Why is Math so special?

[Storm Bay]

Do you HAVE studies which show this, for subjects where performance can be measured objectively (such as math), completely independent from a teacher's personal preferences (such as writing)?

 

I am very sceptical because I am an instructor myself..

 

I'd like to see those studies, too. I teach piano (had no desire to be a concert pianist or a professional musician at all) and it is very clear that there are innate differences in musical and intellectual ability unrelated to practice habits and attitude. Obviously, every student with good practice habits does better than she or he could do without those habits, but even tough I have an arsenal of different ways to teach it, there are very clear differences. This is very clear in the classroom, and kids themselves usually know it, too, as in who in the class is brilliant, who struggles, etc.

[stripe]

I have always wondered about this study that is quoted so much, too. First, I have never seen the study. Second, my guess is that it was done in a general ed elementary school classroom.

I am not an authority on teacher education, or the so-called Pygmalion effect, but the most recent thing I read about this was in Loewen's book Teaching What Really Happened. He makes an interesting point about SAT scores -- namely, if they are designed to predict who will do well in college, then why do male students do better than females, when females do better in college? He has a whole chapter on teacher bias including SAT/standardized testing issues.

 

I also think, anecdotally, some of us homeschool because we are unhappy with the low expectations we see being placed on our children.

 

You make a good point about Math (perhaps more easily measured than, say, history), but I do think the attitude of "we are going to make sure you know this" (a la Jaime Escalante) makes a difference over the "you're all idiots destined to failure," which is an attitude I've heard teachers express. To me, the biggest advantage of grouping by current achievement level is that is would suggest who would benefit by intensive tutoring to bring the students up to speed. I think Urban Prep in Chicago has effectively addressed students' academic deficiencies by having a double-dose of English and lots of tutoring (you can see a video on the grio's article here). That's rarely how it works, however.

Edited December 5, 2010 by stripe

[regentrude]

He makes an interesting point about SAT scores -- namely, if they are designed to predict who will do well in college, then why do male students do better than females, when females do better in college? He has a whole chapter on teacher bias including SAT/standardized testing issues.

 

I have not read this, but it is pretty obvious that the SAT can not be an accurate predictor for college success because it is a snapshot of student performance in a very artificial format, in a narrow field, at a specific instant.

 

The students who fail my class do so for two reasons: inadequate preparation (the material tested on the SAT is not a sufficient preparation to do well in science), and inadequate work ethic/time management/study habits (a much bigger issue which, again, would not be tested in the SAT).

 

Could you paraphrase for me where the author sees teacher bias on the SAT??? Aside from the essay, any other section is multiple choice, so I do not see how a teacher can have an influence on the outcome.

[stripe]

Could you paraphrase for me where the author sees teacher bias on the SAT??? Aside from the essay, any other section is multiple choice, so I do not see how a teacher can have an influence on the outcome.

Bias in test construction, not by teachers per se. He asserts it is deliberate.

[regentrude]

How can the SAT be gender biased in construction? Math is math - for males and females. And both genders should know grammar and recognize bad writing.

Could you elaborate???

[Crimson Wife]

I took a social psychology class from Claude Steele back in college and he talked a lot about his research findings on what he calls the "stereotype threat". Certain groups (most notably African-Americans and females) tend to perform worse on tests when they are told that group differences have been found than they do otherwise. That probably explains some of the gender differences found on the SAT.

 

I make sure to emphasize to my DD that intra-group differences are much, much larger than inter-group differences. That is, there is much greater variation between individual girls than there is between girls on average & boys on average. Knowing the group average tells us very little about how any one particular student will score.

[regentrude]

I took a social psychology class from Claude Steele back in college and he talked a lot about his research findings on what he calls the "stereotype threat". Certain groups (most notably African-Americans and females) tend to perform worse on tests when they are told that group differences have been found than they do otherwise. That probably explains some of the gender differences found on the SAT.

 

 

So do I understand that right: what you're saying is that a girl would do worse on a standardized test if she knows that girls on average perform less well than boys? So this knowledge is somehow impacting her performance? Works like a kind of self-fulfilling prophecy? Interesting.

 

(I am in a very male dominated field and have excelled in subjects girls are not usually supposed to excel at, so I have a hard time wrapping my mind around the mechanism. And I guess I make a good role model for my DD).

 

And you are absolutely right - average in a group tells absolutely NOTHING about an individual.

[Crimson Wife]

How can the SAT be gender biased in construction? Math is math - for males and females. And both genders should know grammar and recognize bad writing.

Could you elaborate???

 

I have heard that it's possible to create a version of the SAT where the overall test average remains the same but the average for girls will be higher than the one for boys, simply by shifting the mix of questions. Girls tend to do better on the algebra questions and worse on the geometry/spatial reasoning ones. I tried to find the reference but was unsucessful.

[Guest]

How can the SAT be gender biased in construction? Math is math - for males and females. And both genders should know grammar and recognize bad writing.

Could you elaborate???

 

This happens in several ways, I think.

 

One is the distribution of "straight" problems, visual/spatial problems, and verbal problems. I believe there have been studies done demonstrating, in general (always exceptions), that boys do better with the first two types, girls with the latter. The population of the gifted/talented programs in our city schools changed dramatically when the test they used for determining the cut-off went from the Stanford-Binet to the Raven (spatial logic). The classes are now filled with many, many more boys and fewer girls than were selected under the previous tests. Ironically, the intent was to increase the numbers of kids identified as gifted who spoke another language besides English as their primary language and thus were at a disadvantage on a more verbal test; its primarily effects turned out to be gender-related instead.

 

In a similar manner, there are a number of studies (not dealing exclusively with math SAT problems, but all problems) which show that the vocabulary of a problem can determine who gets it right. For instance, if you are given a problem whose content is filled with jargon or special language from a sport you aren't familiar with -- sailing, or ice hockey, or whatever -- you are going to have to work doubly hard to get through the language to the math, and you may be utterly confused by the language and not be able to figure out what is being asked. Test-makers can manipulate word problems in favor of any number of subgroups taking the test.

 

Very good instruction might compensate for a number of these effects, but it's rare for kids to have a string of excellent math teachers.

