The Role of Calculus in College Admissions: Addressing Requirements and Expectations

Math serves as a cornerstone in education, equipping students with essential skills applicable across various academic disciplines and everyday life. While not every student may find joy in mathematics, understanding the expectations surrounding math coursework for college admissions is crucial. This article delves into the math classes colleges require, the level of proficiency expected, and how admissions officers evaluate a student's mathematical background, considering differences based on intended major and the availability of advanced courses.

Navigating High School Math Requirements

The minimum math requirements for high school graduation, typically set at three years of math classes, including Algebra II, may not align with the expectations of colleges. While some colleges have minimum academic standards for admission, competitive applicants are expected to exceed these standards.

A-G Requirements

The University of California (UC) system, for example, has specific academic requirements, known as the A-G requirements, that all incoming students must meet to be eligible for admission. These include three years of math study, with a fourth year strongly recommended, covering introductory and advanced algebra, as well as geometry. A score of 4 or 5 on the AP Calculus exam (AB or BC) can satisfy two years of this requirement, excluding geometry. Integrated math courses that cover the required topics are also acceptable. A grade of C or better is required to receive credit for these courses. Keep in mind that taking high school (A-G) courses isn't the only way to satisfy these requirements. You also may meet them by completing college courses or earning certain scores on various acceptable exams.

College Expectations: Beyond Minimums

While the minimum math requirement for most colleges is four years of high school courses, the specific subject matter learned holds significance. Colleges generally expect a proficiency level up to trigonometry. Moreover, they value academic rigor and want to see students challenging themselves with the math courses they choose. The level of math proficiency you need to attain also varies, but most high schools set this as at least Algebra II.

Major-Specific Math Preparation

Certain majors, particularly in engineering, the sciences, and business, demand specific preparation in mathematics, often requiring completion of calculus. Many programs prefer that students have taken calculus in high school to ensure they are prepared for college-level coursework. Social sciences, such as economics and sociology, also rely on significant statistical analysis.

Addressing the Calculus Divide

Calculus is often the highest-level course offered in high schools. Passing this class - or better yet, acing it - can set your transcript apart from other college applicants’, signaling your academic chops to top schools. Prestigious liberal arts institutions build their first-year classes out of applicants who took calculus in high school. For example, of students admitted to Wesleyan University in fall 2021, 86% had taken calculus. Overall, some 20% of high school students take calculus.

The emphasis on calculus in admissions has drawn criticism due to unequal access for students from different socioeconomic backgrounds. A recent report from Just Equations and the National Association for College Admission Counseling argues that emphasizing calculus in admissions limits college access. Calculus is less frequently available to Black, Latino/a, and rural students. These students are also more likely to lack the resources that enable wealthier students to succeed in calculus.

Alternatives to Calculus

For students whose schools do not offer calculus, it is advisable to take the most advanced math courses available. Admissions officers evaluate students within the context of their school's offerings. Students should also consider exploring calculus classes at local community colleges or online platforms like Math Academy.

Calculus for STEM Majors

Students who plan to work in STEM may benefit from high school calculus, however. In majors like computer science, economics, engineering, math, and chemistry, the coursework is highly sequential. Incoming students who have already tackled calculus may have more classes open to them and more flexibility in their class schedule. For some schools, high school calculus is required for admission. At STEM-focused schools like Caltech, for example, applicants who did not take calculus could be at a real disadvantage. The school seeks out students who show “proficient readiness to study math topics beyond calculus.”

If you are STEM-bound but may not take calculus in high school, don’t despair. Most STEM majors take calculus their first year of college, though over 75% of students enrolled in an introductory college calculus course took the subject in high school as well.

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Calculus in College

The pressure to succeed in calculus is even greater in college than in high school. Paul Tough, author of “The Years That Matter Most: How College Makes or Breaks Us”, called first-year college calculus “an important gatekeeper for college success… If you don’t do well in freshman calculus it’s very hard to go on to earn a STEM degree.”

The Movement Away From Gatekeeping Leads to Another Gate

According to Just Equations, the “race to calculus” starts in middle school. Middle school math placement often determines which students will make it to calculus by 12th grade. Otherwise, students who progress through high school math at a standard rate may never get a chance to take calculus. Most learners who want to take high school calculus must forge an accelerated pathway starting in seventh or eighth grade.

Planning High School Math Coursework

High schools often have recommended tracks for students, which may vary by state and school. Some schools use an integrated math curriculum, while others offer AP Statistics as an alternative to AP Calculus. However, even students intending to major in statistics are typically better served by taking AP Calculus.

The Evolving Landscape of College Admissions

As standardized tests like the SAT and ACT lose importance in college admissions, calculus may become an even more critical factor for some admission officers. The increasing percentage of students taking calculus in high school reflects this trend.

