What is the Goal of Requiring Undergraduates to Take Math?

About 50 years ago when university math chairs were surveyed, only 10 percent thought a math course should be a college graduation requirement for all students. Today, virtually every undergraduate is required to take math in order to earn a degree. 

This dramatic change begs the question: Why do we consider it important for college students to learn math?

When math chairs said most students didn’t require a college math course, they were  likely thinking about the specialized math courses that prepare students to major in math, engineering, or physics. However, when colleges adopted general education math requirements, their rhetorical justifications tended to center on something altogether different: the importance of mathematical and quantitative reasoning for understanding and thriving in the contemporary world. 

For that reason, these requirements are often called quantitative reasoning (QR) requirements. A 2016 task force at the California State University system underscored that such requirements support “the ability to reason with and make inferences from quantitative information in order to solve problems arising in personal, civic, and professional contexts.” 

In practice, though, there has often been a disconnect between the stated purpose of these requirements and their implementation by math departments. For the most part, math or QR requirements have historically focused on traditional math sequences requiring hand computation—courses such as precalculus and calculus—as opposed to the sophisticated applications of mathematics or statistics that have revolutionized so many industries. 

Math departments, which were typically responsible for general education math courses, often focused on the content required to become a mathematician or engineer. They weren’t well versed in the uses of math in other disciplines. At many research universities, even statistics occupies its own department distinct from mathematics. 

Fortunately, more and more colleges have gradually expanded their general education math offerings in recent years to include a range of rigorous applied courses, often in collaboration with or offered by other departments. Strategic Visual Thinking at the University of Georgia and Human Language as Computation at University of Southern California are just a couple examples.

The idea that students’ college math courses should be relevant to their area of study is increasingly common, including in the many states working with the Charles A. Dana Center to redesign their math sequences. As Princeton University says about its QR requirement, “Quantitative and computational reasoning is used to some degree in almost every area of learning.”

The existence of relevant and applied math in college, however, doesn’t necessarily tell us how to structure high school math sequences. While some math educators argue that alternative approaches rooted in real-world contexts are key to engaging more students in mathematical learning, others worry that such strategies give short shrift to traditional mathematical content that students may need in college.

As both concerns have merit, they need to be reconciled by examining the essential math skills and knowledge all students need, regardless of their academic and career plans. This leaves room for students to acquire additional skills as they branch into their chosen fields of study. It is important to keep in mind, though, that a list of skills is useful only to the extent that students are engaged enough that they actually master those skills. 

What algebra concepts are needed for success in courses such as Strategic Visual Thinking and Human Language as Computation? At what point do we know whether a student will major in history and take one of those courses, rather than major in physics and choose multivariate calculus? Ideally, we keep those options open for students, while trying to make the content as engaging and meaningful as possible. 

That’s why there are benefits to learning math in the context of engaging, real-world problems, regardless of the math content being taught. Wright State University’s engineering department showed that immersing students in engineering-motivated math content while delaying calculus instruction led to a doubling of departmental graduation rates. 

At the high school level, it’s important to note that there are options that don’t require students to forgo content that could prepare them to major in a STEM subject. For example, a discrete math course that has been offered in the San Diego area includes topics such as cryptography, combinatorics, and graph theory, all of which can lead to more sophisticated math topics and math-intensive majors, such as computer science. 

A recent webinar by our friends at the Data Science for Everyone coalition showed how high school data science lessons can be used to teach key algebra concepts, whether that means infusing algebra content into a data science course or using data science examples in an algebra class. 

Such approaches are still the exception to the rule. We’ve come a long way in the past 50 years in reconciling the disconnect between traditional views of math curriculum and the need for relevant math content. It’s time to bring these new approaches into more classrooms.