By way of Majikthise, I found this excellent post by Abbas Raza about the problem of mathematical illiteracy. But to step back a bit, this trail of links began with the release of new teaching guidelines by the National Council of Mathematics Teachers:
The report urges teachers to focus on three broad concepts in each grade and on a few key subjects — including the base-10 number system, fractions, decimals, geometry and algebra — that form the core of math education in higher-achieving nations.
I think this is exactly the right approach. It’s more important for students to develop specific competencies, such as fractions, decimals, geometry and algebra, than to develop the fuzzy skills often described in state educational standards–‘critical thinking’ being the worst of these. A story by Abbas describes exactly what I mean:
I sometimes tutor students for graduate admissions tests like the GRE or GMAT, and the first time I meet with them they often show me algebraic word problems they got wrong in a practice test. I ask how their junior high math is, and no one ever admits that they can’t do 7th or 8th grade math. Then I ask them to subtract one number from another for me, using a pen and a piece of paper I hand them: say -2and7/8ths minus 1and3/17ths. You’d be surprised how many of them are tripped up and make a mistake in a simple subtraction that any 8th grader should be able to do. The problem is they really cannot do ANY algebra until they are consistently and confidently competent in such simple tasks as adding, subtracting, multiplying and dividing numbers, and yes, this includes fractions, decimals, and negative numbers, but even these college graduates generally are not.
I noted a similar phenomenon when columnist Richard Cohen argued that algebra might not be necessary for a student who failed the class six times. That she could not calculate the correct change without the aid of the cash register, indicated that the problem wasn’t algebra, but subtraction.
Before I get jumped all over for advocating ‘drill and kill’, I’m not. How one teaches these skills can vary, and, given, that people are different in many ways, there probably is no one right way to teach. I myself learned arithmetic without reciting “1+1 is 2, 2 + 2 is 4.” I had all sorts of groovy tactile things in my class including an abacus. You can also teach the notion of different base numerical schemes–creative kids like that.
(An aside: the whole different bases thing also allows you to work in some very cool Mayan archeology. To digress even further, I’m always astonished that archeologists were able to figure out that the Mayans used a base five system without understanding their language.)
What I am advocating is a content-based outcome, which for a long time has been overshadowed by jargon-laden buzzwords (you need to know something before you can critically think about it). Given the importance of basic math for, well, everything, certain content-related skills and knowledge must be mastered. These guidelines sound like a step in the right direction.