Women, men and mathematics
Oh boy.You may recall, back in 2005, some controversial statements from Harvard's President Laurence Summers on the issue of the underrepresentation of women among the faculty of hard science and mathematics departments in top tier research and higher education institutions. Most of the responses to this event were underinformed on the current social science evaluation of factors as well as facts, but one exception to this trend was a debate held at Harvard on The Science of Gender and Science between the cognitive scientists Steven Pinker and Elizabeth Spelke. Fortunately for me, and maybe you, they filmed and transcribed this event, so feel free to catch up if you have a couple of hours before reading my responses.
They spend most of their time debating mathematical aptitude and gender differences, a subject that is near and dear to my mathematically sensitive heart. Both parties agree that there are statistical differences (i.e. trends, not absolute binaries) between the sexes that have biological bases. The conflict in the debate lies in how we can measure mathematical ability, and what impact is made by implicit descrimination.
As a mathematically inclined female with experience, at least as an undergraduate, in the field of mathematics, I was surprised at both the conclusions of the studies they cited and at their assumptions about success in mathematics, and hard science, in higher education and academia.
1. Apparently approximately half of the mathematics degrees awared at the undergraduate level are awarded to women, at least in the States. That is news to me. I was always in the minority in my math classes at McGill, and when the class size got under 12, I was always the ONLY female in the class (teacher included).
2. Pinker seems to think, like many others, that visual rotation of objects is some fundamental part of most higher mathematics. What? First off, from tutoring people of both sexes, I have the impression that there are usually different approaches to understanding the abstract relationships that are the building components of mathematical reasoning, and the analogies need not be strictly or even partially visual. I won't say that my math homework never gave me dreams of dancing polygons, but much of the time I didn't have and didn't need a spatial representation of whatever I was trying to understand. Were spatial metaphores important to the mix of ideas that allowed me to construct these abstract concepts and relations? Undoubtably, not in the same way that spatial rotation is measured by comparing pairs of 2D representations of block structures in a multiple choice test. Often times, what was more important was the number of different logical statements I could keep in mind at any given moment, a matter of memory and perhaps succinctness of metaphores rather than pictures.
3. Spelke suggests that while there are differences in some abilities that relate to how mathematics is evaluated, they do not all point in the same direction. SAT and GRE mathematics tests have struggled to deal with the fact that some kinds of questions seem to favour male students and other favour female students. In order to properly represent
4. This is a matter of exceptions, not rules. As Pinker states, but then ignores, "Most women aren't able to become Harvard mathematics professors because most men aren't able to became Harvard mathematics professors." In the process of the debate, they spent relatively little time exploring what it actually takes to become a professor of mathematics as opposed to a professor of psychology (with strong female representation since the barrier went down) or an accountant (also predominantly female profession as of this last generation of workers). This is forgivable because they are psychologists, not mathematicians, and so don't know what they are talking about, but it still brings up my own questions.
The questions of perception derived biases do come up in my own life. I remember being frustrated from the beginning of my mathematical studies by the fact that most of my peers (i.e. students that were performing comparably well in basic algebra and advanced calculus) had benefited from extensive private study of mathematics prior to beginning this degree. They often had a parent (read father) who was a mathematician or engineer, or had been singled out by a high school math teacher and given extra materials and attention to learn outside of the curriculum. In otherwords, many of my (male) peers had mentors in the field already. While I can explain some of this difference by the fact that I went to public schools rather than private, I do recall getting more of that kind of attention in other subjects, such as english and music, and thus can't really complain. Who knows how much of the difference was circumstance, aptitude, gender bias or obvious overinvolvement in extracurriculars.
Certainly, a big factor in my performance as a math student was a lack of confidence, combined with a fear of competition, which effectively blocked me from working with my peers towards greater understanding. Had I been convinced of my greatness, and had I no alternative source of affirmation, I might have struggled harder and confronted those fears instead of knowingly letting them handicap my education. One fear was tied up in being the sorry representative of this otherwise underperforming sex. I didn't want to be "the girl that couldn't" in the minds of my classmates, for the sake of both my pride and my gender. Oddly enough, I think the resulting bluff worked more often than not, perhaps because most math students have serious confidence issues through assuming everyone else is getting all of this "obvious" material.
