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### 1Yarrow

For the last few weeks I've had a theory going round in my head, and I'd appreciate some thoughts.

I'm female, just completed a good (first class) Maths masters in the UK. I'd often wondered why it was that Maths was much more popular with boys than girls (on a general level) and generally accepted that I must have a 'male brain' in order to be good at it (people tell me that all the time). Thing is, I'm not sure I subscribe to that anymore. I feel like I do maths intuitively (spotting patterns, that sort oft thing), I can almost sense what the result should be, and I've trained myself to construct to logical argument that gets me there. Also, I'm really bad at taking a set of expressions and following them through logically, until I get a useful picture in my head, and then I feel like I can do anything, I almost read off the picture.

Also, I had no idea that this wasn't normal - I thought everyone had a picture of a numberline in their head that they read the answers off (I've been doing that since I can count) but none of my friends on my course had ever done anything like that. When doing simple mental arithmetic (adding 27 + 18 for example) I picture adding one to another on a numberline and then read off the answer. Most people I talk to picture the physical numbers (digits) in their head, and picture writing out the sum.

I was wondering if maybe my way of doing maths (thinking in pictures and patterns) would be a good way for girls to learn. Girls are supposed to think more intuitively than boys, and I wondered whether it wasn't that girls were generally worse at maths, just that they were being taught in a way that was alien to them, and that only the ones with 'male brains' were any good at it.

Anyway, am I making this up? I would be really interested to hear what you all (especially women mathematicians) think.

Disclaimer: I know nothing about gender psychology and I'm just repeating what I've heard/read.

I'm female, just completed a good (first class) Maths masters in the UK. I'd often wondered why it was that Maths was much more popular with boys than girls (on a general level) and generally accepted that I must have a 'male brain' in order to be good at it (people tell me that all the time). Thing is, I'm not sure I subscribe to that anymore. I feel like I do maths intuitively (spotting patterns, that sort oft thing), I can almost sense what the result should be, and I've trained myself to construct to logical argument that gets me there. Also, I'm really bad at taking a set of expressions and following them through logically, until I get a useful picture in my head, and then I feel like I can do anything, I almost read off the picture.

Also, I had no idea that this wasn't normal - I thought everyone had a picture of a numberline in their head that they read the answers off (I've been doing that since I can count) but none of my friends on my course had ever done anything like that. When doing simple mental arithmetic (adding 27 + 18 for example) I picture adding one to another on a numberline and then read off the answer. Most people I talk to picture the physical numbers (digits) in their head, and picture writing out the sum.

I was wondering if maybe my way of doing maths (thinking in pictures and patterns) would be a good way for girls to learn. Girls are supposed to think more intuitively than boys, and I wondered whether it wasn't that girls were generally worse at maths, just that they were being taught in a way that was alien to them, and that only the ones with 'male brains' were any good at it.

Anyway, am I making this up? I would be really interested to hear what you all (especially women mathematicians) think.

Disclaimer: I know nothing about gender psychology and I'm just repeating what I've heard/read.

### 2wyrdchao

I am inclined to believe that the 'gender bias' in math proficiency is almost entirely due to our (low) expectations of what girls are able to learn about math; in my own experience (tutoring 7-10 year olds), there is NO difference at all; in fact, I think girls at that age are better at it (or at least more attentive).

As for how you DO math; whatever works! I myself actually visualize the

I think teaching math effectively really has to do with the quality of the teacher: in the US, primary school math teachers seldom have degrees in math, and therefore tend to be uncomfortable with the subject; this attitude gets passed down to students.

An American actress (from the show 'West Wing' as well as others) has written a new book on girls and math:

Math Doesn't Suck: How to Survive Middle-School Math Without Losing Your Mind or Breaking a Nail by Danica McKellar

Ms. McKellar returned to school after beginning her acting career to complete her Ph.D. in Math, but she 'hated' math (in middle school) until a particularly good teacher helped her 'get it'. The National Public Radio interview of her is here:

http://www.npr.org/templates/story/story.php?storyId=14594340

As for how you DO math; whatever works! I myself actually visualize the

*piece of paper*with the problem written on it, and I proceed from there. In fact my memory seems to be almost entirely associative-visual; reading a book is like watching a movie going in my head with all the characters and scenes fleshed out... As a result of this intense 'movie' I have a very hard time memorizing anything by rote.I think teaching math effectively really has to do with the quality of the teacher: in the US, primary school math teachers seldom have degrees in math, and therefore tend to be uncomfortable with the subject; this attitude gets passed down to students.