Calculus as an Unspoken Standard Hurts Students

In the last two decades, the percentage of students taking calculus in high school has quickly increased. But this growth has been uneven, due to differences in school offerings and student enrollment rates. According to the Just Equations report, about half of all high schools offer calculus, though just 38% of high schools with predominantly Black or Lation/a enrollment offer the course. Students in rural areas are also less likely to have access to calculus.

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Demonstrating Merit Beyond the Curriculum

No matter where a student attends high school, they can demonstrate their merit to college admissions boards by taking the most challenging courses available. However, this may mean looking beyond the high school curriculum. Prospective math, science, computer science, economics, and engineering majors will all need some calculus and are advised to get an early start on this requirement. The standard prerequisite for freshman-level calculus is three years of high school mathematics, including trigonometry and logarithms. Students who need to take calculus and do not have (or wish to forfeit) AP credit, should start with Calculus I.

Calculus Course Options

Options for Calculus I include:

MATH 1106 - Modeling with Calculus for the Life Sciences
MATH 1110 - Calculus I

These courses have different emphases, and each takes a different perspective on the material than AP calculus classes. MATH 1106 is an option for students whose major requires only one semester of calculus. Some topics are covered in less depth than in MATH 1110, while more advanced topics are introduced. MATH 1106 focuses on modeling using examples from the life sciences. It introduces some fundamental concepts of calculus and provides a brief introduction to differential equations. MATH 1110 is the best choice for students who plan to take more calculus and is recommended for students who aren't sure about their plans but want to keep their options open. It goes in depth on the fundamental concepts of calculus, such as limits, derivatives, and integrals. It also uses more computations and algebraic manipulations by hand. After taking Calculus I or earning a 4 or 5 on the AP Calculus AB exam (or equivalent), students typically continue with Calculus II. MATH 1910 is the first course in a sequence designed for engineers that assumes familiarity with differential calculus as taught in MATH 1110. Students not in an engineering program or physical sciences major who take MATH 1910 may decide to continue with MATH 2130 (not offered 2023-2024) or MATH 2210 rather than MATH 1920. MATH 1006, MATH 1011, and MATH 1012 meet weekly to supplement lecture material, answer questions, and provide tips for effectively learning the material in MATH 1106, MATH 1110, and MATH 1120, respectively.

Addressing Placement Challenges in Community Colleges

How should we place students who need mainstream calculus for their intended major? This was one of the questions faced by the California Community Colleges (CCC) as their Chancellor’s office began work on their Multiple Measures Assessment Project for placement into English and mathematics courses. Of course, one cannot expect a single answer. It must depend on a student’s prior experience before matriculating at one of their colleges. Their findings are summarized in Figure 1. Fortunately, the report containing this result, Preparatory Pathways and STEM Calculus Completion: Implication of the AB 1705 Standards, has appendices with extensive breakdowns of the data that were collected, enabling me to do my own analysis. The data are based on the records of CCC students who on matriculation between 2012-13 and 2019-20 had declared an intention to pursue a STEM major for which mainstream Calculus I is required and whose first mathematics course was in the transfer-level calculus pathway (College Algebra, Trigonometry, Precalculus, or STEM Calculus I). They restricted the study to students for which they had complete high school transcripts and either a record of passing calculus at the community college within two years or two full years of records in the CCC system. Students were not required to pass calculus on their first attempt. A few (a total of three) took at least five attempts before they passed, but they had to accomplish this within two years of the start of their first transfer-level course.

Findings from the CCC Study

The CCC study revealed insights into student success in calculus based on their prior math coursework. A small percentage of students, only 8%, enrolled directly in calculus without having seen Algebra 2. These students were highly motivated and likely acquired the necessary knowledge outside of the traditional classroom setting.

The study also highlighted the attrition rate among students pursuing STEM majors. It is amazing that of those who passed trigonometry or precalculus in high school and who needed calculus for their intended major, half never enrolled in calculus. Also, there is very little difference in the pass rates of those who went directly to calculus and those took a preliminary course. There seems little point in asking someone who passed calculus in high school to start with a course below calculus when they get to college, even if it was not a fully college-equivalent course and a placement exam reveals gaps or weaknesses in their preparation. This is especially true if they are serious about aiming for a STEM major that requires calculus. I believe that this is also true for those whose highest high school course was trigonometry or precalculus. It is very possible that they are not fully prepared to succeed in calculus, but they will have more opportunities to identify and address any deficiencies within calculus than in precalculus or its precursors. This probably will require supplemental supports. You still want to keep the path to calculus as short as possible. Students who appear to lack the necessary prerequisites but go directly to calculus and succeed are interesting students who are worth studying. Finally, these data reveal that the traditional sequence of courses designed to prepare students for calculus-College Algebra/Trigonometry/Precalculus-is failing the majority of community college students with aspirations of a STEM major.

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