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Joined: Aug 2010
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Regarding the extreme tails, I mentioned this earlier, but will drop the actual study here: http://www.pnas.org/content/106/22/8801.longAbstract
Using contemporary data from the U.S. and other nations, we address 3 questions: Do gender differences in mathematics performance exist in the general population? Do gender differences exist among the mathematically talented? Do females exist who possess profound mathematical talent? In regard to the first question, contemporary data indicate that girls in the U.S. have reached parity with boys in mathematics performance, a pattern that is found in some other nations as well. Focusing on the second question, studies find more males than females scoring above the 95th or 99th percentile, but this gender gap has significantly narrowed over time in the U.S. and is not found among some ethnic groups and in some nations. Furthermore, data from several studies indicate that greater male variability with respect to mathematics is not ubiquitous. Rather, its presence correlates with several measures of gender inequality. Thus, it is largely an artifact of changeable sociocultural factors, not immutable, innate biological differences between the sexes. Responding to the third question, we document the existence of females who possess profound mathematical talent. Finally, we review mounting evidence that both the magnitude of mean math gender differences and the frequency of identification of gifted and profoundly gifted females significantly correlate with sociocultural factors, including measures of gender equality across nations.
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I have actually come across one or two studies in this general direction. There is some good information there. Unfortunately, I find it troubling that their definition of mathematically talented is 95th percentile (or even 99th percentile). Dr. Stanley's work focused on children who were really at the extreme tail (even well beyond the 99.9 subtest standard used by Davidson). At the nationally competitive level, that's who we are dealing with.
Even my DD, who is not mathematically talented, is consistently at above 99th percentile. She is just not at the extreme like her brother or even her mother.
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Two recent studies directly address the question of whether greater male variability in mathematics is a ubiquitous phenomenon. Machin and Pekkarinen (19) reported that the M:F VR in mathematics was significantly >1.00 at the P < 0.05 level among 15-year-old students in 34 of 40 countries participating in the 2003 PISA and among 13-year-old students in 33 of 50 countries participating in the 2003 Trends in International Mathematics and Science Study (TIMSS). However, these data also indicated that the math VR was significantly less than or insignificantly different from 1.00 for some of the countries that participated in these assessments (e.g., Table 2), a finding inconsistent with the Greater Male Variability Hypothesis That finding is not inconsistent with greater male variability.
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...I find it troubling that their definition of mathematically talented is 95th percentile (or even 99th percentile). Dr. Stanley's work focused on children who were really at the extreme tail (even well beyond the 99.9 subtest standard used by Davidson). At the nationally competitive level, that's who we are dealing with.
Even my DD, who is not mathematically talented, is consistently at above 99th percentile. She is just not at the extreme like her brother or even her mother. Performance on a standardized test or in a math competition seems like a narrow definition of math talent to me. Both of these things require speed; what about people who prefer to approach problems s-l-o-w-l-y and consider many different aspects of an idea? Many things in our society (including chess competitions, tenure decisions, and so) reward speed (e.g. how fast can you make your next move?? How many publications can you get out in the next 5 years??). IMO, when we fail to let people move slowly, we fail as a society in a very important area.
Last edited by Val; 02/11/14 02:17 PM.
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...I find it troubling that their definition of mathematically talented is 95th percentile (or even 99th percentile). Dr. Stanley's work focused on children who were really at the extreme tail (even well beyond the 99.9 subtest standard used by Davidson). At the nationally competitive level, that's who we are dealing with.
