An overemphasis on calculus in high school may be harming students
This year marks the 60th anniversary of the launch by the U.S.S.R. of Sputnik 1, the first artificial satellite to orbit Earth. This important achievement was met in the West with surprise, confusion, and more than a little fear. U.S. civilian and military leadership alike were shocked at how far the Soviet space program had progressed and saw our own efforts lagging. Attention quickly focused on improving math and science education in the United States.
Following President Dwight Eisenhower’s call to match U.S. education needs to the exigencies of the nascent Cold War, Congress passed the National Defense Education Act with bipartisan support in 1958. This act represented the first major foray of the federal government into the U.S. educational system since the Smith-Hughes National Vocational Education Act 40 years prior.
The new law was unprecedented in its scope. Among other provisions, it provided large resource pools for “strengthening science, mathematics, and modern foreign language instruction.” Because a solid grounding in mathematics is required for success in science and engineering programs, the subsequent changes to the curriculum engendered by the NDEA elevated the importance of one subject in particular: calculus.
As the U.S. education system has matured, this push led to an unfortunate byproduct: Knowledge of calculus has become for many—including guidance counselors, college admission officers, and parents—synonymous with “college ready.” This has led high schools to push more students through a calculus course without adequately explaining the purpose of learning the material.
This pressure to complete calculus in preparation for college affects students in a variety of ways. To accommodate the additional material, students are accelerated through the curriculum without adequate mastery of important foundational concepts. Many of the incoming students who score poorly on our pre-calculus placement exam at Dickinson College, where I teach, are surprised and crestfallen because they have already completed a calculus course in high school. And incoming students are often surprised that they can complete a major in mathematics in four years without having completed a calculus course in high school.
“It seems many students are not only not benefitting, but in fact are being harmed under our current system.”
David Bressoud of Macalester College has examined these issues for the Mathematical Association of America. In one study, Bressoud concluded that taking calculus in high school was only beneficial if the student learned it well enough to earn college credit for it, and he found evidence that an introduction to calculus that builds on an inadequate foundation can be detrimental. This observation is important, considering that only 421,000 of the estimated 750,000 high school students who took a calculus course in 2015 took an AP exam, and of those taking the Calculus AB exam (the most popular AP calculus exam), 42 percent received a 1 or 2 out of 5, indicating poor understanding of the material.
Thus, it seems many students are not only not benefitting, but in fact are being harmed under our current system. The net effect can ultimately discourage students from continuing in mathematics and science. With STEM enrollment constituting a national priority, we need to rethink our strategies.
Also important in this debate is the hallowed place of calculus itself. While it remains indispensable to the fields of engineering and the physical sciences and is an incredible achievement of human thought, the vast majority of college majors do not use it at all. What could we replace it with? Many of the students currently in calculus would be better served with a course in statistics, modeling, or computer science.
Even among those students who will eventually need calculus, many are not ready for it in high school and would benefit from additional time with foundational material. In my opinion as an educator, the majority of students in high school calculus are either taking the wrong course or taking it at the wrong time. As education needs have evolved, so must we. It’s time for us to critically reexamine the mathematics curriculum and prepare our students for the future instead of the past.
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