Flipping the Differential Equations Classroom: Changes Over Time

Traditional lecture style courses use class time to deliver new material to students and homework to provide practice. Flipped classrooms, on the other hand, provide new material outside of class and students are then given opportunities to work actively on problems during class time. A flipped classroom design combines active, problem-based learning activities with direct instruction methods, and is seen by many as a teaching method that results in higher student satisfaction, greater retention of knowledge, and increased depth of knowledge [1] . The initial implementation of a flipped classroom can be difficult for teachers. Time is needed to develop instructional materials for students to view outside of class, in addition to the time required for developing constructive in-class activities. Teachers who have persisted with this teaching method often report that their classrooms are not optimized until the third or fourth implementation. This paper describes the three-year progression from traditional lecture style to flipped classroom design of a large enrollment differential equations course at the University of Louisville’s J. B. Speed School of Engineering. The discussion section of the paper reflects on specific implementation difficulties of flipping a classroom, and gives strategic suggestions for instructors who are beginning to design this type of curriculum. Introduction: Course Administration, Content, and Context Differential Equations for Engineers (DE) at the J. B. Speed School of Engineering is the fourth course in a sequence of required mathematics courses for engineering students. The series consists of topics in calculus I through III followed by differential equations, with each course including theory paired with engineering applications and analyses. The first three courses are four credit-hours, and DE is a two credit-hour course. The engineering school has three semesters per year: Fall, Spring, and Summer. Several sections of each engineering mathematics course are typically offered each semester. Though taught by multiple faculty, the sections are coordinated; the faculty team uses the same text, materials, assignments and exams. All sections take the same exam at the same time. A team of student graders, supervised by one or more faculty members, scores the exams. Graders are students who have taken the courses previously and performed well. Faculty members grade parts of the final exam along with graders. Like the other calculus courses offered in the engineering school, DE was designed specifically for engineering students. For every theoretical topic, students are also exposed to common engineering applications. There are five course units (for details, see Appendix A). Upon completion of DE, learners should be able to: 1. Identify the order and type (linear or non-linear) of a given ordinary differential equation and solve it by an appropriate solution technique. 2. Solve first and second order linear difference equations. 3. Demonstrate the application of each of the methods of undetermined coefficients, variation of parameters and Laplace Transforms by solving ordinary or systems of ordinary differential equations.