What do we know about differences in how girls and boys learn?
There are significant
differences in the ways girls and boys learn, differences which are more substantial than age differences in many ways. In other words, a 7-year-old girl and a 7-year-old boy differ, on average, on parameters such as "How long can you sit still, be
quiet, and pay attention?" Those differences between a same-age girl and same-age boy are larger than differences between, say, a 7-year-old girl and a 9-year-old girl. Most American schools segregate kids on the basis of age differences:
they put 7-year-olds in one classroom and 9-year-olds in another classroom. And yet, on some parameters - such as how long
a child can sit still, be quiet, and pay attention - the sex differences (e.g. between the average 7-year-old girl and the average 7-year-old boy) are larger than the age differences
(e.g. between the average 7-year-old girl and the average 9-year-old girl).
The differences appear to be greatest among the YOUNGEST children. If you visit an all-girls kindergarten and then an all-boys kindergarten, you will be struck by how differently the children learn. If you visit
an all-girls 12th-grade classroom and an all-boys 12th-grade classroom, the differences are more subtle. Some 6-year-old boys just have to stand and make buzzing noises in order to learn. It's unusual to find 17-year-old boys
who absolutely have to stand and make buzzing noises in order to concentrate.
There are gender-specific personality traits which affect how children learn.
In the 1960's and 1970's and even into the 1980's, it was fashionable to assume that gender differences in personality were "socially constructed." Back then, many psychologists thought that if we raised children differently --
if we raised Johnny to play with dolls and Sally to play with trucks -- then many of these gender differences would vanish.
However, cross-cultural studies over the past 30 years have provided little support for this hypothesis. On the contrary, a report from the National Institutes of Health (NIH) found that
gender differences in personality were remarkably robust across all cultures studied, including China, sub-Saharan Africa, Malaysia, India, the Philippines, Indonesia, Peru, the United States, and Europe (including specific studies in Croatia, the Netherlands, Belgium, France, Germany, Italy, Norway, Portugal, Spain, Yugoslavia and western Russia). "Contrary to predictions from the social role model, gender differences were most pronounced in European and American cultures in which traditional sex roles are minimized," the authors concluded.
Source: Paul Costa, Antonio Terracciano, & Robert McCrae, "Gender differences in personality traits across cultures: robust and surprising findings," Journal of Personality and Social Psychology, volume 81, number 2, pp. 322-331, 2001.
Educational psychologists have consistently found that girls tend to have higher standards in the classroom, and evaluate their own performance more critically. Girls also outperform boys in school (as measured by students' grades), in all subjects and in all age groups.
Sources: Alan Feingold, "Gender differences in personality: a meta-analysis," Psychological Bulletin, volume 116, pages 429-456, 1994. See also the important paper by Diane Ruble and her associates, "The role of gender-related processes in the development of sex differences in self-evaluation and depression, Journal of Affective Disorders, volume 29, pages 97-128, 1993. For documentation of the fact that girls now outperform boys (as measured by report card grades) in all subjects and age groups, see the chapter by Dwyer and Johnson entitled "Grades, accomplishments, and correlates" in the book Gender and Fair Assessment edited by Willingham & Cole, published by Laurence Erlbaum (Mahwah, NJ), 1997, pp. 127-156.
Because girls do better in school (as measured by report card grades), one might imagine that girls would be more self-confident about their academic abilities and have higher academic self-esteem. But that's not the case. Paradoxically, girls are more likely to be excessively critical in evaluating their own academic performance. Conversely, boys tend to have unrealistically high estimates of their own academic abilities and accomplishments.
Source: Eva Pomerantz, Ellen Altermatt, & Jill Saxon, "Making the grade but feeling distressed: gender differences in academic performance and internal distress," Journal of Educational Psychology, volume 94, number 2, pages 396-404, 2002.
