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CALCULUS for EVERYONE? BY MITCH STOKES SENIOR FELLOW, NEW SAINT ANDREWS COLLEGE
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’m going to briefly argue that every Christian high school student can—and should—learn calculus before graduation. Of course, claiming that K–12 mathematical education should culminate in calculus for everyone is radical, especially for those of us in the United States. Studies consistently show that American students rank below average compared to other developed and developing countries in math and science1, all the while scoring above every nation in selfesteem. But it’s not a lack of intelligence that accounts for the U.S.’s poor showing in mathematics: after all, anyone of average intellectual horsepower can learn the fundamentals of calculus (more on this below). So why is it that only about fourteen percent of our high school students study calculus? Why is calculus seen as a luxury, a delicacy appreciated only by mathematical connoisseurs? For two reasons, mainly. One, we simply don’t understand how central calculus is to Western intellectual culture, especially its relevance to the confl ict between faith and unbelief. Two, we don’t teach calculus nearly as well as we could. Regarding the fi rst, cultural reason, calculus is a mathematical analogy to the works of Shakespeare. Having a basic understanding of calculus—including why it was invented—puts a lot of Western philosophy and science in perspective. In fact, calculus is an ideal place to learn how to teach mathematics classically. The only other bit of mathematics that has had as much impact on the humanities or liberal arts is Euclid’s 1 Drew DeSilver, “U.S. students’ academic achievement still lags that of their peers in many other countries,” Pew Research Center, February 15, 2017, https://www.pewresearch.org/fact-tank/2017/02/15/u-s -students-internationally-math-science.
Elements. (I hate putting it this way since mathematics is a liberal art, a paradigm of the humanities.) In any case, if calculus is analogous to Shakespeare’s Hamlet, Euclid is like unto Homer’s Odyssey. And until our students learn the fundamentals of calculus and Euclid’s Elements, they will never realistically integrate mathematics with the rest of their studies, and therefore never really understand the whole. Indeed, the story of Western philosophy can be told through the (whole) story of calculus, beginning with Thales’s search for unity and stability in a wildly diverse and ever-changing cosmos. This is what I do in my year-long math colloquium at New Saint Andrews College. The second reason calculus is seen as a mere luxury is that we don’t teach it like we ought. A fi rst course in calculus is often so difficult because we make it difficult—at least more than it has to be. For one thing, we cover too many topics too quickly, many of which are unnecessary at that stage of the students’ learning. The National Science Foundation sees this more-asbetter approach as the primary reason for today’s math debacle. In testimony before the House Committee on Science, NSF director Dr. Rita Colwell said, “U.S. textbooks contain many more topics than those in other countries. For example, the science textbooks we give to our eighth graders cover some 67 topics. In Germany, they cover 9 topics. As the saying goes, we are learning less and less about more and more.”2 2 NSF’s FY2000 Budget, Second Hearing on U.S. Math and Science Education—Programs Aimed at Grades K-12, Before the House Science Committee Basic Research Subcommittee, 106th Cong. (1999) (Statement of Rita Colwell, Director of the National Science Foundation), https://www.nsf.gov/about/congress/106/rc90428k_12edu.jsp.
VOLUME FOUR
