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University math faculty figure out a better way to teach calculus
5/31/12

For any college student interested in a career in engineering, science, or mathematics, the make-or-break course may be introductory calculus.

"Many people view first-semester calculus as a ‘weed-out’ course for majors in the sciences and engineering," explained Joseph Petrillo, associate professor of mathematics in the College of Liberal Arts & Sciences at Alfred University (AU).

"Unfortunately, a negative experience in a calculus course can affect performance in subsequent courses and discourage even the brightest students from continuing in math-intensive majors."

Yet demand for people in the sciences, technology, engineering, and mathematics - the so-called STEM disciplines - is higher than ever in the United States, and losing potential employees in those areas because of a first-semester math course is troublesome.

But maybe, thought Petrillo and his colleague, Darwyn Cook, associate professor of mathematics at AU, the real problem with calculus is in the way it is taught. "Even though calculus is notorious for high failure rates, the organization of the course material never seems to get much of the blame," said Petrillo.

He and Cook decided to "rearrange the curriculum to make it more understandable and intuitive."
The traditional curriculum introduces a concept, focuses on it for a lecture or two, and then moves on to the next. The curriculum developed at AU, however, focuses on families of functions and how calculus concepts relate to them. Instead of learning about a concept once, the students are exposed to it "repeatedly throughout the course," explained Petrillo.

The AU Division of Mathematics piloted the new curriculum in two of the four section of Calculus I in the fall of 2011. At the end of the semester, all students took a common final exam, one that had been written for the traditional course.

On average, students in the pilot group scored substantially higher on the final exam than those in the control group. "This evidence suggests that the new curriculum may have a greater impact on understanding and performance when compared to the traditional curriculum," said Petrillo. A paper on the results of the pilot will be written and submitted for publication later this year.

In May of 2011, Petrillo applied for funding from the National Science Foundation (NSF) to create the Alfred University Calculus Initiative (AUCI). He’s just received word that AU has been awarded a two-year grant in the amount of $161,042. The funding will help the AUCI team create what it is calling a "comprehensive calculus experience," the goal of which is to "increase understanding and success in calculus and pre-calculus while maintaining the level of rigor and breadth required for post-calculus courses."

According to the proposal submitted to the NSF, "the AUCI is being informed by current research and trends in STEM education, which include engaging students with visual and online technology, creating an active learning environment in the classroom, and incorporating meaningful applications."

Petrillo will spend this summer developing the lecture portion of the course, which will consist of 42 video lessons, each about 10 to 15 minutes long. Research indicates that students learn better through shorter, more focused lessons. An online quiz taken upon completion of the video lesson indicates to the faculty member that the student has actually watched the video. Some of the advantages of video lessons are that students may view them multiple times and at their own convenience, and that instructors can spend class time engaging students in activities, worksheets, group work, and discussion. Traditional lectures will no longer be part of the classroom experience.

Cook is developing the online quizzes and homework through the WeBWorK homework system, and Addison Frey, associate professor of mathematics at AU, is working on a website through which students will access the videos, examples, and other information.

During the second year of the grant, the Alfred University mathematics faculty will partner with the Greater Southern Tier Board of Cooperative Educational Services, which serves 21 member school districts, including nearby Alfred-Almond Central School. High school students will be able to take the course at their home school and earn Alfred University credit for successful completion.
Petrillo is the principal investigator for the NSF grant, with Cook and Frey as co-principal investigators. David Terry, assistant professor of education, and Danielle Gagne, associate professor of psychology, are the faculty associates who will be evaluating the AUCI project.