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Sunday, February 28, 2016

The Wrong Way to Teach Math

"Think about numbers as a language; we need to learn to be fluent in it." according to Andrew Hacker, teaches political science and mathematics at Queens College and is the author of the forthcoming book The Math Myth and Other STEM Delusions,” from which this article below was adapted.

Photo: Laurie Rollitt

HERE’S an apparent paradox: Most Americans have taken high school mathematics, including geometry and algebra, yet a national survey found that 82 percent of adults could not compute the cost of a carpet when told its dimensions and square-yard price. The Organization for Economic Cooperation and Development recently tested adults in 24 countries on basic “numeracy” skills. Typical questions involved odometer readings and produce sell-by tags. The United States ended an embarrassing 22nd, behind Estonia and Cyprus. We should be doing better. Is more mathematics the answer?

In fact, what’s needed is a different kind of proficiency, one that is hardly taught at all. The Mathematical Association of America calls it “quantitative literacy.” I prefer the O.E.C.D.’s “numeracy,” suggesting an affinity with reading and writing.

Calculus and higher math have a place, of course, but it’s not in most people’s everyday lives. What citizens do need is to be comfortable reading graphs and charts and adept at calculating simple figures in their heads. Ours has become a quantitative century, and we must master its language. Decimals and ratios are now as crucial as nouns and verbs.

It sounds simple but it’s not easy. I teach these skills in an undergraduate class I call Numeracy 101, for which the only prerequisite is middle school arithmetic. Even so, students tell me they find the assignments as demanding as rational exponents and linear inequalities.

I’m sometimes told that what I’m proposing is already being covered in statistics courses, which have growing enrollments both in high schools and colleges. In 2015, nearly 200,000 students were taking advanced placement classes in statistics, over three times the number a dozen years ago. This might suggest we are on the way to creating a statistically sophisticated citizenry.

So I sat in on several advanced placement classes, in Michigan and New York. I thought they would focus on what could be called “citizen statistics.” By this I mean coping with the numbers that suffuse our personal and public lives — like figures cited on income distribution, climate change or whether cellphones can damage your brain. What’s needed is a facility for sensing symptoms of bias, questionable samples and dubious sources of data.

My expectations were wholly misplaced. The A.P. syllabus is practically a research seminar for dissertation candidates. Some typical assignments: binomial random variables, least-square regression lines, pooled sample standard errors. Many students fall by the wayside. It’s not just the difficulty of the classes. They can’t see how such formulas connect with the lives they’ll be leading. Fewer than a third of those enrolled in 2015 got grades high enough to receive credit at selective colleges.

Something similar occurred when the Carnegie Foundation for the Advancement of Teaching created a statistics course for 19 community colleges in 2012. It was advertised as an alternative to remedial algebra, with its sadistic attrition rates. In Statways, as it was called, here is some of what students were asked to master: chi-square test for homogeneity in two-way tables, line multiple representation of exponential models. Even with small classes and extra support, almost half of the students got D’s or F’s or dropped the class.

The Carnegie and A.P. courses were designed by research professors, who seem to take the view that statistics must be done at their level or not at all. They also know that citizen statistics is not the route to promotions. In the same vein, mathematics faculties at both high schools and colleges dismiss numeracy as dumbing down or demeaning. In fact, figuring out the real world — deciphering corporate profits or what a health plan will cost — isn’t all that easy.

So what kinds of questions do I ask my students?
Read more... 

Additional resources

The Math Myth:
And Other STEM Delusions
"The Math Myth expands Hacker’s scrutiny of many widely held assumptions, like the notions that mathematics broadens our minds, that mastery of azimuths and asymptotes will be needed for most jobs, that the entire Common Core syllabus should be required of every student. He worries that a frenzied emphasis on STEM is diverting attention from other pursuits and subverting the spirit of the country." writes Amazon.

Publisher: The New Press (March 1, 2016). 

Source: New York Times

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