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The Bell Curve
Monday, September 14, 2009
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September 14th, 2009
In 1994 Richard Herrnstien and Charles Murray wrote “The Bell Curve," a book that explored the implications of intelligence. The central thesis was that native intelligence, what we call IQ, has a greater effect on the outcome of an individual’s life than any other social or economic factor. In short, the smarter you are, the better you are likely to do in your life. As if that wasn’t a controversial enough idea, the authors went on to say that based on their research there were significant differences between the races in intelligence, although they also pointed out that it is debatable whether nature or nurture account for ethnic differences.

The book was a bestseller and a major controversy. Some accused the authors of scientific racism; some applauded them for telling it like it is. In America we like to believe in an individual’s ability to rise above their circumstances, that the unfettered citizen can do anything just by sheer will. Being told your possibilities are determined by something we believe is largely genetic does not go down well. Yet, it is hard to deny the fact some people are smarter than others and that does make a difference in their lives.
The bell curve refers to a mathematical fact about quantities affected by many random or unknowable things. Take height, for example. Your height is determined by many different factors, age, genetics, nutrition, even gravity, which varies from place to place on the Earth. If you were to take 1,000 men and group those by height, a graph of their heights would look like a perfectly symmetrical hill, somewhat like a bell, which is where the graph gets its name. It is also called a “normal” curve.

The interesting thing about the bell curve is that it is predictable. The top of the hill will be 5 feet 10 inches, the average. Two thirds or about 667 will be within 3 inches of that height (between 5-foot-7 and 6-foot-1).  One sixth are above 6-foot-1, one sixth below 5-foot-7. If you ever wondered why chairs and couches are the heights they are or why certain sizes of clothing seem more common than others, there’s your answer. Those things are built for people and most people are a certain height.
Many things are distributed like height. The speed of people walking across the street. The tire pressure of cars in a parking lot. The life span of a light bulb. The number of miles per gallon your model of car gets.  The scientific consensus on intelligence is that it also fits a bell curve.

Obviously, this has big implications for our education system, but you wouldn’t guess that from the way schools are designed. However, Americans are in denial about the impact of intelligence. Consider this fact: half of American children are below average intelligence. For that matter half of all of us are below average in intelligence. I can hear the keyboards typing angry rebuttals already, but, that is the definition of average ... the middle point. Few want to honestly address this point. No one wants to think their child might be below average and no one wants to point out someone else’s child is less than average. In America we think that if you can’t make the grade, you’re just not trying hard enough.
Last year there was a minor controversy about our local high schools making college preparatory classes standard requirements for graduation. Everyone was going to college or bust. Critics of this plan were accused of fostering mediocrity. But I have to point out; most people are, in fact, mediocre. It doesn’t mean they’re bad. Some people are pretty funny. Some are strong. Some can throw a football with precision. Some are beautiful. Some are just decent.

It seems to me we don’t design our schools to account for the variety of students we have. For instance, differences in intelligence don’t necessarily the ability to master a subject, but rather the time it takes to master it. The brighter you are, the less time it takes to learn something. Yet our school schedules are very rigid. I have 50 minutes to teach the topic of the day. When that time is up, I have to move on because tomorrow I have another topic and I have to be at a certain point by the end of the year. I have a schedule that isn’t necessarily the schedule of my students. 

Another example is how students are grouped. We group students by age. Nearly all 7th graders are 12.  Nearly all 10th graders are 15. This makes sense if you consider maturity, but not if you consider ability.  It’s not such a big deal if we accelerate some students, although many schools resist too much acceleration even when ability warrants it. But, allowing students to proceed more slowly is not OK. It’s considered a humiliation and a punishment. I wish we could abolish grades or make a broader group to account for maturity.

Just like designing clothing or furniture, schools need to accommodate all the variation they get in their student population. It’s nice to think of all of our children as being above average, but if we stocked clothing stores like that, few would find a comfortable fit.
20 comment(s)

russ wrote on Sep 14, 2009 7:42 PM:

" Teacher, Thanks for your lesson in statistics but what is your point?

Should there be advanced education for exceptional students, especially in math, science and language? Do we have that now in our schools?

Are you saying that our educational standards are too high? "

a teacher wrote on Sep 14, 2009 8:43 PM:

" Russ.

My point is that our education system works on the assumption that everyone is above average and that if they are not making the grade, they (or someone else) is not trying hard enough. As a result we have an inflexible school system that doesn't take a wide variation of human intelligence into account.

Consider this.

