Using math to enrich the humanities

How can math help in the study of Dante’s The Divine Comedy? What do numbers have to do with philosophy? And how do quantitative ideas apply to the courses “Colonialism in the Americas,” “Introduction to Classical Art and Archaeology,” and “Women’s Activism”? Just ask the folks at the Mathematics Center in MCEC, where they run labs that enrich the study of the humanities with a dose of math.

Just as every academic discipline requires good writing skills, every major is enriched by the ability to think logically, analytically, and quantitatively. It is this principle of liberal arts education that powers the Math Center program.

The lab on The Divine Comedy, for instance, focuses on geometric principles in this masterpiece, including the geometric structure of the universe Dante envisions and the theorems that The Divine Comedy specifically invokes. In the philosophy course “Medical Ethics,” students participate in a Math Center lab on decision theory and vaccinations. Math Center Director Judith Moran has created several labs for the history course “Colonialism in the Americas.” The labs examine the Mayan math system, the Mayan calendar and its basis on astronomical observation, and Latin American historians’ mathematical attempts—and failures—to estimate the indigenous population of the Americas before the Spanish Conquest.

Two Classics courses incorporate a lab at the Math Center called “Making Sense out of the Shards,” an exercise in sampling procedures and statistics. In this lab, students try to determine the average number of chips in various brands of chocolate chip cookies and attempt to estimate the proportion of brown candies in a package of M&M’s. By understanding sampling, students in “Introduction to Classical Art and Architecture” and “Celtic Britain and the Romans”can gain insight into the ways social scientists learn about ancient cultures.

A model program
The Math Center has served as a model for other colleges that, like Trinity, want to make sure they develop the full range of their undergraduates’ thinking skills. Representatives from other schools often visit the center, and Moran has been invited to discuss the program at a number of higher education conferences. The national math community encourages colleges and universities to foster “quantitatively literate citizens” by integrating math-related thinking into traditionally non-mathematical courses, Moran explains. “The goal is to enable students to see the relationships and bridges between the disciplines, rather than focusing on separate disciplines as islands of self-contained knowledge.”

Trinity’s quantitative literacy requirement goes hand-in-hand with the philosophy behind the Math Center. Incoming students at the College must take a quantitative literacy test during new student orientation. The test evaluates students’ proficiency in four areas: numerical relationships, statistical relationships, algebraic relationships, and logical relationships. Forty-five to 50 percent of incoming students pass three or all four of the sections, according to the Math Center faculty. Students who fail only one of the sections usually are assigned a study unit on their weak area, which they can complete on their own in the Math Center.

Students who pass one or two sections of the test are assigned to take half-credit courses that pertain to their weak spots. Students who pass none of the sections, about one-quarter of incoming students, must take Math 101, “Contemporary Applications.” The semester course taught by the Math Center faculty and designed to give these students the quantitative skills they will need no matter what major they pursue.

Concepts in an imperfect world
Some of Trinity’s brightest students have benefited from the Math Center program, initiated in 1987 with a grant from Aetna Life and Casualty Foundation. “In the half-semester logic course, you have kids with 750 math SAT scores,” says Lecturer Margaret Cibes.  They just have not been exposed to statistics or logic or the relevant mathematical terminology.

Cibes uses the example of a New Yorker article that states, “‘The number of filibusters in the Senate has been growing exponentially.’ What does exponentially mean?” To understand the article, one must understand the math.

Math classes posed no problem for Rachel Ach ’04 when she attended Columbia Preparatory School in Manhattan.  “I did really well in math in high school.  I was a big studier,” she says. She also scored well on the math portion of the SAT’s.  But translating these abilities to college proved more difficult, and after passing one of the four sections on the proficiency test, she enrolled in Math 101.

Ach’s case is not unusual, according to Cibes and Math Center Assistant Director Charlotte Gregory. Good algebra students expect their answers to come out as neat, reliable numbers, but projections in the real world usually don’t come out evenly, Cibes notes. And good math students don’t necessarily remember the concepts they mastered in 6th grade. “You don’t do percentages in calculus,” she quips.

Besides successfully completing Math 101, Ach took full advantage of the other Math Center resources, including drop-in student tutoring, study groups, and frequent conversations with the Math Center faculty. She says she appreciates the support she received from everyone she encountered at the center, including student tutor Andy Lumb ’02. “They really want to help you. They want to see you do well,” Ach says.

In addition to Gregory, Cibes, and Moran (who is on leave this term), Lecturer Cathy Zucco-Teveloff and Visiting Lecturer Susan Ricciuti teach at the center.

“A second home”
Lumb, a math major, started tutoring at the center this year and is assigned specifically to help Math 101 students. “A lot of my teachers had mentioned that it was something I should do,” he says. In addition to the financial benefits—tutors are paid for their work—helping other students has been personally rewarding for Lumb. It’s a great feeling, he says, for a student he helped to approach him a couple of days later and say how well he or she did on a math test.

Peer tutoring, available from 2 to 5 p.m. and 7 to 10 p.m. Monday through Thursday and from 7 to 10 p.m. on Sundays, offers an unintimidating avenue for math students to seek help. “I may not know as much as a professor, but it’s more relaxing,” says Lumb, one of about a dozen student tutors.

Many students who first encountered the Math Center for a course or a tutoring session keep coming back long after they passed the course or the test. Gregory says students often come to the Math Center faculty who taught their Math 101 course, for instance, when they need help with a concept in a higher-level math class or an economics course. And students often gravitate toward the center’s round tables and bright, pleasant study atmosphere.

“It’s like a little second home for some people,” Cibes says.

--Becky Purdy