Foreword

By Amber M. Northern and Michael J. Petrilli

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. Mind you, most students will not take an advanced math course by the time they graduate high school. So, this is primarily a study about 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.

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, in 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.

1. Rising Popularity of Statistics. Participation in statistics has risen rapidly as access to coursework has expanded, while calculus enrollment has remained relatively flat.
2. 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.
3. 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.
4. 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.
5. 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 8 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 four percent. By year 10, the raw difference declines to $1,622 annually (three percent) but the difference is no longer statistically significant (nor are there any statistically significant differences in salary after that point, up to roughly 18 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 8th grade, Geometry in 9th, Algebra II in 10th grade, Pre-Calculus in 11th, and Calculus in 12th 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.

Introduction

For decades, research has documented a strong link between the math courses students take in high school and their post-secondary outcomes. Taking rigorous math courses has been associated with a higher likelihood of attending a four-year college,[2] majoring in and persisting within a STEM field (i.e., science, technology, engineering, or mathematics),[3] achieving strong academic performance in college,[4] and attaining higher long-term earnings.[5]

Despite such benefits, however, prior research also shows that participation in these courses has been low and unequal across student subgroups. Data from the National Center for Education Statistics suggests that, nationally, less than 20 percent of students complete Calculus in high school, and only 35 percent even take Precalculus.[6] Students of low socioeconomic status (SES) and students of color are more likely to be placed in lower mathematics pathways, thus impacting their ability to reach college-preparatory level math courses.[7] The issue is not simply about students opting for different pathways or even being underprepared to succeed in them. High schools with a majority of students of color and/or low-income students are also less likely to offer calculus courses, which can be required for college admission and access to STEM majors, and which some of their students might have been well prepared to succeed in.[8]

The benefits of advanced math courses, combined with unequal access to them, have also led to calls to reconceptualize the types of math courses available to students. Francis Su, past president of the Mathematical Association of America, said that each math pathway “should be designed with a strong focus on deep mathematical understanding, rigorous problem solving, and smart use of computational tools.”[9] He argues for updating high school mathematics pathways that have seen little change in decades, noting that: “In a world where we are regularly updating our software, our devices, and our lexicons, why wouldn’t we want the same for our children’s math education?”

Some contend that requiring calculus for admission to selective colleges has led it to function much like mastery of Latin functioned for earlier generations: Many students take it not because the course confers indispensable skills for future academic and professional success but rather because passing it has become a signal of elite ability.[10] Indeed, as Dr. Su pointed out, “In college, two-thirds of all high school calculus students retake calculus or take a more foundational class, suggesting that a rush to calculus isn’t beneficial for most students.”[11] Recent studies, too, find that statistics skills are often more applicable to today’s job market than calculus skills (or advanced algebra).[12] What’s more, AP Statistics has been one of the fastest-growing courses offered by the College Board over the past twenty years, suggesting that statistics could serve as a calculus alternative for advanced students.[13]

Some math educators are working to reform secondary math pathways to create space for different types of advanced math coursework. For example, the Charles A. Dana Center at the University of Texas at Austin is focused on modernizing Algebra II to serve as a foundation for multiple rigorous pathways, including one that moves from advanced algebra to calculus and another that emphasizes statistics and data science.[14]

Alongside these efforts to modernize and diversify advanced high school math, concerns about equity in access, participation, and achievement in advanced math have driven another set of policy responses.[15] For example, worries that advanced math course access in middle school exacerbated racial and socioeconomic achievement gaps drove some districts to prohibit students from taking Algebra I until ninth grade,[16] a policy so controversial in the San Francisco Unified School District that it was reversed by a local ballot initiative in 2024.[17] Sometimes, concerns about racial and socioeconomic equity have intersected with initiatives to modernize math, such as the now-abandoned 2021 Virginia Math Pathways Initiative, which emphasized data literacy and statistical reasoning while eliminating opportunities for accelerated coursework.[18]

In other cases, policymakers have offered math alternatives that lacked clear content standards. In 2017, for example, California began allowing Introduction to Data Science to replace Algebra II in the core courses used to determine admission to the state’s higher education system, only to have it reversed in 2024 by the University of California due to confusion about course content.[19] Still, other states, including Ohio, Oregon, New Jersey, and West Virginia, are piloting high school data science courses or adding them to their K -12 math standards.[20] Note, too, that no state requires calculus coursework for high school graduation, meaning that students who have already completed most traditional high school math can opt for Statistics rather than Calculus as their capstone course, as long as their school offers it.

Yet, very little is known about what happens when students pursue different pathways. Focusing on the final step of the traditional high school pathway, this report draws upon roughly twenty years of student-level education and employment data from Texas to provide new evidence of the evolution of advanced math pathways in high school and how these courses relate to students’ postsecondary outcomes.

Using data from public schools in Texas, we aim to address the following questions:

1. How have high school math course offerings and course participation evolved in recent years?
2. How have inequalities in math course participation changed in recent years?
3. To what extent is math course participation correlated with postsecondary outcomes, including educational and workforce outcomes?
4. How do post-secondary outcomes, both educational and in the workforce, differ for similar students who take AP Statistics and those who take AP Calculus?

Organization of the report

After discussing the Texas data used in this report and the methods used to produce the present analysis, we present trends in school-level access to – and student-level participation in – advanced math courses. Then, we address the critical question of whether changes in the availability of advanced math courses have led to changes in historic patterns of inequality between racial/ethnic, socioeconomic, and gender groups in their participation rates.

Next, we focus on AP course-takers to examine the relationship between students’ participation in AP Calculus or AP Statistics and their postsecondary education and employment outcomes.[21] As we show, these groups of students are already quite similar in demographics and prior academic characteristics. However, we use techniques to create “observably equivalent” groups of students taking each course to better isolate the relationship between course-taking and postsecondary outcomes. We conclude with the study’s implications for educational policy, practice, and research.

Methods

This section provides a brief overview of our research methods. See Appendix A for greater detail, including variable definitions, sample inclusion/exclusion procedures, descriptive characteristics of our entire sample, and details on statistical models and robustness checks.

Data and Sample

We use data from Texas’s statewide longitudinal data system called the Texas Education Research Center (TERC). It contains data on every public school student (both charter and traditional public) going back decades, including their demographic characteristics, standardized test scores, and high school courses taken. We follow students out of high school into college and the workforce by linking their K-12 records with data from the Texas Higher Education Coordinating Board (THECB, for in-state college data), the National Student Clearinghouse (or NSC for out-of-state college data), and the Texas Workforce Commission (for in-state employment data). Table 1 describes the entire sample, which includes every student who graduated from a Texas public high school between 2003 and 2020, totaling 5,220,078 students.

We use the entire sample for descriptive analyses of course offerings and student course-taking. For other analyses, we apply various restrictions:

1. Inferential analyses for course-taking: Limited to students enrolled in Texas public schools with 8th-grade standardized assessment scores.
2. College enrollment and attainment: Limited to post-2015 high school graduates since NSC has data for out-of-state enrollments starting then.[25]
3. Attainment analyses: Further limited to cohorts eligible for a specific outcome (e.g., 2015-2017 cohorts for six-year baccalaureate attainment).
4. Earnings analyses: Limited to earlier cohorts to examine earnings 7.5 to 17.5 years post-graduation and to students remaining in Texas. This is due to the availability of unemployment insurance (UI) records.

These restrictions help control for prior achievement, ensure data completeness, and account for time-dependent outcomes.

Table 1: Texas Highschoolers at a Glance

Note: The data in this table reflect all 5,220,078 students in the sample, including the graduating cohort classes of 2003 through 2020. The category of underrepresented minority students (URM) refers to underrepresented racial/ethnic minority students, including Black, Hispanic/Latino, Native American/Alaskan Native, Native Hawaiian/Pacific Islander, and Multiracial students.

Category	Characteristic	Percentage
Demographics	Asian	4.1
	Black	13.3
	Hispanic/Latino	43.6
	Multiracial	0.7
	Native American	0.4
	Pacific Islander	0.1
	White	38.3
	Underrepresented Minority	58.1
	Female	50.1
	Male	49.9
	ESL Status	4.6
	Immigrant	1.6
	Special Education	8.5
	Economically Disadvantaged	46.4
Ninth-Grade Math Course	Algebra 1	62.3
	Geometry	24.6
	Algebra 2	2.8
	Other Math	0.2
	Missing Data	10.2
Highest Math Taken	Algebra 2 or Below	57.1
	Precalculus	28.8
	AP Calculus AB	6.3
	AP Statistics	3.2
	Statistics and Calculus	1.9
	AP Calculus BC	1.6
	Regular/Regular Statistics	1.1
Academics	Ever designated as "gifted"	7.2
	Completed Career/Technical Cluster	82.4
High School Graduation Type	Distinguished/Advanced	9.6
	Recommended/Regular	73.7
	Minimum	13.7
	IEP (Individualized Education Program)	3.0
College Enrollment and Major	Enrolled in any college/university in first year after HS	68.5
	Public 4-year institution (among first-year enrollees)	39.7
	Private 4-year institution (among first-year enrollees)	7.8
	2-year or less institution (among first-year enrollees)	52.3
	Attended a 4-year institution right after HS	26.6
	Any bachelor’s degree (by end of study window)	21.8
	Bachelor’s degree in a STEM subject	8.1

Analysis

We analyze math course-taking trends and predictors using descriptive and inferential methods. To describe access to coursework, we calculate percentages of schools offering specific math courses and graduates completing them. To examine how student characteristics relate to advanced math course completion, we use linear probability models that control for student factors and the high school a student attended.

To assess changes over time, we use two approaches:

1. Disaggregate the sample and calculate group differences (by race, gender, and SES) in course completion rates.
2. Interact demographics with different high school cohorts to see whether certain student groups are more or less likely to complete advanced math courses now compared to the past and whether the gap in advanced math course completion between groups has changed over time.

Because the descriptive patterns in approach one are roughly similar to the results from the statistical model in approach two (which are more difficult to interpret accurately), we focus our discussion on the first approach and include the results for the supplemental analyses in Appendix B.

To estimate the relationship between the highest math course a student took in high school and that student’s postsecondary outcomes, we use linear probability models that control for student characteristics, the high schools students attended, and the graduation year. Student characteristics include:

• Demographics (free-or-reduced-price lunch eligibility, race/ethnicity, gender, gifted, special education);
• Math and reading test scores measured in eighth grade; and
• Measures of course-taking:
  • math course taken in ninth grade,
  • total high school credits,
  • failed credits,
  • math and science credits,
  • AP/IB credits,
  • and dual-enrollment credits.