 

I have a couple of books on the make-up and effects of IQ and achievement tests, and can go try to dig the titles up if you're interested.

[Crimson Wife]

So do I understand that right: what you're saying is that a girl would do worse on a standardized test if she knows that girls on average perform less well than boys? So this knowledge is somehow impacting her performance? Works like a kind of self-fulfilling prophecy? Interesting.

 

(I am in a very male dominated field and have excelled in subjects girls are not usually supposed to excel at, so I have a hard time wrapping my mind around the mechanism. And I guess I make a good role model for my DD).

 

And you are absolutely right - average in a group tells absolutely NOTHING about an individual.

 

Yes, that's correct. IIRC you grew up outside the U.S. so you probably didn't experience as much anti-female bias in math & science as those of us who were raised here.

 

Even in the 1980's and early 1990's, I experienced a lot of not-so-subtle bias in math and physical sciences. I was good at math & science, but my guidance counselor didn't push me to double-up on those courses the way she did my friend Rob. Instead, she pushed me to use my electives on a 2nd foreign language and more humanities classes.

[Storm Bay]

Yes, that's correct. IIRC you grew up outside the U.S. so you probably didn't experience as much anti-female bias in math & science as those of us who were raised here.

 

Even in the 1980's and early 1990's, I experienced a lot of not-so-subtle bias in math and physical sciences. I was good at math & science, but my guidance counselor didn't push me to double-up on those courses the way she did my friend Rob. Instead, she pushed me to use my electives on a 2nd foreign language and more humanities classes.

 

The bias was HUGE when I went to high school in the 1970s. Sexism was still more overt and it was one of the reasons I was kept with my age peers for my math (there were a pair of boys who were allowed to go 3 grades ahead, and that's when I quite bothering with math.)

[FairProspects]

In a similar manner, there are a number of studies (not dealing exclusively with math SAT problems, but all problems) which show that the vocabulary of a problem can determine who gets it right. For instance, if you are given a problem whose content is filled with jargon or special language from a sport you aren't familiar with -- sailing, or ice hockey, or whatever -- you are going to have to work doubly hard to get through the language to the math, and you may be utterly confused by the language and not be able to figure out what is being asked. Test-makers can manipulate word problems in favor of any number of subgroups taking the test.

 

 

This. Completely this.

 

When I was working with my GRE tutor, there were a number of what she called "money words" on a separate list that I had to study. They were words that regularly appeared on the test (including in one of the questions I missed in my pretest) that were commonly used in wealthy households because they had to do with money management. My tutor explained that people with a wealthy background generally picked up this vocabulary from their lifestyle/hobbies, while the rest of us had to actually learn and study the meanings of these words.

 

To me this was just one clear example of how the test is structurally biased towards certain groups of people. I'm sure there are equally relevant examples that apply to other demographics of gender, race, etc. as well.

[regentrude]

IIRC you grew up outside the U.S. so you probably didn't experience as much anti-female bias in math & science as those of us who were raised here.

 

No, but there were very interesting effects which lead me to believe that not all differences are due to bias.

I grew up in East Germany where, for various reasons, there was a HUGE push towards getting girls into science and engineering. 95% of women worked jobs, SAHM were a rarity. Girls were actively encouraged to do math and science and become engineers. When I went to university, however, the ratio or freshmen who majored in physics was 1 girl: 6 guys, roughly the same as here in the US... all that push and encouragement had absolutely no effect on the numbers.

[Ester Maria]

For instance, if you are given a problem whose content is filled with jargon or special language from a sport you aren't familiar with -- sailing, or ice hockey, or whatever -- you are going to have to work doubly hard to get through the language to the math, and you may be utterly confused by the language and not be able to figure out what is being asked. Test-makers can manipulate word problems in favor of any number of subgroups taking the test.

I constantly hear this argument, but I never fully understood it. Personally, I think that the SAT is a nonsense, but for completely different reasons - I don't consider it biased.

 

Let's take a linguistically nonsenous problem: Gino and Lea have each three bicchieri containing each five cani and nine gatti. The value of each cane is 1/3 the value of two gatti. The value of half gatto is 40 units.

Determine (let's look at a few possible options):

a) The total unit value of one bicchiere.

b) The total unit value of the sum of all bicchieri of Gino and Lea.

c) The total unit value of a bicchiere in which two gatti are are absent.

 

How is this biased? Even if you have no idea what the words mean (it's about cups which contain dogs and cats, by the way :D), it can be solved. I'm simplifying, but you can also just replace bicchiere with A, cane with B and gatto with C. Those are just labels, nothing more. Even if they take a specialized term, they ultimately have to explain in the problem what do you need to do, how many specialized terms contains another specialized term, etc. Or am I missing something? :confused:

 

Sorry to hijack your post, I just really don't get HOW can the test be biased in the math section. While tests are by default biased in language sections, in math the language is just in the use of something "greater", the point of the problem, not to test one's vocabulary or cultural knowledge per se. You can solve a math problem without having the slightest idea what it talks about just by understanding the language of the context.

[patchfire]

Even in the 1980's and early 1990's, I experienced a lot of not-so-subtle bias in math and physical sciences. I was good at math & science, but my guidance counselor didn't push me to double-up on those courses the way she did my friend Rob. Instead, she pushed me to use my electives on a 2nd foreign language and more humanities classes.

 

I had the opposite problem. I went to an all-girls school, and the prevailing attitude was one of "If you are good in math and/or science, you OWE IT to your fellow females to concentrate in that area! You're being selfish if you take over 'their' strengths in the humanities just because you like it better."

 

I didn't fully realize the impact of it all until I was 3/4 of the way through a science degree at Georgia Tech, and came to the conclusion I would have been happier at a LAC studying poli sci. Oops.

[Guest]

 

How is this biased? Even if you have no idea what the words mean (it's about cups which contain dogs and cats, by the way :D), it can be solved. I'm simplifying, but you can also just replace bicchiere with A, cane with B and gatto with C. Those are just labels, nothing more. Even if they take a specialized term, they ultimately have to explain in the problem what do you need to do, how many specialized terms contains another specialized term, etc. Or am I missing something? :confused:

 

 

Yes, you are simplifying. An example: there have been test questions in the past which assume knowledge of, for instance, how football is scored. How can you figure out how many touchdowns, touchbacks, and kick points were made for a given total score if you have never seen or played football and do not know how it is scored? This goes beyond the issue of terminology. I have a very good friend who worked for ETS for a number of years, and he confirmed that the test question writers are largely male, white, upper middle class, university educated. Their questions are going to be biased, inevitably, according to their experiences and background. It takes someone from outside that group to point out what has been assumed.