My partner math teacher works next door to the gifted 6th grade class. Every year she gets a student or two from that class to take her 7th grade math class. They usually do well and when they go to 7th grade they take 8th grade math (algebra). The problem is that next year they have no math class. We have to move heaven and earth to get them to a high school. It seems like it should be easier. My guess is that 5% to 10% of our students could graduate a year or two, but there is no provision for that.

On the other side I get students who have failed sometimes three years in a row, and yet, are passed on. What do you think their chances of passing my class are? There is only one type of 7th grade math, it's either pass or keep on failing.

Nearly a third of students are dropping out of high school. There are many different reasons. I wonder how many would stay in if they could go a little slower?

I think that setting expectation high for all is unrealistic. "

pharper wrote on Sep 14, 2009 11:08 PM:

" I think that rather than forcing students to take all their classes in a linear fashion, schools should require certain classes (or a certain number of classes in a particular subject, like 2 math classes, 2 English, etc.) but let the student decide when to take them. A high school freshman could take calculus if s/he was prepared, and then take the easier math classes during his/her senior year so it's not as stressful. That way students could take classes when they feel that they are ready, and still get a well-rounded education. It would be a little more like college in that the student's schedule isn't hand-picked for them, and they can customize their schedules in order to make the classes they are taking relevant to graduation requirements but still at their own level. "

Cadence wrote on Sep 15, 2009 11:07 AM:

" Why not group students of similar abilities regardless of age? Seems to me that it might be a far more efficient use of resources and teacher time. "

glenroy wrote on Sep 15, 2009 11:28 AM:

" I like it....but I'm stumped.

How can half the population be below average without half the population being above?

If the bell works average should be the top of the curve?

It would seem to me using a national intelligence average bell curve….darn near impossible for more than half to be on either side of the curve.

Another interesting piece of work Teach….very well written…of course my writing skills were always left of center....curve wise.

BTW: What is the average IQ? "

a teacher wrote on Sep 15, 2009 1:48 PM:

" Half of the population is indeed above average. It's a symmetrical curve. One way of thinking about is that a person with an IQ of 130 or higher, a little more than 2% of the population is as unique as a person with an IQ 0f 70 or lower, also about 2% of the population.

The average IQ is 100. That is a "normed" score, that is what ever the average score is on intelligence tests, we'll call that 100. In other words, intelligence is "curved". 2/3's fall with in 15 points of 100 (2/3 are between 85 and 115) and 95% fall with in 30 points of average(95% between 70 and 130).

I read an article last year where the author claimed that human intelligence is increasing. The person of average intelligence today would score higher than a person 100 years ago. "

alucawanza wrote on Sep 15, 2009 1:49 PM:

" As a sixth grade teacher I had many students who were ready for 7th grade pre-algebra. Fortunately Redwood was very helpful and loaned me books. These kids had separate lessons although they mostly taught themselves or each other. They were very talented. When they went to Redwood they had to pass the pre-algebra test to take algebra. Then most of the parents drove them to Vintage for Geometry. The parents of these kids were very active in their child's education. One of them had started their child on Kumon Math, a Japanese program, when he was very young. It made him almost intuitive about math. There weren't many of these kids, but I sure enjoyed watching their success. It was fun to work with them.

Glenroy: a teacher, please correct me if I'm wrong, but I believe the average IQ is any number between 95 and 105.
However, there are other forms of IQ. I believe there are seven: including number intelligence, word fluency, verbal meaning, memory, reasoning, spatial perception and perceptual speed. "

a teacher wrote on Sep 15, 2009 3:00 PM:

" Alucawanza:

Years ago I went to a talk by Howard Gardener, who is the fellow who came up with multiple intelligences. I heard him on the radio a while ago saying he believes that there are as many as 20 or so different types of intelligence.

Other psychologists use one measure to discuss intelligence.

It all boils down to the same thing though. Humans are individuals with common characteristics and a vast variety of differences. "

glenroy wrote on Sep 16, 2009 10:04 AM:

" Alucawanza
I don’t know what the national IQ average is or trends related to it. I am a little surprised just 2% on average would score 130 or above…. Or is that 2%=130?

BTW: A wonderful 6th grade teacher…Mr. Eggers….don’t know of a student that ever had a bad word to say about this Gentlemen.


Teach…
Did Gardener develop the EQ test?

