January 28, 2025
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Rethinking Math

Math as a Gatekeeper: Examining the Evidence

by
Pamela Burdman
,
Math as a Gatekeeper: Examining the Evidence

Making education—specifically math education—more accessible and more equitable is the ultimate goal of our work at Just Equations. We always seek to understand why math education is such a source of inequity, because identifying root causes of disparities by race and income is ultimately a key to reducing them. 

Numerous explanations for education inequity in general—beginning with differential access to educational resources, such as high-quality teaching—of course apply to math education. But, as I’ve spelled out before (here and here, for example), math education seems to be especially stratifying: Various policies and practices reinforce its role in conferring pedigree, which only preserves privilege and rations opportunity. 

It’s not that math learning isn’t important, it’s that its importance for professional opportunities is sometimes exaggerated. Math achievement can function more as a golden ticket to advanced opportunity than as a source of essential skills, an idea that is explored in two articles that recently came to my attention. 

The first is a 2017 journal article by sociologists Daniel Douglas and Paul Attewell that lends credence to the notion that math education serves a pernicious gatekeeping function.

Analyzing two 2011 sources of labor data, the authors show that very few workers reported needing or using advanced math on the job. At that time, only 2 percent of the population said that their jobs required math more sophisticated than that needed to “calculate the square footage of a house,” according to one of the data sources (O*NET). About 42 percent of educated Americans required the numeracy needed to balance a checkbook. And, according to the second data source (OECD’s PIAAC), 81 percent of employees and 62 percent of those with a bachelor’s degree reported never using advanced math. Douglas and Attewell conclude: 

The topics and substance of high school and college-level math—geometry, algebra, trigonometry, calculus—appear only rarely in contemporary workplaces and seem to be the purview of very small numbers of workers. … The advanced math that plays a prominent role in determining educational outcomes is not prevalent in the workplace.

This conclusion leads the authors to cast suspicion on common assumptions about the value of math education. These assumptions derive from human capital theory, which posits a straightforward connection between the knowledge and skills we acquired through education and our future work opportunities and earnings. Under this theory, the math skills that students acquire through school and college are necessary qualifications to perform effectively in many high-paying jobs. 

Instead of human capital theory, the authors credit competing explanations—those based on signaling theories developed by behavioral economists such as Nobel Prize winners Michael Spence and George Akerlof. These theories postulate that, rather than directly enhancing productivity in the workplace, an educational benchmark functions more like a signal. In Douglas and Attewell’s words, 

What matters is that this signal exacts a cost on all applicants; it must be difficult and/or expensive to obtain. Those who complete a college education signal that they may be superior employees, while those who fail in the educational “rat race” signal that they lack persistence, resourcefulness, or effort. In this framing, the content of formal education is irrelevant, as long as the route to a credential is difficult and many students fall by the wayside. 

One version of this theory is credentialism, in which managers who control access to jobs favor individuals from their own status group based on class-related social networks. Over time, increasing reliance on credentials effectively rations access to these professions, especially as the cost of earning credentials rises. Another version, called “cultural reproduction,” suggests that schools tend to privilege the culture and habits of the elite, while devaluing the cultural capital of lower-class students, replicating inequities across race and income lines. 

When Douglas and Attewell used federal education data (NCES’ ELS) to assess these theories, they found that students’ high school math performance was substantially linked to college outcomes. These associations, they say, are significant, robust, and persistent, even when they control for “demographic markers, other forms of social advantage, and students’ general academic performance and level of engagement in high school.” Interestingly, the link is mainly significant for higher income students (those whose socioeconomic status scores are one standard deviation above average) in determining access to elite colleges. It is also strongest with respect to Latinx and Asian students.

The authors conclude,

Despite its limited labor market value, math has a particular gatekeeper role in determining adult outcomes. … School mathematics seems to play a preeminent role in our educational sorting process precisely because of its apparent objectivity as a yardstick, along with long-standing western cultural beliefs about its relationship to innate talent as well as its perceived independence from family circumstances. The fact that school math performance has a stronger effect than SES on outcomes such as admission to four-year and selective colleges suggests that math is acting as a gatekeeper even among relatively privileged families for access to the most sought-after educational opportunities. 