 

There is also the matter of the distribution of types of questions, which can hugely impact overall test scores -- I mentioned in my earlier post the effects on GT populations in my city when the tests were changed from largely verbal to visual-spatial.

 

Many studies have shown that despite the fact that women score lower than men on the math section of the SAT -- in general -- women in general receive higher grades than men in first year college courses. Yet the SAT claims to correlate with first year college grades. There's a discrepancy here, and many researchers find it in the wording and distribution of SAT problems.

 

You can find on-line discussions of this issue at FairTest, the web sites of Alfie Kohn and Susan Ohanian, the New York Times archives, Scientific American, and various universities.

[Ester Maria]

An example: there have been test questions in the past which assume knowledge of, for instance, how football is scored. How can you figure out how many touchdowns, touchbacks, and kick points were made for a given total score if you have never seen or played football and do not know how it is scored? This goes beyond the issue of terminology.

I toyed with that idea, actually - that it's worded that way - but I guess I dismissed it based on the fact I never saw anything like that in any SAT practice tests I've seen, so I assumed that, if there were such things, they were long ago removed or reworded differently; I've also never really seen (though I've searched online) concrete examples that appeared on a test recently and were biased (not just paraphrasing what's wrong, but a full, concrete problem that actually appeared and for which we have data that specific subgroups failed to solve it while managing to solve non-biased problems, etc., to see exactly how it's worded and what's the problem). For all the ones I saw, seriously, it can be an unknown word for me because I don't speak English as my first language and didn't grow up in an Anglo culture, but I can still solve the problem without knowing what it means, thus the analogy.

 

But, don't they have entire groups nowadays whose sole purpose is to detect the bias and remove it?

(I agree with SAT not being a good predictor of anything, it doesn't surprise me. I was just curious about this math bias.)

Edited December 5, 2010 by Ester Maria

[regentrude]

Many studies have shown that despite the fact that women score lower than men on the math section of the SAT -- in general -- women in general receive higher grades than men in first year college courses. Yet the SAT claims to correlate with first year college grades. There's a discrepancy here, and many researchers find it in the wording and distribution of SAT problems.

 

 

My experience as a college instructor suggests that - as I wrote previously- a large contributor to student success are time management, work ethic and study habits. On average, my female students are more diligent, attend class more regularly, have a higher homework completion rate. That goes a very long way towards success (and may outweigh natural aptitude), particularly since college instructors are strongly encouraged to give points for homework and attendance instead of simply testing cumulative mastery in one final exam. So, looking at average scores I would not be surprised to see female students score higher on average than male students on average.

OTOH, out of the many hundreds of students I have taught, the truly outstanding students who display extraordinary abilities have almost all been male.

 

Btw, I think the flaw is ascribing the SAT too much predictive power. (Just as an extreme example: my 12 y/o DD's SAT score was in the 90th percentile of college bound seniors - but I do not think she would have been a successful college student in 7th grade!)

[Guest]

I used the football example as an extreme instance of how acculturated people can get, how much they can assume about what is and is not common knowledge. That is an older item that was taken off long ago; the problem of finding current bias is indeed subject to committees tasked with examining the questions.

 

One problem is that these committees all consist of highly educated people who have already gone through the system, so they are already losing track of what is and is not known by kids growing up in inner cities, by immigrants from certain cultures, by kids whose parents are working class, etc. In other words, if you have people who think inside a particular group mentality trying to discover what is problematic for people outside that group, there are going to be items whose inappropriateness or bias is overlooked.

 

I don't think this is as large a problem in math as it is in the language sections of the test; nevertheless, the fact that so many test items are thought up every year but prove faulty and need to be thrown out, or which are answered by one segment of the population and not others, shows that this is a recurring difficulty.

 

A lot of scientists, psychologists, and educational theorists are out there working on what is widely acknowledged to be a rather large issue in the US testing industry; it's not just a few people with a chip on their shoulder claiming bias.

[EKS]

Except that haven't studies shown that even average students perform miraculously well when the teachers are told they are gifted?

 

I don't know if studies have shown this definitively, over long periods. However, I can share a personal story that relates to this.

 

My older son was being evaluated for the umpteenth time (he is 2E) two years ago. When I came to get him after the IQ test, the psychologist took me aside and said, "He is absolutely brilliant!" Um, what? He is bright, but brilliant enough for a psychologist who deals with highly gifted kids all the time to get worked up over, not so much.

 

She proceeded to show me the scores she had calculated that morning. The GAI was in the profoundly gifted range, and that was without extended scoring. This was about 20 points off from what I thought it would be.

 

Anyway, for the next week my son seemed brilliant. Truly. Everything he said or did had a touch of brilliance to it.

 

A week later we went back for more testing. I asked for the raw scores so that I could figure the GAI using extended scoring. When I went home to do this, the raw scores were lower than what was on the table. I assumed that things were linear and calculated what I thought the GAI would be, based on what she gave me--20 points lower than what she had told me, which turned out to be correct. It turns out she had been looking at scoring tables for significantly younger kids (and it wasn't consistent).

 

But that experience taught me that my perception of something is heavily influenced by my own preconceived ideas.

[Bostonian]

Regentrude wrote:

"OTOH, out of the many hundreds of students I have taught, the truly outstanding students who display extraordinary abilities have almost all been male."

 

According to IQ tests, the dispersion of intelligence is higher in males than females, although the means are about the same. There are more extremely dumb males than females, but also more extremely smart ones. On the SAT there are more males with near-perfect scores. The higher dispersion in males may be one reason that in many intellectual fields, men have made most of the breakthrough discoveries.

 

The above argument is not PC, of course. Then-Harvard-president Larry Summers was demonized for expressing it.

[Guest]

Regentrude wrote:

"OTOH, out of the many hundreds of students I have taught, the truly outstanding students who display extraordinary abilities have almost all been male."

