American History and Practical Math

The Math Myth and Other STEM Delusions
Andrew Hacker

Let’s be honest: math can be terrifying. I’m not an engineer because I couldn’t wrap my head around integral calculus.

But I  know some things about myself. One is that when it comes to math–the kind they care about on standardized tests–I’m in the 85% percentile. That’s not too shabby.

Then again, it’s also humbling, because it means there are potentially a billion people on the planet better at it than I am.  Some of them have much more math than my three semesters of graduate level statistics.

I’d bet that most of that billion avoided the sweaty palms, stomach aches and general level of anxiety I experienced. It was, in a word, unpleasant

Why should anyone have to experience that if they didn’t have to?  Andrew Hacker would probably nod in agreement with my question.

The Administration Building (I believe) at Queens College, the CUNY Campus where Andrew Hacker teaches. I like the original buildings.

Professor Hacker teaches at Queens College where he is a member of the political science faculty.  Queens is one of the ‘senior’ colleges of the CUNY system, a group which includes Brooklyn, City and Hunter colleges.

Queens has a particularly strong social science faculty. So strong, in fact, that  as both an undergraduate and graduate student I took courses there despite graduating from elsewhere in the CUNY/SUNY universe.

Professor Hacker’s reputation within the system and, to judge from the acknowledgments pages, New York academic circles, is well-established. In plain English he’s no crank and worth listening to.

What he’d like to get you thinking and talking about is math. Specifically, he’d like to get you thinking about math, and the rest of the STEM acronym, in a critical manner. That means letting go of the idea that math “…will armor our workforce in a merciless world.” (p. 2)

The obverse view. Hey, I’d sell the view, too. And I’ve lived in Queens and like the school.

Hacker is  pretty clear right from the start that he believes this idea has taken on a life of its own. So much so that he references Charles Mackay‘s 19th century classic: Extraordinary Popular Delusions and the Madness of Crowds. When the subject at hand has been lauded by two presidents, the educational establishment and most every corporate leader those amount to fighting words.

Yet his argument is not without merit.  How much, Hacker asks, of everyday life and business requires knowledge of advanced mathematics? Arithmetic, surely, but what the British call maths? If you think about it you’ll quickly conclude that you almost never use advanced algebra or geometry let alone trig, calculus, differential equations and the like.

Trouble is, STEM isn’t just a delusion, it’s public policy.  Forty-two states have adopted the Common Core Standards Initiative, a testing-heavy approach to assessing whether American students are making adequate progress in key areas.

Show me an everyday activity in which you need to apply an asymptote in any orientation. If you can, have I got an azimuth for you.

None figures more prominently than math and Hacker wonders whether we are doing more harm than good.  Nor is he alone. Hacker demonstrates he is not the only one asking how we wound up in such a place.

One of the design features of the book is a page or spread at the end of each chapter labelled ‘Voices.’ Shown as cartoon ‘talk bubbles,’ these are actual, though anonymous, quotes from readers of columns Hacker has penned on the subject.

I admittedly found this annoying at first but came to embrace it as I realized these pages functioned like pages of verbatim extracts culled from focus groups or in-depth interviews. Here’s one, just to give you a flavor of the commentary:

Unlike literature, politics, and music, mathematics has little relevance to everyday life. And I say that as a professor of mathematics.

None of this would matter if it there were good reasons for enacting such a program or if the consequences were benign. Hacker shows that neither is the case.

When it comes to justification a circular reasoning takes hold: in our technology-driven world, success requires disciplined application of reasoning; math requires disciplined, logical thinking; therefore, we should require as much math as possible if we want to be a successful society. It’s a syllogism that doesn’t stand up to reality.

Hacker suggests that you need not teach quadratic equations and first derivatives to get the benefit of numerate, as opposed to mathematical, thinking. Or even to learn how to apply higher-level math. My favorite example of those given is carpet installers. They have to apply geometry and accounting in equal parts and they learn to do so on the job.

Andrew Hacker
Does this look a radical to you?

How did we get here? The experts, of course. It’s fashionable, at the moment, to recoil in horror at dismissing expertise but somewhere between instant dismissal and unquestioned acceptance is where we probably belong.

Hacker claims that a high-caste, he calls them Mandarins, of mathematics professors dominates the important discussions. What should be taught in a K-12 math curriculum? Why anything that an aspiring graduate student in mathematics might require. Even experiments in simplifying the curriculum are dominated by this group.

Hacker suggest this is as much about preserving privilege and class enrollments as anything else. After all, when math is a requirement so are math professors. There’s room here for a Bourdieu argument or even a Randall Collins one. Strangely, Hacker, a social scientist, makes neither.

Hacker demonstrates that we are at risk of creating a nation of dropouts and that a major driver of that is math requirements. The book’s most telling vignette showcases a middle school student from Florida who has the temerity to ask Governor Jeb Bush— a vocal STEM/Common Core advocate–what the angles are in a 3/4/5 triangle. His answer–to use a word that many math advocates claim to love for its clarity–is wrong.

In the book’s last chapter Hacker tells of a real-world semester-long experiment he ran with the agreement of his colleagues in the math department. He contrives to use arithmetic to undertake some pretty advanced studies and exercises. The approach was novel, engaging, though-provoking and effective

That ought to get us thinking.

 

 

 

 

 

 

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