Math Needs a Makeover
Too many first-year students struggle with calculus because we fail to teach it well.
Opinion by Oussama Safadi
Why do some students ace calculus in high school yet founder as first-year engineering undergraduates? Consider the young woman who literally came crying to my office. She had enrolled in Calculus III after receiving credit for Advanced Placement Calculus I and II – only to get a D on her first exam. This former straight-A student figured she must not be smart enough for aerospace engineering and wanted to change her major or withdraw from the university altogether.
As a faculty adviser and mentor, I’ve witnessed similar sagas, and it always breaks my heart to see bright, energetic students thinking about quitting school because of a calculus course. After all, the subject wasn’t always required of engineers – just look at the pyramids, amphitheaters, and other enduring structures designed and built centuries before the mathematics of integrals and derivatives debuted in 17th-century Europe. Still, it’s hard to break with a U.S. academic engineering tradition dating back to Rensselaer Polytechnic Institute’s founding in 1824.
That doesn’t mean calculus must be a “make it or break it” course. Indeed, our experience at the University of Southern California (USC) suggests it can be taught better and made more enjoyable. There are two main reasons calculus can seem unbearable to newly admitted engineering students. The first is poor preparation for the rigorous math taught in a large research institution, coupled with poor advising that places students like my tearful advisee in an inappropriate calculus class. More typically, however, the math faculty lacks sensitivity when teaching calculus to nonmath majors.
Universities too often let students down by not ensuring they get quality teaching in this foundational “language,” without which they cannot understand physics or read engineering textbooks that cover such vital topics as quantum mechanics, vibration analysis, and magnetism. Pre-med students can struggle in calculus and still become successful physicians. Though less numerous, there are engineering undergraduates who do not enjoy their math course, but whose talents – imagination, leadership skills, or hands-on design – propel them to bright careers as entrepreneurs, inventors, and even managers in top engineering companies.
To encourage rather than exclude such innovators, we must change the way we teach calculus. Some engineering schools now offer calculus with an engineering slant or have engineering faculty teach math. Neither approach is practical. Moreover, engineering students benefit enormously from seeing calculus applications in other fields. I’m also against the current trend of using graphing calculators in exams. Students need to be able to sketch a function by hand, determining the points of inflection and intersection, upward concavity, and asymptotes.
In 2010, USC established the Center for Excellence in Teaching Calculus (CETC) to improve instruction in courses ranging from Calculus I to Linear Algebra and the Mathematics of Physics and Engineering. These are taken by a huge number of students, most of them nonmath majors. The center provides a forum for faculty to exchange ideas, methods, and techniques. It also holds workshops, seminars, and debates, and serves as a vehicle for mentoring new faculty and teaching assistants assigned to teach calculus.
In one workshop I conducted, I picked a calculus concept that stymies many students and asked the TAs to prepare and deliver a 10-minute blackboard presentation. The group discussed each presentation, provided feedback, and got to see and learn different approaches from each other in a cheerful and fun environment.
For calculus instruction to improve, universities must take the training of teaching assistants more seriously. Like research assistantships, it’s a form of scholarship. Sadly, the position is often granted to bright students who excel at research without considering their ability to teach. I frequently hear that a TA is unable to communicate with his or her students. I’ve even noticed faculty urging TAs to cut back on class preparation so they can concentrate on their research!
Through the CETC, we sought and found ways not only for students to learn calculus better but also to enjoy the experience. An added bonus: Retention improved across a variety of majors, including engineering. Reforming the way calculus is taught requires a collective effort, but the systemwide rewards are worth it.
Oussama Safadi, director of the University of Southern California’s Center for Excellence in Teaching Calculus, is an associate professor of engineering practice in the aerospace and mechanical engineering department at the Viterbi School of Engineering.