To address our research question about how postsecondary outcomes, both educational and in the workforce, differ for similar students who take AP Statistics and those who take AP Calculus, we focus on the comparison between AP Calculus AB (equivalent to one semester of college calculus)[26] and AP Statistics, restricting the sample to these students. An advantage to this approach, as shown below, is that these two groups are quite similar to begin with and require fewer adjustments to make them comparable. We use a technique called augmented inverse probability weighting (AIPW) to create two “observably equivalent” groups of students who took either course and then estimate the differences in long-term outcomes between them.[27]

Postsecondary Outcomes

We examine two categories of outcome variables, subsequent math course-taking and postsecondary outcomes, specifically:

• Whether students enrolled in any of the following their first year after high school…
  • any college or university
  • any 4-year college or university
  • any private 4-year college or university
  • any selective or very selective college or university
• College major, measured using two-digit Classification of Instructional Program (CIP) codes;[28]
• Baccalaureate attainment within four or six years;
• Quarterly earnings;[29] and
• Industry of employment.[30]

High School Math Coursework

Math coursework data come from two sources, the Texas Education Agency (TEA) and the THECB. The former collects course-level data for all courses completed by students that confer high school credit, and the latter collects data on dual-credit courses, which are high school courses that can confer college credit. Because middle school course data are inconsistent and often missing, we focus on high school math courses.

We use course transcript records to examine every course that students completed (i.e., enrolled in and passed) in high school, as well as whether students completed any calculus course, any statistics course, and the highest math course students completed.[31]

Table 2 below displays the most common high school math courses taken (rather than counts of students) by Texas high schoolers graduating from 2003 to 2020, as well as the percentage of their course records that were taken as dual-credit, meaning that students could earn college credits as well as high school credits for completing the courses. Algebra I, Geometry, and Algebra II comprise roughly three-quarters of all high school math courses and are rarely taken as dual-credit. (Some of these courses, such as Algebra I, can also be taken prior to matriculation to high school.) Precalculus is the next most common math course, with 4.7 percent of courses taken as dual-credit. Although dozens of other math courses are available in Texas, the courses in Table 2 comprise over 99 percent of the math course records.

Table 2. Geometry, Algebra II, and Algebra I are the most common high school math courses.

After reviewing the Texas education standards, we classify these courses into three categories: typical math, including Geometry, Algebra I, Algebra II, and Precalculus; advanced math, including Statistics, AP Statistics, AP Calculus AB, and AP Calculus BC (there is no non-AP Calculus); and a remainder category of other supplementary or remedial math courses, such as Mathematical Models with Applications. All calculus courses in the TERC are identified as “AP.” AP Calculus AB focuses on the core ideas of differential and integral calculus, while AP Calculus BC includes much of the same content, along with added topics such as sequences, series, and parametric equations.

We will focus on the typical and advanced courses. In some of the analyses, we will combine AP Calculus AB and AP Calculus BC into a dichotomous “any calculus” variable and combine AP Statistics and regular Statistics into a dichotomous “any statistics” variable. (For more information on how we categorize advanced high school math courses, see Appendix A).

Finally, in analyses comparing calculus and statistics in relation to students’ postsecondary outcomes, we focus specifically on comparing students who completed AP Calculus AB or AP Statistics and did not take Calculus BC. As shown in the next section, these two populations of students are quite similar demographically and in terms of prior academic characteristics. We classify students based on whether they took AP Statistics or AP Calculus AB as their highest math course and exclude others from this analysis (including if students completed both courses, comprising one percent of the entire sample). These analyses, therefore, restrict the sample to the approximately ten percent of students who took one of these courses but did not complete both courses or AP Calculus BC in high school.

Results: Advanced Math Access and Participation

We begin by addressing a foundational question: How has access to advanced mathematics coursework – particularly calculus and statistics – changed over time? We analyze advanced math course offerings and school completion rates and how patterns differ by various student and school characteristics. [32]

Finding 1: Statistics participation has risen rapidly as more students have gained access to statistics coursework, while calculus participation has been flat.

From 2003 to 2019, the percentage of schools offering AP Calculus AB and AP Calculus BC both declined by roughly eight percentage points, from 60 to 52 percent for AP Calculus AB and from 32 to 24 percent for AP Calculus BC. The percentage of schools offering AP Statistics remained relatively constant at just above 30 percent.

In contrast, the availability of regular Statistics shows a V-pattern. It first declined from roughly one-quarter of schools offering statistics in 2003 to less than ten percent in 2015. After that, statistics rose rapidly, surpassing AP Calculus BC and coming neck-and-neck with AP Statistics by 2019. By 2020, over 40 percent of schools offered AP Statistics and regular Statistics.[33]

Figure 1. The percentage of schools offering AP or regular Statistics has increased, while the percentage offering either type of AP Calculus has declined somewhat.

Note: N =32,662 school-by-year observations. Schools were considered to have offered a course if at least one student was enrolled for the given year. AP Calculus AB focuses on the core ideas of differential and integral calculus, while AP Calculus BC includes much of the same content, along with added topics such as sequences, series, and parametric equations.

Figure 2 shows trends in the percentage of high school graduates who completed Precalculus, any statistics course (regular or AP), and any calculus course (AP Calculus AB or AP Calculus BC) for the 2003 to 2020 cohorts. Roughly two decades ago, only 30 percent of students completed Precalculus in high school. Yet, students were three times as likely to take calculus compared to statistics (nine percent versus three percent). As discussed in the sidebar, Mathematics Policy in Texas, the 4x4 curriculum policy that went into effect in 2011 increased the required number of math courses to be completed in high school from three to four, resulting in the jump in Precalculus course-taking that year. At their peaks, 48 percent of students completed Precalculus in the class of 2017, and 11 percent of students completed any calculus course in the class of 2018.

Figure 2. While statistics participation has increased steadily since 2003, calculus participation has remained stagnant.

Note: N = 5,220,078. This analysis included the entire sample of students who graduated from Texas public high schools between 2003 and 2020.

However, two notable changes have arisen in recent years. First, the share of high school graduates completing Precalculus began to decline, coinciding with Texas’s passage of HB5 and the adoption of the FHSP that reduced the math requirements in the default curriculum starting with the graduating class of 2018. By the 2020 cohort, only 41 percent of students had completed Precalculus in high school. Second, statistics-takers surpassed calculus-takers in the class of 2019. Since then, a larger percentage of students in each class has completed any statistics course compared to any calculus course.  

Figure 3 removes Precalculus and disaggregates the specific calculus and statistics courses. It displays the percentage of all students who completed these courses, allowing them to be counted in multiple categories if they completed multiple courses. Similar to the previous analyses of course offerings at the school level, regular Statistics appeared to be declining in popularity until the class of 2015. At that point, it saw a rapid rise, surpassing AP Calculus BC for students in the class of 2018 and approaching AP Statistics for the class of 2020. Although less of a dramatic increase, the percentage of students completing AP Statistics also nearly tripled over this time span from roughly two to six percent of students completing the course. However, between the classes of 2003 and 2020, the percentage of students completing AP Calculus AB declined slightly, while AP Calculus BC showed a one percentage point increase, from two to three percent of students completing the course.

Figure 3. Participation in both regular and AP Statistics increased dramatically between 2003 and 2020.  

Note: N = 5,220,078. This analysis included the entire sample of students who graduated from Texas public high schools between 2003 and 2020.

Finding 2: Expanded access to advanced math was a “rising tide” that lifted all boats but has not reduced socioeconomic and racial disparities in participation

Given the importance of math in shaping students’ postsecondary outcomes and the long-standing inequalities in advanced math course-taking, a key question is whether expansions in overall access and course participation rates have translated into reduced disparities by race, SES, and/or gender. This analysis includes the demographic characteristics and test scores of our entire 2003-2020 high school graduate sample. It places students into mutually exclusive categories based on the highest math course they completed.

Not surprisingly, those who complete AP Calculus BC or take both Calculus and Statistics score nearly a full standard deviation (SD) higher on the state math test than students who only complete Algebra II or below (Figure 4). Students who do not progress beyond Algebra II score roughly 0.15 SD lower on the eighth-grade math assessment than the statewide average; the comparable score for students who complete AP Calculus AB or take both statistics and calculus is 0.70 SD. Notably, students who complete Precalculus are somewhat higher achieving on average than students who complete regular Statistics. Whereas Precalculus students score roughly 0.20 SD higher in math, regular Statistics students score very close to the statewide average on reading and math in eighth-grade. In contrast, students who progress into advanced math courses are much higher achieving than average, scoring 0.40 to 0.50 SD higher in reading and 0.45 to 0.60 SD higher in math. Notable, too, is that AP Calculus AB students are somewhat higher achieving than AP Statistics students.

Figure 4. Students who participate in advanced math courses score considerably higher than the statewide average on standardized assessments.

Note: N =4,317,426. This analysis included the sample of students who graduated from Texas public high schools between 2003 and 2020, were enrolled in Texas public schools in eighth grade, and completed eighth grade standardized assessments. Students who completed the Grade 8 exams before eighth grade are included in the sample. The standardized exams used (TAAS, TAKS, or STAAR) vary based on the cohort students graduated in and the testing and accountability regime in effect at the time the student was in eighth grade.

Figure 5 shows that advanced math course-taking is stratified by class and race and, to a lesser extent, by gender. Underrepresented minority (URM, signifying Black, Hispanic/Latino, Native American/Alaskan Native, Native Hawaiian/Pacific Islander, or Multiracial students) and economically disadvantaged students are more likely to terminate with Algebra II or a lower class than their White and non-economically disadvantaged counterparts. In contrast, economically disadvantaged and URM students are much less likely than other students to be enrolled in AP courses, and female students are much less likely than male students to take AP Calculus BC and both a statistics and calculus course.

Figure 5. Math course-taking is highly stratified by race, class, and—to a lesser extent—gender.   

Note: N =4,317,426. This analysis included the entire sample of students who graduated from Texas public high schools between 2003 and 2020, were enrolled in Texas public schools in eighth grade, and completed the State of Texas Assessments of Academic Readiness (STAAR) exams in math and reading. Students who completed the STAAR Algebra I End-of-Course (EOC) exam in lieu of the Grade 8 Mathematics exam are included in the sample. URM refers to underrepresented racial/ethnic minority students, including Black, Hispanic/Latino, Native American/Alaskan Native, Native Hawaiian/Pacific Islander, and Multiracial students.

Figure 5 also highlights the substantial distinction between regular Statistics and AP Statistics regarding the courses’ demographic composition. Indeed, students who completed Precalculus or regular Statistics as their highest math course are demographically similar to the overall student population. In contrast, both AP Statistics and AP Calculus AB students are disproportionately White and non-economically disadvantaged. This analysis suggests that statistics versus calculus may not be the primary stratifying mechanism in advanced math pathways. Rather, students’ demographic characteristics relate more to whether students take these courses as AP or not.

Next, we examine the extent to which sociodemographic disparities in advanced math course-taking persist even after including differences in prior achievement and school characteristics as controls. We conduct a regression that controls for students’ demographic characteristics, eighth grade test scores, the math course they enrolled in during ninth grade, high school graduation year, and which high school they attended (see Methods for more).[34]

Figure 6 depicts differences in the likelihood that various student groups will complete any calculus or statistics course in high school, controlling for other variables. Compared to similar White students, Black, Hispanic/Latino, and Native American students are significantly less likely to take calculus or statistics. In contrast, Asian students have the highest likelihood (by a margin of 17 percentage points). Compared to their non-disadvantaged peers, economically disadvantaged students are just 2.6 percentage points less likely to take advanced math, after applying controls. In comparison, students identified as “gifted and talented” are 16.5 percentage points more likely compared to non-gifted students. There are no significant differences between male and female students, and the differences for students receiving special education services or identified as limited English proficient (LEP) are less than one percentage point from the reference group (non-SPED and non-LEP, respectively).