An American actress (from the show 'West Wing' as well as others) has written a new book on girls and math:

Math Doesn't Suck: How to Survive Middle-School Math Without Losing Your Mind or Breaking a Nail by Danica McKellar

Ms. McKellar returned to school after beginning her acting career to complete her Ph.D. in Math, but she 'hated' math (in middle school) until a particularly good teacher helped her 'get it'. The National Public Radio interview of her is here:

http://www.npr.org/templates/story/story.php?storyId=14594340

### 3chellerystick

I don't have an answer. But I think before I even look for an answer I need more information:

1. the different ways that mathematically inclined people think. Even talking to the guys, there are a lot of different ways--some verbal, some symbolic, some spatial, etc. How can we talk about this until we have some sense of the categories?

2. how much of the difference is due to things like stereotype threat. I don't know how much of a difference there is compared to a perceived difference (because most people do not have a grasp of bimodal distributions--they see that the means are different or they see the exaggerated difference at the extremes and then if any woman at all is good at math or if a man is not they get all ZOMG!!!).

1. the different ways that mathematically inclined people think. Even talking to the guys, there are a lot of different ways--some verbal, some symbolic, some spatial, etc. How can we talk about this until we have some sense of the categories?

2. how much of the difference is due to things like stereotype threat. I don't know how much of a difference there is compared to a perceived difference (because most people do not have a grasp of bimodal distributions--they see that the means are different or they see the exaggerated difference at the extremes and then if any woman at all is good at math or if a man is not they get all ZOMG!!!).

### 4scottja

>1 Yarrow: There are small but real biological differences in mean cognitive abilities between men and women. There are some cognitive skills (spatial skills, in particular) that men tend to be a little better at then women, and these may relate directly to mathematical inclination and skill. Research is suggestive of this effect, but really not conclusive because there are so many potentially confounding variables. (This is all "on average," of course - individuals of both sexes vary widely around the means.)

An interesting essay on this subject is here.

>2 wyrdchao: I'm pretty sure McKellar only has a bachelor's degree in math.

>3 chellerystick: I think your point #2 is right - people get carried away with the whole sex difference thing.

An interesting essay on this subject is here.

>2 wyrdchao: I'm pretty sure McKellar only has a bachelor's degree in math.

>3 chellerystick: I think your point #2 is right - people get carried away with the whole sex difference thing.

### 5eileen82

Short presentation: I'm swedish, female and study at university-level to teach high school mathematics and swedish.

I don't think the way you all seems to do at all.. I never visualize numbers or lines or pieces of paper but rather in parts of numbers. Ex. 27+18 becomes (20+10)+(7+8). When numbers add up to an even 10, ex. 23+17 I sometimes get the feeling (not a picture but a feeling) of the numbers being like pieces in a jigsaw, or even closer: Tetris-blocks, fitting together perfectly.

On the subject of boys being better than girls at math: Gender studies often describe our perception of genders as being opposites: male - female. There are also a multitude of other pairs of opposites that correspond to these: hard - soft, sense - sensibility, logic - irrationality, science - every day life, order - chaos. The previous ones are supposedly related to the male characteristic, the latter to the female. As we can see, both "logic" and "science" are considered to be related to the male gender, rather than the female. And, sadly, parents unconsciously carry these values on to our children, teachers to their students etc. The children perform the way we expect them to, and we see what we expect to see.

This is, of course, not true in every case, but it's a general tendency. To know more, read for example Evelyn Fox Keller - Reflections on Gender and Science.

(please excuse my somewhat feeble grasp on mathematical expressions in english.)

I don't think the way you all seems to do at all.. I never visualize numbers or lines or pieces of paper but rather in parts of numbers. Ex. 27+18 becomes (20+10)+(7+8). When numbers add up to an even 10, ex. 23+17 I sometimes get the feeling (not a picture but a feeling) of the numbers being like pieces in a jigsaw, or even closer: Tetris-blocks, fitting together perfectly.