Anyway, there are plenty more comments to be made on the debate, but my soup is getting cold.
They spend most of their time debating mathematical aptitude and gender differences, a subject that is near and dear to my mathematically sensitive heart. Both parties agree that there are statistical differences (i.e. trends, not absolute binaries) between the sexes that have biological bases. The conflict in the debate lies in how we can measure mathematical ability, and what impact is made by implicit descrimination.
As a mathematically inclined female with experience, at least as an undergraduate, in the field of mathematics, I was surprised at both the conclusions of the studies they cited and at their assumptions about success in mathematics, and hard science, in higher education and academia.
1. Apparently approximately half of the mathematics degrees awared at the undergraduate level are awarded to women, at least in the States. That is news to me. I was always in the minority in my math classes at McGill, and when the class size got under 12, I was always the ONLY female in the class (teacher included).
2. Pinker seems to think, like many others, that visual rotation of objects is some fundamental part of most higher mathematics. What? First off, from tutoring people of both sexes, I have the impression that there are usually different approaches to understanding the abstract relationships that are the building components of mathematical reasoning, and the analogies need not be strictly or even partially visual. I won't say that my math homework never gave me dreams of dancing polygons, but much of the time I didn't have and didn't need a spatial representation of whatever I was trying to understand. Were spatial metaphores important to the mix of ideas that allowed me to construct these abstract concepts and relations? Undoubtably, not in the same way that spatial rotation is measured by comparing pairs of 2D representations of block structures in a multiple choice test. Often times, what was more important was the number of different logical statements I could keep in mind at any given moment, a matter of memory and perhaps succinctness of metaphores rather than pictures.
3. Spelke suggests that while there are differences in some abilities that relate to how mathematics is evaluated, they do not all point in the same direction. SAT and GRE mathematics tests have struggled to deal with the fact that some kinds of questions seem to favour male students and other favour female students. In order to properly represent
4. This is a matter of exceptions, not rules. As Pinker states, but then ignores, "Most women aren't able to become Harvard mathematics professors because most men aren't able to became Harvard mathematics professors." In the process of the debate, they spent relatively little time exploring what it actually takes to become a professor of mathematics as opposed to a professor of psychology (with strong female representation since the barrier went down) or an accountant (also predominantly female profession as of this last generation of workers). This is forgivable because they are psychologists, not mathematicians, and so don't know what they are talking about, but it still brings up my own questions.
The questions of perception derived biases do come up in my own life. I remember being frustrated from the beginning of my mathematical studies by the fact that most of my peers (i.e. students that were performing comparably well in basic algebra and advanced calculus) had benefited from extensive private study of mathematics prior to beginning this degree. They often had a parent (read father) who was a mathematician or engineer, or had been singled out by a high school math teacher and given extra materials and attention to learn outside of the curriculum. In otherwords, many of my (male) peers had mentors in the field already. While I can explain some of this difference by the fact that I went to public schools rather than private, I do recall getting more of that kind of attention in other subjects, such as english and music, and thus can't really complain. Who knows how much of the difference was circumstance, aptitude, gender bias or obvious overinvolvement in extracurriculars.
Certainly, a big factor in my performance as a math student was a lack of confidence, combined with a fear of competition, which effectively blocked me from working with my peers towards greater understanding. Had I been convinced of my greatness, and had I no alternative source of affirmation, I might have struggled harder and confronted those fears instead of knowingly letting them handicap my education. One fear was tied up in being the sorry representative of this otherwise underperforming sex. I didn't want to be "the girl that couldn't" in the minds of my classmates, for the sake of both my pride and my gender. Oddly enough, I think the resulting bluff worked more often than not, perhaps because most math students have serious confidence issues through assuming everyone else is getting all of this "obvious" material.
Anyway, there are plenty more comments to be made on the debate, but my soup is getting cold.