There has been a lot said so far about Andrew Hacker’s argument for de-emphasizing algebra, and I’ll have more to say about that later this week. But one thing I’ve noticed anecdotally is that when students say they have difficultly with algebra, that’s usually not the entire story. Typically, that means they have also trouble with arithmetic. There’s a reason why the ability to do long division is correlated with long-term mathematics performance: you have to master the basics.
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 -2 and 7/8ths minus 1 and 3/17ths. 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.
The problem isn’t algebra per se. It’s more basic than that.