Numbers to Live By

Many students -- even A students -- used to consider one great thing about being accepted to college that they would never have to study math again. That possibility is disappearing at a growing number of institutions.

Some colleges are refusing to let a student cross the stage without some math on the brain, even if the student is a literature major who came in with a 5 on the Advanced Placement calculus exam.

Plenty of colleges have a math general education requirement, but even some students who take math courses have trouble with “quantitative literacy,” or applying their knowledge of numbers to things they encounter outside of class. The movement for quantitative literacy, a theme identified by the Association of American Colleges and Universities in its 10-year campaign to redefine and promote liberal education, is afoot.

“It’s a small movement, but it’s a movement,” said Lynn Arthur Steen, professor of mathematics at St. Olaf College, in Minnesota, and a former president of the Mathematical Association of America.

One of the first things students have to do upon setting foot on campus at Wellesley College is to take a quantitative reasoning assessment. Some questions, judging from past exams, are basic algebra, while others test a student’s ability to apply numerical concepts. One question from a past exam gives the New Jersey hate crime rate -- 13 crimes per 100,000 residents -- as cited in a New York Times article, and asks how many hate crimes were committed in New Jersey in 1994 if the population was 8 million.

“The test is looking for students who are weak,” said Corrine Taylor, director of Wellesley’s quantitative reasoning program, which began in 1997. Taylor and other experts agreed that life in the 21st century is awash in numbers that people need to understand not only for their professions, but also to be competent citizens.

If students fail the test at Wellesley, which about 6 to 8 percent of students do each year, Taylor said, they have to take an intro to quantitative reasoning course. For those who make the grade, they can go straight to a “quantitative overlay” course, such as Statistical Analysis of Education Issues. Those who failed will join them following a basic skills course. As part of the push to bring quantitative thinking to every department, Wellesley has begun a quantitative reasoning speaker series, thanks to a donation from a math major alumna who, Taylor said, “wished she’d been taught math in an applied way.” One speaker, a quilter, Jinny Beyer, who talked about the mathematics of quilting tessalations. “She demystified [M.C.] Escher for us,” Taylor said.

Judith Moran, director of the Math Center at Trinity College in Connecticut, “started life,” she said, as an art major. Now, like several of the faculty members questioned, Moran said she wants all students to be able to assess numbers in The New York Times. Trinity students also get their quantitative feet held to the fire on day one, with quantitative literacy assessment. Students who fail any part of the exam, “logical relationships,” for example, have to take a course that will help them “wake up and smell the quantitative roses around them,” Moran said. If a student aces the quantitative literacy test, they’re done with the requirement. But Moran is pushing to make sure quantitative roses spring up beneath their feet no matter what department they enter.

For example, she worked with Dario Del Puppo, director of Italian programs at Trinity, so he can talk math with students studying Dante. When Dante, at the end of Paradise, is confronted with the vision of God, he tells readers that he cannot possibly explain the image, no more than a geometer can square a circle. “Squaring the circle is one problem from ancient Greece that has been proven undoable,” Moran said. “It’s a perfect analogy to impossibility. If someone doesn’t know math that Dante thought his readers would know, they miss out.”  

In another case, Moran, working with Latin American history students, examined figures in scholarly works given as the number of Hispaniola natives wiped out after first contact with Europeans. The numbers, she said, “are remarkably varied. One of the estimates would give much of Mexico higher population density at that time than England. There’s hundreds of papers written, and yet the math underpinnings, if not spurious, are at least questionable.”

Steen said that even advanced calculus students need to have applied math concepts worked into their courses. “If you look at a typical calculus book, you have a sophisticated body of mathematics, but the problems are really simple,” he said. “You can’t look in the book for a formula for avian flu.” Steen said he thinks that growing recognition that traditional math courses don’t equip students with “what they need as citizens,” and the rise of computers which have made data easy to gather and disseminate are driving the quantitative reasoning push. Institutions, sensing the need, are getting creative about working QR in.

Carleton College requires students to submit a writing portfolio for evaluation at the end of the sophomore year. Now the college has started examining those same portfolios for quantitative reasoning where numerical concepts apply. For example, professors might look to see whether a student uses numerical arguments when doing so would clearly bolster an argument. Macalester College is running a pilot program -- Quantitative Methods for Public Policy -- that organizes groups of courses from different departments around a particular theme that incorporates quantitative reasoning. A recent theme: “Policies Affecting the Immigrant Experience in Minnesota.”

Using a National Science Foundation grant, Len Vacher, a geology professor at the University of South Florida, is leading the “Spreadsheets Across the Curriculum” project. That endeavor invites professors from community colleges and research universities to work on developing courses that have students solving applied math problems with spreadsheets.

According to Education Department statistics –--provided by Clifford Adelman, a researcher with the department’s Office of Vocational and Adult Education -- though some of the interdisciplinary quantitative reasoning programs are new and novel, students from all disciplines have been ramping up their math for years. A national survey of about 800,000 people from the high school class of 1982 who went on to get bachelor’s by 1993, 60 percent of business students took more than 4 credits of college level math, as did 52 percent of biosciences students, and 16 percent of humanities students. In a more recent survey -- about 920,000 people from the high school class of 1992 who got bachelor’s degrees by 2000 --  the definition of “college level math” changed a bit, but Adelman said there was certainly an increase. That survey had 84 percent of business students, 82 percent of biosciences students, and 31 percent of humanities students taking more than 4 math credits.

Even some of the nation’s top math students aren’t exempted from math in college anymore. Following a 2003 report from the Committee on Yale College Education, Yale University, starting in fall 2005, began requiring even students who score a 5 on the Advanced Placement calculus exam to take math. “The best high school writer still has a way to go to become the writer he or she could be. Further, when the development of these powers stops with high school, the result can be a going backward, not a standing still. Students who do not use their math ... skills in college commonly lose abilities they once had and can graduate knowing less than when they arrived,” the report reads.

The University of Pennsylvania also put an end to AP exemption. “College education is different from high school education,” said Dennis DeTurck, dean of Penn’s College of Arts and Sciences. “Studying math with a mathematician goes beyond sort of the basic facts and formulas and equations.”

The wave of quantitative literacy may wash in a New York Times readership full of statistical acumen, but there’s still some work to be done, perhaps on the other side of the grey lady. According to Steen, “journalism is another place where there’s a lot of need.”