On the subject of boys being better than girls at math: Gender studies often describe our perception of genders as being opposites: male - female. There are also a multitude of other pairs of opposites that correspond to these: hard - soft, sense - sensibility, logic - irrationality, science - every day life, order - chaos. The previous ones are supposedly related to the male characteristic, the latter to the female. As we can see, both "logic" and "science" are considered to be related to the male gender, rather than the female. And, sadly, parents unconsciously carry these values on to our children, teachers to their students etc. The children perform the way we expect them to, and we see what we expect to see.

This is, of course, not true in every case, but it's a general tendency. To know more, read for example Evelyn Fox Keller - Reflections on Gender and Science.

(please excuse my somewhat feeble grasp on mathematical expressions in english.)

### 6pw0327

Danica McKeller does have a BA in mathematics from UCLA, she is also a coauthor of a paper titled:"Percolation and Gibbs states multiplicity for ferromagnetic Ashkin–Teller models on Z2".

Here is a link to her website for a PDF version of the paper.

http://www.danicamckellar.com/math/percolation.pdf

There is also an English girl, Sarah Flannery, who came up with a way to implement the Cayley-Purley Algorithm, which is a faster cryptographic method than the RSK algorithm, although that algorithm has been cracked. She wrote a book about math and her upbringing. It seems that in her case it was more a case of nurture than nature, her dad would bring home math puzzles for the family to solve together.

http://www.amazon.com/Code-Mathematical-Journey-Sarah-Flannery/dp/1565123778/ref...

Here is a link to her website for a PDF version of the paper.

http://www.danicamckellar.com/math/percolation.pdf

There is also an English girl, Sarah Flannery, who came up with a way to implement the Cayley-Purley Algorithm, which is a faster cryptographic method than the RSK algorithm, although that algorithm has been cracked. She wrote a book about math and her upbringing. It seems that in her case it was more a case of nurture than nature, her dad would bring home math puzzles for the family to solve together.

http://www.amazon.com/Code-Mathematical-Journey-Sarah-Flannery/dp/1565123778/ref...

### 7plantluvver Primeira Mensagem

I think in patterns, but not in pictures. More along the lines of performing actions, such as rotating things, moving them around, matching, etc.

I live in the USA and have a BA with majors in Mathematics and Science.

I remember in grade school, that there wasn't much distinction between boys and girls unnntil about the sixth grade. After that, the boys did mostly better than the girls, except for 2 or 3 clearly exceptional girls. I didn't know I was among them, because I was relatively slow. In fact, I was in fear of failing my math class in sixth grade, because the teacher expected us to perform timed drills on multiplication and addition basics. I struggled to pass the addition drills, I probably tried twenty or thirty times. I never did pass the multiplication drills.

My memory for numbers seems rather poor. I love to see patterns and relationships. In everything, knitting patterns, fabric textures. I think I am rather tactile. I can imagine graphs, but I think this is only because I have been taught these tools. I tend to count on my fingers, and I now like to estimate numbers. (It took me a long time. I think this was due to a wish that mathematics be exact, and have one correct answer.) But I think approximating things is more my true nature. I am very poor at giving directions, because I don't remember the exact order of streets. Instead I remember that one location will be on the way toward another location.

I don't know if this makes any sense, but that is my impression of how I do math.

Also, my university has about an even split between men/women students, at least at the undergraduate level. I asked my advisor about this once, whether it was true elsewhere. He said that he forgets about this difference, until he visits his alma mater, where the sexes are not balanced.

I had difficulties in the actuarial profession. I was a divorced woman, and even men who I had been friends with became distant after they married. I won't mention the absolute chauvinists, (and many of them were young), who would bond over their "Sports Illustrated Swimsuit Edition," joke about how someone had given up golf, after losing to his girlfriend.

I think much of the gender imbalance has to do with social and cultural aspects of mathematics.

I live in the USA and have a BA with majors in Mathematics and Science.

