By: David Bressoud @dbressoud

The third installment of My Mathematical Journey: Pólya’s “Let Us Teach Guessing”, was released on February 15 to free up the March Launchings for this column.

I have often written of how the rush to calculus has distorted and damaged the high school curriculum in mathematics. It has increased inequalities between privileged and disadvantaged students and made it far more difficult to expand opportunities that engage all students. This year has seen a significant setback in the effort to broaden the curriculum, a setback to which C. Allen Butler and Ken Ono have responded eloquently in “Virginia students and businesses need modern mathematics.”

Much of the pressure to study calculus while in high school comes from the widespread belief that it will improve the chances of admission to selective colleges and universities. There has been little hard evidence of this, but a recent report by Veronica Anderson and Pamela Burdman of Just Equations, A New Calculus for College Admissions, published in partnership with the National Association for College Admission Counseling (NACAC), presents evidence that this is often the case. Beyond the elite technical universities such as MIT, no one explicitly requires calculus for admittance, and even there exceptional students can be admitted without it. But we now see that it does weigh in these decisions.

As one admissions officer admitted,

“Calculus is an easy answer to a complicated question. Institutions are looking for a simple gatekeeper. We are looking for ways to determine excellent and extraordinary students.” (Anderson and Burdman, 2022, p. 8)

This matters for several reasons. One is that access to calculus in high school is highly unequal. Only 38 percent of high schools with predominantly Black or Latinx enrollment offer calculus. In those that do, tracking and implicit bias often close off access to calculus. As shown in Figure 1, Black and Latinx students are significantly underrepresented among those who study calculus in high school. These students are not only disadvantaged when they apply to college, if they do enroll in calculus when they get to college, they find themselves competing against students who are retaking a course in which they have already succeeded.

The second reason this matters is that it greatly distorts calculus instruction. For the top students, about the top fifth, calculus is taken because they really love the subject and want to learn calculus. Many other students take it less for the love of the subject than as a means of preparing for the single variable calculus they will need to take for their intended major in college. But the overwhelming majority of high school calculus students are taking it for a combination of the desire to strengthen their college application and because that is what is expected at their high school for high-performing students. As Dan Teague of the North Carolina School of Science and Mathematics has said,  "Most students don't want to take AP Calculus; they just want to have taken AP Calculus.” The result is students who are less interested in learning calculus than achieving sufficient proficiency to pass the course and, ideally, earn a 3 or higher on the AP exam .

The third reason this matters, and the motivation behind the Just Equations report, is that it consumes the oxygen that is needed to support alternative pathways through the secondary school curriculum. We know that many students are better served by courses that focus on statistics or data science or discrete mathematics. Statistics or data science can help students who have had strongly negative experiences in high school algebra to re-engage with mathematics. They see how a broader understanding of what constitutes the mathematical sciences can illuminate situations about which they care. Taught well, these courses can be fully rigorous and prepare students for credit-bearing courses in the mathematical sciences when they get to college. Such pathways hold tremendous potential for broadening preparation and participation in the mathematical sciences, helping to ensure that no students are cut off from the opportunity to participate fully in the modern economy.

But these efforts are running up against the fears of many parents that opportunities outside the traditional calculus track will limit access to high school calculus for their children. As Matt Taibbi recently recorded in “Loudon County, Virginia: A Culture War in Four Acts”, the dramatic shift toward the Republicans in northern Virginia in the 2021 gubernatorial election had a great deal to do with popular perceptions of infringements on gifted and talented programs, of which AP Calculus sits at the heart.

The Virginia Math Pathways Initiative, announced in 2019, began the exploration of various combinations of courses in the mathematical sciences for grades 11 and 12 that could meet the spectrum of needs for mathematical preparation. While this did include an accelerated track toward calculus in high school, that was not clear to many parents. In Governor Youngkin’s first Executive Order on taking office, “On Ending the Use of Inherently Divisive Concepts, Including Critical Race Theory, and Restoring Excellence in K-12 Public Education in the Commonwealth”, he ordered the Superintendent of Public Instruction to end the Virginia Math Pathways Initiative.

The fact remains that if we are to prepare the workforce we will need for the future, we need to broaden our conception of high school mathematics, as supported by the Butler and Ono column referenced at the opening of this column. Accelerated tracks to calculus will continue to be needed for some. But this cannot be the only rigorous and challenging mathematics offered to students. The challenges are many. We must work to build these courses and prepare those who will teach them. And there must be recognition by the mathematical community, policy makers, and school leaders of the importance of providing these options. This is a task that extends beyond a five- or ten-year horizon. It is a challenge for a generation, a challenge that must draw on the expertise of our best and brightest in the mathematical sciences and from those who labor in mathematics education. It is a challenge for all of us now.

Anderson, V., & Burdman, P. (2022). The calculus of college admissions: How policy, practice, and perceptions limit equity in high school mathematics. Just Equations

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