Figure 6. Race/ethnicity, economic background, and gifted status – but not gender – correlate with taking at least one advanced math course, even after controlling for other demographic factors.

Note: N = 5,220,078. This analysis includes the entire sample of students who graduated from Texas public high schools between 2003 and 2020. The figure plots coefficients from a linear probability model indicating whether or not students completed any calculus or statistics courses in high school. The reference group for Race/Ethnicity is White students. In addition to the variables shown, the model controls for students’ 8th grade reading and math test scores, the highest math course students completed in 9th grade, the cohort students graduated from, and high school fixed effects. Standard errors are clustered at the high school level. Error bars represent 95 percent confidence intervals.

Next, we investigate the extent to which participation in advanced math has become more equal among groups over time.[35]

Figure 7 shows that, from the classes of 2003 through 2020, the advanced math course-taking rate more than doubles for both disadvantaged and more affluent groups (from five to 13 percent and from 13 to 27 percent, respectively). Still, the larger increase for the latter means that the gap in advanced math course-taking also grew substantially during that time. For the class of 2003, this gap was about eight percentage points, but by the class of 2020, it had doubled to 16 percentage points. However, the relative gap in participation remained roughly the same, meaning more affluent students were 2.3-2.5 times as likely as disadvantaged students to complete calculus or statistics across all years.[36] (To see rates of course-taking for individual courses broken out by socioeconomic status, see Figure B2 in Appendix B.)

Figure 7. The rate of taking any calculus or statistics course increased from 2003 to 2020 for students regardless of socioeconomic status, but the increase for non-economically disadvantaged students was much larger than that for economically disadvantaged students.

Note: N = 5,220,078 This analysis included the entire sample of students who graduated from Texas public high schools between 2003 and 2020. To visualize the gap between groups, see Figure B1 in Appendix B.

Figure 8 shows a similar pattern by race and ethnicity for taking any calculus or statistics course. The rate of Asian students doing so has increased by roughly 20 percentage points since the class of 2003, and more than half of Asian students now take calculus or statistics. The percentage of White students increased by roughly nine percentage points during this time to 22 percent by the class of 2020. The rates for Black, Hispanic/Latino, and Native American students increased by a larger percent in relative terms, roughly doubling, but from a much lower baseline, meaning that the absolute increases of 5 to 6 percentage points are more modest, with gaps between these groups’ rates and those of White and Asian students widening substantially during this period.

Figure 8. Black, Hispanic/Latino, and Native American students’ rates of calculus or statistics course-taking rose considerably, but still much more slowly in absolute terms than those of Asian and White students.

Note: N = 5,220,078. This analysis included the entire sample of students who graduated from Texas public high schools between 2003 and 2020. URM refers to underrepresented racial/ethnic minority students, including Black, Hispanic/Latino, Native American/Alaskan Native, Native Hawaiian/Pacific Islander, and Multiracial students.

Figure 9 shows changes in racial/ethnic inequalities for specific advanced math courses. For simplicity, we focus on students who are underrepresented minorities (URM), meaning Black, Hispanic/Latino, Native American, and Pacific Islander students, comparing them with White students, the largest student group in the sample over the entire period.[37] In many respects, this figure looks similar to Figure 8, which presents socioeconomic gaps, albeit with two notable differences.

First, Calculus AB course-taking among URM students increased slightly over time, from four percent to five percent of students. In contrast, the percentage of White students taking that course remained flat at 10 to 11 percent until the class of 2018 and then declined to nine percent by the 2020 cohort (see the teal lines in Figure 9). This results in the gap between these groups narrowing from nearly six percentage points to about four percentage points in the most recent year. In contrast, Calculus BC course-taking increased slightly for White students but was flat for URM students (see the blue lines). Second, for both regular Statistics (salmon lines) and AP Statistics (gold lines), both groups experienced large increases. Still, the rate of growth for White students (broken lines) was roughly double that of URM students (solid lines), resulting in the largest racial/ethnic gaps for the class of 2020. (To see these rates of course-taking for individual courses broken out by socioeconomic status instead of race, see Figure B2 in Appendix B.)

Figure 9. Gaps between URM and non-URM students in advanced math course-taking have grown larger over time for all courses but AP Calculus AB.

Note: N = 5,220,078 . This analysis included the entire sample of students who graduated from Texas public high schools between 2003 and 2020. URM refers to underrepresented racial/ethnic minority students, including Black, Hispanic/Latino, Native American/Alaskan Native, Native Hawaiian/Pacific Islander, and Multiracial students.

Finally, the differences in advanced math course-taking by gender are much smaller than differences by SES or race/ethnicity. As Figure 10 shows, female and male students have nearly identical rates of taking either course until the arrival of the class of 2012. At that point, girls began to take advanced courses at slightly higher rates than boys and were roughly one percentage point more likely than boys to take calculus or statistics in the class of 2020.

Figure 10. Girls have begun to surpass boys in their likelihood of taking any calculus or statistics course.

Note: N = 5,220,078. This analysis included the entire sample of students who graduated from Texas public high schools between 2003 and 2020.

However, Figure 11 reveals differences by gender in math course-taking. Boys and girls had nearly equivalent rates of taking Calculus AB and regular Statistics starting in the class of 2003 through the class of 2020 cohort, but their rates of taking other advanced math courses diverged. Boys were already more likely to complete Calculus BC in the class of 2003, and that gender disparity has grown since. Conversely, girls and boys had roughly equivalent rates of taking AP Statistics until the class of 2010, when the girls began taking that course at higher rates than boys. The growth in the female AP Statistics advantage roughly coincides with the increase in the male Calculus BC advantage, although we cannot say whether the trends are causally related.

Figure 11. Gender gaps in advanced math course-taking have remained relatively consistent over time for all courses but AP Statistics, in which females gained a considerable advantage over time.

Note: N = 5,220,078 . This analysis included the entire sample of students who graduated from Texas public high schools between 2003 and 2020.

The rise of statistics during the study period contributes to more students of all groups taking advanced math over time. The results for equity, however, are a mixed bag – or a Rorschach test. More economically disadvantaged students and URM students are taking advanced math in high school than ever before. Still, these increases have not kept pace with the even larger increases among other groups, resulting in widening gaps.

How Calculus vs. Statistics Relate to Postsecondary Outcomes

The previous section documented the considerable rise in statistics, the stagnation of calculus course-taking, the growth in socioeconomic and racial/ethnic disparities in most advanced math course-taking, and the growing female advantage in AP Statistics combined with the increased male advantage in Calculus BC. The implications of these trends depend on the relationship between advanced math course-taking in high school and students’ postsecondary outcomes, the topic to which we now turn.

Finding 3: Students who complete higher math courses in high school tend to have better postsecondary educational outcomes and earnings.

Descriptive results in Figure 12 show that students who completed AP Calculus or AP Statistics are much more likely to enroll in a four-year postsecondary institution, and a selective institution, than students who finish high school with Algebra II, regular Statistics, or Precalculus. Students completing any of these AP math courses are also much more likely to complete a bachelor’s degree within four or six years than other students.

There are also differences among the non-AP students, with those completing regular Statistics or Precalculus much more likely to experience these postsecondary outcomes than students who complete only Algebra II or a lower class. Among the AP students, the students who take Calculus generally outperform the students who only take Statistics. Students who take AP Calculus BC have the highest rates of attending a four-year institution, attending a very selective institution, and completing a degree, whether in four or six years. AP Statistics students have levels of overall college-going that are similar to those of calculus students, however (see the first group of bars marked “First-Year Any College”).

Figure 12. The highest math course students take is strongly correlated with the attainment of a bachelor’s degree and other post-secondary educational outcomes. 

Note: N = 5,220,078. This analysis included the entire sample of students who graduated from Texas public high schools between 2003 and 2020. “Statistics and Calculus” refers to the group of students who take any statistics and any calculus course. Higher education institutions include both public and private institutions.

A similar pattern holds for long-term earnings, which are shown in Figure 13. AP math students strongly outearn students who took Algebra II or Precalculus as their terminal high school math course. Still, there is variation within the AP courses that is similar to that of the postsecondary educational outcomes in Figure 12: Students who complete an AP calculus course tend to outearn the AP Statistics students, although the difference between AP Statistics students’ earnings and those of the students taking the most common AP calculus course, AP Calculus AB, is only about $2,000 per year. The earnings of AP Calculus BC students ($69,000 per year) and those of students who take an AP calculus course and AP Statistics ($71,000 per year) are the greatest.

Figure 13. Ten years after graduation, AP math students outearn students whose highest high school math course was Algebra II or below by $21,000 to $33,000 annually.

Note: N = 1,557,905. This analysis included students who graduated from Texas public high schools between 2003 and 2012, had at least 10 years (40 quarters) between when they graduated high school and the last observable quarter of wages at the time the analysis was conducted, and were employed in Texas with non-zero wages reported through Texas’s Unemployment Insurance (UI) wage data collection in their fortieth quarter after high school graduation.

Finding 4: Calculus students are more likely to enroll in selective colleges and pursue STEM majors but are no more likely than statistics students to earn a degree.

For these analyses, we focus specifically on whether students completed AP Statistics or AP Calculus AB given that 1) those two groups of students are already similar, 2) this represents a common “fork in the road” in math course-taking for students who have completed Precalculus, and 3) the rise of statistics previously documented raises the question of the benefits of calculus versus statistics. As indicated in the Methods section, we restrict our sample to students who completed either of these courses and graduated from 2015 to 2020, given the availability of out-of-state college enrollment data from the National Student Clearinghouse (NSC).[38] We also apply a rich set of control variables, including student demographics, 8th grade assessment scores, prior course-taking, and school-specific effects, to help mitigate selection effects.

Figure 14 shows the estimated advantage of taking AP Calculus AB compared to AP Statistics on several postsecondary outcomes. Each teal bar represents the estimated difference between the two groups of students on the specified outcome. In contrast, the horizontal bars represent the confidence intervals of our estimates (i.e., how precise they are). The red vertical line is centered at zero and estimates whose confidence intervals cross zero are not statistically significant. Estimates to the left of the vertical line suggest an AP Statistics advantage, whereas estimates to the right imply a Calculus AB advantage. (Thus, negative values signify a disadvantage for AP Calculus AB and an advantage for AP Statistics.)

Overall, we find no statistically significant differences between Calculus AB and AP Statistics students in their probability of attending any college, attending any 4-year institution, or completing a bachelor’s degree. However, AP Statistics students are roughly two percentage points more likely to attend a private 4-year institution (last bar). In comparison, Calculus AB students are 6 percentage points more likely to enroll in a very selective institution (first bar). Given that selective institutions tend to have higher completion rates than less selective institutions, it’s worth noting that Calculus AB students are no more likely to complete a bachelor’s degree. (Moreover, while the raw differences depicted in Figure 12 suggest a Calculus AB advantage over AP Statistics in bachelor’s attainment, those differences disappear after applying controls).