 

According to IQ tests, the dispersion of intelligence is higher in males than females, although the means are about the same. There are more extremely dumb males than females, but also more extremely smart ones. On the SAT there are more males with near-perfect scores. The higher dispersion in males may be one reason that in many intellectual fields, men have made most of the breakthrough discoveries.

 

The above argument is not PC, of course. Then-Harvard-president Larry Summers was demonized for expressing it.

 

This is interesting to think about, but perhaps more complex than it appears. When dd had her IQ tests I remember the neuropsych telling us that IQs of roughly 130-140 were apparently some kind of ideal, in that almost all Nobel laureates fell into that category (I don't know where the study is that got hold of their test scores!); people with higher IQs, in general, were NOT the ones making the big breakthroughs.

 

Then of course there are the multiple factors of women not being allowed in universities until relatively recently in history, being barred from grad programs and/or jobs as recenty as the 1940s and 1950s, and subject to all kinds of behaviors and attitudes that created extra obstacles in their paths, from harassment to not being able to find mentors to being barred from publication.

[HeidiD]

The higher dispersion in males may be one reason that in many intellectual fields, men have made most of the breakthrough discoveries.

 

And in males, the region of the cerebral cortex which correlates with math ability is larger.

 

The above argument is not PC, of course. Then-Harvard-president Larry Summers was demonized for expressing it.

 

Well, the PC crowd can demonize him all they want, but they're just shooting the messenger - it is what it is. :)

 

Anyway, as Regentrude points out, there are other important factors contributing to success. Dedication and work ethic can help to level the playing field, and have nothing to do with gender.

 

Regarding bias, my son was recently tested and one of the questions the evaluator related to me afterward as an example of information a "typical 15 yo would be expected to know" was regarding tipping in a restaurant. Obviously there are kids who would, for socio-economic reasons, be unaware of the correct answer, but there are probably also kids dining regularly in restaurants who have no idea the tip is on the credit card. :lol:

 

Regarding the SAT word problems, unfamiliarity with "labels" or descriptions/situations outlined in particular problems can have a detrimental effect on a person's overall speed, which on a timed test can clearly impact scores.

[smrtmama]

Regentrude wrote:

"OTOH, out of the many hundreds of students I have taught, the truly outstanding students who display extraordinary abilities have almost all been male."

 

According to IQ tests, the dispersion of intelligence is higher in males than females, although the means are about the same. There are more extremely dumb males than females, but also more extremely smart ones. On the SAT there are more males with near-perfect scores. The higher dispersion in males may be one reason that in many intellectual fields, men have made most of the breakthrough discoveries.

 

The above argument is not PC, of course. Then-Harvard-president Larry Summers was demonized for expressing it.

 

 

Gee, that certainly couldn't be at ALL culturally-related. Couldn't have anything to do with disparity in the way girls/boys are raised and how they are treated in academia. It's surely just that women are stupider than men. /sarcasm

[Halcyon]

Gee, that certainly couldn't be at ALL culturally-related. Couldn't have anything to do with disparity in the way girls/boys are raised and how they are treated in academia. It's surely just that women are stupider than men. /sarcasm

 

:iagree:

Personally, I think IQ tests are a bunch of hooey.

[EKS]

This is interesting to think about, but perhaps more complex than it appears. When dd had her IQ tests I remember the neuropsych telling us that IQs of roughly 130-140 were apparently some kind of ideal, in that almost all Nobel laureates fell into that category (I don't know where the study is that got hold of their test scores!); people with higher IQs, in general, were NOT the ones making the big breakthroughs.

 

Then of course there are the multiple factors of women not being allowed in universities until relatively recently in history, being barred from grad programs and/or jobs as recenty as the 1940s and 1950s, and subject to all kinds of behaviors and attitudes that created extra obstacles in their paths, from harassment to not being able to find mentors to being barred from publication.

 

Just to point out, statistically, there are far more people in the 130-140 range than in the 140+ range. If I calculated this correctly, approximately 95% of the people with IQs over 130 will have an IQ between 130-145.

[Guest]

Just to point out, statistically, there are far more people in the 130-140 range than in the 140+ range. If I calculated this correctly, approximately 95% of the people with IQs over 130 will have an IQ between 130-145.

 

Right, but you'd expect the over 140s to put in more of a presence even accounting for statistics -- or at least, I expected that, and apparently it doesn't come out that way.

[Guest]

Well, the PC crowd can demonize him all they want, but they're just shooting the messenger - it is what it is. :)

 

Anyway, as Regentrude points out, there are other important factors contributing to success. Dedication and work ethic can help to level the playing field, and have nothing to do with gender.

 

.

 

Well, yes and no. The University of California has an ongoing commission that is dealing with some fairly serious problems women scientists and aspiring scientists report, one of which is simply that the older men in top positions do not want to mentor them. This will likely change as the age of the professorial population changes, but it's still a problem at this very moment.

[regentrude]

Well, yes and no. The University of California has an ongoing commission that is dealing with some fairly serious problems women scientists and aspiring scientists report, one of which is simply that the older men in top positions do not want to mentor them. This will likely change as the age of the professorial population changes, but it's still a problem at this very moment.

 

I think the biggest problem for female scientists is the conflict between career and family. Even if you choose to take family leave, even if your university has a policy that extends time for tenure if you have children, you still compete with single men and with men who have a wife who is a SAHM or works shorter hours and who are able to put in 14 hour days at the office or lab. There is no way to prohibit these people to work that much (and hence publish more).

It is doable for a woman- but it is much harder. And I do not think there is any way around this.

[regentrude]

Gee, that certainly couldn't be at ALL culturally-related. Couldn't have anything to do with disparity in the way girls/boys are raised and how they are treated in academia. It's surely just that women are stupider than men. /sarcasm

 

I do not see why it is such a holy cow to accept cognitive differences between the genders. I have no problem accepting that men are, on average, physically stronger and that women have a longer life expectancy. Why should I have a problem that women are, on average, better at verbal tasks, better at social interactions and more inclined towards fields that require empathy (and hence more drawn to fields like teaching and nursing) - and men better at spatial reasoning and abstract tasks (and may be more inclined to invent or build things)? After all, these different traits have served the human race well for thousands of years.