I remember in grade school, that there wasn't much distinction between boys and girls unnntil about the sixth grade. After that, the boys did mostly better than the girls, except for 2 or 3 clearly exceptional girls. I didn't know I was among them, because I was relatively slow. In fact, I was in fear of failing my math class in sixth grade, because the teacher expected us to perform timed drills on multiplication and addition basics. I struggled to pass the addition drills, I probably tried twenty or thirty times. I never did pass the multiplication drills.

My memory for numbers seems rather poor. I love to see patterns and relationships. In everything, knitting patterns, fabric textures. I think I am rather tactile. I can imagine graphs, but I think this is only because I have been taught these tools. I tend to count on my fingers, and I now like to estimate numbers. (It took me a long time. I think this was due to a wish that mathematics be exact, and have one correct answer.) But I think approximating things is more my true nature. I am very poor at giving directions, because I don't remember the exact order of streets. Instead I remember that one location will be on the way toward another location.

I don't know if this makes any sense, but that is my impression of how I do math.

Also, my university has about an even split between men/women students, at least at the undergraduate level. I asked my advisor about this once, whether it was true elsewhere. He said that he forgets about this difference, until he visits his alma mater, where the sexes are not balanced.

I had difficulties in the actuarial profession. I was a divorced woman, and even men who I had been friends with became distant after they married. I won't mention the absolute chauvinists, (and many of them were young), who would bond over their "Sports Illustrated Swimsuit Edition," joke about how someone had given up golf, after losing to his girlfriend.

I think much of the gender imbalance has to do with social and cultural aspects of mathematics.

### 8pw0327

That is very interesting plantluvver. I am a male and I was never particularly quantitative either, although I did do well enough to get by in math. I too, am a patterns and relationships kind of a person. Always trying to make connections and seeing the bigger patterns.

I am not sure how much of the degradation of girl's math skills is due to teacher/societal bias, I suspect there is a lot of it, but it boggles my mind to think that this is the sole reason. I don't think there has been any study that can precisely pinpoint the nature vs. nurture argument in this respect.

I think also, that once they reach the middle school age, math becomes much more of a contest, a competition for grades since the quantitative part of math is ideal for this type of viewpoint since they are dealing with absolutes, and absolutes lend nicely to competition. Nice girls don't compete, at least that is the implicit societal message.

I do know that in my dealings with some students that the stigma of math is wearing off somewhat. It still isn't cool for a girl to be doing math, but most of the math types don't really care about that.

I am not sure how much of the degradation of girl's math skills is due to teacher/societal bias, I suspect there is a lot of it, but it boggles my mind to think that this is the sole reason. I don't think there has been any study that can precisely pinpoint the nature vs. nurture argument in this respect.

I think also, that once they reach the middle school age, math becomes much more of a contest, a competition for grades since the quantitative part of math is ideal for this type of viewpoint since they are dealing with absolutes, and absolutes lend nicely to competition. Nice girls don't compete, at least that is the implicit societal message.

I do know that in my dealings with some students that the stigma of math is wearing off somewhat. It still isn't cool for a girl to be doing math, but most of the math types don't really care about that.

### 9plantluvver

I don't know if gender bias would degrade a girl's skills. But if a girl ran into a difficulty, it would be more acceptable for her to give up. I think most boys are taught to overcome obstacles, and to feel accomplished.

I was taught that it wasn't "nice" to be proud, and that it was always important to consider other peoples feelings. Once, I was assigned a seat next to a girl who was doing very poorly, and I would feel terrible when I received an A. I would hide my paper quickly to spare her feelings. I don't think many boys would assume personal responsibility for her sadness.

WowSum

I was taught that it wasn't "nice" to be proud, and that it was always important to consider other peoples feelings. Once, I was assigned a seat next to a girl who was doing very poorly, and I would feel terrible when I received an A. I would hide my paper quickly to spare her feelings. I don't think many boys would assume personal responsibility for her sadness.

