Walk by Nancy Baxter Hastings’ Workshop-Calculus classroom, and you’ll never believe that she’s teaching math.
|Nancy Hastings’ accessible approach to math is meeting with great success among all majors at Dickinson. Above, Hastings (left) discusses a concept in the calculus lab.
That’s because Hastings, holder of the Theodore & Catherine Mathias Chair in Mathematics and Computer Science, cleverly crosses boundaries, replacing traditional lectures with an innovative learning environment where students “read, write and discuss math”—and even enjoy it.
What does reading, writing and discussing math entail? “Students learn by doing,” Hastings explains. “Instead of my going up to the board and telling them how to do a particular problem, students work together on activities that are designed to help them understand new ideas. As a result, they develop a sense of ownership of the material.”
This approach to teaching was inspired in the early ’90s by Dickinson’s Workshop-Physics program, which already fostered activity- and observation-based learning. In 1991, Hastings, then associate professor of mathematics Allan Rossman and Physics Professor Priscilla Laws received their first three-year grant from the U.S. Department of Education’s Fund for Improvement of Postsecondary Education (FIPSE) for development of a similar workshop program for mathematics.
“The idea was that, to start, we’d spend a year designing activities, a year testing them, a year revising them and then we’d be done,” Hastings says. “But the project kept going and, since that initial grant, we’ve had continuous funding for our project from the National Science Foundation (NSF) and FIPSE.”
Along with the workbooks she developed—including Workshop Calculus: A Guided Exploration with Review—Hastings creatively uses technology to help students learn calculus concepts. For example, her students use motion detectors—box-like devices that emit signals to detect movement—to understand graphic representations.
“I watched [Laws’] students use a motion detector to think about velocity,” Hastings recalls. “I thought, ‘Hey, our students could use this to think about graphs and functions.’
“If you walk in front of the box, the box measures and graphs how far away you are from it,” Hastings explains. “If you increase your distance, it draws a curve that goes uphill. If you decrease your distance, the curve goes downhill. Using this, students develop an understanding of the shape of graphs—they develop a mental image of what ideas mean. And they even have fun in the process.”
And no, Hastings isn’t only talking about mathematics majors. In fact, the workshop curriculum was designed for students who use calculus outside of the discipline—students pursuing fields in pre-medicine, economics or chemistry.
“Of course, the primary goal [of the workshop program] is to provide students with a firm understanding of calculus concepts,” she says. “But a secondary goal, which to me is equally important, is to help students develop confidence in their ability to do math. If they need to use mathematics outside of the course, I want them to say, ‘OK, I can figure this out.’
“My personal goal is to have students leave Workshop Calculus feeling that they had a positive experience in a math class,” Hastings continues. “My hope is that in the future, if they meet a mathematician at a party, they will say, ‘Yeah, I enjoyed math.’ Or if one of their children does poorly on a math test, instead of responding, ‘I didn’t do well in math, either!’, they will say, ‘I know you can do this. Let’s think about how to help you understand.’ ”
So far, Hastings’ approach is working. Since she started the program, she says, she has received “volumes of positive feedback.” Enthusiastically, she recalls a letter from a recent student, a biology major who took Workshop Calculus as a pre-medicine requirement. The student, who had always struggled with math, “really turned around—she worked hard, she got an ‘A’ and she wrote to me: ‘I finally understand calculus. Thank you!’ ”
Hastings’ program crosses borders even beyond the limestone walls. Over the years, she has regularly spoken at conferences and hosted workshops to teach educators how to implement the approach at their institutions. California State University at Hayward, Indiana University, Knox College, Loyola Marymount University and Gettysburg High School are among those that have adopted her approach, either in calculus, precalculus or both.
Her reputation as a national innovator earned her yet another honor this summer. On June 21, Hastings and two students—Jeff Goldsmith ’07 and Carley Moore ’06— presented the project to members of Congress in Washington, D.C.
“The Mathematics Association of America has 30,000 members, and it asked Dickinson to be its representative [at the event],” Hastings comments. “It was a real compliment.”
Hastings and her students spent the day meeting with congressional leaders like Sen. Rick Santorum (R-Pa.) and Rep. Ralph Hall (R-Texas) and discussing their project, along with 30 NSF-funded members of other science organizations, at a reception and poster session.
“It was great fun,” Hastings recalls of the event. “We talked to congressional representatives about the impact of undergraduate funding on education at four-year, liberal-arts colleges. We talked about how NSF funding has enabled us to do things that we couldn’t otherwise do. We thanked the representatives for supporting funding for science education.”
The project has received more than $1 million in federal grants, says Workshop Mathematics Project Manager Joanne Weissman, who has worked with Hastings for the last 12 years. “These grants have enabled us to develop our innovative, activity-based curriculum materials, which help students learn,” Hastings says.