31.3.16

LET'S ENABLE INEPTITUDE.

A retired professor of political science, Andrew Hacker, wrote a column for New York's Times a few years ago proposing to change the way the elementary schools teach mathematics.  It involves less algebra.
Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white. In New Mexico, 43 percent of white students fell below “proficient,” along with 39 percent in Tennessee. Even well-endowed schools have otherwise talented students who are impeded by algebra, to say nothing of calculus and trigonometry.
There is a research project here, identifying the effect of diminished proficiency with mathematics on income inequality.  Perhaps there are more effective and less effective ways of developing proficiency.  Focus, for instance.
It’s true that students in Finland, South Korea and Canada score better on mathematics tests. But it’s their perseverance, not their classroom algebra, that fits them for demanding jobs.
The challenge, however, is in disentangling persistence from persistence at learning algebra. Or other quantitative skills, which is where Mr Hacker was going.
This need not involve dumbing down. Researching the reliability of numbers can be as demanding as geometry. More and more colleges are requiring courses in “quantitative reasoning.” In fact, we should be starting that in kindergarten.
There's some of that quantitative reasoning, or estimating, or approximating, in the Common Core approach to math. But because there's a lot of Common Core being done in a formulaic or non-intuitive way, it's not catching on.

Meanwhile, Mr Hacker has expanded his column into a book, The Math Myth: And Other STEM Delusions, and Slate's Evelyn Lamb suggests he's written a bad polemic.
As much as the content of his conclusions, though, the arguments Hacker uses to reach them are disingenuous. Over and over again, he relies on the reader’s ignorance or fear of mathematics to make mathematics education sound scarier than it is. These repeated misunderstandings and misrepresentations undermine his credibility. I know much more about math than I do about pedagogy, policy, and other topics he addresses. If a huge amount of what he says about math is incorrect or misleading, why should I trust him on the other subjects?

Throughout the book, Hacker uses jargon to make math topics sound more intimidating. Students, he laments, are asked to master “associative properties.” It sends shivers down the spine … unless you know that the associative property of addition is the one that says 5+1+3=6+3=5+4—that is, it doesn’t matter whether you add the first two numbers together and then the third or the last two and then the first. This is a basic property of addition that most students should learn in elementary school.
I've read enough press coverage of train wrecks to have a similar distrust of the press more generally.

There's still work to be done.
Taken individually, each of these examples might seem like an insignificant misstep, but the book is littered with them. I almost hope they’re Easter eggs for numerate people and that Hacker has a secret agenda of improving math education to the point that everyone can recognize that his arguments are full of crap.

Where does that leave us? Few mathematicians or educators would argue that the math curriculum is perfect or perfectly taught. Hacker is not the first to recognize or call attention to the problem; there are thousands of talented and passionate math teachers working to address the math phobia that permeates our culture and gets handed down from generation to generation, teachers working to make their classrooms places where students will see the utility, beauty, and fun of doing mathematics. Of course we should work to make mathematics education better. But while we consider the options, we shouldn’t let our emotional reactions to math terminology lead us to accept shoddy arguments from Hacker or anyone else.
Precisely. The enabling of math phobia contributes to rendering young people unemployable.

And perhaps it's the pedagogy, not the subject, that's done badly.  Stanford's Keith Devlin summarizes.
First though, I should repeat what I said in my HuffPost article about his algebra piece. Just as his essay actually amounted to a strong argument in favor of teaching algebra to all students (albeit not the rule-based manipulations of formulas so often presented in place of algebra), so too his book includes a strong argument in favor of Common Core Math. In the same way that Hacker mischaracterized algebra in 2012, so too his portrayal of the CCSSM (Common Core State Standards for Mathematics) is totally at odds with the real thing—though not quite so far off if you turn your attention from the Standards themselves to some implementations of the CC.
Yes. You can have the best set of tools in town, and yet, if you don't know how to use them, your projects will turn out badly.

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