Douglas Meade’s office in the historic LeConte College tells the story of change for the College of Arts & Sciences mathematics professor.
Rolled up in one corner is a poster describing Maplets for Calculus, an online tutoring program Meade helped develop with a colleague at Texas A&M. A table is covered with a variety of small cube formations built with business cards, part of a student project.
Both of those are emblematic of his 14 years as undergraduate director for the Department of Mathematics at the University of South Carolina. On July 1, he began a year-long sabbatical from the position.
On his desk sits the 10th edition of a classic textbook - “Elementary Differential Equations and Boundary Value Problems” by William E. Boyce and Richard C. DiPrima. One of the original authors has died, and another is ready to hand over the chores of updating the text. Among Meade’s sabbatical projects is bringing that text into the digital age. He also plans to finish a calculus textbook he has worked on for years.
“Math is one of the historical liberal arts,” Meade says. “It does not prepare you for a specific career, but it prepares you for just about any career that you are motivated enough to want to pursue - law school, medical school, banking and finance, national labs. Their job title may not include mathematics or mathematician, but the mathematics provides the good foundation to be able to do the banking or the business or the medicine.”
Some College of Arts & Sciences mathematics majors pursue careers as actuaries in the insurance and finance industries. Some go into teaching. In both cases, programs were tweaked during Meade’s tenure as undergraduate director to better prepare students for those professions. The actuarial pathway now includes more business and finance courses than typical for a mathematics major, and the secondary education track was changed to allow students to become certified to teach at the secondary level by completing a BS in Mathematics and an MT in Secondary Education.
Meade also played a role in improving the mathematics placement test procedures and establishing the Carolina Core course guidelines for the analytical reasoning and problem solving (ARP) learning outcomes.
Meade, who grew up in Ohio, earned his undergraduate degrees in mathematics and computer science at Bowling Green State University in Ohio. He did his graduate work at Carnegie Mellon University in Pittsburgh, earning a M.S. in Applied Mathematics and a Ph.D. in Mathematics. He had a post-doctoral appointment at Purdue University in Indiana. He left the Midwest for a job at the University of South Carolina in 1991 and found Columbia an ideal place to live and to raise a family.
Growing up he never expected a career in academics, but the more he delved into it, the more passion he developed for mathematics research and education. While serving in his role as undergraduate director, he taught almost exclusively undergraduate courses, and his scholarly writing has dealt with innovations in teaching mathematics – particularly those that involve computer algebra systems.
One of the keys is for students who fall behind to have a way to catch up. Maplets for Calculus (M4C) makes that easier. (A “Maplet” is an applet developed in Maple, a computer algebra system.)
“The curse and the beauty of math is that everything is based on something more fundamental, so if you do not understand the fundamentals, you do not understand the things later on,” Meade says.
The M4C can take the place of a private tutor. Each Maplet presents a common calculus problem and helps students work it, providing feedback for each step. The student has to get the first step right to be allowed to move on to the next step. Hints are available, or the student can ask for the system to enter the correct answer. Maplets coaches the user through the process to the answer.
Developed with Philip Yasskin of Texas A&M, the Maplets program is free for USC and Texas A&M students and available for a small fee for others, including high school students.
The other key to mathematics education is to engage students who exhibit an aptitude and desire to customize their undergraduate experience.
The cubes on the table in Meade’s office represent one project with that goal. They are pieces of a Menger sponge – a three-dimensional device used to illustrate a variety of math concepts. The face of a cube is divided into nine squares and the central square of each face removed. The result is a cube with less volume and more surface area. By repeating the process of removing the central square on each of the smaller cubes that result, the sponge keeps adding surface area and losing volume. Conceptually, in the limit, the Menger sponge has infinite surface area and zero volume.
The South Carolina High Energy Mathematics Teachers’ Circle (SCHEMaTC), a local mathematics teachers’ circle created to develop a support network for local middle-level mathematics teachers, has begun work on a large Menger sponge built out of business cards. The cards are folded to create small cubes (called a level 0 Menger cube). Twenty level 0 cubes can be assembled to form a level 1 Menger cube.
The teacher circle got the effort started and now the Gamecock Math Club and Pi Mu Epsilon Mathematics honorary are recruiting students to get involved with the construction of level 3 Menger cube. This object will measure 4 ½ x 4 ½ x 4 ½ feet, and will require more than 60,000 business cards. Meade envisions putting the finishing touches on the model in a public spot on campus, hopefully the mezzanine level of the Thomas Cooper Library.
Meade’s work as the Undergraduate Director for the Department of Mathematics clearly does not focus solely on educating within his department; rather, his passion for mathematics and teaching reaches out through all of USC. His focus on building from fundamentals shows his interest in all students’ potential and ability to apply mathematics to their fields of study and futures.