WowSum

### 10chellerystick

So we have several different bits of thinking here:

1. pictures, spatial manipulations of geometric objects--such as 1-D number line, 3-D rotations, blocks

2. tactile manipulations

3. feeling of "completeness" or "rightness" (Eileen may have a better word)

4. picturing the written version of a calculation

As for me, I tend to calculate "in real life" by mumbling. It is similar to number four except that 1. it is not visual and 2. I avoid keeping track of more than one carry, sum, etc. as I have a great deal of trouble walking and chewing gum. So 27 + 18 is often mumbled "twenty... seven... eighteen... five... thirty... forty. Forty-five." 27 * 18 would be "twenty seven... eighteen... twenty... fifty four... times ten...five forty... minus fifty four... five hundred... minus fourteen... four hundred... ninety... eighty six. Four eighty six." Unless I happen to notice that it's 27 and 18 and therefore it's just 81... 6... 486.

Similarly if someone is reading a proof aloud I tend to stop and repeat each phrase "for all x in R2..." to absorb it, which drives my boyfriend crazy in general but he'll (mostly) put up with it for the sake of doing math together. Simple things like "for all x in R2" just go into my head, but if it's a complicated situation, I might be like this is in this over here, and that is there, okay, next phrase--more spatially. I do this less if I can just read it.

1. pictures, spatial manipulations of geometric objects--such as 1-D number line, 3-D rotations, blocks

2. tactile manipulations

3. feeling of "completeness" or "rightness" (Eileen may have a better word)

4. picturing the written version of a calculation

As for me, I tend to calculate "in real life" by mumbling. It is similar to number four except that 1. it is not visual and 2. I avoid keeping track of more than one carry, sum, etc. as I have a great deal of trouble walking and chewing gum. So 27 + 18 is often mumbled "twenty... seven... eighteen... five... thirty... forty. Forty-five." 27 * 18 would be "twenty seven... eighteen... twenty... fifty four... times ten...five forty... minus fifty four... five hundred... minus fourteen... four hundred... ninety... eighty six. Four eighty six." Unless I happen to notice that it's 27 and 18 and therefore it's just 81... 6... 486.

Similarly if someone is reading a proof aloud I tend to stop and repeat each phrase "for all x in R2..." to absorb it, which drives my boyfriend crazy in general but he'll (mostly) put up with it for the sake of doing math together. Simple things like "for all x in R2" just go into my head, but if it's a complicated situation, I might be like this is in this over here, and that is there, okay, next phrase--more spatially. I do this less if I can just read it.

### 11chellerystick

Another question might be the specialties you enjoy. Is there a correlation to thinking styles? I did a BA in math, really liked algebra, math logic, and topology (point-set and algebraic), did not like a cal (i.e. undergrad analysis, though it had some cool moments), baby stats, diffeq.

### 12pw0327

Going back to the discussion on competition. Overcoming obstacles is a part of what being competitive teach people and I think that with more girls participating in things that are competitive: sports, music, knowledge bees etc. Girls are getting better at competing and best of all, not having to apologize for being competitive.

My $0.02

My $0.02

### 14szarka

Speaking of both girls doing math in general and Danica McKellar in particular, here's a recent discussion on Science Friday:

http://www.sciencefriday.com/pages/2007/Sep/hour2_092107.html

http://www.sciencefriday.com/pages/2007/Sep/hour2_092107.html

### 16lokum

In response to eileen82: I feel the same way about addition. I split numbers up and recombine them to do arithmetic. I am also a female math major at a university.

### 17Toolroomtrustee

#7 I remember in grade school, that there wasn't much distinction between boys and girls unnntil about the sixth grade. After that, the boys did mostly better than the girls, except for 2 or 3 clearly exceptional girls.

__________

I'm aware of some research that corroborates plantluver's experience, and goes on to say that this dropping off of interest in math by girls has repurcussions for the kinds of professions they eventually enter, and the salaries they earn from them. Simply put, a lot of the high-paying jobs require at least some coursework in the hard sciences, and to enter such programs in university, students need to have done well in math (and physics) throughout secondary school.

I'm a (secular) homeschooler for my daughter and son, and the topic of this thread is something I think about a lot. Unaware of how university programs work, my daughter constantly asks why math is needed for the veterinary program she wants to enter. Maybe her dislike of the subject is from my teaching, maybe it's part of an aversion to math that many girls feel as they enter puberty ... I just don't know, but I'm not going to let her give it up.