Putting together business teams we used so many tests it made my head spin, or spin faster… it seemed to us a high EQ score indicated effective use of ones IQ…. "

a teacher wrote on Sep 16, 2009 11:11 AM:

" Glenroy: The best way to think of the Bellcurve and IQ is to think about how likely a particular measurement is. With a bell curve the further away you get from the average, the rarer the measurement is. If you think about height, most men are around 5 foot 10 inches. Very few men are above 6 foot 10 inches, very few are below 5 feet.

For intelligence, If you have a group of 10,000 random people, you would expect 214 to have an IQ of 130 or above. Of those 10,000, 13 have an IQ of 145 or above. I have a friend whose daughter has an IQ of 164, she is 1 in 100,000, very rare indeed.

Bill Gates once made an observation about China. He said just by it's sheer size (population wise), China has over a million geniuses. The same would be true of India.

Gardener did not invent the term EQ, although his work got the ball rolling in talking about multiple types of intelligence. I don't know much about it, but from what i can gather it appears that some believe that there is a connection between "emotional intelligence" and job performance. However that appears to be quite a controversial claim. "

vocal-de-local wrote on Sep 16, 2009 2:47 PM:

" People don't always like facing truth. But we must take into consideration that the bell curve strictly revolves around scholastic intelligence. Other types of intelligence do exist.

For example, an engineer with a strong math mind (note that autistic children are most often the offspring of an engineer parent), would not be particularly effective at sales jobs which require a great deal of social skill. Nurses, on the other hand, must have a combo of nurture and brain power to navigate through chemistry, anatomy and physiology and still maintain an element of care. Nurturing physicians are often weeded out by the educational system which requires quiet a bit of calculus (I'm generalizing here) because math brains often do not have natural nurture. Of course, there are exceptions.

Our educational system generally does not recognize other types of intelligence. But here's the honest truth. There are a certain percentage of people out there who lack both social and scholastic intelligence. We tend to think that they can "will" themselves out of it. They can't.

So either we admit this truth or we continue having a significant amount of our population sitting at home, being taken care of by others, because they've spent an entire eighteen years brainwashed by a system that says that they "can" get ahead if they try hard enough. When they discover that they don't have what it takes to be what we define as "successful", they resort to selling drugs or doing nothing at all.

The level of intelligence a person is born with is fairly static. Sure, a person can do brain exercises and open up some pathways, but the boundaries are still limited by genetics. Our educational system is unwilling to acknowledge this truth. "

winemd wrote on Sep 16, 2009 4:02 PM:

" Pat Wolfe (a Napa local) has done a lot to integrate brain research in to educational models. Her website is www.patwolfe.com.

The level of academic intelligence is somewhat static, but there are windows of learning when the intelligence can be maximized by learning certain things. Newsweek had an article about that in February 1996. Stuck with me, can you tell? For instance the research shows that the more words a child hears by the age of 2, the larger the vocabulary will be. And apparently, this applies to "live" language, not TV. For music, the best age to start learning an instrument is 3-10.

My 2 older children have very different strengths in terms of intelligence. So traditional acedemics is great for one and just okay for the other. So we try to work out different ways for him to get the concepts down. "

glenroy wrote on Sep 17, 2009 4:46 PM:

" Great reading and great posts.... "

winemd wrote on Sep 19, 2009 5:54 PM:

" You know, this is interesting based on the magnet school comments thread. So are the students at PVA more scholastically intelligent than the ones in the regular Pueblo Vista program? If the study is correct, then yes. The demographics of the groups being quite different won't matter (either economic or ethnic). Merging the 2 programs under the magnet program would not then help the underacheivers or hurt the ones at the top of the scores (PVA). If you look at the example of NVLA, you might indeed see evidence that this is true. The scores for the white students at NVLA are similar to PVA. (NVLA 919, PVA 902)
Here is the breakdown for NVLA vs. PV Regular program: Hispanic students NVLA 729, PV 748; Socioeconomically disadvantaged NVLA 699, PV 741; English learners NVLA 688, PV 729.

If you compare to Bel Aire/ BVA, all of the scores in these catergories are lower than NVLA. So NVLA students are in the middle.

It's hard to find any other schools in the NVUSD where there are numerically significant populations of both groups for comparison purposes. We don't know what the few white children at Phillips score nor the Hispanic children at Vichy.

So it could be argued that if the English language learners were in an English only program it probably woudn't change their scores much. Which means that it is based on something other than the program they are in, which could be intelligence, economic factors, or social factors.

No answers here, just questions... "

browns valley wrote on Sep 21, 2009 4:10 PM:

" The average Japanese math student's level of achievement is as high as our highest achieving students. It's not IQ, it's process.

