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Tuesday, January 09, 2007


Local Schools to Study Whether Math - Topics = Better Instruction via Phil

A couple thoughts on this:

1) It is absolutely infuriating when supposedly well-educated and informed journalists say things like this:
"Some scholars say the American approach to math instruction has allowed students to fall behind those in Singapore, Japan and a dozen other nations. "

This is a tired loquation, familiar to anyone who has ever read an article detailing literally any facet America's public education. It is a way for an author to add interest by inserting a "sky is falling" mentality into an otherwise innocuous article, which seems to be just about the only thing they teach in journalism schools any more. What they do not note, is that the comparison between the American education system and those of virtually any other country in the world are utterly inexact. Take, for example, the Office for Economic Cooperation and Development study. This study is typical of this category of investigations, and belies one of the basic issues with testing across cultures: namely, it can't really be done.

At the risk of sounding racist, the educational systems of many countries (especially Korea, Japan and China) tend to be much more tightly focused on operational math; that is, addition, subtraction, graph interpretation, and so on. Largely this tends to be a function of working within the confines of a country with a hypercompetitive higher-educational admission process. In the US, the difference between an A and a B can be the difference between MIT and Carnagie-Mellon; in many Asian countries, it can be the difference between getting into Nanjing University and not going to college. The difference is a mathematical culture that is fairly well built with an eye for admissions testing, which tends to fit the same mold as evaluatory testing.

Moreover, tests that want any modicum of comperability cannot test subject matter. Someone in 11th grade who has taken AP Calculus but not Geometry is going to come across on many exams as being worse at math than someone who has the reverse. The solution testmakers have found is to create a test that is solely "reasoning." This has two fairly immediate consequences: first, countries that do not have a democratically integrated education system have a massive advantage. Finland, who consistently ranks first in mathematics, doesn't have the "everyone goes to college" mentality of the US. Instead, they track into higher-education and vocational schooling. In China, those who are not going to go on to University commonly drop out to work. I am not saying those systems are worse than the US system - indeed, I think we would all be significantly better off just accepting that not everyone needs a four-year degree - but they do make a huge difference in testing.

Finally, studies consistently show a robust correlation between poverty and poor performance. This should be a suprise to absolutely nobody, and seems to be consistent without reference to school funding or overall institutional quality. (One of the findings of the above referenced study was that intra-school variation in the US is bigger than almost any other country). Yet the US has a Child poverty rate almost 7% higher than Canada, and 20% higher than Sweden. And considering the difference in quality and quantity of social programs (see: socialized healthcare) poverty in the US, in addition to being more prevailant, is also much more debilitating.

The basic result of these studies, in other words, seem to be: countries that have fewer poor kids taking the test tend to rank ahead of countries with more poor kids taking the test. You can eliminate poor kids from taking the test by tracking (removing the poor or underperforming ones early) or by tackling poverty head on, and making sure children are able to get an education because they are not systematically deprived of basic human rights. The US doesn't seem particularly interested in either of these, since preventing children from developing crippling illness by giving them health insurance is not democratic, and kicking them out of school is too obvious. But it does mean that focusing on curriculum and textbooks may never get to the real root of the problem.

2)This quote is also important:
"One group, led by mathematicians, has argued that children must learn a sequence of basic skills, including times tables and some memorization, if they are to have a fighting chance at college-level math study.

The other camp, led by math educators, has urged children to understand the theory behind math problems and to find solutions in their own way."

It's really unsuprising that the group that wants to teach basic skills is mathematicians, and the one that wants kids to understand "theory" and find solutions in their own way is educators.

Here's the thing: a first grader will never, ever, ever, unless they are an absolute prodigy, be able to understand the "theory" behind addition and subtraction. The actual theory behind addition tends to involve either a set-theoretical approach, invoking the cardinality of sets, or a number-theoretical approach, which tends to necessitate the introdution of the Dedekind-Peano axioms.

In fact, this is true for most math up until roughly the sophomore year of college. In order to understand the "theory" behind geometry, you need calculus. In order to understand the "theory" behind calculus, you need real analysis. These are not elementary school topics.

So what are educators really advocating? What they're going for is "New New Math" - like the disaster that is PSSM. It's a system of approaching mathematics as a social science, removing "right" and "wrong" answers in favor of elevating the explanation over the result. The problem is, this method is utterly bad. It is, for the less mathematical among you, like teaching upper-level linguistics to a kindergartener to help them understand sentences. The abstraction of these principles does not help anyone comprehend methodology, whereas familiarity with the methodology is instrumental in comprehending the abstractions.

The point I'm trying to make is: there are a lot of problems with education. But if the country is looking for real reforms, start by paying teachers more, and eliminating teachers unions. It's the sort of answer that is unappealing to people, precicely because it is obvious and tends to hurt the bottom line. But as someone with a ludicrous amount of math education, I face the choice in the coming year of working for $96,000 a year at Booz Allen, or $27,500 a year in DC public schools, where I will be able to teach Algebra I to 9th graders while someone with a degree in Communications struggles through higher-level classes because he has seniority. Guess which one I'm leaning towards.

The other point: stop letting people who don't know math or science create the curriculum for math and science. The things they teach in science classrooms these days are so utterly detached from anything meaningful, it's embarassing. And you don't need a study talking about Japan to prove it. There is far too much public interference in education, and that evolution/creationism is the hot topic is proof of that.

cranked out at 9:01 AM | |

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