Are high school students better served by completing their math studies with calculus or statistics? This question has provoked lively debate in the education world, in the mathematics world, and in the college admissions world. But remarkably little is known for certain about what difference—if any—it actually makes.
For years, selective college admissions offices have looked for calculus on applicants’ transcripts. In fact, 92 percent of admissions officers in 2024 said that “faculty places a high priority on calculus for demonstrating a rigorous math curriculum,” and about three-quarters of them ranked AP Calculus in the top four math courses that carry the most weight in admissions decisions. Yet, paradoxically, 95 percent of them also acknowledged that “calculus is not necessary for all students.” This tension recently led The Hechinger Report’s Jill Barshay to ask, “Is calculus an addiction that college admissions officers can’t shake?”
Like all addictions, this one may be detrimental, especially if it eclipses statistics (or other rigorous data science courses) that also teach valuable quantitative skills that may be more easily transferable to any number of other career fields: skills like evaluating data to identify patterns, trends, and biases; being able to test a hypothesis; and understanding probability and distributions.
Some believe that college students who plan to major in STEM careers should continue to take calculus, but that non-STEM majors will be better served—with more careers open to them—if they choose a different math pathway, including Statistics as the capstone course.
But is that true?
Today we know too little about how high schoolers’ participation in calculus or statistics influences their future outcomes, much less about that smaller pool of students who take advanced courses in either subject. To help fill this knowledge gap, we’re releasing a new study today, Calculus or Statistics: Does it Matter? It addresses primarily a small but influential segment of the American college-going population—a population that is integral to our country’s economic growth and competitiveness, as they are tomorrow's leaders, scientists, and innovators.
In the study, we ask a host of consequential questions about this special world of mostly college-bound high achievers and their choice of advanced courses. Do students who choose one path over the other attend and graduate college at the same rates? Do they earn comparable salaries? Do they end up employed in similar industries? Knowing what the future holds for otherwise similar, high-achieving students strikes at the heart of the calculus-versus-statistics debate: Does the choice actually matter in the long run?
Fortunately, three talented scholars were also interested in investigating these questions: Associate Professor Matt Giani from the University of Texas-Austin, his research assistant Franchesca Lyra, and Fordham’s National Research Director Adam Tyner. Dr. Giani specializes in social mobility research and has extensive experience analyzing statewide longitudinal data through UT Austin’s Education Research Center (ERC). We’ve had the pleasure of working with him previously on a study about industry-recognized credentials, on which Dr. Tyner also collaborated as project manager.
Using data from over 5.2 million Texas public high school graduates from 2003 through 2020, the researchers first analyzed course-taking patterns and inequalities in math course participation. To ensure fair comparisons in their analysis of postsecondary outcomes, they focused on the roughly 178,000 students who took either AP Calculus AB (equivalent to one semester of college calculus) or AP Statistics from 2015–2020. That’s roughly 3.4 percent of the much larger sample. Those two groups of students already shared a number of characteristics, but by applying additional weighted adjustments, the analysts were able to create two “observably equivalent” groups. These adjustments accounted for a wide range of factors, including student characteristics, prior performance, course-taking patterns, high school attended, and graduation year.
Their analysis yielded five key findings.
- Rising Popularity of Statistics. Participation in statistics has risen rapidly as access to coursework has expanded, while calculus enrollment has remained relatively flat.
- Persistent Equity Gaps. Although broader access to advanced math is a “rising tide” that lifts all boats, it has not reduced socioeconomic or racial disparities in participation.
- Better Outcomes with Advanced Math. Students who complete relatively higher math courses in high school tend to achieve better postsecondary educational outcomes and higher earnings.
- STEM Advantage for Calculus Students. Calculus takers are more likely to enroll in selective colleges and pursue STEM majors but no more likely than statistics students to earn degrees.
- No Long-Term Earnings Edge for Calculus. Despite its STEM advantage, taking AP Calculus AB does not lead to higher long-term earnings compared to AP Statistics (at least after eight years).