Figure 14. AP Calculus AB and AP Statistics students have equivalent college enrollment and bachelor’s degree attainment rates, but Calculus AB students are more likely to enroll in selective institutions.

Note: N = 177,986.  Augmented Inverse Probability Weighting. The sample was limited to students in the 2015-2020 cohorts, for whom NSC data on out-of-state college enrollment is available, and to students who participated in AP Statistics or AP Calculus AB. Estimates found to the left of the vertical line suggest an AP Statistics “advantage,” whereas estimates to the right imply a Calculus AB “advantage.” Lines extending from the bars represent 95 percent confidence intervals. Models control for the math course taken freshman year, whether a student took AP Statistics or AP Calculus, percent of students in school enrolled in Precalculus, percent of students in school enrolled in AP Statistics, percent of students in school enrolled in Regular Statistics, percent of students in school enrolled in AP Calculus AB, percent of students in school enrolled in AP Calculus BC, number of passed course credits, number of failed course credits, number of math course credits, number of science course credits, number of advanced course credits, number of dual-credit course credits, standardized reading test scores, standardized math test scores, cohort, race/ethnicity, economic background, special education status, gender, and “giftedness” status. Those whose freshman year math course was “AP Statistics/Regular Statistics,” and “Calculus AB/BC” were excluded from analyses. Higher education institutions include both public and private institutions.

When it comes to majoring in STEM fields, we find an obvious advantage for calculus students. Figure 15 shows that students who completed AP Calculus AB are roughly 11 percentage points more likely to declare a STEM major than AP Statistics students. Notably, only 15 percent of observably equivalent AP Statistics students major in STEM, meaning that AP Calculus AB students are 75 percent more likely to major in STEM in proportional terms.

This overall STEM advantage for calculus students is driven by their increased likelihood of majoring in Engineering (five percentage points), Biological Sciences (three percentage points), and Computer Science (two percentage points). For Engineering and Computer Science, they are twice as likely to major in these subjects compared to AP Statistics students. The one exception is Psychology, in which AP Statistics students are significantly more likely to major compared to AP Calculus AB students. Still, the difference is modest (less than one percentage point). Results for all other majors are either small (less than 1 percentage point) or not statistically significant.

Figure 15. AP Calculus AB course-takers are significantly more likely to major in STEM fields than observably equivalent AP Statistics course-takers.

Note: N = 177,986.  Augmented Inverse Probability Weighting. The sample was limited to students in the 2015-2020 cohorts, for whom NSC data on out-of-state college enrollment is available, and to students who participated in AP Statistics or AP Calculus AB. Lines extending from the bars represent 95 percent confidence intervals. Models control for the math course taken freshman year, a flag for whether a student took AP Statistics or AP Calculus, percent of students in school enrolled in Precalculus, percent of students in school enrolled in AP Statistics, percent of students in school enrolled in Regular Statistics, percent of students in school enrolled in AP Calculus AB, percent of students in school enrolled in AP Calculus BC, number of passed course credits, number of failed course credits, number of math course credits, science course credits, advanced course credits, dual-credit course credits, standardized reading test scores, standardized math test scores, cohort, race/ethnicity, economic background, special education status, gender, and “giftedness” status. Those whose freshman year math course was “AP Statistics/Regular Statistics,” and “Calculus AB/BC” were excluded from analyses.

Figure 16 shows that the patterns for STEM degree attainment closely mirror the patterns for STEM enrollment. Calculus AB students are roughly ten percentage points more likely to earn any STEM bachelor’s degree compared to observably equivalent AP Statistics students. Similarly, this calculus advantage is mostly driven by higher rates of earning degrees in Engineering (five percentage points), Biological Sciences (three percentage points), and Computer Science (two percentage points). As with STEM enrollment, the one STEM field where AP Statistics students are more likely to earn a bachelor’s degree is Psychology, with a difference of roughly one percentage point. Overall, AP Calculus AB students are more likely to both major in and complete bachelor’s degrees in STEM fields compared to AP Statistics students.

Figure 16. AP Calculus AB students are more likely to earn STEM bachelor’s degrees compared to observably equivalent AP Statistics students.  

Note: N = 177,986. The sample was limited to students in the 2015-2020 cohorts, for whom NSC data on out-of-state college enrollment is available and who participated in AP Statistics or AP Calculus AB. Lines extending from the bars represent 95 percent confidence intervals. Models control for the math course taken freshman year, whether students took AP Statistics or AP Calculus, percent of students in school enrolled in Precalculus, percent of students in school enrolled in AP Statistics, percent of students in school enrolled in Regular Statistics, percent of students in school enrolled in AP Calculus AB, percent of students in school enrolled in AP Calculus BC, number of passed course credits, number of failed course credits, number of math course credits, number of science course credits, number of advanced course credits, number of dual-credit course credits, standardized reading test scores, standardized math test scores, cohort, race/ethnicity, economic background, special education status, gender, and “giftedness” status. Those whose freshman year math course was “AP Statistics/Regular Statistics,” and “Calculus AB/BC” were excluded from analyses. Augmented inverse probability weights were applied.

Finding 5: Despite the STEM advantage, taking AP Calculus AB does not lead to better long-term earnings than taking AP Statistics.

In our final set of analyses, we investigate students’ long-term earnings and industry of employment after applying a rich set of control variables.

AP Calculus AB students are estimated to outearn their AP Statistics peers 7.5 years (30 quarters) after graduation (Figure 17). At that point, AP Statistics students earn $47,756 annually with AP Calculus students outearning them by $1,888 annually, an advantage of about four percent. By year 10 (40 quarters after graduation), the raw difference had declined to $1,622 annually, with AP Calculus students earning about three percent more than observably equivalent AP Statistics students, although the difference is not statistically significant. Thereafter, no differences in income between AP Statistics and AP Calculus students were statistically significant. At 17.5 years (70 quarters after high school graduation), AP Statistics students are estimated to earn roughly $2,000 more per year than AP Calculus AB students, but, again, the estimate is not statistically significant.

In short, we do not have sufficient evidence to conclude that taking AP Calculus AB over AP Statistics provides long-term earnings benefits. (We obtain similar results when examining the log of earnings, although the coefficient at 17.5 years is positive in that estimation; see Figure C7 in Appendix C.)

Figure 17. AP Calculus AB students have an initial earnings advantage over AP Statistics students, but the advantage fades eventually.  

Note: N =177,986.  The sample was restricted to students who participated in AP Statistics and AP Calculus AB in earlier cohorts, for whom long-term earnings data are available. The sample was also restricted to students who remained in Texas, given that the wage records come from the TWC. Error bars represent 95 percent confidence intervals. Models control for the math course taken freshman year, whether a student took AP Statistics or AP Calculus, percent of students in school enrolled in Precalculus, percent of students in school enrolled in AP Statistics, percent of students in school enrolled in Regular Statistics, percent of students in school enrolled in AP Calculus AB, percent of students in school enrolled in AP Calculus BC, number of passed course credits, number of failed course credits, number of math course credits, number of science course credits, number of advanced course credits, number of dual-credit course credits, standardized reading test scores, standardized math test scores, cohort, race/ethnicity, economic background, special education status, gender, and “giftedness” status. Those whose freshman year math course was “Other,” “AP Statistics/Regular Statistics,” and “Calculus AB/BC” were excluded from analyses. Augmented inverse probability weights were applied.

Finally, we examine whether or not taking AP Calculus AB versus AP Statistics in high school is linked to the industries in which students are employed ten years after graduating from high school.[39] Figure 18 shows that AP Calculus AB 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. We find no 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, Computer Systems Design, Management, and Scientific Research and Development.

Interestingly, we also do not find a clear advantage of calculus or statistics course-taking in math-intensive industries overall. Although fields where AP Calculus AB students have an advantage (such as Oil and Gas) may be heavily reliant on math (e.g., engineering), AP Statistics students are more likely to work in other math-intensive industries, including Finance and Insurance, as well as Information. In other words, differences in industries of employment between AP Calculus AB and AP Statistics students do not clearly align with math-intensive versus less math-reliant fields.

Figure 18. There are some significant differences between calculus and statistics students in their industries of employment, but not in the Professional and Scientific industries.

Notes: N = 119,524. The sample was restricted to students who completed AP Calculus AB or AP Statistics, who graduated high school between 2003 and 2011, and for whom employment information ten years after high school graduation (Q40) is available. The sample was also restricted to students who remained in Texas, given that the wage records come from the TWC. Lines extending from the bars represent 95 percent confidence intervals. Models control for the math course taken freshman year, a binary indicator regarding whether the student took AP Calculus or AP Statistics, percent of students in school enrolled in Precalculus, percent of students in school enrolled in Regular Statistics, number of passed course credits, number of failed course credits, number of math course credits, number of science course credits, number of advanced course credits, number of dual-credit course credits, standardized reading test scores, standardized math test scores, cohort, race/ethnicity, economic background, special education status, gender, and “giftedness” status.

Implications: Developing Diverse High School Math Pathways

For decades, the high school math hierarchy was evident: calculus reigned supreme as the gold standard for advanced students. But this report tells a different story—one where statistics is rising rapidly, eclipsing calculus as the most common advanced math course in Texas by 2020.

This shift presents both an opportunity and a challenge: how can we ensure that expanded pathways do not come at the expense of rigor, equity, or economic mobility? We offer four ideas.

First, a non-calculus pathway can be rigorous and effective, but it must be buttressed by strong standards, curricula, and assessments. High school math pathways focusing on statistics and data science hold great promise as data literacy becomes increasingly necessary for most Americans. Indeed, coursework centered on statistical thinking is valuable and relevant, helping citizens to interpret political polls, engage with data visualization, make inferences from samples, and understand the concept of probability.

Critics have raised concerns that alternative math pathways could dilute rigor and leave students underprepared. California’s recently repealed data science initiative, for instance, lacked clear standards and accountability, raising legitimate concerns about whether students were mastering essential math concepts.[40]

Yet the College Board’s AP program provides a counterexample: AP Statistics students – who follow a structured, externally validated curriculum – perform just as well as their Calculus-taking peers in long-term outcomes, including college enrollment, degree completion, and earnings. This underscores the need for rigorous standards and common assessments in all advanced math pathways, including emerging data science programs and other math courses for non-accelerated students. Without clear benchmarks, alternative pathways risk becoming weaker tracks that exacerbate, rather than address, educational inequities.

More directly, the long-term success of AP Statistics students also demonstrates that statistics can be an equally valuable alternative to calculus, at least for students planning to pursue non-STEM fields after high school.

Second, diversified math pathways will not necessarily close equity gaps. In our Texas sample, growing access to statistics has corresponded with increased overall participation in advanced math among all student groups. Still, it has not reduced socioeconomic or racial/ethnic disparities. In fact, some gaps in advanced math course-taking have widened as statistics course-taking has increased. That’s because higher-income, White, and Asian students are more likely to enroll in these courses than their peers. The real equity challenge, then, is not about calculus versus statistics: it is ensuring that students from all backgrounds have access to rigorous advanced math. Broadening access means starting earlier and thinking bigger, including investing in middle school algebra pipelines, supporting teacher capacity, and confirming that students and families understand their options.