 

My mentally retarded brother, who certainly has been raised without any push towards scientific or technical education (he can not even write his name, so my parents had other things to worry about) was the kid who took things apart and who could figure out how to work any radio or stereo in a few minutes - because of his disability, there is no cultural component there (he is the youngest and ended up inheriting my sister's and my girl toys).

 

The important thing is that these are always statements about the average, which enable no prediction about the abilities of any individual. But I do not believe these differences are purely cultural - and I don't see any harm in acknowledging that.

[rlugbill]

You do have a point, however there are some explanations, as people here have said. My dd (12) is advanced in both math and music, so I do have some basis for my opinion.

 

We purposely did not have her advance as much in math as in music. We tried the EPGY program in math. It advances the child rather quickly into higher math. It's easy to advance a grade level in 6-8 weeks. But, we went back to using CLE math- workbooks. She is a year "ahead" in math, using the CLE 800 lightunits. CLE has continuous review of prior material and we felt it was more important that she remember what she learned than that she advance into higher math at an early age.

 

We have friends whose dd went through the EPGY math and quickly went on to higher math- algebra, geometry, etc. at a very young age. Now, the mom confided in me that she wished they hadn't progressed so quickly. Their dd can do higher math, but doesn't know how many quarts are in a gallon. All of the elementary math was quickly forgotten.

 

And that's the math that people actually use in everyday life. And it's also the math that children are tested on for their age/grade level. Sixth graders are not tested on their knowledge of algebra or geometry and if they are studying higher math, they might actually do worse on standardized testing.

 

As far as music, we did not put any limits on how quickly our dd advanced. However, her teacher didn't try to teach emotional expression in her music, because in his opinion, younger children just aren't capable yet of expressing their emotions through music until they are a little older. She has just started expressing herself emotionally in her music.

 

Also, in music, she has done the Suzuki method, where you keep reviewing the elementary material once in a while, but apply the new techniques you have learned to the repetoire.

 

Basically, I might be on the wrong board here, but I think it's more important for gifted children to branch out and learn lots of different things than to go for higher level material in a few subjects. For example, they can learn some other languages, take up several musical instruments, several different sports, play lots of different games, read lots of different books, etc. I think the variety is both stimulating and interesting.

 

I don't think you should hold a child back, but perhaps expose the child to lots of varied activities so they can learn a greater variety of things. Nothing wrong with going into higher level math per se, but it shouldn't be at the expense of trying out lots of other things.

 

For example, my dd is very advanced in violin, but also plays flute and piano and she used to play cello.

 

Anyway, I do understand your point, but at the same time we actually did choose to not accelerate too much in math in order to ensure she remembered the basics. It's hard to say what would have happened had we taken a different route because we don't have twins to experiment on, but it has worked fine for our dd.

[regentrude]

I want to preface this by saying that I in no means want to criticize your decision about your child's math education ... but there were a few things in your post that I feel the need to comment on. Nothing personal.

 

We have friends whose dd went through the EPGY math and quickly went on to higher math- algebra, geometry, etc. at a very young age. Now, the mom confided in me that she wished they hadn't progressed so quickly. All of the elementary math was quickly forgotten.

Then you look at a case of a poorly designed math education- either too rushed, or not based on true mastery. There is no way to master advanced math without a firm grasp on arithmetic, and without using arithmetic on a constant basis. It is impossible that my kids forget their elementary math because they need it every single day to solve their algebra problems.

 

Their dd can do higher math, but doesn't know how many quarts are in a gallon. And that's the math that people actually use in everyday life.

 

Well, to be honest, I have not needed to know how many quarts are in a gallon EVER. I find it useful, however, to understand exponential functions in order to understand my mortgage calculations...an ability that would actually benefit many people.

By your argument, we could stop teaching math after 4th grade because many people may not used higher math. Same goes for advanced science, languages, literature...

OTOH, there are plenty of people (including me) who need calculus for a living.

 

And it's also the math that children are tested on for their age/grade level. Sixth graders are not tested on their knowledge of algebra or geometry and if they are studying higher math, they might actually do worse on standardized testing. .

And that defines a quality education? Passing a very low level standardized test?

Again, I do not buy it that accelerated children have to do worse on elementary math. In my experience as an instructor, it is often so that understanding of material beyond a certain topic actually enhances understanding of the basics... I observe that every semester.

[patchfire]

YBasically, I might be on the wrong board here, but I think it's more important for gifted children to branch out and learn lots of different things than to go for higher level material in a few subjects. For example, they can learn some other languages, take up several musical instruments, several different sports, play lots of different games, read lots of different books, etc. I think the variety is both stimulating and interesting.

 

I don't think you should hold a child back, but perhaps expose the child to lots of varied activities so they can learn a greater variety of things. Nothing wrong with going into higher level math per se, but it shouldn't be at the expense of trying out lots of other things.

 

I think this is a false dichotomy. My daughter's acceleration in math in no way precludes her from trying "lots of different things;" I don't feel the need to rattle out all of her activities here, but suffice it to say she participates in a variety of activities in a variety of different areas. She generally spends a bit more time on math than on any other single activity, yes, but she's by no means spending time on math in lieu of other worthwhile activities.

 

A tangential point is that the child who is gifted or accelerated in math may not, in fact, be gifted or accelerated in those other areas. Not everyone is globally gifted. Some kids may be 2E. Etc.

Edited December 7, 2010 by patchfire

[regentrude]

I don't think you should hold a child back, but perhaps expose the child to lots of varied activities so they can learn a greater variety of things. Nothing wrong with going into higher level math per se, but it shouldn't be at the expense of trying out lots of other things..

 

Forgot to comment on this: why should advancing in a subject mean that the kid can not be doing varied activities? Advancing in math does not mean the child has to spend more time. My DD is spending 3-4 hours on math per week - just on material that is a few grades above her age level. She does not spend MORE time, she is just progressing faster. It does not have to come at the expense of following deep interests (for example, DD is passionate about riding horses and spends 15 hours a week at the barn - way more than on math-, sings in choir, is bilingual, writes books for fun, studies languages....)

[Carol in Cal.]