Based on these results, Dr. Giani and co-authors drew several useful implications, including the need to strengthen popular but often unstandardized non-calculus pathways with robust standards, curricula, and assessments. They also reiterated that diversified math pathways alone will not close equity gaps. That’s because higher-income, White, and Asian students are still more likely to enroll in advanced courses than their peers. So, the real challenge is ensuring that students from all backgrounds are prepared to succeed in and have access to rigorous advanced math (more on that below).
We offer three additional takeaways based on the study’s findings.
First, students, families, and admissions counselors need to know that AP Statistics is not inferior to AP Calculus, at least when it comes to long-term earnings and choice of industry or career field. At about eight years after college graduation, AP Calculus students are estimated to outearn their AP Statistics peers by $1,888 annually, an advantage of about 4 percent. By year ten, the raw difference declines to $1,622 annually (3 percent), but the difference is no longer statistically significant (nor are there any statistically significant differences in salary after that point, up to roughly eighteen years when our study period ends).
The report finds that AP Calculus students are more likely to be employed in manufacturing, health care, oil and gas, and construction, whereas AP Statistics students are more likely to be employed in finance and insurance, accommodation and food services, administrative services, information, real estate, and arts and entertainment.
Yet neither calculus nor statistics takers have cornered the market in math-intensive industries. While calculus students have an edge in engineering-heavy fields like oil and gas, statistics students excel in data-driven sectors like finance and IT. Nor are there significant differences between the two groups in their probability of employment in professional and scientific industries, which include many prestigious sub-industries such as legal services, accounting, and scientific research and development. This suggests that both pathways can lead to success in quantitative careers—and that there’s work to be done to educate parents, families, and admissions officers about data science and its practical benefits.
Second, we need to adjust the standard math sequence to prepare high achievers for either advanced statistics or calculus as their capstone course. Advanced students tend to take Algebra I in eighth grade, geometry in ninth, Algebra II in tenth grade, pre-calculus in eleventh, and calculus in twelfth grade. But if both calculus and statistics can lead to successful careers in mathematics, we should adjust course pathways so that students are prepared to take either of them as their capstone class.
Critical to those efforts is reworking Algebra II to include statistics, probability, and other topics relevant to data science. CSU-Northridge math professor Kate Stevenson explained to EdSource that few of today’s Algebra II teachers find time for statistics standards, “So what would a third year look like with a better balance between statistics and algebraic skills? Could we repeat less of Algebra I if we did the integrated pathway? Or what parts of the algebra curriculum could really belong in pre-calculus rather than in Algebra II?”[1]
Similarly, if students aren’t planning on taking calculus, pre-calculus might be replaced with a trigonometry and probability course or perhaps introductory programming for data analysis.
Finally, we must start building a wider pipeline of advanced math students. To address the persistent equity gaps found in the report, we turn our attention to the overwhelming majority of high school students who did not take an advanced math class. In 2019, just 16 percent of high school graduates took calculus and 17 percent took probability and statistics. Of the calculus takers, 46 percent were Asian, 18 percent were White, 9 percent were Hispanic, and 6 percent were Black.
We can stipulate that not all students will be attracted to college or even to math-centric fields. But they should make those choices based on their interests and capabilities, not because of meager opportunities and weak mathematics instruction. So if we want to increase the numbers above, we’ll need to also increase access to advanced course-taking in low-income schools. Equally or more importantly, we must start building a wider pipeline of advanced math students in the early elementary grades. For starters, that means allowing early entry into kindergarten for kids who are ready; universally screening all students for “gifted” services; automatically enrolling students into higher math courses if their test scores indicate readiness; and encouraging grade skipping for those who are already exceeding grade-level standards.
Too few states are implementing these policies. And that needs to change. That’s because all of us should not only be concerned about the minority of students for whom advanced math courses are relevant, but the majority whose K–12 mathematics preparation may render those courses out of reach.
[1] Some states and districts are already redesigning middle and high school mathematics, often working with the Dana Center, located at the University of Texas at Austin. Over twenty states are working together to make mathematics more relevant to students and useful to their future careers.