Third, equitable math options are facilitated by policies that prioritize access, quality control, training, and transparency. The data make clear that state policy plays a powerful role in shaping math course-taking. Texas’s 4x4 curriculum in 2007 drove an increase in precalculus enrollment, while the shift to the Foundation High School Program (FHSP) in 2014 corresponded with a rise in statistics and a decline in precalculus. Future policy should focus on ensuring that all students have access to rigorous advanced math options, including:

• Building a wider pipeline of advanced math students: The decision to enroll in AP Calculus or AP Statistics during high school depends on factors and opportunities encountered earlier in a student’s academic career. For example, if students have not taken Algebra I by eighth grade, it is nearly impossible for them to take advanced courses during high school. One promising strategy to expand access is auto-enrollment policies, such as Texas’s SB 2124 and similar laws in a few other states,[41] that require districts to place high-achieving middle school students into advanced math courses automatically. Prior to participating in rigorous middle school math, however, students must master fundamental skills in elementary school mathematics (such as basic operations, place value, and fractions) that will help propel them into this pipeline.[42]
• Establishing clear learning standards: The lack of standardized expectations in some alternative math pathways risks creating low-quality tracks. States should develop rigorous, common end-of-course assessments to ensure transparency and accountability.[43]
• Strengthening teacher capacity: As with other courses, advanced math courses are only as strong as the educators teaching them. States should invest in teacher training for both calculus and statistics, particularly in schools serving low-income and underrepresented students.
• Guiding students and families: Many students and parents lack clear information about how different math choices impact college and career opportunities. Schools should provide better advising to help students make informed decisions.

Fourth, calculus remains the optimal choice for many students, especially those considering a STEM major in college. The rise of statistics should not be interpreted as a reason for schools to shift away from offering calculus. The data corroborate what has long been understood: calculus retains unique value for high school students eyeing STEM majors in college. AP Calculus AB students are significantly more likely than AP Statistics students to attend selective colleges, major in STEM, and pursue careers in engineering, computer science, and physical sciences. At the same time, statistics is integral to a broad range of careers in finance, healthcare, and social sciences.[44] Even within STEM, advanced statistics skills are increasingly in demand, and mastery of statistics and data science is a competitive advantage in nearly every industry. Rather than an either-or debate, the goal should be to equip students with the quantitative reasoning skills they need for their chosen paths, including both calculus and statistics when appropriate.

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The rise of statistics presents an opportunity to modernize high school math education for a data-driven world. But simply offering more options is not enough. Ensuring quality, equity, and transparency must be central to any reform efforts. Policymakers should embrace a both-and approach: expanding rigorous alternatives like statistics and data science while preserving strong calculus pathways for students who plan to focus on STEM. We all lose if the future of high school math is a clash between calculus and statistics rather than a system that prepares all students for success in college, careers, and an increasingly quantitative world.

Appendices

Appendix A: Technical Notes on Methodology

Data Source and Sample

To address our research questions, we use administrative data from the Texas Education Research Center (TERC) at the University of Texas at Austin. TERC maintains Texas’ statewide longitudinal student data system, which links K-12 data collected by the Texas Education Agency (TEA), postsecondary data collected by the Texas Higher Education Coordinating Board (THECB), and employment data collected by the Texas Workforce Commission (TWC). Every student who attends a public school in Texas between early elementary and high school graduation is included in the K-12 data and is trackable through postsecondary education (anywhere in the country) and into the workforce (in Texas) with a unique identification number. THECB data only covers students who enroll in college in-state. To track students who left Texas for college, we use data from the National Student Clearinghouse (NSC). Our full sample consists of 5,220,078 individuals who graduated from a high school in Texas between 2003-2020. 

Math Course Variables

Given that high school math course-taking is the focus of our study, math-specific course credit variables were created from TEA’s course transcript records found in the ERC. Although the course data does not include the grade students received in the course, it does include the broad (e.g., math) and more specific (e.g., statistics) subject of the course, unique course titles, whether the course was taken as Advanced Placement or dual-credit, and whether the student passed the course. We define course completion as students attempting and passing a course, although for the ninth grade math course variable (described below) we use the course that a student enrolled in, whether or not they passed the course. 

To measure school-level course offerings, we aggregated the student-level dichotomous course indicators at the school-by-year level. If at least one student completed a course in a given school and a given year, we treated that school as having offered the course. Although schools could technically offer a course without having any students enroll, we cannot distinguish between schools not offering a course at all and offering a course with zero enrollments.

TEA’s course records contain several variables that allow us to determine the specific courses students completed. All courses are assigned a subject area code that represents the broad subject of the course (e.g., ELA, math, science), a more specific subject code (e.g., physics, chemistry, biology), and unique service codes. These service codes correspond to specific courses (e.g., Algebra I, Geometry, Algebra II) and allow us to distinguish between courses in the same subject (e.g., regular Statistics vs. AP Statistics). In addition, course records indicate whether the course was considered advanced (AP or IB) or taken as a dual-credit course.

Some high school math courses have vague titles. We consulted the Texas Essential Knowledge and Skills (TEKS), Texas’s education standards, to determine which courses should be considered “advanced.” According to TEKS, Mathematical Models with Applications is a course “designed to build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I” and “provides a path for students to succeed in Algebra II.”[45] The course can only be taken after the completion of Algebra I and before the completion of Algebra II. Independent Study in Math is a course where students “extend their mathematical thinking beyond the Algebra II level in a specific area of mathematics such as theory of equations, number theory, non-Euclidean geometry, linear algebra, advanced survey of mathematics, or history of mathematics.”[46] This course requires students to have completed Geometry and Algebra II. Advanced Quantitative Reasoning “consists primarily of applications of high school mathematical concepts…in applied situations involving numerical reasoning, probability, statistical analysis, finance, mathematical selection, and modeling with algebra, geometry, trigonometry, and discrete mathematics.”[47] This course also requires students to have completed Geometry and Algebra II. College Prep Mathematics is a course primarily for high school seniors who have not demonstrated college readiness and reviews foundational algebraic and geometric concepts. Finally, Algebraic Reasoning is a course designed for students to “continue developing mathematical reasoning related to algebraic understandings and processes.”[48] Students must have completed Algebra I before taking the course.

Based on their content, we conclude that Mathematical Models with Application, College Prep Mathematics, and Algebraic Reasoning are all non-advanced courses, typically offered to students who need additional instruction to master foundational algebraic and geometric concepts. Because these courses do not include statistics or calculus content, they are not considered advanced math courses in our study. Independent Study in Math can be an advanced math course and has the highest rate of courses taken as dual-credit out of all math courses, but calculus and statistics content is not heavily reflected in the learning objectives of the course. Finally, Advanced Quantitative Reasoning does include statistical concepts, but the emphasis is on applied data analysis for problem-solving rather than providing students with a thorough treatment of statistical concepts. This course is also not offered as AP and rarely as dual-credit (0.6% of course records).

We use this course data to create several variables representing math coursework used in our analyses. First, we create a categorical variable capturing the highest math taken by each student. The categories included: Algebra 2 or Below (57.13 percent), Precalculus (28.83 percent), Regular/Regular Statistics (1.10 percent), AP Statistics (3.16 percent), AP Calculus AB (6.32 percent), AP Calculus BC (1.61 percent), and Statistics and Calculus (1.85 percent). The latter category indicates that the participant took both a Calculus and Statistics course. This allows us to place all students into one of the mutually exclusive categories indicated by the variable.

Second, we create dichotomous indicators of whether students completed specific courses (Precalculus, Regular/Regular Statistics, AP Statistics, AP Calculus AB, and AP Calculus BC). These variables are equal to one if the student completed the course and zero otherwise. These dichotomous variables are used in analyses examining student- and school-level factors that relate to the probability of course-taking. In this case, the dichotomous variables are not mutually exclusive. For example, students who completed both AP Statistics and AP Calculus AB would have a one for both dichotomous variables.

Third, for some analyses, we create a dichotomous indicator designed to directly compare the outcomes of students who took AP Calculus AB or AP Statistics as their highest math course. This variable is equal to one if the student took AP Calculus AB and did not take AP Calculus BC or AP Statistics, and is equal to zero if the student took AP Statistics and did not take AP Calculus AB or AP Calculus BC. The variable is missing for all other students, meaning analyses including this variable are restricted to these two groups of students.

Finally, we create a categorical variable indicating the highest math course a student completed in ninth grade, which we use as a control variable. The categories of this variable are: Other Math (0.14 percent), Algebra 1 (62.3 percent), Geometry (24.6 percent), Algebra 2 (2.8 percent), Precalculus (0.08 percent),), AP Statistics/Statistics (0.00 percent),), AP Calculus AB/BC (0.01 percent), and Missing (10.2 percent). These categories are mutually exclusive. We note that students in the “Missing” category may be missing because they were not enrolled in a Texas public high school in ninth grade (e.g. students who moved to Texas after ninth grade) or because they were enrolled but did not take any math course in ninth grade.

A peculiarity of the Texas data is that courses are often taken simultaneously as AP and dual-credit. For example, we would expect the rate of dual-credit course-taking in AP Calculus AB, AP Statistics, and AP Calculus BC to be zero, but we find that a small percent of these courses (all less than 5 percent) are taken as dual-credit. Anecdotally, we have heard that some districts list the course as both AP and dual-credit so that students may still receive college credit for the course through the dual-credit mechanism even if they do not score high enough on the associated AP exam for a college to confer them college credit. However, because these courses are defined as AP in the service codes, we treat them as AP courses rather than dual-credit.

As mentioned above, if students took the course for dual-credit, a record of the course is also collected by THECB. THECB’s course records capture all courses provided by colleges and universities in the state, including dual-credit, developmental education/non-credit, and technical credit courses. Because Independent Study in Math has a high rate of dual-credit course-taking and it is not immediately apparent what students taking those courses are learning, we explored THECB’s dual-credit math course data. Although some of these independent study course records indicated they were Statistics or Calculus courses, roughly 83 percent did not fall into either of these categories. Approximately 63 percent of these dual-credit math courses were identified as College Algebra, with smaller percentages for courses such as Plane Trigonometry (7.8 percent), Precalculus (5.0 percent), Math for Business and Social Science (4.4 percent), and Contemporary Mathematics (2.9 percent). For this reason, we do not consider Independent Study in Math primarily based on calculus or statistics. Because our primary interest lies in examining calculus and statistics coursework, we focus on the four TEA courses unambiguously considered to be aligned with those subjects: AP Calculus AB, AP Calculus BC, AP Statistics, and regular Statistics.

College enrollment and degree attainment

Several variables were created to capture college enrollment and degree attainment patterns. We measure first-year college enrollment by examining the college enrollment records in the year after the student graduated from high school. A dichotomous variable was equal to one (68.5 percent) if the student was enrolled in any college or university in their first year after high school graduation and zero otherwise (32.5 percent). To identify the institution type of the university which the participant attended, we created a categorical variable with the following 3 categories: Public 4-year institution (39.7 percent), Private 4-year institution (7.8 percent), and lastly, institutions that were limited to degrees that can be attained in two years or less (52.3 percent). Note that these percentages are out of the 2,922,163 who attended an institution their first year after graduating high school. An additional dichotomous flag captured whether a participant attended a 4-year institution right after high school (26.6 percent) or not (73.4 percent).

