The Math Myth: And Other STEM Delusions by Andrew Hacker
The New Press 240 pp. $25.95
By Charlie Gofen
At my kids’ high school, the top math students study calculus while the less mathematically inclined take a course in basic finance. If you’re in the latter group, you learn useful skills for personal budgeting, selecting a mortgage, and buying life insurance. If you’re in the former group, you’re left to contemplate less common scenarios such as how quickly your conical bathtub would overflow if, for some reason, you simultaneously left the faucet running and the drain open.
Calculus and the classes leading up to it (algebra, geometry, trigonometry and functions) remain the core of math education in the United States even though it’s often difficult to understand why we study these topics. Very few of us have ever had an occasion to use math beyond the most basic algebra after leaving school.
Conversely, courses designed to promote math literacy – or “numeracy,” as the mathematician John Allen Paulos has called it – are rarely required even though they are relevant for all high school students regardless of whether those students are headed to M.I.T., community college, or straight into the workforce.
And this is where Andrew Hacker steps in. Hacker, an emeritus professor at Queens College and author of more than 10 books, first raised the question “Is Algebra Necessary?” in a controversial op-ed piece published in the New York Times in 2012. (Short answer: no.) He has expanded the argument in his latest book, The Math Myth, which is a worthwhile read, even if you are among the educators who become apoplectic at the suggestion that students shouldn’t have to grapple with polynomial functions.
Hacker contends that the math currently required of high school students is largely irrelevant to their educational and professional careers, and is in many ways harmful. He argues that students would be better served studying personal finance, statistics, and other topics that promote relevant math literacy. Before we get to his replacement ideas, though, we need to consider his animated attack on algebra.
The Math Myth is essentially a broadside against the mandated pre-calculus math curriculum in U.S. high schools. Hacker’s first volley focuses on how difficult the study of math can be for many students. Excessive requirements in algebra, geometry, trigonometry, and functions create significant stumbling blocks. One out of five kids in the United States doesn’t finish high school. Of those who do go on to college, nearly half leave without a degree. “At both levels,” he says, “failure to pass mandated mathematics courses is the chief academic reason they do not finish.”
“Our goal,” Hacker says, “should be to keep our young people in high school and later in college where they can discover and develop their talents. At this point, we’re telling them that they must unravel reentrant angles and irrational numbers if they want a high school diploma and a bachelor’s degree.”
Even community colleges, Hacker notes, frequently deny students a certificate or diploma because they fail advanced math, regardless of whether the math is in any way relevant to their educational or career plans.
The mathematics required by the Common Core standards – and the math needed to succeed on the SAT, ACT, and in admissions to many top colleges and universities – puts students whose aptitudes and interests lie outside of math at a huge disadvantage, he says. “Students who show promise in art history or postmodern criticism won’t even have their applications opened if they faltered in geometry.” (It’s worth noting, though, that many colleges have changed their admissions policies so that the SAT and ACT are now optional.)
Hacker next argues that only a small percentage of jobs require any math beyond arithmetic and basic algebra. In a chapter titled, “Does Your Dermatologist Use Calculus?” he notes that many top medical schools require applicants to have taken calculus even though doctors almost never need it in their careers.
In addition, he says, engineers and scientists rarely need the math they are required to master. There is a “deskilling” trend in which engineers and other professionals are able to create equipment, software programs, and processes that eliminate the need for operators and implementers to have as strong a mathematical background.
The disconnect between math requirements and the reality of the working world creates unnecessary barriers to entry for many careers. Hacker quotes the biologist E.O. Wilson saying that math hurdles have “deprived science of an immeasurable amount of sorely needed talent.”
Hacker also notes that the way we use standardized tests to assess mathematical abilities effectively discriminates against girls. “A proclivity for speed and a readiness to guess are rewarded in clock-driven tests,” he says. “And it’s traits like these, not knowledge or skill in mathematics, that raise boys’ scores.”
Hacker attempts to preemptively counter key arguments of his opponents.
It is widely believed that because math requires logic and reasoning, it enhances problem solving and critical thinking skills more generally, but Hacker says there is no proof that this is true, and he believes there are better ways than studying advanced math to build these non-math capacities.
Some educators argue that the drudgery and difficulty of math is character-building, but Hacker says math should be interesting and relevant, and ultimately a process of discovery, rather than an additional cause of the growing rate of student burnout. “Job one for teachers, at all grades and levels, is to excite their pupils, especially those who arrive not caring much about the subject,” he says.
