Creating an interactive, digital calculus textbook

It started as a crazy idea. Well, it actually started before that.

Dr. Matt Cathey and Dr. Joseph Spivey teach a lot of calculus, and they — along with their colleagues from around the world — have followed a model for teaching the subject that dates back more than a century.

“About five years ago, we realized that we kept running into the same big problems,” says Cathey, an associate professor in the Department of Mathematics.

Wofford’s 13-week semesters were not conducive to covering differential and integral calculus together. Differential calculus and the associated theory were covered in Calculus 1 then integral calculus in Calculus 2. Further, the single textbook used for both semesters was expensive.

Many students were taking Calculus 1 but not completing the sequence with Calculus 2, which means they were not getting a thorough treatment of the subject.

Students who placed into Calculus 2 at Wofford were bored by the repeated material that they already had seen in high school, then overwhelmed when the class started something unfamiliar. The department was losing potential mathematics majors because of it.

“These are national problems,” says Spivey, associate professor of mathematics. “We ran the numbers, and only 20 to 30 percent of students were seeing the whole sequence. That meant only 20 to 30 percent were well served.” Cathey and Spivey decided to conceptualize, write and code (a skill each learned for the project) their own interactive, digital textbook. It's now on Wofford's Digital Commons, free for anyone.

“We came up with this crazy idea on our own, but we couldn’t have done it by ourselves,” says Cathey. “Our department was very supportive. We all have to teach out of the same playbook if we’re preparing students in a common way, so I appreciate the faith they have had in us.”

Cathey and Spivey worked on various pieces of “Calculus: An Integrated Approach” during their sabbaticals. The online homework system is a huge advantage for students because of its diversity of problems and instant feedback. Three-dimensionality is built into the program to better demonstrate concepts, and both differential and integral calculus are taught side-by-side for a more complete, but uniformly challenging first semester. The second semester is highly theoretical and designed for students who want to consider a major in mathematics.

“Now both semesters tell a more compelling story,” says Spivey. “There wasn’t a textbook (until now) that does this. It’s given us an opportunity to serve our students better and in a really cool way, and it’s made calculus even more fun to teach.”

Promoting student opportunity

Cathey, Spivey and their new interactive calculus textbook illustrate what happens when faculty remain active and engaged in their disciplines. Students reap the rewards of more stimulating classes when faculty stay intellectually fueled. They benefit when academic spaces hold both traditional knowledge and innovative thought. When faculty attend conferences and make connections with others in the larger academic commons, students discover opportunities for internships, research, presentations and publication.

For example, in August Dr. Dawn McQuiston, associate professor of psychology and one of the college’s pre-law advisors, took three students to the American Psychological Association’s 126th annual convention in San Francisco, Calif. The students attended sessions, watched McQuiston’s address and panel discussion on the implications of comfort animals in the courtroom, bought books, picked up materials from graduate schools and even found time to tour Alcatraz. McQuiston has been interviewed by CNN, The New York Times, the Boston Herald, ABC Radio, Science Daily, Newsy and the APA on her research that focuses on juror reactions to dogs that comfort vulnerable witnesses during trial and the reliability of eyewitness testimony.

The entire Department of Psychology stays active in research, and much of their research involves students.

Dr. Kara Bopp, chair of the department, is in the second year of an Intergenerational Connections Grant, funded through the Council of Independent Colleges and the AARP Foundation, that involves Wofford students serving Spartanburg’s low-income, older adult population to reduce social isolation. Her research interests are in cognitive aging.

Dr. John Lefebvre researches pain and the role of worry on the experience of pain. He is collaborating on new research into student mental health and resilience with Dr. Patrick Whitfill in the Department of English and with the Rev. Dr. Ron Robinson on belongingness.

Dr. Cecile Nowatka's current research involves the experience of depression and suicidal thoughts among college students.

Dr. Dave Pittman ’94 studies the neural signals of taste and how they affect feeding behaviors. He has received grant funding from the National Institutes of Health and has developed a school-based nutrition education curriculum to promote healthy eating for elementary-aged children.

Dr. Alliston Reid ’75 focuses his research on the basic mechanisms of learning and memory across species. In February he is the keynote speaker at the 11th Annual Art and Science of Animal Training Conference in Hurst, Texas.

Dr. Katherine Steinmetz runs a progressive student research assistant program modeled after similar programs in graduate schools. Her research seeks to understand the neuroscience behind emotional influences on attention and memory.

Challenging stereotypes

The diversity of research at Wofford spans the academic spectrum. The James-Atkins Student Managed Investment Fund is, in effect, a working research group in which students gain real-life investment experience by managing an investment portfolio. The group’s advisor, Dr. Philip Swicegood, the R. Michael James Family Professor of Finance, has published research with students as have others in the department. Both environmental studies and sociology are conducting research in the Northside and Glendale communities through the Milliken Sustainability Initiative. Dr. Rachel Vanderhill, associate professor of government and international affairs, contributes to her department’s scholarly portfolio with timely research on international politics.