To me, it makes sense that math skills are important, even if their importance is overstated in certain contexts. After all, there is little question that some degree of mathematical or quantitative ability is an important qualification for an educated citizenry. Quantitative fluency is necessary for anything from managing one’s finances and making health care decisions to following competitive sports and participating in the democratic process. It would be silly to argue that quantitative abilities have no value in our lives and careers. 

By the same token, there is no lack of smart people—including some mathematicians— who question whether “school math,” the actual mathematical skills students are expected to learn and the methods by which they are taught, actually enhances most students’ math understanding—and their lives more broadly. Examples include Andrew Hacker, Christopher Edley Jr., Uri Treisman, and Conrad Wolfram

If such arguments are correct, any changes in math curriculum still need to be accompanied by changes in corresponding policies, such as admissions. 

There is much we still don’t know. For example, how different would the sociologists’ results have been if the study had been conducted in 2024 with more recent data? And, importantly, what if the study focused not on all students, but on the narrower slice who pursue STEM majors—given that content taught in algebra, precalculus, and calculus appears to be needed for those majors? 

The second article—forthcoming in March in the Journal for Research in Mathematics Education—attempts to address that question. Its provocative title, “When Am I (N)ever Going To Use This? How Algebraic Functions Are Used in STEM-Related Careers,” hints at the answer. Among the findings: 

  • The use of linear functions is “ubiquitous” across STEM fields.
  • Other functions, such as quadratic and logarithmic functions (core topics in high school algebra), are used rarely. 
  • In contrast to limited explicit use of algebra, mathematical modeling in messy real-world situations was important. 
  • Calculations and formulas are more central than equations. 
  • Visual representations such as charts and graphs are important. 

While a single study is rarely conclusive, this one reinforces the need to scrutinize common assumptions about math requirements. According to the authors, 

A key argument for continuing to teach advanced algebra courses, one given by both our STEM practitioners and society at large, is that advanced mathematics courses teach logic and problem-solving skills essential to careers and everyday life. Our review of research and theories of transfer casts some doubt that this is the case. The STEM practitioners themselves often endorsed this view, citing algebra as essential to their careers, while struggling to give specific applications that fit with what they conceptualized algebra to be. 

I hope research on these questions continues to emerge. The study points to several avenues for future study, including: 

  • Examine the impact of having statistics and data analysis as a more central part of STEM education, including engineering, given the movement toward the use of big data in workplaces. Algebraic functions could highlight the connection between algebra and these fields. 
  • Explore the idea of teaching mathematics through problems that emphasize authentic mathematical modeling and the messiness of real-world uses of mathematics. 
  • Consider the impact of “deemphasizing concepts such as quadratic formula; factoring; synthetic division; writing, simplifying, and solving nonlinear equations … and the effects this might have on future STEM practitioners, including on the pool of people who choose to go into and persist in STEM, as well as on their on-the-job attitudes and skills.” 

To get a fuller picture, I encourage readers to read both articles.

One logical question to raise is this: Couldn’t the same critique be made about any number of education requirements? That is, does being an educated person really entail reading Shakespearean sonnets, dissecting frogs and pigs, or memorizing the original 13 colonies? The distinction appears to be that most subjects are less frequently the cause of a student failing a course, not getting accepted to a particular college, or being weeded out of a given college major. 

While the actual content of math may be important, learning it also serves as a rite of passage—a price of entry independent of its intrinsic relevance. This is what math education may have in common with finishing school and fraternity hazing. It affords access to certain universities or fields—not to high society or social clubs. 

If education in general is stratifying, math education is apparently more so. The literature on topics such as math anxiety, math identity, and math belonging has arisen out of a concern about that stratification. This literature focuses on math as a social activity, which some dismiss as not rigorous or too touchy-feely. But the point isn’t to make kids feel good instead of teaching actual math skills. The point is that feeling alienated in class is counter to learning. Some degree of engagement is a precondition for development of math skills. 

Since stratification is a social phenomenon, why wouldn’t the response to it be at least partly social in nature?

Ultimately, if math requirements are used to sort and rank students—and especially if they privilege certain racial and socioeconomic groups over others—it is reasonable to scrutinize those requirements for relevance and validity: It’s not that we shouldn’t require math, it’s that we should be requiring math that is relevant to a student’s future pursuits and valid as a measure of the student’s ability to succeed in those pursuits.

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