Bitter controversy has recently swirled around California’s revised Mathematics Framework, a set of recommendations about how math should be taught in the state’s K-12 schools. At stake are hot-button issues involving equity, privilege, socioeconomic class and gender, ethnicity and race.
There’s no disagreement about the need to improve math fluency and reduce performance gaps. In 2019, during the last statewide assessment prior to the pandemic, just 34 percent of California students over all and 18 percent of Black students and 20 percent of Latino students met or exceeded the state’s math standards.
An altered approach is essential, according to the proposed framework’s advocates, because “traditional math instruction turned off many students by stressing rote memorization of ‘meaningless formulas’ and procedures; along with being boring, it was disconnected from students’ lives and experiences.”
To better motivate students and prepare more students for success in STEM fields, the initial draft framework recommended:
- Detracking math instruction by mixing students with different levels of prior math performance and eliminating advanced, lower-performing and remedial math classes.
- A slower progression through middle school and high school math to ensure that students master the conceptual frameworks that underlie algebra and geometry.
- The elimination of accelerated and gifted programs for high-achieving math students before the 11th grade.
- A data science pathway as an alternative to the standard Algebra II, precalculus and calculus sequence.
- A math pedagogy that emphasizes inquiry, discussion, collaborative problem-solving and conceptual understanding rather than memorization.
With words that stirred an intense counterreaction, the initial draft declared that:
- “We reject ideas of natural gifts and talent” and “the cult of genius.”
- Math instruction “has much to correct [because] the subject and community of mathematics has a history of exclusion and filtering, rather than inclusion and welcoming.”
- “Do not include homework … as any part of grading. Homework is one of the most inequitable practices of education.”
- “The push to calculus in grade twelve is itself misguided.”
Critics, which included hundreds of faculty members and academic staff at four-year colleges and universities, including faculty at UC Berkeley, Caltech and Stanford, signed a statement criticized the proposed framework as an assault on excellence that will ill prepare “students for college-level math courses and exacerbate existing racial and gender disparities in STEM.” Among the criticisms:
- That the report lacked sound research to support its claim that its approach will advance equity.
- That the framework cherry-picked, misrepresented and distorted the cited literature in neuroscience, acceleration, tracking and assessment.
- That the document’s authors were biased toward data science while downplaying other areas of math.
- That the report denigrated procedural skills, downplayed the importance of math homework and substituted subjective measures of learning (such as portfolios) for more objective methods of assessment.
Controversies surrounding math education are not, of course, confined to California. in 2015, just 25 percent of 12th-grade students nationwide performed at or above proficiency in math, according to the National Assessment of Educational Progress.
Nor are arguments over how math should be taught new. I myself suffered through the new math in middle school. Rather than simply trying to teach students how to use numbers to solve everyday challenges, like making a budget, balancing a checkbook or paying taxes, K-12 mathematics was increasingly viewed not as a series of techniques and procedures to be applied, but as concepts (like set theory and numerical bases) that needed to be understood and, even more importantly, in the wake of Sputnik, as a key to scientific understanding and technological advancement.
An exchange in a Peanuts comic strip captured the backlash to the new math that prompted a “back to basics” counterreaction.
Linus: New math is too much for me.
Lucy: You’ll get onto it. It just takes time.
Linus: Not me. I’ll never got onto it. How can you do new math problems with an old math mind?
At stake in today’s math wars, even more than in the literacy wars, are fundamental concerns over equitable access to many of the fastest-growing fields. After all, students who lack a solid background in calculus and statistics are not only closed out of programs in business analytics and financial technology, engineering, epidemiology and health informatics, machine learning and the quantitative social sciences, but even medical, dental and nursing school.
Among the debates:
- Should all students be exposed to advanced mathematics, or should there be different pathways for those who do not intend to enter math-intensive fields?
- Will differentiated math tracks—with one path leading to calculus and another to statistics and cultural relevant mathematics—become “pathways for students of color” that reinforce racial and class-based inequalities?
- How should the pandemic-induced learning losses in mathematics and the deepened income and ethnic and racial disparities best be rectified?
Underlying these controversies is a bigger issue: Is possible to bring many more students, not just those gifted in mathematics, to an appropriate level of competence? Are some students simply more talented in math and should they be placed in more demanding math classes, while other students aren’t “math persons” and would benefit from a different pathway better aligned with their interests?
Society doesn’t expect all students to be equally talented at art, music or athletics. Should we expect all students to become proficient in math and statistics?
There can be no doubt that many Americans find math difficult and anxiety-inducing. According to one often-reported statistic from 2009, 17 percent of the general population has high levels of anxiety involving mathematics. Anywhere from 3 to 7 percent are thought to suffer from a math-specific learning disabilities like dyscalculia. This is the math equivalent of dyslexia; those with dyscalculia find it difficult to grasp number-related concepts, perform accurate math calculations and reason and problem-solve with numbers or statistics.
Dyscalculia doesn’t explain the gaps in math performance in the general population—which appear to be more a matter of the quality and forms of instruction and deeply embedded attitudes and beliefs. This has led math education reformers to the conclusion that math achievement can be raised through better teaching, mind-set training, extra attention and a more relevant and culturally responsive curriculum.
So what does this mean for colleges and universities?
- Our campuses need to recognize that fluency with quantification, probability, statistics and data is essential. Facility with analytics, data mining, data visualization, informatics and probability isn’t a luxury. It’s necessary. A college graduate should be able to locate and understand data sources, derive meaningful information from data, interpret data visualizations (including graphs and charts), critically assess, analyze and evaluate statistical claims, and recognize when data are misrepresented.
- Colleges and universities should infuse numeracy and statistics across the curriculum. Just as writing is too important to be left to one or two courses in rhetoric and composition, so, too, math is too important to be left to a few introductory math classes. Many disciplines outside math are well equipped to incorporate mathematics and statistical analysis into many of their classes. Even humanities courses can integrate computational thinking, data mining, data visualization, geospatial analysis, time series network analysis, provenance, data privacy, 3-D digital reconstructions and simulation modeling into their classes.
- Institutions should offer more opportunities for students to take discipline- and career-aligned courses in applied mathematics. These include classes in biostatistics, climatology, computational modeling of behavior, computational social science, epidemiology, finance, genomics, investment analytics, materials science, medicine, risk management and supply chain analysis.
Wellesley College’s Quantitative Reasoning Program makes an assertion that I think we should all embrace: “The ability to think clearly and critically about quantitative issues is imperative in contemporary society.” While it may not be literally true that “quantitative reasoning is required in virtually all academic fields … [and] most every profession,” as the Wellesley website claims, the fact is that in an increasingly data-driven society, the ability to analyze data, statistics and charts and graphs is a key component of critical thinking.
Quantitative literacy is not, of course, the only literacy that needs strengthening. Fluency in social science thinking and scientific methods is also essential. But there’s no reason to prioritize one literacy over another. All are necessary.
Resolving the math wars won’t be easy. As we’ve seen, they’re not new. The math wars persist because all sides recognize that mathematical illiteracy imposes a glass ceiling that limits possibilities and potential.
We mustn’t echo Teen Talk Barbie, with its dismissive catchphrase “Math class is tough.” Yes, math is tough, but it’s also vital. As Galileo noted, the book of nature is written in the language of mathematics. Quantitative literacy needs to become a shared responsibility that permeates the curriculum.
Steven Mintz is professor of history at the University of Texas at Austin.