We arrive at one of the most robust paradoxes teachers face: the girl who gets straight A's but thinks she's stupid and feels discouraged; the boy who's barely getting B's but thinks he's brilliant. Consequently, the most basic difference in teaching style for girls vs. boys is that you want to encourage the girls, build them up, while you give the boys a reality check: make them realize they're not as brilliant as they think they are, and challenge them to do better.
Educational psychologists have found fundamental differences in the factors motivating girls vs. factors motivating boys. Researchers have consistently found that "girls are more concerned than boys are with pleasing adults, such as parents and teachers" (Pomerantz, Altermatt, & Saxon, 2002, p. 397). Most boys, on the other hand, will be less motivated to study unless the material itself interests them.
Source: E. T. Higgins, "Development of self-regulatory and self-evaluative processes: costs, benefits, and trade-offs." In M. R. Gunnar & L. A. Sroufe (editors), Self processes and development, Minneapolis: University of Minnesota Press, 1991, pp. 125-165. See also the more recent paper by Eva Pomerantz and Jill Saxon, "Conceptions of ability as stable and self-evaluative processes: a longitudinal examination," Child Development, volume 72, pages 152-173, 2001.
Girls and boys experience academic difficulties very differently. Here are the findings of Eva Pomerantz, Ellen Alterman, and Jill Saxon (2002, p. 402):
"Girls generalize the meaning of their failures because they interpret them as indicating that they have disappointed adults, and thus they are of little worth. Boys, in contrast, appear to see their failures as relevant only to the specific subject area in which they have failed; this may be due to their relative lack of concern with pleasing adults. In addition, because girls view evaluative feedback as diagnostic of their abilities, failure may lead them to incorporate this information into their more general view of themselves. Boys, in contrast, may be relatively protected from such generalization because they see such feedback as limited in its diagnosticity."
Girls tend to look on the teacher as an ally. Given a little encouragement, they will welcome the teacher's help. A girl-friendly classroom is a safe, comfortable, welcoming place. Forget hard plastic chairs: put in a sofa and some comfortable bean bags. Let the girls address their teacher by her (or his) first name.
Context enhances learning for most girls, but often just bores the boys. The choir director of the National Cathedral School for Girls and the St. Alban's School for Boys told us that when he's teaching the high school girls a new song, he'll start by sharing a story about why the composer wrote this piece, who it was written for, or maybe how the choir director himself felt 20 years ago when he goofed the solo part. "Giving the girls some context, telling them a story about the piece, gets them interested. The boys are just the opposite," he said. "If you start talking like that with the boys, they'll start looking at their watches, they'll start getting restless. Then one of them will say, �Can we please just get on with it already? Can we please just learn the song already?'"
Teaching math and science
Best practices for teaching math differ significantly for girls and boys - particularly in arithmetic, algebra, and number theory. With boys, you can stimulate their interest by focussing on the properties of numbers per se. With girls, you want to tie what you're teaching into the real world. Keep it real and keep it relevant. Let's consider how you would teach the same topic -- Fibonacci series as an introduction to number theory -- to girls and to boys.
Teaching Fibonacci numbers to boys:
Pose this question:
"I'm thinking of a number between 1 and 2. The reciprocal of that number is equal to that same number minus 1. We can write that statement in equation form, like this:
1/x = x - 1
Can you tell me what number I'm thinking of?"
After a couple minutes, one of the boys will figure out that the equation above can be simplified if you multiply both sides by x, yielding:
1 = x2 - x
Subtracting 1 from both sides yields:
x2 - x - 1 = 0
You can then use the quadratic formula to solve for x:
x = (1 +/- [squroot of 5])/2
We're looking for a number between 1 and 2, so we choose the positive solution:
= (1 + [squroot of 5])/2
Tell the boys that mathematicians refer to this number as Phi. Sure enough, this number Phi has the characteristic we were looking for: the reciprocal of this number exactly equals this number minus 1:
= 0.5 + 1.11803398874989. . .
= 1.61803398874989 . . .
1/1.61803398874989. . . = 0.61803398874989. . .
