The Math Myth: And Other STEM Delusions
reviewed by Andrea McCloskey - November 17, 2016
Are Americans delusional about mathematics? Is our collective obsession with STEM based on well-intentioned, but mistaken, assumptions at best? Or instead, is it based on more cynical capitalistic and militaristic interests at worst? In The Math Myth: And Other STEM Delusions, author Andrew Hacker offers a convincing argument that the American public in general and our educational system in particular have bought into a misguided mythology. My own relationship to Hackers thesis (which in a nutshell is: most, if not all of the United States attention to mathematics teaching and learning in schools is wrong-headed and harmful to the democratic aims of our educational system) is perhaps surprising. I currently work as a university-based faculty member in mathematics education. I have devoted my professional life to studying what does and should happen in K12 mathematics classrooms. Nevertheless, I am largely sympathetic to Hackers claims. The bulk of my lecturing responsibility consists of teaching mathematics content and instructional methods courses to pre-service elementary, middle, and high school teachers. As such, I confront indications of our countrys deep ambivalence towards mathematics and schooling through my students concerns on a daily basis.
I have studied this ambivalence and have written about the largely non-rational perspectives held by education professionals and the general public alike when it comes to mathematics in schools. One of my favorite personal anecdotes relates to a conversation I had with a parent who disapproved of the mathematics textbooks her son was using in his elementary classroom. This mother told me that she did not want her son to be learning how to compute and perform basic operations through reasoning, sense making, or problem solving. Instead, she wanted him to be shown the standard algorithms (e.g., the ones that she had learned in school) and then to practice. When I asked her why she valued computational algorithms, she told me that it was because she wanted him to be able to perform calculations quickly. So I asked, If your goal is for your son to perform calculations quickly, how would you feel if he were taught to use calculators? After all, using technology is the quickest way to find an answer to a three-digit by three-digit multiplication problem." She responded by clarifying that when she said the quickest method, she meant the quickest paper-and-pencil method, not the quickest method in general.
This exchange exemplifies just how contradictory people are about the mathematics we want our children to be learning in school. We want them to have better mathematics experiences than we did, but we also want their homework to look like ours did (or at least how we think we remember ours did!). We want students to learn to use appropriate technology, but do not want them to depend too much on technological tools. While the annual PDK/Gallup polls repeatedly reveal ways that Americans hold contradictory opinions about schooling, my experiences confirm the delusions Hacker has documented here, where STEM and mathematics serve as unique arenas for this ambivalence to play out.
In each chapter, Hacker sets his sites on a particular source, instantiation, or effect of this positioning of mathematics. For example, he takes on the often cited, but seldom verified, claim that mathematical proficiency contributes to the development of more general critical thinking. He also bravely calls out research mathematicians, whom he dubs the mandarins (p. 97), for their similarity to ancient Chinas elite class. These researchers protect their own interests by maintaining mathematics status as the most essential and most honorable, yet least accessible, of the disciplines.
Other writers, including mathematicians, have already critiqued aspects of Hackers book, so there is no need for me to echo these same observations. My disappointments were more related to my perspective as a mathematics education researcher. For example, Hacker admits early on he occasionally uses the term algebra as a surrogate for the full mathematics sequence. He seems to use this term to approximate any mathematical content that is beyond arithmetic. I agree that algebra has come to play a particular role within American schooling when understood as a curriculum and distinct course of study. Hacker does an effective job making this case. He shares statistics about how many students fail algebra, thereby sealing their fate for post-high school failure. The author also proceeds to demonstrate how familiar arguments in favor of requiring algebra for all (Students need Algebra in order to . . .) do not hold water when we take the realities of modern life into account, such as ubiquitous technology.
However, Hacker and other journalistic writers who have joined the let's cut algebra down to an appropriate size argument would do well to consult the mathematics education research literature to see excellent scholarship arguing that algebra is more than a curricular course studied in a year so students can meet their graduation requirements. Instead, algebra is a distinct way of reasoning about and representing quantities and relationships that should permeate the entire K12 curriculum. In other words, we should not just think of algebra as a course. Instead, we should think of it as a habit of mind serving to both support and exemplify more general mathematical proficiency.
All this is to say that my main critique of Hackers book is that he remains largely oblivious to the wealth of scholarship that my colleagues in mathematics education have conducted in our short history as a field of study. For example, he does not seem to realize that his final chapter where he details his own experimental teaching of a university-level introductory mathematics course based on quantitative reasoning has much in common with a problem-solving approach that emerged as a focus of research by mathematics educators years ago. Drawing on this initial body of research, my colleagues have continued conducting detailed analyses of classroom activity so that we now have more knowledge about what types of assessment practices, discourse patterns, and community contexts support the successful implementation of problem-based approaches. But rather than relating his own teaching experience to this larger body of research, Hacker allows his approach to remain a singular and idiosyncratic one-off.
There are other smaller misconceptions that Hackers book propagates. He overstates the gatekeeping influence schools of education play when it comes to certifying and granting access to the profession of teaching K12 students. This was the case at one point in time, but neoliberal forces have permitted people to become teachers through as many paths as a free market allows. The author also makes a subtle but telling error when he cites the 2001 report by the National Research Council as claiming that, mathematics instills procedural fluency, productive dispositions, conceptual understanding, strategic competence, and adaptive reasoning (pp. 8182, emphasis in original). These five strands are indeed important. I teach them to all of my pre-service teacher students in their university classes, but they are not the product of the discipline of mathematics. Rather, these strands are characteristics of people who are authentically and meaningfully mathematically proficient. Our schools currently do not do enough to foster the development of all five strands through mathematics instruction.
Despite the shortcomings discussed above, I found The Math Myth: And Other STEM Delusions to be a convincing call to action for my colleagues who work in mathematics education and myself. For example, in what ways have we remained oblivious of, or even actively contributed to, the uncritical reverence for mathematics? Have we added to the discourse that mathematical proficiency is more important for our students than the development of historical understanding, aesthetic appreciation, technical and mechanical skills, and emotional wellness? My field has certainly benefitted from the funding that is available to causes and projects fueled by the STEM hysteria. We are more apt to gain funds when we lean on the argument regarding our nations security being dependent on the mathematical achievement of our students. But can we in good conscience continue to make such claims, especially in light of the arguments made by Hacker and others that the overemphasis of mathematics, especially procedural mathematics, propagates inequitable achievement across race, gender, and socioeconomic lines? My hope is that Hackers book can help those of us who care about mathematics and its overall effect in schools to reach broader and more influential audiences beyond our ivory towers.