The Japanese society and education system has a belief in "effort over ability". The US has bought the "ability myth" hook line and sinker. Yes some people are born with superior abilities but that is irrelevant. In Singapore they teach Algebra in sixth grade to all of their students.

Anyone can run faster if they practice. Michael Jordon was cut from his high school basketball team so he worked harder. "

a teacher wrote on Sep 21, 2009 9:25 PM:

" Couple of things, Browns Valley. IQ is not all there is, motivation is surely important. But it is not all there is either. Believing that because you want it, you can get it is magical thinking. Like you say, everyone can run a mile faster, but not everyone can run a four minute mile, it doesn't matter how much they try.

I greatly admire how the Japanese teach Mathematics. It's very elegant. But, it works because it's Japanese, I don't think you can duplicate it here.

And no, Singapore does not teach Algebra in the 6th grade. You can look up their curriculum on line. Their scope and sequence is about the same as California's, except it's much narrower. They teach Algebra in 8th grade (standard 2 - it's modeled after the British system, which I've taught). "

pharper wrote on Sep 21, 2009 10:53 PM:

" We also have to consider the fact that education is EVERYTHING in most Asian countries. Unlike the United States, the Chinese and Japanese especially hold teachers in the highest regard - education is sacred and it is not just hoped for, it is expected that students will excel in everything they are taught. However, I am given to understand that Japanese and Chinese students are selected according to who is the smartest and will go furthest academically, once a certain level of education has been reached. The rest go into vocational training. This, I think, has everything to do with IQ or "book smarts" than it does with effort, otherwise most, if not all students would continue to rise through the higher levels of education.

Certainly, more emphasis is put on effort than on raw talent for learning, but intelligence plays an enormous factor in any system of education - except, apparently, the United States system, where everyone is expected to learn at the same rate, in the same capacity, and the same material. "

JustAnotherManicMonday wrote on Sep 23, 2009 3:35 PM:

" Teacher- I'm now 40 and realizing I'm just average. I'm learning to be OK with it. When I was younger, I thought I was smarter, but the older I get, the more I realize I'm not.

I had a hard time with geometry and advanced algebra in high school. I got through first year algebra by a very kind teacher, and going over it again and again. I needed a lot of extra help as I didn't "get it" the first time she explained it. I had her for geometry too. Then I changed schools, had a man teacher, and he would only explain it one way, and wasn't kind when I couldn't "get it" the first time.

I did better at learning Spanish than Math. "

steph wrote on Sep 23, 2009 4:52 PM:

" Aye, that Bell Curve study really rubbed me the wrong way, and not because I'm not Asian.

Hah!

Inherent intelligence, in the traditional sense, the ability to reason, is only one part of a very complicated mix of factors that contribute to success (whatever that is.)

There's a certain imperiousness or egotism that comes from being "smart" or good on tests in school, and it's these "smart" folks who are defining "intelligence". It's biased in its chauvinism ("My intelligence is the yardstick by which we will measure intelligence because it's the only intelligence I understand".) But it's only academic.

Economist James Heckman has interesting things to say about education.

There are a lot of folks out there who never stood a chance, because as children they were not read to, never told they were intelligent, rarely smiled to, were stressed from day 1, etc. Some of this is cultural, some socio-economic. IQ studies can't be controlled for all the various input factors.

And IQ is only one kind of intelligence, of which there are several, as mentioned above by your other posters, all of which intermingle and overlap--and what does it all mean, anyway?

All I know is, I've tried to curb some of the insular arrogance in my own children, the kind that comes from being book smart and praised for it constantly. I'm trying to get my children to recognize strengths come in various forms: hard work, loyalty, artistic ability, sense of humor, compassion, altruism, athletic ability, beauty, intuition, emotional stability, and I could go on and on.

Anyway, teacher--that's God's work you're doing, working with children to give them education and self esteem. "

napablogger wrote on Sep 24, 2009 9:30 AM:

" teacher, great article and I totally agree with you. It is insane the way we try to push every kid into college.

It also ties into something I think about in many contexts, sort of how in the box we are with everything.

When I look down from a plane I always think how weird it is that all the land is divided into perfect boxes. Humans are very comfortable with living in linear, straight defined environments both physically and mentally.

There is a lot of talk about getting outside the box, very little real doing so.

We are so inside the box we don't even know it.

In politics everyone tends to line up on one side of the fence or the other, and argue over how correct their box is.

Reality is a lot more circular and indefinite. "

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