences that exist take place only on the SAT
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and
the AP examinations (in 2002 the average score of girls was 3.3 compared to boys’ 3.5). In England, a country with a similar education system, girls used to achieve at lower levels than boys on examinations, but now they achieve at higher levels in all subjects. In fact, the results for girls and boys in England have shifted in interesting ways over time. In England, at age sixteen, almost all students take the General Certificate of Secondary Education (GCSE) examination in mathematics. As mathematics is compulsory until age sixteen, equal numbers of boys and girls take this examination. In the 1970s, boys passed the mathematics GCSE examination
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in higher numbers and achieved more of the highest grades; in the 1990s, girls and boys passed the exam in equal numbers but boys achieved more of the highest grades. By the 2000s, girls were passing the exam at higher rates than boys and achieving more of the highest grades.
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In England, girls now perform at equal or higher levels than boys in mathematics and physics, on the GCSE and beyond, and they now achieve more of the highest grades in the most demanding high-level examinations.

Girls are doing very well now in the United States, England, and many other countries, but their strong performance hides a worrying fact—most mathematics classrooms are not equitable environments and girls often do well despite inequitable teaching. This is the reason that girls often opt out of mathematics even when they are achieving at high levels and even though a mathematical or scientific career could be very good for them. In high-level courses and mathematical jobs, the statistics are quite alarming. In 2009, women made up only 31 percent of mathematics PhDs, and in 2005 only 18 percent of mathematics faculty were women. The low numbers of women working as researchers and scientists across Europe is one of the priority areas for the European Union. Fifty-two percent of higher education graduates across Europe are women, but only 25 percent
of these women take science, engineering, or technology subjects. Girls do well in math and science because they are capable and conscientious, but many do so through endurance, and math classroom environments are far from being equitable. Indeed, it is the impoverished version of mathematics that is offered to students that turns many people, female and male, away from the subject.

Other Barriers

Of course, the lack of opportunity to inquire deeply is not the only barrier to girls and women in mathematics and science. Mathematics classrooms in schools are considerably less gender stereotyped than they were twenty years ago, when sexist images prevailed in textbooks and mathematics teachers were found to give boys more attention, reinforcement, and positive feedback,
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but still girls in some classrooms experience stereotyped attitudes and behaviors, contributing to their low interest and participation in math. Some school mathematics and science classrooms are also highly competitive, which deters many young women.

In university math departments the situation is worse. Abbe Herzig, a professor at the State University of New York at Albany, has produced evidence of the ways in which the climates of university mathematics departments can be icy cold toward women and minority students.
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Herzig notes that women face many issues including sexism, stereotyped ideas about women’s capabilities, feelings of isolation, and lack of role models,
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especially at the graduate level. By and large, math departments in the United States remain a male preserve where the underrepresentation of women among students is eclipsed only by the underrepresentation of women among the faculty. There could not be a clearer statement about the absence of women
in the history of the department or the lack of concern for their sense of inclusion now.

The teaching in mathematics departments can also be highly rule-based, which again denies girls the opportunity to ask why and how, as Julie, one of the young women who had given up on her mathematics degree at Cambridge University, explained to me:

I think it was my fault because I did want to understand every single step and I kind of wouldn’t think about the final step if I hadn’t understood an in-between step. . . . I couldn’t really see
why
they,
how
they got to it. Sometimes you want to know; I actually wanted to know.

For Julie, who had won awards for her mathematics achievement prior to attending Cambridge, her desire to understand how and why methods worked stopped her from going forward with the subject.

Societal Stereotypes

In addition to the problems in university mathematics departments and schools, young women and men suffer from the stereotypes that are perpetuated in society, particularly by the media. Ideas such as girls being too nurturing and caring to work in the hard sciences are based on incorrect ideas about women and about the ways mathematics and sciences work. Girls and women do not need a softer version of mathematics. Indeed, the sorts of inquiries women need could be said to epitomize true mathematical work, with its need for proof and rigorous analysis of ideas.

When girls went ahead of boys in mathematics and science (and all other subjects) in England, alarm bells rang everywhere.
Suddenly there was government money to look into gender relations in math and science, something that had never happened when girls were underachieving. It was interesting that, whereas people had always decided that the underachievement of girls in math and science was due to their intellect, when it was boys who were underachieving, people looked to external reasons—with suggestions that the books must be biased, the teaching approaches favored girls, or that teachers must be encouraging girls more. Nobody suggested that boys did not have the brains for math or science. Michele Cohen, a historian, gives an interesting perspective on the tendency of people to locate girls’ underachievement
within
girls. She points out that this has been done throughout history and that in the seventeenth century scholars went to enormous lengths to explain away the achievement of girls and the working classes, as it was boys, specifically upper-class boys, who were believed to possess true intellect. People at that time explained that the superior verbal competence noted among girls was a sign of weakness and that the English gentleman’s reticent tongue and inarticulateness was evidence of the depth and strength of his mind. Conversely, women’s conversational skills became evidence of the shallowness and weakness of their mind.
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In 1787, the Reverend John Bennett, from the Church of England, argued that boys appeared slow and dull because they were thoughtful and deep and because “gold sparkles less than tinsel.”
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The tendency to locate sources of underachievement within girls and to construct ideas about female inadequacy is also characteristic of much of the psychological research on gender. In my interviews with high school students, I frequently encounter stereotypes about the potential of girls and boys. But it is particularly disturbing when I find that ideas about girls being mathematically inferior have come from the reporting of research. In a recent interview with a group of high school
students in California, I asked Kristina and Betsy about gender differences:

JB:
Do you think math is different for boys and girls or the same?

K:
Well, it’s proved that boys are better in math than girls, but in this class, I don’t know.

JB:
Mmm, where do you hear that boys are better than girls?

K:
That’s everywhere—that guys are better in math and girls are, like, better in English.

JB:
Really?

B:
Yeah. I watched it on
20/20
[a television current affairs program] saying girls are no good, and I thought, “Well, if we’re not good at it, then why are you making me learn it?”

The girls refer to a television program that presented the results of research on the differences between the mathematical performance of girls and boys. The problem with some research on equity is not that researchers noted that girls were achieving less than boys, or that girls displayed less confidence in math classrooms, but that such findings were often presented as being due to the nature of girls rather than any external sources. This led educators to propose interventions that were well intentioned but that aimed to change girls. The 1980s spawned numerous programs that were intended to make girls more confident and challenging.
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The idea behind such programs is often good, but they also lay the responsibility for change at the feet of the girls rather than mathematics teaching environments or the broader social system. On July 5, 1989, the
New York Times
ran the headline “Numbers Don’t Lie: Men Do Better than Women” with an article discussing gender differences in SAT scores. But this article, like many others, used performance
differences to suggest that women were mathematically inferior, rather than questioning the teaching and learning environments—as well as the biases they themselves were helping to create—that caused the underachievement of women. Now that women are ahead in most areas, it is interesting to note the absence of any analogous headlines proclaiming women’s innate superiority.