In addition to college enrollment, we created indicators representing whether students majored in specific STEM subjects or any STEM subject using Classification of Instructional Program (CIP) codes for students’ majors found in the THECB enrollment data. CIP codes can range from two to six digits, with 2-digit CIP codes representing broad majors (e.g., Engineering) and 6-digit CIP codes representing more specific majors (e.g., Biomedical Engineering). We used the Department of Homeland Security (DHS) STEM-designated degree program list to identify majors categorized as STEM. The DHS list only designates four 2-digit CIP codes as fully STEM, while all other 2-digit CIP codes may include some STEM and some non-STEM majors. For example, Agricultural Science includes some 6-digit CIP codes designated as STEM while others are not considered STEM. For simplicity, we used 2-digit CIP codes in which most 6-digit majors were designated as STEM. The specific STEM subjects we created dichotomous indicators for include Biological and Biomedical Sciences, Computer Science, Engineering, Engineering Technology, Math and Statistics, Physical Sciences, and Psychology. The dichotomous Any STEM variable was equal to one if the student majored in any of those disciplines as well as Agriculture Science, Interdisciplinary, Natural Resources and Conservation, or Science Technologies. We did not create separate dichotomous variables for those subjects because very few students enrolled in those majors.

Dichotomous flags were also made to capture any bachelor's degree attainment (21.8 percent) and whether students earned a bachelor’s degree by the 4th, 6th, or 8th year following their graduation from high school. Similarly, STEM versions of these variables were created to specifically measure STEM degree attainment. Of the analytic sample, 8.1 percent attained a bachelor’s degree in a STEM subject.

Wages

Post-graduation wages were retrieved from Texas Workforce Commission (TWC). Earlier cohorts have more wage data, given that more time has passed since their high school graduation date. Our primary outcome is the wages students earned in a particular quarter. We use both the raw wage records to examine actual earnings, as well as a variable that takes the natural logarithm of wages to transform the variable into one with a near-normal distribution. We examine wage outcomes in increments of 10 quarters (e.g., 2.5 years) from students’ high school graduation semester.

General academic variables

A multitude of academic variables were used to unveil the academic journeys of our participants. Firstly, a variable captured what grade students were in upon graduation. Of our analytic sample, 99.3 percent were registered in the 12th grade. An additional variable provides their specific date of graduation. A cohort group was defined by the latter year of the academic year. For example, the academic year spanning from fall 2002 to spring 2003 is coded as 2003 in the cohort variable. A dichotomous flag captured whether a student was documented as Gifted (7.2 percent) or not (92.8 percent). Graduation type was recorded with the following categories: Distinguished/Advanced (9.6 percent), Recommended/Regular (73.7 percent), Minimum (13.7 percent), and IEP (Individualized Education Program) (3.0 percent). This variable was derived from a previous variable that included much more specific graduation types. For simplicity and clarity, it was collapsed into the aforementioned categories. For reading and math tests, variables capture the standardized scores which were derived from TAAS, TAKS, and STAAR (dependent upon year of exam taking).

School-level variables

For school identification, each district and campus had a unique numeric code. Our sample includes 2,891 distinct schools.  Furthermore, dichotomous variables captured whether or not a specific math course was offered by the schools in our sample (Precalculus (83.4 percent), Regular Statistics (56.73 percent), AP Statistics (56.80 percent), AP Calculus AB (64.41 percent), and AP Calculus BC (53.68 percent)). The following are the percentages of students in our sample who are enrolled at a school which offers the following math courses: Precalculus (98.7 percent), Regular Statistics (39.2 percent), AP Statistics (70.4 percent), AP Calculus AB (89.2 percent), and AP Calculus BC (61.5 percent). Based on these percentages, it seems that larger schools (with a higher populous) tend to offer more advanced math courses (i.e., only 64.4 percent of schools offer AP Calc AB, but 89.2 percent of the sample is enrolled at a school which offers it).

Additional course variables

In addition to general academic characteristics, we also had access to information on the course history of our participants. Course credits from high school were calculated to be additive for each full/partial credit received. Points were proportional to semester length (i.e., a one semester course is assigned 0.5 and a whole year course is assigned 1). One variable captured all passed course credits, while another accounted for the quantity of failed course credits. Individual variables also calculated the total amount of advanced and dual credit course credits received.  Subject-specific course credit variables captured the total credits received for each respective subject area. These subjects included: English Language Arts (ELA), Math, Social Studies, Science, Physical Education, Foreign Language, Arts, Computation, CTE (Career and Technical Education), “Other”, Advanced ELA, Advanced Math, Advanced Social Studies, Advanced Science, Advanced Physical Education, Advanced Foreign Language, Advanced Arts, Advanced Computation, Advanced CTE, Advanced “other,” Dual Credit ELA, Dual Credit Math, Dual Credit Social Studies, Dual Credit Science, Dual Credit Physical Education, Dual Credit Foreign Language, Dual Credit Arts, Dual Credit Computation, Dual Credit CTE, and Dual Credit “Other.” Further, additional variables addressed cluster concentrations regarding CTE (Career and Technical Education). Most of our sample did not claim a CTE cluster concentration (82.4 percent). Categories of cluster concentrations included the following: “Agriculture, Food, and Natural Resources,” “Architecture and Construction,” “Arts, A/V Technology,” and Communications,” Business Management and Administration,” “Education and Training,” “Finance,” “Government and Public Administration,” “Health Science,” “Hospitality and Tourism,” “Human Services,” “Information Technology,” “Law,” “Manufacturing,” “Marketing,” “STEM,” “Transportation, Distribution, and Logistics,” and “Multiple (having multiple CTE concentrations).” Each category had a respective variable with the total course credit amount for that specific category. Finally, a categorical variable includes the number of participants in each concentration category. 

Demographic variables

Our study included a multitude of demographic control variables. The Race/Ethnicity of participants was self-selected, with categories including Asian (4.1 percent), Black (13.3 percent), Hispanic/Latino (43.6 percent), Multiracial (0.7 percent), Native American (0.4 percent), Pacific Islander (0.1 percent), and White (38.3 percent). The measure of sex was binary, with 50.1 percent categorized as female and 49.9 percent as male. Another binary variable indicated whether a participant had an ESL status or not. This variable was created from two separate ESL variables, as the ESL variables changed over time from one to the other. A value of zero indicated that the student had never participated in an ESL program, while the value of 1 indicated participation in any ESL program (including both “pull-out” and “content-based" models). Of the analytic sample, 4.6 percent of participants had an ESL status, and the remaining 95.4 percent did not. Another binary variable captured whether a student was documented as an immigrant (1.6 percent) or not (98.4 percent).

Further, a binary variable indicated whether a student had a special education status (8.48 percent) or not (91.52 percent). A dichotomous flag for economic disadvantage was derived from a prior variable which contained four categories, including “Not identified as economically disadvantaged,” “Eligible for free meals under the national school lunch and child nutrition program,” “Eligible for reduced-price meals under the national school lunch and child nutrition program, and “Other economic disadvantage (including Food Stamps eligibility and other government metrics).” The latter three categories were collapsed into one, which indicated an economically disadvantaged participant (46.4 percent).

Methods

At a high level, we use three methodological approaches to address our research questions. First, we use ordinary least squares (OLS) models that control for high school fixed effects to account for between-school variation in outcomes. For dichotomous outcome variables, such as whether students took a specific math course, these models can be considered linear probability models, and the estimates represent percentage point differences in the likelihood of the outcome occurring. Because we control for high schools in the models, the estimates from these models can be interpreted as the relationship between the variable and the outcome for students who graduated from the same high school. We control for the other courses students completed, their 8th grade standardized test scores, and demographic characteristics as described in the previous sections.

To better account for selection bias, we use a technique called augmented inverse probability weighting (AIPW) in our analyses estimating the relationship between math course-taking and postsecondary outcomes. This technique proceeds in three stages. First, a prediction model estimates the probability that a student will experience a “treatment,” such as taking AP Calculus AB instead of AP Statistics (the “control”). We use logistic regression for the prediction model and include demographic characteristics, 8th grade test scores, and the highest math course a student completed by 9th grade. The logistic regression model produces a predicted probability (or “propensity score”) for each student in the analytic sample, which represents the probability that the student would experience the treatment (i.e., taking AP Calculus AB instead of AP Statistics). The sample is then “weighted” based on the inverse of these propensity scores, which is similar to the application of survey weights. This procedure results in the “treatment” and “control” groups being observably equivalent on all variables controlled for in the prediction model. AIPW then fits a model on the weighted sample to an outcome, such as whether students enrolled in college or their earnings in a particular quarter. This outcome model includes the same control variables as the prediction model and additional variables (e.g., other courses taken in high school). Because of this two-step procedure, AIPW is described as a “doubly robust” method, meaning that it can produce unbiased estimates of the effect of the “treatment” even if either the prediction or the outcome model is misspecified.

Finally, to address whether the introduction of new math courses at the school-level influences students’ postsecondary outcomes, we create time-varying school-level variables that indicate whether specific math courses were offered in a particular year. By controlling for school and year fixed effects, we isolate how the addition (or removal) of course offerings relates to postsecondary outcomes. Because it is unlikely that schools beginning to offer advanced math courses would have much (if any) effect on the outcomes of students who are not eligible to take the courses, in some analyses, we restrict the sample to higher-ability students, specifically those who were enrolled in Geometry or higher in ninth grade. We explored the possibility of using course offerings in an instrumental variable (IV) approach. Still, these estimates were too noisy to produce compelling evidence of the relationship between course offerings and post-secondary outcomes for the subset of students induced to take the courses by the school beginning to offer the course.

Appendix B: Supplemental Analyses of Longitudinal Trends in Advanced Math Inequalities

As discussed in our methods and results in Part I, the primary method we used to examine changes in inequalities related to advanced math course participation was to disaggregate the sample based on students’ demographic characteristics and calculate the raw differences in each group’s probability of completing advanced math courses. To better isolate the relationship between students’ demographic backgrounds and the probability of completing advanced math courses over time, we also fit linear probability models that added interaction terms between the demographic and cohort variables. These interactions allow us to examine how the magnitude of inequalities changed over time, controlling for other factors that may shape course completion. In the figures below visualizing these interactions, we note that the 2003 base year indicates the initial magnitude of the disparity between groups. Estimates for all subsequent years are in relation to the base year.

Despite broadening access to advanced math coursework, socioeconomic and racial/ethnic inequalities in course-taking have grown. For both low-income and URM students, the gaps in advanced math course-taking between their non-disadvantaged and white peers, respectively, have been predominately driven by statistics courses. In contrast, girls have gradually surpassed boys in their propensity to complete advanced math courses, although advanced math courses remain somewhat stratified by gender. Female students have increased their participation in AP Statistics faster than male students, whereas the male advantage in Calculus BC has grown over time.

Figure B1: The estimated gap between economically disadvantaged and non-disadvantaged students by roughly six percentage points from 2003-2020.