While there is a common belief that there is a shortage of qualified U.S. citizens to fill positions in computer programming and engineering, and thus a pressing need for more students to go into STEM (science, technology, engineering, and math) subjects, Hacker argues that companies maintain the fiction of a shortage because they prefer to hire foreigners at lower salaries.
The argument Hacker has the most difficulty countering is that relaxing academic standards will create a subordinate track for students who are already marginalized. He attempts to dismiss this argument by noting that there is no evidence that algebra and pre-calculus “will be the lingua franca of the future,” and perhaps he’s right, but for now, these math skills signal to colleges, graduate schools, and potential employers a certain level of educational sophistication. If these classes are no longer required, students who are already at a disadvantage in our society will have even more difficulty competing with their more privileged peers in gaining admission to college and landing desirable jobs.
Rather than radically lowering expectations, we would do better to maintain meaningful standards for everyone and find ways to support struggling students more effectively. That is not to say, however, that our math requirements shouldn’t be changed.
Hacker makes a strong case that promoting math literacy is preferable to forcing everyone down the pre-calculus track. We could just pile on additional requirements, but students have a limited number of classroom hours for math.
Perhaps the longer-term solution is to meet Hacker halfway and maintain requirements for geometry and one year of algebra as essential building-block topics, but then replace the rest of the mandated pre-calculus track with applied math coursework grounded in statistics and finance. Students would still have the option of studying trigonometry, functions, and calculus.
For this change to work, we would need a more rigorous curriculum to promote math literacy. If these offerings continue to be viewed as Mickey Mouse classes, they won’t ever develop the necessary level of support either in high schools or among the gatekeepers at colleges and universities.
The relevant topics for math literacy seem to fall into three categories – finance, statistics, and more general quantitative reasoning. Finance at the high school level (or “consumer math,” as it was once called) has the feel of inferiority because of its practicality, but there is no shame in understanding compound interest, stocks and bonds, and the cost of student loans. And this area of study doesn’t need to be reserved for less mathematically inclined students; the math can be plenty complex in calculating present value and discount rates.
Statistics has already generated greater interest in recent years because of our growing recognition of the importance of learning how to gather and interpret data, analyze risk, and make sense of the real world. In addition, statistics requires some background in algebra and doesn’t face the stigma of high school “consumer math.” (The Common Core standards, which roughly 40 states have signed on to, now include statistics and probability, with an explanation that studying these topics will help students make informed decisions that take quantitative data into account.)
The final area, quantitative reasoning, is a catch-all category aimed at helping students develop comfort with numbers, support an argument quantitatively, and appreciate the role of math in the real world. Hacker devotes his last chapter to describing a course in quantitative reasoning that he designed and taught in conjunction with his school’s math department.
His course covered topics ranging from how the government spots tax fraud to how political parties use gerrymandering to make some votes count more than others. It’s a math course I would love to have taken as a student, and it’s easy to develop compelling course content, particularly in an election year in which we are besieged by polls and predictions.
Everyone has a math story – a memory from school that left them with either a positive charge or a negative charge as they reflect back on their math education. Here’s mine.
I was in my first semester of graduate school in public policy, in an introductory statistics course. The professor, Malcolm Sparrow, challenged us to develop a method of surveying a large number of doctors nationwide to determine the percentage who had ever performed an abortion. Because some of the doctors feared repercussions if they responded in the affirmative, not trusting that their responses would remain confidential, we had to design an approach that would give us an accurate answer while taking the doctors’ concerns into account.
Our solution, with a bit of guidance from the professor, was to direct all the doctors to flip a coin. If it showed heads, they should tell the truth in their survey response. If it showed tails, they should flip the coin a second time. If the second flip showed heads, they should answer yes to the survey question, regardless of the actual truth, and if the second flip showed tails, they should answer no. We could then use the so-called Law of Large Numbers to assume that half of the responses were generated by the second flip of the coin and eliminate those responses from the tally. As an example, if we received 10,000 total responses, of which 3,000 were yes, we would eliminate 5,000 of the total responses and 2,500 of the yes responses, leaving us with 5,000 total “honest” responses and 500 “honest” yes responses, which would indicate that 10% of the doctors were in the yes category.
The actual math involved in the doctor survey was just basic arithmetic, but the problem required some creativity and mathematical reasoning and offered real world applicability. Not a bad approach. As I head back to grad school this year for my 25th reunion, I remember this imaginative solution as if we had discussed it just yesterday.
Charlie Gofen is an investment counselor in Chicago who has taught high school, been a newspaper reporter, and served as Board Chair of the Latin School of Chicago.