Even my DD, who is not mathematically talented, is consistently at above 99th percentile. She is just not at the extreme like her brother or even her mother. Performance on a standardized test or in a math competition seems like a narrow definition of math talent to me. Both of these things require speed; what about people who prefer to approach problems s-l-o-w-l-y and consider many different aspects of an idea? Many things in our society (including chess competitions, tenure decisions, and so) reward speed (e.g. how fast can you make your next move?? How many publications can you get out in the next 5 years??). IMO, when we fail to let people move slowly, we fail as a society in a very important area. Actually, Val, I don't disagree with you on this point. The standardized tests and competitions are one way to catch many of those with math talents. Certainly, some are missed, especially twice exceptional kids. At the same time, speed does matter in some situations. It may seem unfair, but if I were hiring, I would give preference to an applicant who can think and act fast, all other abilities being equal. More to the point, my post is consistent with yours to the extent that I don't believe doing well on a standardized test or math competition (at the 95th or even 99th percentile) necessarily translates to math talent. That was my point regarding DD. My judgment was not based just on standardized test scores and math competition awards but on more informal demonstrations of DS versus DD's innate abilities from toddlerhood. DS ponders independently and arrives at math concepts without being taught. DD needs to be taught - she learns very quickly and is very bright but that innate talent is missing. Incidentally, I am not so presumptuous as to assume that DS will ultimately fall within that extreme tail either as he is no Terrence Tao - only time will tell whether his minor math talent develops into a significant talent as an adult.
Last edited by Quantum2003; 02/11/14 03:00 PM.
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Ahh. Fair enough. Thanks.
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Even my DD, who is not mathematically talented, is consistently at above 99th percentile. She is just not at the extreme like her brother or even her mother. Am I the only one who found it amusing that "not mathematically talented" and "above 99th percentile" were in the same sentence?
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No, for the simple reason that it's just not possible to control for all the cultural factors, so you can't do a study using a control group that does not exist.
However, we DO know that cultural attitudes about gender stereotypes have been changing over time, and we've seen that the performance gap changes over the same time period. We also know that cultural attitudes about gender stereotypes are different from culture to culture... and sure enough, we find that the performance gaps reflect those different attitudes as well.
So basically, we've proven beyond reasonable doubt that stereotypes play a significant role in gender differences in math, and in chess. We know that as attitudes skew closer to equality, the performance also skews closer to equality. That's a closed case. All good points. I agree with most of what you said. The question I have is whether there is still gender stereotyping going on in math today (leave chess aside for a moment), given that girls outperform boys in school. My limited view is that there is no longer gender stereotyping in math today. In our high school, there are as many girls in honors math as there are boys, and perhaps even more girls get As than boys. But interestingly, when it comes to competition math, the boys still dominate. And nationally, on the SAT, the mean score for boys is about 30 points higher than girls. I can't explain that either. All that's left now is to hypothesize about an imaginary culture in which no gender stereotypes exist, would some biological factor pre-select males for dominance at the very highest echelons of math and chess?
My hunch is: no. I have no opinion of what "truth" actually is. I would happily accept that there are no differences, or that there are inherent differences.
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Even my DD, who is not mathematically talented, is consistently at above 99th percentile. She is just not at the extreme like her brother or even her mother. Am I the only one who found it amusing that "not mathematically talented" and "above 99th percentile" were in the same sentence? No-- I also found it amusing that "talented" was equated to "autodidactic" in the same post. I was not aware that those things were necessarily synonymous. 
Schrödinger's cat walks into a bar. And doesn't.
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Even my DD, who is not mathematically talented, is consistently at above 99th percentile. She is just not at the extreme like her brother or even her mother. Am I the only one who found it amusing that "not mathematically talented" and "above 99th percentile" were in the same sentence? Glad to be of service. Definitions and standards make a difference. I don't equate high IQ and/or high achievement with math talent. In my experience, it is possible to be both without having math talent and perhaps more controversial, to be without neither (at least not super high) and yet have a certain math talent. My DD is very smart and she is able to leverage that to do very well in math, including 99 percentile on measures like MAP (250 Fall 5th grade). It is very possible that she will maintain that level of achievement through high school. However, she is only 10 so it is also possible that her "ability/achievement" will decline relatively speaking as she approaches high school. Elementary and even middle school math do not necessarily draw upon the same skill set as high school/college math. Many students excel in elementary and even middle school before hitting a wall in high school. Conversely, some genuinely talented math students struggle in elementary and middle school and sometimes even high school but soar in college once they hit calculus, differential equations, linear algebra and higher level math. DS is technically/numerically more verbally gifted than DD but DD is by far more talented as a writer. Talent is not high IQ or high achievement on standardized tests.
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