Questioning the status quo has always been fraught, even deadly. The furor around Andrew Hacker’s, The Math Myth, is no exception (though as far as I know Hacker has not been physically attacked or threatened). The accepted truth Hacker challenges is the sequence of math courses that almost all US high school students take – commonly called Algebra I, Geometry, and Algebra II – and which a slightly smaller number retake, as remedial or developmental courses, when they enter college.
These courses are designed to lead students toward calculus, a worthy goal as one of the great scientific and mathematical achievements of the last 500 years, but one that, to be fair, is not crucial to function effectively as a citizen of the 21st century. Instead, this math curriculum is the result of a Sputnik-era concern over the threat of Soviet competition in space and science more broadly.
As such, Hacker’s book asks us to reconsider our lock step requirements for all students in math and offers an alternative based in the thinking of a numerically literate social science professor. Here in essence is his argument, as I see it:
- Currently, the US requires all students to take math leading to calculus.
- This curriculum teaches skills and knowledge that are not used in most people’s everyday life.
- This curriculum teaches skills and knowledge that are rarely used, even by scientists, engineers, computer scientists, actuaries, or any other work we typically think of as needing mathematics.
- This curriculum is not improving the quantitative literacy or reasoning of our society.
- The transfer of math skills and thinking to other fields, as is often claimed, is unproven at best.
- Mathematical proof is abstract and unrelated to the way we in fact establish truth in the world, for example scientific proof or legal proof.
- The cost of forcing all students into the same math curriculum is too high, in terms of preventing too many otherwise talented students from completing their studies and entering the professional workforce.
- Therefore, we should offer rigorous alternatives to the current math curriculum that promote improved quantitative literacy and reasoning.
Along the way, Hacker includes some thoughts about why the status quo is what it is. Tradition is a big piece of it, as is using math as a surrogate for precision and rigor, something I have often observed. In addition, our math curriculum represents a de facto form of tracking for students, keeping out the “unwanted” from professional careers. You should read that as African-American, Latino/a, and other non-white students who are disproportionately stuck in the math pipeline. The status quo also serves mathematicians by giving them many jobs teaching all the students forced into those classes. Finally, Hacker argues that preventing students in the US from completing their degrees keeps the flow of foreign-born workers, often willing to work for less money than their US-born counterparts, open and strong.
Whether you agree with Hacker’s premises or not, he presents an array of evidence that is not easily dismissed. In fact, critics of the book mostly do not attack the ideas I’ve outlined above. Instead they focus on Hacker’s use of terms, which admittedly is not always careful from a mathematical perspective. That said, in no serious critique of the book have I seen anyone disagreeing with the basic premise that teaching math as we currently do in the US is costing our society the loss of many talented students who excel in many areas, but are denied access to college degrees because they do not complete the math requirements.
Keith Devlin, an educator, Mathematical Association of America-sponsored columnist, and a voice I respect, explicitly agrees with Hacker that “Algebra as typically taught in the school system is presented as a meaningless game with arbitrary rules that does more harm than good.” Devlin’s critique of Hacker draws a distinction between what is taught in US schools as “algebra” and algebra as it was historically developed and currently practiced by mathematicians. This distinction is useful as a defense of algebra as a whole, but not as a critique of Hacker’s work, precisely because Hacker’s argument is about how algebra is taught and used by our educational system. I say, for those that are concerned by Hacker’s use of “algebra” as a convenient metaphor representing “the current state of math education in this country,” substitute the longer phrase.
From my perspective, The Math Myth is titled provocatively for the purpose of creating controversy and selling books. Hacker does not attack the importance of math overall, but does question the current math establishment. As a thoughtful voice from outside the discipline, we should listen, broaden our thinking, and be open to the constructive message he brings. It is the students, as Hacker points out, who pay the price for our insistence on the status quo.