I think the biggest problem for female scientists is the conflict between career and family. Even if you choose to take family leave, even if your university has a policy that extends time for tenure if you have children, you still compete with single men and with men who have a wife who is a SAHM or works shorter hours and who are able to put in 14 hour days at the office or lab. There is no way to prohibit these people to work that much (and hence publish more).

It is doable for a woman- but it is much harder. And I do not think there is any way around this.

 

This is certainly part of it, but not all of it.

 

When I left my engineering career to raise my daughter, I had been a successful employee for 20 years. I had only had one year where I was working and raising a child, so my income was not effected by family obligations. I was a hard worker, effective, and consistently got very good reviews, promotions, and some awards as well. And I was underpaid, significantly.

 

Now, we were not supposed to talk about our pay, so I didn't know what everyone else made. And we were not supposed to see the pay grids, so I don't really know what I was supposed to make. But annually at my review I would ask whether I was being paid commensurately with my performance and the answer was always a plan to get there, rather than the affirmative. I thought that this was just how things were, and that since I had gotten promoted relatively quickly it was taking them a while to catch me up.

 

I never really talked about this with anyone except my boss until I was quitting. He again admitted that I was low for level, and that really burned me. I had significantly more responsibility that many of the others, and excellent reviews, and a long list of solid achievements. So when an executive woman took me aside and asked why I was leaving I told her that I was underpaid and that although I was clearly well-appreciated, that was not reflected in my pay. She investigated and came back and agreed that I was underpaid and that there was no reason for it. She indicated that she would help fix my pay if I stayed. They really wanted me to do so, and offered me a half time job and a 10% increase as well as another increase in 6 months if I would reconsider.

 

It was too late--I already had one foot out the door and was looking forward to being home with my dd.

 

So, for the first time, I did talk about salary with others. And guess what? Every single guy said, "Wow, that's not right." And every single other woman engineer in my area, EVERY SINGLE ONE, told me that she was significantly underpaid, too. We all were, and we all thought we were the only one. Now, in that group was the older woman who had no children and worked as her hobby as well as her job. There were others with children who worked desperately hard to make sure that no one could ever say that they slacked because of their families. There were others who had not had any children yet. There was no one who was incompetent or 'an affirmative action hire' or not doing a great job. They were ALL underpaid relative to the objective criteria of the company, they all knew it, and the guys were not.

 

I think I figured it out. The guys were threatening and posturing. The managers verbally deplored this, but they still catered to it. Someone would say that they would leave if they didn't get more money, and magically the grids would be set aside and large raises would ensue. By and large, the women did not do this. And it made the management complacent about them. That's what I think happened. But I'm not really sure.

 

Still, I'm glad I had my engineering job as long as I did. It enabled me to travel, to buy my first home, and to save up enough to stay home with DD, which I dearly loved. But we do have a ways to go to be able to call this field fully congenial for women, and it's not just because of the child care issue.

[Storm Bay]

:iagree:

Personally, I think IQ tests are a bunch of hooey.

 

Well, yes and no. The University of California has an ongoing commission that is dealing with some fairly serious problems women scientists and aspiring scientists report, one of which is simply that the older men in top positions do not want to mentor them. This will likely change as the age of the professorial population changes, but it's still a problem at this very moment.

 

 

IQ tests are inherently limiting, and one of the original IQ test writers was skeptical himself. Now I've forgotten it it was Binet or not.

 

While I do think that there are general differences in the brains of men and women, they tend to fall into 80-20 ratios. This fits fairly closely to the 1 in 6 physics majors being women, too.

 

However, there is no test which measures all areas of intelligence, even in just the intellectual area, and this may bear directly on some of this. I suspect that there are areas not tested where you would find more domination by women, but these aren't in the areas we're discussing. The entire childbearing aspect has to be considered for career choices, regardless of IQ discrepancies--I'd like to see the numbers on this, for curiosity. Even one of my brothers, who has his Ph.D. in Physics (so somewhat doubly appropos) had to choose between continuing in research and time for a family life, and chose family life although he continues to work full time. This is less common for men to do than women, and so this is a relevant point. This type of decision can come up in many fields, not just in adademia and/or research. I have a cousin who is brilliant, but loved cooking so much that she became a chef after getting her BA in History (with a minor in English) who has just given up that career to get a regular full time job because she'd like to have a family and it would be far too difficult with the hours she was keeping.

 

The mentoring factor is also important as are the attitudes of professors in a number of scientific fields.There are still a number of fields where there is strong "boys club."

 

As for new innovations, etc, I think that it may well be that males are more inclined to have the three areas considered important to be a successful innovator. A good read on what makes someone an good innovator is the book Iconoclast: A Neuroscientist Reveals How to Think Differently by Berns.

Edited December 7, 2010 by Karin

[wapiti]

We have friends whose dd went through the EPGY math and quickly went on to higher math- algebra, geometry, etc. at a very young age. Now, the mom confided in me that she wished they hadn't progressed so quickly.

 

About EPGY, I'm finding in my dd's case, as we move from afterschooling to hs-ing, that it doesn't have as much practice as my dd happens to need. So we'll be dropping EPGY (or at least not relying on it as the main math curriculum for dd) and doing Singapore. I love EPGY for forging ahead, something my younger boys need as well, so I may sign up for another three months for them, but I would like them to get more pencil-and-paper practice, as they move into the abstract (they attend a montessori school, so the EPGY is supplemental). I'm afraid that while EPGY has many advantages, it's not the right stand-alone curriculum for my dd at this time. I want her preparation to be rock solid; indeed it's the primary reason I'm pulling her from school next week - what she's getting there is not rock solid.

 

Nothing wrong with going into higher level math per se, but it shouldn't be at the expense of trying out lots of other things.

My perspective is that I don't want well-roundedness to come at the expense of my child's strengths (one of which happens to be math); in other words, I don't want to round off her strengths. However, I don't really believe it's an either/or question - it's not as though solid preparation and acceleration in math takes the same kind of time commitment as something like ice skating at a high level, or even playing an instrument at a high level - the time for doing math is already a part of the academic schedule.