Now, you change the subject (or appear to change the subject). You tell them about the Fibonacci series. Recall that a Fibonacci series is formed by adding two numbers to yield a third number, and reiterating the process to form a sequence. The simplest Fibonacci sequence is:
1 + 1 = 2
This yields the series: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 . . .
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
Now, ask your boys to take each number in the Fibonacci series and divide it by the number before it, starting with 3, and list their answers.
3/2 = 1.5
Now you can point out to the boys (if they haven't noticed already) that this process seems to be converging on Phi. Why is that? you ask them.
5/3 = 1.666. . .
8/5 = 1.6
13/8 = 1.625
21/13 = 1.61538 . . .
34/21 = 1.61905. . .
55/34 = 1.61764 . . .
89/55 = 1.61818 . . .
144/89 = 1.617977 . . .
233/144 = 1.61805. . .
While they're thinking about that, draw a circle. Inscribe a pentagon within the circle. Then draw an isosceles triangle within the pentagon. The hypotenuse of the triangle (line AB in the figure at left) is exactly equal to the base of the triangle (line BC) multiplied by Phi. Why is that?
While the boys are pondering this question, you can step over to the girls' classroom to cover the same material.
Teaching Fibonacci numbers to girls
In order to get girls the same age excited about "pure" math and geometry, you need to connect it with the real world. Remember that in girls, geometry and "pure" math appear to be instantiated in the cerebral cortex, the same division of the brain which mediates language and higher cognitive function. So you need to tie the math into other higher cognitive functions. Here's how you might teach the same lesson about Phi and Fibonacci numbers to girls. You'd begin by explaining how a Fibonacci series is formed:
1 + 1 = 2
And so forth. You write down the first twelve numbers in the Fibonacci series: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 . . . In preparation for this session, you've asked your girls to bring in any of the following: artichokes, sunflowers, pineapples, and pinecones.
For your artichokes, pinecones, etc., the number of rows counted vertically or obliquely will, again, be a number in the Fibonacci series. You can get more examples like these from the book Fascinating Fibonacci by Trudi Hammel Garland. Older girls may enjoy The Golden Ratio: the story of Phi, the world's most astonishing number by Mario Livio. Or you might even let them read Dan Brown's suspense thriller The DaVinci Code, and challenge them to verify or invalidate each of the many claims made in that book about Phi and the Fibonacci series. Show them examples of natural phenomena which manifest Phi, phenomena such as a dying leaf or a spiral nebula. At this point, you might also mention the fact that
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
Phi - 1 = 1/Phi
But don't expect the girls to ooh and aah over that fact the way the boys do. 12-year-old girls are likely to be more interested in the real-world applications of number theory than in remote abstractions. The girls are also more likely than the boys to be interested in the beliefs of the ancient Pythagoreans regarding the magical and mystical properties of Phi.
Now these girls will start asking questions. Why do numbers in the Fibonacci series keep showing up when you count the petals on a delphinium, or the bracts on a pinecone? Why is it the case that a dying poinsettia leaf and a spiral nebula share similar structural features? How can abstract number theory explain these similarities? And you will have accomplished something really worthwhile: you've got a classroom of 12-year-old girls excited about number theory.
This example illustrates an important point. There are no differences in what girls and boys can learn. But there are big differences in the best way to teach them. At the end of the day, you will have taught both girls and boys about the properties of Phi, using the Fibonacci series as an introduction to number theory. Girls and boys are equally capable of learning that material. But if you teach that material the way it's usually taught (the way we taught it to the boys in my example above), then many of the girls will tune out and be bored. Conversely, if you bring in pinecones for the boys, many of the boys will snicker and start throwing the pinecones around like hand grenades. "Incoming!"
Regarding "story problems": "Story problems" are a good way to teach algebra to many girls. Putting the question in story format makes it easier for girls to understand, and more interesting as well. "Story problems" often don't work as well for boys; indeed, for many boys,
embedding the algebra question in a linguistic context makes the problem more difficult.