“I teach in a field that is constantly evolving and changing, so in order for me to be the best possible teacher, I need to stay actively engaged with the research. Research is essential for me to be a good teacher,” says Vanderhill.

In addition to several smaller research projects, Vanderhill is working on a book-length manuscript that considers the use of new technology and social media in authoritarian regimes — how resistance movements use social media to challenge authoritarian regimes and how authoritarian regimes use new media to stay in power, particularly in regard to surveillance. Vanderhill’s current research involves both post-Soviet states and the Middle East and North Africa (MENA) region, which also informs her teaching in the college’s MENA program.

While research certainly informs and inspires teaching, sometimes teaching stimulates research as well. Dr. Britt Newman and Dr. Amanda Matousek in the Department of Modern Languages, Literatures and Cultures have been doing research into the assessment of teaching.

“We’re trying to figure out varied and effective ways to assess how well we’re achieving some of the learning goals for intercultural competence we have in our department,” says Newman. “Partly this research came out of curiosity. We want to understand the work we do better. We want to do a good job as teachers.”

Matousek began to realize the importance of this type of pedagogical research when she took a closer look at the study abroad experience.

“We have discovered that the things we think students are getting are not automatic. We have to make sure we’re preparing them for these experiences and helping them reflect afterward,” she says. “As we talked more about the skills we want students to get out of a study abroad experience, I began to realize that the skills students need for intercultural competence are what students also will need in other classes or to be successful in a new job.”

Because they’re creating their own system for determining intercultural competence, Newman and Matousek recruited student help this summer from Elizabeth Blackhall ’19, a German, environmental studies and international affairs major from Cartersville, Ga., and Nefi Aguilar Aguilar ’21, a Spanish major from Greenville, S.C.

“They did essentially what we did,” says Newman, referring to the hours of learning, benchmarking, reading, evaluating, coding and recoding. “We all felt good putting effort into it. Intercultural competence really is vital to society at this moment.”

In the visual arts, research takes on still other forms.

According to Jessica Scott-Felder, assistant professor of studio art, research in visual arts means exploring materials and art-making processes as well as doing historical and conceptual research.

“I often find myself learning new skills and collecting a wide range of materials, books and images when starting and completing a work,” says Scott-Felder, who spent the four weeks before the semester began in a residency at the Vermont Studio Center in Burlington, Vt. “Exhibitions also are integral aspects of research as I gain further insight on how my work creates a psychological mark, influences the perception of time and alters physical space.”

This summer she explored silverpoint drawing using rings her grandfather wore.

“I am exploring how an object’s history will affect the type of mark it makes. As a result of this visual research, I could continue to work with other rings, watches or similar objects in order to develop a new body of drawings,” she says. “My research and professional studio art practice ensures that art-making techniques are current and that contemporary conversations are present in my courses.”

Scott-Felder’s colleague in studio art, Michael Webster, completed two residencies this year — at the Penland School of Crafts in Spruce Pine, N.C., and at the Hambidge Center for Creative Arts and Sciences in Rabun Gap, Ga. The experiences gave him time to create work using different facilities and equipment. He networked with other artists and spread Wofford’s reach as well.

“Research for artists may mean making physical objects or images, learning different techniques or trying to generate affect or emotion with viewers to some degree,” says Webster. “There’s a lot of subtlety and crossover with other disciplines.”

Collaborating across disciplines

When Dr. Patrick Whitfill, assistant professor of English, completed his doctoral degree in creative writing–poetry, he expected to spend his time and effort teaching and writing, something he’s done successfully with excellent reviews from students in his classes and poems published in the Kenyon Review Online, Subtropics, Best New Poets and other journals. Then he received a call from a colleague that made him consider his work in a whole new way.

“Our goal has been to create a curriculum that will let us teach the craft of poetry as a therapeutic technique,” says Whitfill. “It’s invigorating to do something that I had never thought about doing in relation to my field.”

The plan is to combine the poetry workshop model with the therapeutic practice of writing poetry.

“It’s not just writing about feelings, but learning to write about feelings in a lasting, therapeutic way,” says Whitfill. “For example, a person undergoing anxiety or trauma in a college setting can shift their feelings of alienation, illuminating the experience without brooding.” The experience becomes fuel to create. “The person can start seeing themselves as an artist instead of a victim.”

The research closely followed the Pulse nightclub shooting. Whitfill and his colleagues, including Dr. John Lefebvre in psychology, since have given strategic thought into collaboration across disciplines to offer another option for students on college campuses, often places where stigma abounds but mental health resources are limited. Next steps, according to Whitfill, are to correlate the data already collected and do control group testing this fall at Wofford. The plan is to roll out a pilot curriculum in the spring.

“I appreciate the opportunity to serve the college from my role as a member of the faculty in a way that will help alleviate some of the pressure on the mental health professionals on campus,” says Whitfill. “I’m learning, which is exciting to me, and this new research has allowed me to be helpful in the process.”