[Storm Bay]

I do not see why it is such a holy cow to accept cognitive differences between the genders. I have no problem accepting that men are, on average, physically stronger and that women have a longer life expectancy. Why should I have a problem that women are, on average, better at verbal tasks, better at social interactions and more inclined towards fields that require empathy (and hence more drawn to fields like teaching and nursing) - and men better at spatial reasoning and abstract tasks (and may be more inclined to invent or build things)? After all, these different traits have served the human race well for thousands of years.

.

:iagree: On average is the key here. Of course you can find people who aren't average, such as highly ematahetic, sensitive men, mathematicians such as Sophie Germain, women who are physically stronger than many men, etc.

 

PC does cause some trouble. There is a middle ground between PC and oppression, hate, etc.

[MissKNG]

Math is special to me because I'm thrilled my big girl excels in it. Math didn't come very easily to me but as a mom, I'd rather have my girls have the "math brains".

[Guest]

I do not see why it is such a holy cow to accept cognitive differences between the genders. I have no problem accepting that men are, on average, physically stronger and that women have a longer life expectancy. Why should I have a problem that women are, on average, better at verbal tasks, better at social interactions and more inclined towards fields that require empathy (and hence more drawn to fields like teaching and nursing) - and men better at spatial reasoning and abstract tasks (and may be more inclined to invent or build things)

 

I agree with you to a certain extent, but then I diverge: one of the interesting findings of recent research is that -- in general -- math is taught in a way that favors the visual-spatial thinking patterns that are -- again, generally -- a strength for boys. I have read about a few very preliminary studies that show when girls are taught math with more verbal input, in a way that plays to their (general) strengths, the gender difference in math scores tends to lessen. Imagine if this were the case throughout the school years, and if a boys' club, as another poster put it, were not still in effect in grad school and professional life. I don't think that anyone yet understands the full and complex interactions between biological and cultural factors.

 

I think it's also really important to remember what women have struggled against and continue to some extent to struggle against, factors which also have meant that often wealthy, elite males have gotten credit for discoveries and inventions that were in part or largely the result of work done by women or men from working class backgrounds. Just to mention one famous instance: Alexander Graham Bell was one of several people who invented working telephones, and only gets historical credit for its "discovery" or "invention" because he beat another man to the patent office by a matter of hours -- the other man had to scramble for the funds to file a patent. History is positively full of stories like this one, but they don't make it into history textbooks and it has taken a lot of work by scholars to uncover the extent to which this is true.

 

The Age of Wonder by Richard Holmes is a recent book that uncovers the crucial role of unacknowledged women in the scientific achievements of their male family members. Young Romantics, by Daisy Hay, discusses the way that women paid the social and professional price for the radical domestic and sexual philosophies of their husbands, fathers, and brothers. The books don't set out to claim or prove these things; they are just inevitable results of the research the authors did.

[Ester Maria]

I've been trying to wrap my mind around this topic on and off in the past days.

 

I actually have a completely different view of math acceleration - I would say it's one of the least problematic areas for a child to be accelerated in. I also do not notice that people tend to single it out so much, at least not people we've spoken to about this topic (being that both of our daughters are working above supposed grade level in math, one of them quite above that level), they all seem to think that math acceleration is much easier a "fate" for a parent of a bright child, than acceleration in many other areas. And here is why. The thing about math, as I understand it and as most people I know understand it, is that it requires certain intellectual maturity to comprehend it, i.e. to work on a level that's not a blind automatism deprived of an understanding ("math by the scheme"), but a conscious work paired up with conceptual understanding.

 

On the other hand, a child who pursues greater interest in humanities, particularly in areas such as philosophy or literature, needs not only intellectual, but also emotional maturity to be able to deal with what they learn. Many of the topics and things discussed in those areas are just so uncongenial for a mindset and life experience of a child, even a very bright one, and while mathematical proofs can "bug" a child while they're working on it, it's only an intellectual "bugging"; OTOH, there is something inherently more emotionally involving in attempting to "resolve" a legal-theological problem of a high level or dealing with a particular aspect of bioethics or discussing the specific representation of some aspects of human experience in art. For these reasons, I have always been much more careful about accelerating humanities than accelerating math - math never bothered me in particular, as it's a pure intellectual experience, while literature, philosophy or theology aren't only intellectual experiences and by the virtue of the discipline they tend to "soak" the student into the problem on much more potentially-problematic levels. I've never had a child in mute terror over an intellectual experience of a proof in trigonometry; I did have a child in terror over books, over ideas, over the symbolic baggage of the heritage that formed their world.

 

Accelerating math? As long as a child can function cognitively on the required level, absolutely. But for some other areas, not only cognitive but also emotional aspect should be considered - and maybe, sometimes, one really isn't to rush in all directions possible at a certain age.

[nmoira]

 

The Age of Wonder by Richard Holmes is a recent book that uncovers the crucial role of unacknowledged women in the scientific achievements of their male family members.

Here's a recent article in The Observer by Holmes. I do find it somewhat ironic that his book is getting big play, when there have been numerous women commentators who have made substantially the same points. :glare:

[Spy Car]

Here's a recent article in The Observer by Holmes. I do find it somewhat ironic that his book is getting big play, when there have been numerous women commentators who have made substantially the same points. :glare:

 

Yea, but he's a man so he must be smarter :D

 

Bill (who is going back into his hole :tongue_smilie:)

[Guest]

Here's a recent article in The Observer by Holmes. I do find it somewhat ironic that his book is getting big play, when there have been numerous women commentators who have made substantially the same points. :glare:

 

Exactly! He is a fairly big name in literary studies -- over twenty or thirty years he's produced what are considered to be the standard biographies of Coleridge and Shelley, so he gets press whenever he publishes something. But I can imagine it's teeth-gritting to women who have been there before. (And the woman who supervised my dissertation is one of them; a few years ago she wrote a book called For the Love of Animals, which includes a large section on Margaret Cavendish.)

Edited December 8, 2010 by Guest

[regentrude]

in general -- math is taught in a way that favors the visual-spatial thinking patterns that are -- again, generally -- a strength for boys. I have read about a few very preliminary studies that show when girls are taught math with more verbal input, in a way that plays to their (general) strengths, the gender difference in math scores tends to lessen

 

I can not even begin to comprehend how one could teach math "with more verbal input" - a geometry problem IS inherently about spatial relationships between points and lines and no amount of narrating about triangles is going to make it less so. An understanding of a derivative as the rate of change and slope of a curve, and of an integral as an area under a curve are also inherently spatial concepts which must be understood as such, or a full understanding of the concept is not achieved.