Note: N= 4,319,870. Fixed effects regression model. Models include an interaction term for economic background and cohort. Models control for the math course taken freshman year, standardized reading test scores, standardized math test scores, cohort, URM status, economic background, special education status, LEP status, gender, and “giftedness” status.

Figure B1 shows that we estimate no significant difference between economically disadvantaged and non-disadvantaged students in the 2003 base year. However, a gap emerges and becomes statistically significant by 2005, continuing to grow thereafter. By 2019, low-income students were estimated to be six percentage points less likely than their non-disadvantaged peers to complete any calculus or statistics course, controlling for all other variables in the model.

Figure B2 examines socioeconomic inequalities by specific math courses. Statistics course-taking has increased for less affluent students (dotted pink and yellow lines), but the rate of increase for more affluent students (solid pink and yellow lines) is far more significant in absolute terms. In contrast, both Calculus AB and Calculus BC course-taking is largely unchanged for less affluent students between 2003-2020 (dotted teal and navy lines), while it increased somewhat for more affluent students (though not to the extent that their statistics course-taking increased). Thus, the widening socioeconomic gaps in advanced math are explained by both the stagnancy of less affluent students taking calculus and the extent to which more affluent students have outpaced their disadvantaged peers in statistics coursetaking.

Figure B2. Less affluent students’ calculus course-taking is unchanged, and their increase in statistics course-taking has not kept pace with their more affluent peers.

Note: N = . This analysis included the entire sample of students who graduated from Texas public high schools between 2003 and 2020.

Figure B3 displays the results of separate models estimating the probability of completing specific calculus and statistics courses. The patterns for AP Statistics and AP Calculus BC are similar. Both courses began seeing increases in economic inequality shortly after the 2003 reference year, and these inequalities have grown over time. Although the socioeconomic gap for AP Statistics is larger in real terms compared to the gap in AP Calculus BC, the gaps are roughly similar in proportional terms. In contrast, there was essentially no gap between economically disadvantaged and non-disadvantaged students in the likelihood of taking regular Statistics until 2015, when the gap began to grow. By 2020, the economic gap in regular Statistics equaled the gap for AP Calculus BC. AP Calculus AB is the only course where economic gaps have remained stable.

Figure B3: Economic gaps in the completion of all calculus and statistics courses have widened over time, apart from AP Calculus AB.

Note: N= 4,319,870. Fixed effects regression model. Models include an interaction term for economic background and cohort. Models control for the math course taken freshman year, standardized reading test scores, standardized math test scores, cohort, URM status, economic background, special education status, LEP status, gender, and “giftedness” status.

Figure B4 plots the interaction between the cohort variable and the dichotomous underrepresented minority (URM) variable to examine changes in racial/ethnic inequalities in completing any calculus or statistics course. The trend is quite similar to the one found in Figure B1, examining socioeconomic inequalities. One key difference is that URM students were already less likely to complete calculus or statistics than white students in the base year, and the gap has only grown since then. Because of this disparity in the base year, URM students were estimated to be roughly six percentage points less likely to complete calculus or statistics by 2020 compared to white students.

Figure B4: The gap between underrepresented minority students and white students in the probability of taking any calculus or statistics course has grown over time.

Note: N= 4,319,870. K= 2,832. Fixed effects regression model. Models include an interaction term for URM status and cohort. Models control for the math course taken freshman year, standardized reading test scores, standardized math test scores, cohort, URM status, economic background, special education status, LEP status, gender, and “giftedness” status.

Figure B5 presents the parallel analysis comparing the gaps between URM and non-URM students in advanced math course-taking over time. Once again, the patterns in racial/ethnic gaps are quite similar to the estimates of economic gaps from the previous analysis. Gaps between URM and non-URM students taking AP Statistics and AP Calculus BC have grown steadily since 2003. There was essentially no racial/ethnic gap in taking regular Statistics through 2015, at which point the gap began to grow. The racial/ethnic gap in taking regular Statistics was not quite as large by 2020 as the economic gap, however. Once again, we also find essentially no change in the differential likelihood of taking AP Calculus AB over time, meaning the roughly two-percentage-point gap between URM and non-URM students in 2003 remained constant through 2020.

Figure B5: Racial/Ethnic gaps have grown fastest in AP Statistics and AP Calculus BC.

Note: N= 4,319,870. K= 2,832. Fixed effects regression model. Models include an interaction term for URM status and cohort. Models control for the math course taken freshman year, standardized reading test scores, standardized math test scores, cohort, URM status, economic background, special education status, LEP status, gender, and “giftedness” status.

The final two analyses in this section examine trends in the gender gaps of advanced math completion. As shown in Figure B6, female students were about 0.5 percentage points less likely than male students with equivalent academic and other demographic characteristics to take Calculus or Statistics in the 2003 base year--a statistically significant difference. This gap stayed relatively constant from 2004-2006 and even appeared to begin widening in 2007 and 2008. However, from that time, the gap began to close and eventually reversed. By 2012, female students became more likely to take calculus or statistics compared to similar male students, as evidenced by the estimate for 2012 being positive and of greater absolute magnitude than the negative estimate in the 2003 base year. Although the gender gaps are not nearly as large as the economic or racial/ethnic gaps, it is a promising sign that girls have become even more likely than boys to complete calculus or statistics once prior academic achievement, early math course-taking, and all other variables in the statistical models are controlled for.

Figure B6: Girls were marginally less likely to complete calculus or statistics in 2003 but have gradually surpassed boys.

Note:  N= 4,319,870. K= 2,832. Fixed effects regression model. Models include an interaction term for gender and cohort. Models control for the math course taken freshman year, standardized reading test scores, standardized math test scores, cohort, race/ethnicity (reference group= White), economic background, special education status, LEP status, gender, and “giftedness” status.

Figure B7 examines the longitudinal trends in the female-male gaps in advanced math course-taking. We first must call attention to the difference in y-axis scales between this figure and the previous ones. For gender, the largest gap we identify is at most one percentage point, in contrast to the four percentage point gaps found in the analyses of economic background and race/ethnicity. In addition, in this case, there are essentially no gender gaps in the completion of regular Statistics throughout this time period, and only a modest 0.5 percentage point gap in taking AP Calculus AB in 2003, which remains mostly constant throughout. The gap in AP Calculus BC was also roughly 0.5 percentage point in 2003 but grew by another 0.5 percentage point by 2020, resulting in a one percentage point gap that year. Although that point estimate is small, we note that only two to three percent of students complete AP Calculus BC, suggesting a one-percentage-point gap may not be inconsequential. In contrast, females and males had equivalent rates of taking AP Statistics in 2003, and the female advantage grew over time. By 2020, females were roughly one percentage point more likely than males to complete AP Statistics. Thus, while the analysis in Figure 9 suggested that the female advantage in taking any calculus or statistics course has grown over time, the results in Figure 12 suggest this advantage has come almost exclusively from increased AP Statistics course-taking.

Figure B7: The growing female advantage in advanced math has been primarily driven by AP Statistics, whereas the male advantage in AP Calculus BC has increased over time.

Note: N = 4,319,870. Fixed effects regression model. Models include an interaction term for gender and cohort. Models control for the math course taken freshman year, standardized reading test scores, standardized math test scores, cohort, race/ethnicity (reference group= White), economic background, special education status, LEP status, gender, and “giftedness” status.

Appendix C: Supplemental Analysis of Advanced Math Course Access and Postsecondary Outcomes

This report examines patterns of access to and participation in advanced math courses, as well as the relationship between the completion of advanced math courses and students’ postsecondary outcomes. Although we used methods designed to produce fairer comparisons between calculus and statistics students in their postsecondary outcomes, those results may still be biased by unobservable factors. For example, suppose students take calculus over statistics because they already know they want to pursue a STEM field. In that case, differences in STEM outcomes between calculus and statistics students may be due to differences in their underlying aspirations rather than their course-taking. 

A different approach enables us to help eliminate this concern. Rather than examining the relationship between course-taking and post-secondary outcomes, we link changes in course offerings at the school level with these outcomes. In this case, our key independent variables are not whether students took a course but whether their school began offering (or discontinued offering) a course in a given year. By controlling for time-invariant high school fixed effects, we are exploiting year-to-year changes in course offerings as a potential source of exogenous variation that may induce changes in students’ advanced math course-taking. This approach also addresses a policy-relevant question: What is the effect of expanding access to rigorous math courses on students’ postsecondary outcomes?

Although this approach has some benefits over the methods used in the body of the report, two additional concerns persist. The first is using the correct year(s) to measure course access. If we define course access as the school offering a course in any of the years in which the student was in high school, our results may be biased because the student did not have the opportunity to take the course. Given that students often take AP Calculus AB and AP Statistics in their junior and senior years of high school, we tested two versions of the school-level course offering variables: 1) the course was offered in students’ senior year of high school; 2) the course was offered in students’ junior year of high school (course access with a lag of one). Because our results were similar regardless of which version of the course access variables we used, we report results from models that defined course access in the senior year.  

The second concern is appropriately identifying the student sample we wish to generalize to. We would not expect increased access to advanced math courses to have much (if any) effect on students with lower math achievement or those who enrolled in Algebra I in ninth grade, given that their chances of enrolling in advanced math courses in high school are low. We, therefore, fit models to the sub-sample of students who enrolled in Geometry or above in ninth grade, as well as models fit to the entire population of high school students. We present results from both approaches in the following sections.

We find that advanced math course access is not reliably related to college outcomes.

The body of the report examines the relationship between course access and college outcomes for the entire population of students who graduated in 2015 or later (because NSC data is only available for these years). As shown in Figure C1, there are few statistically significant relationships between course access and college outcomes. The point estimates are small and not statistically significant for both AP Statistics and AP Calculus AB. For regular Statistics, the results suggest that adding the course related to a 0.5 percentage point increases the likelihood that a student will earn a bachelor’s degree within six years of high school graduation. However, the estimates for the other five college outcomes are not statistically significant. Perhaps unexpectedly, the offering of AP Calculus BC was associated with a very slightly lower probability of any college enrollment (0.7 percentage point) and six-year bachelor’s degree attainment (0.6 percentage point).

Figure C1: Advanced math course access is not a good predictor of postsecondary academic outcomes. 

Notes: N =1,711,689. K= 2,109. Fixed effects regression model. The sample was limited to students in the 2015-2020 cohorts, for whom NSC data on out-of-state college enrollment is available. Models control for the math course taken freshman year, if school offered AP Statistics, if school offered Regular Statistics, if school offered AP Calculus AB, if school offered AP Calculus BC, passed course credits, failed course credits, math course credits, science course credits, advanced course credits, dual-credit course credits, standardized reading test scores, standardized math test scores, CTE cluster concentration category, diploma pathway (minimum, recommended, or advanced), cohort, race/ethnicity, economic background, special education status, gender, and “giftedness” status.

The next analysis uses the same statistical modeling approach but restricts the sample to students who completed Geometry or above by ninth grade, referred to as advanced math ninth graders. In this case, none of the estimates for regular Statistics, AP Statistics, or AP Calculus AB are statistically significant. We find suggestive evidence that the offering of AP Calculus AB may be associated with a one percentage point increase in baccalaureate attainment. Still, the error in those estimates prevents firm conclusions from being drawn. Similarly, while the offering of AP Calculus BC appears to be inversely related to college outcomes, the majority of those estimates are not statistically significant. The one significant difference is a one percentage point decrease in the probability of any college enrollment when schools offer AP Calculus BC. However, because that is the only statistically significant estimate out of the 24 models included in this analysis, we would caution against drawing strong conclusions about it.

