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2. False. Four students score 1, 7, 8, 9. Average is 25/4 = 6.25. Only one is below average.
As a math teacher, I, too, take some issue with the wording of his second point, which clearly won't always be true. That said, I suspect he is loosely referring to the median.
Why would I waste my money to support some pop-political writer?
Has his work been peer reviewed? No. That's because his "peers" are talking heads on TV, politicians, and other writers of political polemics.
Do you disagree with his points, or are you just taking issue with his political background? Because guess what? There are a lot of teachers, many of whom would describe themselves as being "liberal," that would wholeheartedly agree with most of his aforementioned arguments.
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2. False. Four students score 1, 7, 8, 9. Average is 25/4 = 6.25. Only one is below average.
I think Murray assumes a gaussian (bell curve) or close to gaussian distribution of ability (however measured) among the students. It seems a reasonable assumption but I'm no expert.
I actually think number 2 could be flat out wrong. In order for that to be true, "children" would have to not be normally distributed with a long high tail (if children were normally distributed, then you would have a median and mode at mean, and less than half of children would be below average). In other words, we would have to have a large amount of exceptionally high performers compared to the number of exceptionally low performers. I think the opposite is true, we have more children who perform exceptionally badly than perform exceptionally well. The former takes purposeful lack of effort while the latter takes purposeful effort. That would mean that more than half of children are actually above average.
Uhm, in normal distribution half the people are below the mean, half are above. That is part of the definition of normal distribution.
Look at a standard curve, by definition half of the population will be to the right of the mean, half to the left.
2. False. Four students score 1, 7, 8, 9. Average is 25/4 = 6.25. Only one is below average.
This confuses sample mean with distribution mean or expected value. From these four numbers, you cannot determine the mean of the distribution -- 6.25 is only a rough estimate of the distribution's mean (see the "Law of Large Numbers"). In other words, you cannot tell much of anything about the average value of all students' abilities (if that is the right word -- perhaps "accomplishments" would be a better choice in this context) from only four data points. It could be that all of these four scores are above the mean, or that all four are below the mean, although neither outcome would be terribly likely).
Last edited by Hamish Forbes; 11-25-2013 at 03:43 PM..
I would say our future depends less on how we educate the "academically gifted" than it does on how we educate those in the bottom part of the class. Talents have a way of coming out on their own. Its the kids without much talent that are going to need all the help we can give them to succeed in a world that has become frightfully specialized and competitive in ways I could not have begun to imagine as a child in the 1960s.
We need to bring back vocational training and remove the stigma associated with it. That will take care of the majority of the left half of the curve. The gifted otoh, are frequently ignored and left to figure it out on their own. This maybe part of the reason gifted students can be more depressed, are more likely to feel isolated and to be underachievers.
2. False. Four students score 1, 7, 8, 9. Average is 25/4 = 6.25. Only one is below average.
That is not a normal distribution. If we are talking a population such as, the intelligence of every child on the planet, than it is a normal distribution and mean/average, median, etc would all be the same place. Half of the students would be to the right of the mean (aka below average) and half to the left.
Because he has empirical data and legitimate statistical analysis to back up everything in his books. Have you actually read Coming Apart?
Correlation is not causation.
In all likelihood it isn't the marriage that is the deciding factor but rather the SES that goes along with the income of having two parents. It is a universal truth, regardless of marital status, children raised in wealthier homes do better academically.
This is from a book written five years ago, but I think some of the material is as relevant today as ever. Here they are, in a nutshell:
1. (Student) Ability varies.
2. Half of the children are below average.
3. Too many people are going to college.
4. America's future depends on how we educate the academically gifted.
I haven't read the book and I think it's important that we're careful about how we apply these "truths," but it seems like these are things that are worth having a conversation/debate about instead of simply accepting the current narrative and expectations that are in many ways unrealistic.
My four educational truths:
Schools don't vary as much as the students' performance does ($/student, facilities, teacher educational level, etc are all about the same)
"Good" schools are good because smart kids attend them - wealthy neighborhoods are wealthy because smart people live in them and smart people have smart kids which results in the schools being "good".
Majoring in practical major from a no name school is a lot more valuable than majoring in some softology from an expensive football or prestigious school.
Your kids' future depends on how much more the demand for their services will be in comparison to all the other kids in America. Nobody cares about America's kids. The worse (the rest of) America's kids do, the more the demand your kids' services will be.
In all likelihood it isn't the marriage that is the deciding factor but rather the SES that goes along with the income of having two parents. It is a universal truth, regardless of marital status, children raised in wealthier homes do better academically.
Of course, and nowhere did I say anything that mistakes correlation for causation. Nor did I mention marriage. Moreover, i think that you are wrong -- kids from single parent households do not do as well in life, on average, as kids from stable, two-parent families, ceteris paribus. Murray talks about this, citing numerous studies, and addressing specifically the effect of correcting for differences in SES (page 158 of Coming Apart).
But I would claim that people with low cognitive ability and, especially, dysfunctional cultural values generally have low SES, low income, unsuccessful life partnerships (e.g., marriage), and underachieving offspring. One of the surest routes to poverty is for a girl to drop out of high school and begin having a sequence of illegitimate children with various fathers. Had that very same girl completed high school and waited until marriage or at least a stable, monogamous relationship before having children, she would likely be far better off in terms of SES, etc., as would the children.
Last edited by Hamish Forbes; 11-25-2013 at 05:06 PM..
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