Maybe I'm dense, I don't get where "verbal" can come in. Could you give me an example?

[EKS]

Their dd can do higher math, but doesn't know how many quarts are in a gallon. All of the elementary math was quickly forgotten.

 

And that's the math that people actually use in everyday life.

 

Actually, the math people use in everyday life is that which has been learned deeply. Most adults in this country peaked out in second grade as far as math is concerned.

[Guest]

I can not even begin to comprehend how one could teach math "with more verbal input" - a geometry problem IS inherently about spatial relationships between points and lines and no amount of narrating about triangles is going to make it less so. An understanding of a derivative as the rate of change and slope of a curve, and of an integral as an area under a curve are also inherently spatial concepts which must be understood as such, or a full understanding of the concept is not achieved.

Maybe I'm dense, I don't get where "verbal" can come in. Could you give me an example?

 

As I understand it, the studies I have read have proposed that you can teach kids (particularly girls) to verbalize their way through a problem (in far more flexible and different ways than asking "what do you do next?" or "what theorem applies here?"); you can use writing as a tool to help kids understand and express their understanding; you can encourage kids to discuss and work out problems in small groups -- strategies that largely are not pursued in US schools. (Interestingly enough, I've read that many of these strategies are used in elementary math in Japan.) I have a child that learns through talking her way through things, so I'm perhaps more aware of this than I would have been had I been working with a different kid.

 

It's also interesting to me as a person with training in literature and language how differently written are many of the math textbooks I encounter (I'm trying not to call it bad writing, although that's what it often seems like to me). It truly seems they are written by and for someone with a completely different way of using language/thinking with language than myself and my dd. Marilyn Burns has come closest to using language to talk about math in a way that makes sense to both me and dd; she was also one of the first people to urge writing about math (along with working problems) as an important learning tool. Working through dd's geometry textbook, we often spend much of our time asking what the authors are trying to say, and then rewording it in a way that we can understand.

 

So it isn't a matter of somehow changing the visual-spatial nature of a geometry problem, for instance, as it is showing kids with verbal strengths or language-based ways of thinking how to harness those to deal with the visual-spatial problem. If you're being taught by a book, a lecturer, a DVD, a tutor, or anyone who already has strong visual-spatial skills, they are almost inevitably going to assume a lot of things that won't be obvious or apparent to anyone else who thinks that way already. It will only be clear to people who are otherwise wired, or who are more verbal learners, that they don't get it. Is this clear as mud?

[regentrude]

Thanks for explaining, KarenAnne. I think I get what you say.

 

That's why it is so important to have somebody else to explain difficult concepts to! I am using this in my physics classes: I let the students form groups, give them conceptual problems, and make them discuss the possible answers. The goal is to get them to talk - because even for a spatially minded person, discussing the material organizes the thoughts and brings misconceptions to light. It is very hard initially to make them talk, because they are not used to discussing physics - just to working problems.

 

I think one reason is that you organize material differently in your head when you talk about it using words instead of just formulas. I know for sure (and I share this experience with many colleagues) that I have never fully understood a subject until I began to teach it to somebody else.

[Storm Bay]

I think it's also really important to remember what women have struggled against and continue to some extent to struggle against, factors which also have meant that often wealthy, elite males have gotten credit for discoveries and inventions that were in part or largely the result of work done by women or men from working class backgrounds..

This is correct. Clara Schumann was a better composer than her brother, according to her brother, but which one do we think of when we hear te name Schumann?

Here's a recent article in The Observer by Holmes. I do find it somewhat ironic that his book is getting big play, when there have been numerous women commentators who have made substantially the same points. :glare:

 

Yea, but he's a man so he must be smarter :D

 

Bill (who is going back into his hole :tongue_smilie:)

:lol::lol::lol:

 

I can not even begin to comprehend how one could teach math "with more verbal input" - a geometry problem IS inherently about spatial relationships between points and lines and no amount of narrating about triangles is going to make it less so. An understanding of a derivative as the rate of change and slope of a curve, and of an integral as an area under a curve are also inherently spatial concepts which must be understood as such, or a full understanding of the concept is not achieved.

Maybe I'm dense, I don't get where "verbal" can come in. Could you give me an example?

 

My ds has had to do a lot of math verbally in order to understand it; he used to have to do all of his arithmetic out loud while he did the work. This isn't at the level you're discussing, but I found it interesting. I can't answer your question as I'm very spatial, but I do know that my highly visual-spatial middle dd struggled with the linguistic aspects of math which hindered her computation of multi-step word problems when she got SM 6 in particular and in Challenging Word Problems. We took a year to work on the linguistic aspects of math.

 

This has been very enlightening since my birth siblings and I are the opposite of the norm with the math and science aptitudes, but my parents fit in with the stereotype.

 

Edited because I had to add "birth" before it looked like I was contradicting myself.

Edited December 7, 2010 by Karin

[Guest]

Thanks for explaining, KarenAnne. I think I get what you say.

 

That's why it is so important to have somebody else to explain difficult concepts to! I am using this in my physics classes: I let the students form groups, give them conceptual problems, and make them discuss the possible answers. The goal is to get them to talk - because even for a spatially minded person, discussing the material organizes the thoughts and brings misconceptions to light. It is very hard initially to make them talk, because they are not used to discussing physics - just to working problems.

 

I think one reason is that you organize material differently in your head when you talk about it using words instead of just formulas. I know for sure (and I share this experience with many colleagues) that I have never fully understood a subject until I began to teach it to somebody else.

 

I agree completely! Sometimes when dd and I are reading her textbook -- which I quite like actually, compared to others I've seen -- it feels like we have to actually translate it; it feels almost like it does when I'm working with a foreign language. And I've had math all the way through calculus, getting A's.

 

This is why, I think, the studies I've read, and people like Marilyn Burns, believe not only in having someone able to explain to you, but in having kids have huge amounts of experience in wording it themselves, in ways that make sense to them. It's then another huge step to be able to explain it to someone else!