Figure C2. Few statistically significant relationships exist between access to advanced math courses and college outcomes for advanced math ninth graders.

Notes: N =518,447. K= 1,965.  Fixed effects regression model. Sample was limited to students in the 2015-2020 cohorts, for whom NSC data on out-of-state college enrollment is available.  Models control for the math course taken freshman year (restricted to those who took Algebra 2 or Geometry in their freshman years), if school offered AP Statistics, if school offered Regular Statistics, if school offered AP Calculus AB, if school offered AP Calculus BC, passed course credits, failed course credits, math course credits, science course credits, advanced course credits, dual-credit course credits, standardized reading test scores, standardized math test scores, CTE cluster concentration category, diploma pathway (minimum, recommended, or advanced), cohort, race/ethnicity, economic background, special education status, gender, and “giftedness” status.

The results from the previous chapter suggested that AP Calculus AB students did not have better college outcomes overall compared to observably equivalent AP Statistics students, but they did have better STEM outcomes. We also investigated whether schools’ offering of advanced math courses was associated with STEM outcomes. In Figure C3, we estimate the relationship between math course offerings and the probability that high school graduates majored in any STEM field (the dark blue estimates) as well as select specific STEM majors. Overall, we find no relationship between schools offering advanced math courses and the probability that their graduates will major in a STEM field in college.

Figure C3. There is no relationship between access to advanced math courses and the likelihood that high school graduates will major in a STEM field.

Notes: N =. Fixed effects regression model. The sample was limited to students in the 2015-2020 cohorts, for whom NSC data on out-of-state college enrollment is available. Models control for the math course taken freshman year, if school offered AP Statistics, if school offered Regular Statistics, if school offered AP Calculus AB, if school offered AP Calculus BC, passed course credits, failed course credits, math course credits, science course credits, advanced course credits, dual-credit course credits, standardized reading test scores, standardized math test scores, CTE cluster concentration category, diploma pathway (minimum, recommended, or advanced), cohort, race/ethnicity, economic background, special education status, gender, and “giftedness” status. 

We repeat this analysis and restrict the sample to advanced math ninth graders, the results of which are found in Figure 22. Once again, we find null results. None of the estimates of the relationship between advanced math course offerings and STEM majors are statistically significant, and all of the point estimates are between negative 0.5 percentage points and positive 0.5 percentage points. Although not shown in figures, when we fit similar models to outcomes of whether students earned degrees in STEM fields, we similarly found no significant relationships between advanced math course offerings and STEM degree attainment. Overall, we find no compelling evidence suggesting schools improve their students’ college outcomes by adding any of the calculus or statistics courses we included in our analyses.

Figure C4. Access to advanced math courses is not related to the likelihood of majoring in STEM for advanced math ninth graders.  

Notes: N = 387,217. Fixed effects regression model. The sample was limited to students in the 2015-2020 cohorts, for whom NSC data on out-of-state college enrollment is available. The sample was further restricted to students who completed Geometry or above in ninth grade. Models control for the math course taken freshman year (limited to those who took Algebra 2 or Geometry in their freshman years), if school offered AP Statistics, if school offered Regular Statistics, if school offered AP Calculus AB, if school offered AP Calculus BC, passed course credits, failed course credits, math course credits, science course credits, advanced course credits, dual-credit course credits, standardized reading test scores, standardized math test scores, CTE cluster concentration category, diploma pathway (minimum, recommended, or advanced), cohort, race/ethnicity, economic background, special education status, gender, and “giftedness” status.

Finally, we examine the relationship between school-level offerings of advanced math courses and students’ earnings. Similar to our previous approach, we fit models to the entire population of high school graduates and the sub-sample of students who completed advanced math coursework in ninth grade. Once again, we find no compelling evidence that school-level variation in advanced coursework offerings is associated with changes in student outcomes. As shown in Figure C5, none of the estimates of the relationship between regular Statistics, AP Statistics, or AP Calculus AB and quarterly earnings are statistically significant. For AP Calculus BC, there is suggestive evidence that course access is related to short-term earnings, as the estimates for Q30 and Q40 are statistically significant. However, the point estimates are modest – a school offering AP Calculus AB is associated with a $100 per quarter ($400 per year) increase in earnings in Q30 and a $150 per quarter increase in Q40. However, the estimates for AP Calculus BC are no longer significant by Q50 and the point estimate is near zero by Q60. We would be hesitant to conclude that a school offering AP Calculus BC (or any other math courses we analyzed) would improve students’ long-term earnings outcomes.

Figure C5. There are few significant relationships between math course access and earnings, and those that exist are modest and statistically weak.

Note. The sample size in the analyses varies depending on the outcome, with each model restricted to the sample eligible for that outcome. The sample size ranges from N = 1,518,498 for the analysis of earnings at quarter 30 to N = 115,490 for the analysis of earnings at quarter 70. The school sample size in the analyses varies depending on the outcome, with each model restricted to the school sample eligible for that outcome. The sample size ranges from N = 2,158 for the analysis of earnings at quarter 30 to N = 1,585 for the analysis of earnings at quarter 70. Fixed effects regression model. The sample was restricted to students in earlier cohorts for whom long-term earnings information is available. The sample was also restricted to students who remained in Texas, given that the wage records come from the TWC. Models control for the math course taken freshman year, if school offered AP Statistics, if school offered Regular Statistics, if school offered AP Calculus AB, if school offered AP Calculus BC, passed course credits, failed course credits, math course credits, science course credits, advanced course credits, dual-credit course credits, standardized reading test scores, standardized math test scores, CTE cluster concentration category, diploma pathway (minimum, recommended, or advanced), cohort, race/ethnicity (reference group= White), economic background, special education status, gender, and “giftedness” status.

We repeat this analysis of course access and earnings while restricting the sample to students enrolled in advanced math courses in ninth grade. Figure C6 shows that the estimates are noisy and none is statistically significant. Once again, we cannot draw firm conclusions regarding the relationship between school offerings of advanced math courses and students’ postsecondary outcomes.

Figure C6. Access to advanced math courses is also unrelated to earnings for advanced math ninth graders.

Note. The sample size in the analyses varies depending on the outcome, with each model restricted to the sample eligible for that outcome. The sample size ranges from N = 428,762 for the analysis of earnings at quarter 30 to N = 32,965 for the analysis of earnings at quarter 70.  K= The school sample size in the analyses varies depending on the outcome, with each model restricted to the school sample eligible for that outcome. The sample size ranges from N = 1,968 for the analysis of earnings at quarter 30 to N = 1,337 for the analysis of earnings at quarter 70. The sample was restricted to students in earlier cohorts for whom long-term earnings information is available. The sample was also restricted to students who remained in Texas, given that the wage records come from the TWC. Models control for the math course taken freshman year (restricted to those who took Algebra 2 or Geometry in their freshman years), if school offered AP Statistics, if school offered Regular Statistics, if school offered AP Calculus AB, if school offered AP Calculus BC, passed course credits, failed course credits, math course credits, science course credits, advanced course credits, dual-credit course credits, standardized reading test scores, standardized math test scores, CTE cluster concentration category, diploma pathway (minimum, recommended, or advanced), cohort, race/ethnicity (reference group= White), economic background, special education status, gender, and “giftedness” status.

Because models of actual earnings may be biased by outliers (e.g. extremely high-earners that skew the distribution), we begin with the most robust models (i.e., AIPW) where the outcome is the natural logarithm of earnings (log-earnings) at different timeframes post-high school graduation.[49] Quarter 30 (Q30) represents 7 ½ years since students graduated from high school, Q40 represents quarterly earnings ten years out, and so forth. In this case, the estimates represent the difference in log-earnings between the two groups, which can be interpreted as percent differences in earnings. Each data point in Figure C7 represents the point estimate from a separate statistical model estimating the relationship between taking Calculus AB versus AP Statistics on a different quarter of earnings. Readers may refer to Appendix A for a discussion of this approach.

As shown in Figure C7, Calculus AB students out-earn AP Statistics students ten years after high school graduation (Q40), but only by about 3 percent. In later years, there were no statistically significant differences between the groups. Although the point estimates are larger for later quarters, suggesting a continued earnings advantage for Calculus-takers, these estimates are still modest (less than ten percent) and not statistically significant. (Later estimates are noisier because the sample of students eligible for those outcomes is smaller, as, for example, we only observe Q60 earnings for students who graduated before 2008.)

Figure C7. An initial earnings advantage for AP Calculus AB students compared to AP Statistics students is small and statistically significant in later years.

Note: The sample size in the analyses varies depending on the outcome, with each model restricted to the sample eligible for that outcome. The sample size ranges from N = 197,313 for the analysis of earnings at quarter 30 (Year 7.5) to N = 17,910 for the analysis of earnings at quarter 70 (Year 17.5). The sample was restricted to students in earlier cohorts, for whom long-term earnings information is available. The sample was also restricted to students who remained in Texas, given that the wage records come from the TWC, and those who participated in AP Statistics and AP Calculus AB, which are similar—and therefore comparable—groups. Models control for the math course taken freshman year (reference group= Algebra 1), percent of students in school enrolled in Precalculus, percent of students in school enrolled in AP Statistics, percent of students in school enrolled in Regular Statistics, percent of students in school enrolled in AP Calculus AB, percent of students in school enrolled in AP Calculus BC, passed course credits, failed course credits, math course credits, science course credits, advanced course credits, dual-credit course credits, standardized reading test scores, standardized math test scores, cohort, race/ethnicity (reference group= White), economic background, special education status, gender, and “giftedness” status. Those whose freshman year math course was “Other,” “AP Statistics/Regular Statistics,” and “Calculus AB/BC” were excluded from analyses. Error bars represent 95 percent confidence intervals.

Endnotes

About this Study

This report was made possible through generous support from the Barr Foundation and our sister organization, the Thomas B. Fordham Foundation. We express our gratitude to Matt Giani and Franchesca Lyra for their fastidious data work and diligence in crafting the report. We also thank Elizabeth Huffaker and Doug Sovde for their thoughtful feedback on drafts of the report. And here at Fordham, we thank Adam Tyner for managing the project and co-authoring the final report, Chester E. Finn, Jr. and Michael J. Petrilli for providing feedback on the draft, Stephanie Distler for managing report production and design, and Victoria McDougald for overseeing media dissemination. Finally, kudos to Rebecca Mahoney for copyediting and Dave Williams for laying out the report’s figures.

The research presented here utilizes confidential data from the Texas Education Research Center (TERC) at The University of Texas at Austin. The views expressed are those of the authors and should not be attributed to TERC or any of the funders or supporting organizations mentioned herein. Any errors are attributable to the authors alone. The conclusions of this research do not reflect the opinion or official position of the Texas Education Agency, Texas Higher Education Coordinating Board, the Texas Workforce Commission, or the State of Texas.