Should math instruction switch to “adult arithmetic” and “citizen statistics”?
DOI: 10.1063/PT.5.8184
Andrew Hacker’s dispute with members and supporters of the math establishment—including math “mandarins,” a word he reportedly uses—has burgeoned this year in the media. He wants not just to change math education, but to revolutionize it.
A February New York Times interview article began by identifying him:
[He] has taught political science at Queens College, City University of New York, for nearly 45 years, plus quantitative reasoning for the last three. Not one to decelerate, at 86 he is doing nothing less than taking on the mathosphere, where, he admits, he has few fans. His experimental course requires no geometry, algebra or calculus; instead, he teaches facility with numbers. He calls it adult arithmetic, and it involves statistics, analytic thinking and rigorous computation. Further challenging convention, his new book, The Math Myth and Other STEM Delusions ... argues against the requirement that all high school students take a full menu of math.
Hacker’s campaign isn’t new. He promoted it in 2012 in a high-visibility New York Times commentary . In an illustration dominating the top half of a Times Sunday Review front page, three hands reached up from beneath waves of numbers and mathematical symbols. Above the drawing appeared the headline “Is algebra necessary?” Beneath the fold, alongside the opening paragraphs of Hacker’s commentary, appeared the subhead: “There is no good reason to force students to master quadratic equations. Doing so holds them back.”
In that commentary Hacker stipulated, “Mathematics, both pure and applied, is integral to our civilization.” He simply believes, he wrote, that for most students outside college-level STEM studies, defense of algebra, geometry and calculus is “largely or wholly wrong” and “based on wishful logic.” He said his aim was “to call attention to the real problems we are causing by misdirecting precious resources.” Algebra, he argued, is the major reason for student failure. Moreover it’s not clear, he asserted, “that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job.” He added:
Certification programs for veterinary technicians require algebra, although none of the graduates I’ve met have ever used it in diagnosing or treating their patients. Medical schools like Harvard and Johns Hopkins demand calculus of all their applicants, even if it doesn’t figure in the clinical curriculum, let alone in subsequent practice. Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status.
Hacker continued promoting his vision of general numeracy and quantitative literacy in the Times in February 2016. His op-ed drew a lot of media notice. It began, “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.” He wrote:
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.
In that 2016 Times op-ed Hacker advocated education in statistics, but indicted the pedagogy:
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 AP 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.
In calling for rethinking math education in the 2012 Times piece, Hacker had promoted practical statistics:
[M]athematics teachers at every level could create exciting courses in what I call “citizen statistics.” This would not be a backdoor version of algebra.... Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives.
It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted—and include discussion about which items should be included and what weights they should be given.
It would be misleading to portray the overall controversy as focusing on the Consumer Price Index, but after Hacker’s 2012 Times commentary stirred things up, a Slate piece appeared under the headline “Don’t let economists and politicians hack your math: Of course kids need to learn algebra.” Author Edward Frenkel, a Berkeley math professor, observed:
Ironically, in a recent op-ed in the New York Times, social scientist Andrew Hacker suggested eliminating algebra from the school curriculum as an “onerous stumbling block,” and instead teaching students “how the Consumer Price Index is computed.” What seems to be completely lost on Hacker and authors of similar proposals is that the calculation of the CPI, as well as other evidence-based statistics, is in fact a difficult mathematical problem, which requires deep knowledge of all major branches of mathematics including … advanced algebra.
Frenkel emphasized a larger point: “In this brave new world, in which formulas and equations play a much bigger role than ever before, our ignorance of mathematics is being abused by the powers that be, and this will continue until we start taking math seriously for what it is: a powerful weapon that can be used for good and for ill.” Immediately he added, “Alas, instead of recognizing this new reality, we keep giving forum to paragons of mathematical illiteracy.”
“Paragons of mathematical illiteracy”? This year, another critic lobbed similar harshness at Hacker. In a March Huffington Post op-ed , Stanford mathematician Keith Devlin, the “math guy ” on NPR’s Weekend Edition, charged that although Hacker makes good observations about math education, he’s misled in his prescriptions by his own “dramatic misunderstandings about mathematics.” Devlin charged further that Hacker has “no idea what algebra is or how significant it is in today’s world.” At the end concerning political scientist Hacker, mathematician Devlin tossed in some sarcasm: “MEMO TO SELF: Don’t write essays or books on revolutionizing political science education.”
Mathematician Evelyn Lamb offered if not harshness, at least bluntness. Her Slate subhead declared that Hacker “should check his calculations.” That article characterized his book as “shoddy.” Her Scientific American subhead charged that he “makes a lot of mistakes.” Her text in that case explained in detail how Hacker bungled, as she reported it, what he intended to be an illustrative story about public discussion of a trigonometry question on a Florida state math test.
At the Atlantic, math education writer A. K. Whitney offered “Debunking the myths behind ‘The Math Myth.’” Her article ‘s subhead, in the style of a thumbnail summary, ended with “Here’s why he’s wrong.” In her text Whitney complained, “Hacker’s solution to repackage math and strip it of its more abstract elements, whether useful or not, will do little to ease this country’s belief in the myth that math is for geniuses.”
Other coverage has been more neutral. An article at National Geographic summed up this way:
A lot of math teachers would agree with Hacker that how the subject is taught is more important than what is taught—that a culture of exploration and inquiry is more important than mindlessly solving equations. But we can’t abandon advanced math entirely and ignore the students who excel at it and go on to work in fields that require it. Giving students more valuable and engaging options is the real solution.
A 2 August interview segment on PBS’s NewsHour toggled back and forth between two guests: Hacker and a somewhat skeptical Diane Briars, president of the National Council of Teachers of Mathematics. A Slate piece by Dana Goldstein, who recalls bewilderment and frustration in struggling through calculus, offered a mostly sympathetic view. Goldstein reported anecdotally on how Hacker himself teaches:
[He] asked students to investigate the gerrymandering of Pennsylvania congressional districts by calculating the number of actual votes Democrats and Republicans received in 2012. The students discovered that it took an average of 181,474 votes to win a Republican seat, but 271,970 votes to win a Democratic seat. In another lesson, Hacker distributed two Schedule C forms, which businesses use to declare their tax-deductible expenses, and asked students to figure out which form was fabricated. Then he introduced Benford’s Law, which holds that in any set of real-world numbers, ones, twos, and threes are more frequent initial digits than fours, fives, sixes, sevens, eights, and nines. By applying this rule, the students could identify the fake Schedule C. (The IRS uses the same technique.)
Judging by the media coverage, Hacker’s controversial ideas don’t appear to have drawn attention from school boards, math departments, or other curriculum authorities.
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Steven T. Corneliussen, a media analyst for the American Institute of Physics, monitors three national newspapers, the weeklies Nature and Science, and occasionally other publications. He has published op-eds in the Washington Post and other newspapers, has written for NASA’s history program, and was a science writer at a particle-accelerator laboratory.