Why Calculus? Why Indeed?

Why does high school calculus, generally AP Calculus, play such an outsize role in the access to competitive colleges? And should it?

Clearly the reason for the dominance of Calculus is not that all students who take AP Calculus in high school go on to major in the STEM (Science, Technology, Engineering, and Mathematics) fields that actually require them to know calculus. Nationally, only 20 percent of university students earn undergraduate STEM degrees.

Nor is it the case that students taking AP Calculus in high school necessarily go on to take a higher-level math course in college, the outcome that AP courses were designed to facilitate. As David Bressoud has shown (see p. 5), fewer than 20 percent of students taking AP Calculus do so. In fact, a large majority of students taking Calculus in college are taking it for the second time, and even so, don’t necessarily earn an A or B.

As for the remaining half of the students who took AP Calculus in high school, either they take no math at all, or they end up taking remedial math or non-STEM math courses like statistics. At UC Berkeley, for example, the fastest growing course in campus history has been Foundations of Data Science, which doesn’t require calculus at all.

The primary purpose of calculus is to prepare students to pursue advanced courses in fields such as physics, engineering, and of course, mathematics. It is no secret, however, that a key reason students actually take AP Calculus is to give them a boost in applying to competitive colleges, even if they’re not particularly interested in learning calculus or entering a field that uses it. In fact, according to a survey (p. 33), one of the top reasons given by Rutgers students for taking AP Calculus was that it “looks good on college applications.” Some systems, such as the University of California, offer a “GPA bump” by allowing an extra point for AP courses (so that an A garners 5 points, instead of the usual 4).

In this way, AP Calculus bears a large responsibility for distorting middle school and high school math pathways. Unlike in most subjects, students can’t reach an AP Calculus course in high school without accelerating through the curriculum. This fact once encouraged moves by states such as California to place all students in algebra by eighth grade.

Based on their mixed results, such policies are now being rolled back in some places, including California: Since many students were not ready for algebra in eighth grade, the practice exacerbated inequities (see p. 15). In just one example, among students who entered ninth grade in 2009, white students were two and a half times as likely to complete Calculus as African American students.

In fact, equity concerns are one reason the math establishment is taking increasingly cautious positions about the role of calculus in high school. So is the knowledge that most students who successfully pass calculus in high school are not generally positioned to progress in a math sequence. Increasingly, policies favor using eighth grade to teach more foundational content to ensure students are fully prepared to master the content of high school math. And that means thwarting the race to calculus.

“Although calculus can play an important role in secondary school, the ultimate goal of the K–12 mathematics curriculum should not be to get students into and through a course in calculus by twelfth grade but to have established the mathematical foundation that will enable students to pursue whatever course of study interests them when they get to college,” according to a joint 2012 statement of the Mathematics Association of America and the National Council of Teachers of Mathematics.

The University of California’s board of admissions weighed in four years later, noting that it “strongly urges students not to race to calculus at the cost of full mastery of the earlier math curriculum. A strong grasp of these ideas is crucial for college coursework in many fields, and students should be sure to take enough time to master the material. Choosing an individually appropriate course of study is far more important than rushing into advanced classes without first solidifying conceptual knowledge.”

If these positions are news to you, that’s no surprise. Notwithstanding their eloquence and meticulous reasoning, such statements appear to have had little effect on the behavior of high school students seeking admission to prestigious colleges. Nor is there evidence that admissions offices have begun ignoring the presence of Calculus on students’ transcripts.

So, whether or not it’s in students’ best interest, the pressure to accelerate remains. For now. That translates into pressure on middle schools and high schools to thread the needle—limiting unnecessary middle school acceleration and simultaneously creating options for students to reach AP Calculus.

Promising innovations are emerging. One model is the approach to “de-tracking” adopted by districts such as San Francisco Unified. In a controversial move, San Francisco decided to stop offering Algebra 1 courses in middle school, to ensure students could be steeped in the eighth grade content of the Common Core State Standards. That content is considered more rigorous than the previous eighth grade curriculum and foundational for success in high school math.

“For so long, people have held up this idea that AP Calculus is the gold standard,” SFUSD’s math supervisor told the San Francisco Chronicle. “Faster is not better.”

Instead of accelerating in middle school, San Francisco students now have various options for accelerating their math learning during high school—such as compressing Algebra 2 and Pre-Calculus into a single course. The district reports that more students than ever before are reaching an AP course (Calculus or Statistics) by their senior year.

Such approaches deserve to be studied—and, assuming the evidence continues to validate them—replicated. However, while they may represent improvements, they fail to address the underlying problems with the race to Calculus and its role in inequitable college opportunity.

As long as admissions practices drive aspiring college students to speed ahead on the calculus track, regardless of their interest in math or future aspirations, it will be hard to for calculus to claim its proper role in the high school and college math curriculum.

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