I'll get to the rest of Bruce's post later (maybe), but let's address the numbers first:THE UPPER HALF OF ALL SCHOOLS OUTPERFORM THE AVERAGE OF ALL SCHOOLS!!!!!or … Good schools outperform average ones. Really?Why should that be any different for charter schools (accepting a similar distribution) that have a similar average performance to all schools?This is absurd logic for promoting charter schools as some sort of unified reform strategy – Saying… we want to replicate the best charter schools (not that other half of them that don’t do so well).Yes, one can point to specific analyses of specific charter models adopted in specific locations and identify them as particularly successful. And, we might learn something from these models which might be used in new charter schools or might even be used in traditional public schools.But the idea that “successful charters” (the upper half) are evidence that charters are “successful” is just plain silly.
We have a serious case of innumeracy in this country. It starts with the media: over and over and over and over (I could go on) again, the media has shown it cannot deal with numbers. That's not just true in education; it's true in every facet of life the media covers. Worse, the media is incapable of explaining what data may show in clear and comprehensible ways: Bob Somerby has been writing about this for some time.
I'm not saying your average reporter should be able to run a regression analysis (although I don't think it's too much to ask that they know what that means), but some basic understanding of statistical analysis should be the minimum knowledge required to work in the press.
That said, I do think this problem runs deeper than the press; a modern, functioning democracy requires its citizens to be able to understand some basic mathematical and statistical concepts that just seem to be lacking in our political discourse. And we educators need to look at how we are teaching math to see if we can do something about it.
This is going to come off as boorish to some of you, but take this article in today's NY Times:
Sharasha, I can tell you that in my 40-something years in the planet, as someone who done quantitative analysis, worked in business, and designed computer software:Hunching over her notebook at Borough of Manhattan Community College, Sharasha Croslen struggled to figure out what to do with the algebra problem in front of her: x2 + 2x – 8 = 0.It was a question every ninth grader is expected to be able to answer. (For those who have erased the ninth grade from memory, the answer is at the end of the article.) But even though Ms. Croslen managed to complete three years of math and graduate from high school, she did not know how to solve for x.“It’s incredibly frustrating,” she said during a break from her remedial math course, where she has spent the last several weeks reviewing arithmetic and algebra. “I know this is stuff I should know, but either I didn’t learn it or I forgot it all already.”
I have never in my adult life had to factor a polynomial.
Yes, yes, yes, I know... you have to know this stuff for any of the sciences. It's the stepping stone to advanced math; you won't get to calculus without it. I get that. I'm not saying Sharasha shouldn't have to know this if she wants to go on to college. But there are plenty of people in this nation who are productive, engaged, well-informed citizens who do not need this.
However, I contend no one can claim to be any of those things and not be able to apply knowledge of the difference between a median and a mean.
One of my pet peeves is how few people seem to understand the difference between a marginal rate of taxation and a real rate. Or how few people stop to consider the difference between real dollars and current dollars.
That's innumeracy just as much as not being able to complete a geometric proof. And it a type of innumeracy that allows politicians and pundits to make bad policy and get away with it because their constituents can't see the illogic of decisions.
We need a mathematics curriculum that teaches analysis as much as computation. But computation is much, much easier to test, so in this 'formed world of eduction, we're not likely to get it anytime soon.