One thing has made learning math a lot easier and that is the textbooks available from Singapore for a song: http://www.singaporemath.com/

Their approach is astonishingly clear, and very visual. We just finished a section on word problems fractions aimed at Grade 5 students which I didn't learn until I was in high school.

I would be very interested in knowing whether this alleged gender gap in math applies to countries like Singapore, China and Taiwan, whose students do extremely well in the subject.

__________

I'm aware of some research that corroborates plantluver's experience, and goes on to say that this dropping off of interest in math by girls has repurcussions for the kinds of professions they eventually enter, and the salaries they earn from them. Simply put, a lot of the high-paying jobs require at least some coursework in the hard sciences, and to enter such programs in university, students need to have done well in math (and physics) throughout secondary school.

I'm a (secular) homeschooler for my daughter and son, and the topic of this thread is something I think about a lot. Unaware of how university programs work, my daughter constantly asks why math is needed for the veterinary program she wants to enter. Maybe her dislike of the subject is from my teaching, maybe it's part of an aversion to math that many girls feel as they enter puberty ... I just don't know, but I'm not going to let her give it up.

One thing has made learning math a lot easier and that is the textbooks available from Singapore for a song: http://www.singaporemath.com/

Their approach is astonishingly clear, and very visual. We just finished a section on word problems fractions aimed at Grade 5 students which I didn't learn until I was in high school.

I would be very interested in knowing whether this alleged gender gap in math applies to countries like Singapore, China and Taiwan, whose students do extremely well in the subject.

### 18Jesse_wiedinmyer

*I'm aware of some research that corroborates plantluver's experience, and goes on to say that this dropping off of interest in math by girls has repurcussions for the kinds of professions*

There have also recently been studies that indicate that boys/men perform more poorly when faced with the idea that they're supposed to be better at math than females.

### 19LolaWalser

*why math is needed for the veterinary program she wants to enter*

May I ask what do you tell her? I'm not sure what you mean by how uni programs work. I'm not a veterinarian, but I assume they study animal biology, physiology and biochemistry (among other things), and in those subjects math applications come up in many places. This is not to say that vets use math a lot (wouldn't know anything about that), only that certain fundamental concepts will require understanding of mathematic formulae--e.g. in cardiology, blood flow, structure, genetics, epidemiology... and let's not forget medication, drug dosage--I'd want a vet who knows how much to prescribe for an elephant vs. a cat, and why.

### 20Toolroomtrustee

#19

I agree with everything you say, but she's just not at the stage yet to appreciate the skills required for systematic research. I tell her things along those lines, but it'll take time.

By "how university programs work", I mean that certain programs receive so many applicants that the those with strong performances in calculus and physics as well as chemistry and biology may have an edge over those with good grades only in chemistry and biology. That, I have been told by an unsuccessful applicant, is how it "works" in Canada, where only two universities offer vet programs in English. Those who can afford it take advantage of the wider opportunities in the States.

I agree with everything you say, but she's just not at the stage yet to appreciate the skills required for systematic research. I tell her things along those lines, but it'll take time.

By "how university programs work", I mean that certain programs receive so many applicants that the those with strong performances in calculus and physics as well as chemistry and biology may have an edge over those with good grades only in chemistry and biology. That, I have been told by an unsuccessful applicant, is how it "works" in Canada, where only two universities offer vet programs in English. Those who can afford it take advantage of the wider opportunities in the States.

### 21Toolroomtrustee

Esta mensagem foi marcada como abusiva por vários utilizadores e por isso não é mostrada (mostre)

#18

(I jumped the gun on this one, due to previous debates with someone else).

(I jumped the gun on this one, due to previous debates with someone else).

### 22Toolroomtrustee

>20 Toolroomtrustee:

Sorry, when I wrote that, I didn't realize you're in Toronto.

Sorry, when I wrote that, I didn't realize you're in Toronto.

### 23Jesse_wiedinmyer

Wow. Talk about coming out of left field.

### 24LolaWalser

Yeah, I'm not following either... Anyway, good luck to the little girl in realising her dreams!

### 25Toolroomtrustee

Jesse and I have a history ...

### 26Jesse_wiedinmyer

I guess I'll have to take his word on that. Not sure how that plays into gender stereotypes and all, but...