A Flipped Course in Partial Differential Equations and Boundary Value Problems

A Flipped Course in Partial Differential Equations and Boundary Value Problems

Academic Year:
2013 - 2014 (June 1, 2013 through May 31, 2014)
Funding Requested:
Project Dates:
Overview of the Project:
The goal of this project is to develop an enhanced version of an existing course, Math 454, Boundary Value Problems for Partial Differential Equations, that is "flipped": students will spend much of their time outside class learning course material through supplementary instruction designed to replace the core of the standard classroom lectures, leaving the majority of time in class for active learning, primarily through collaborative work in teams that solve problems based on the material and then present their solutions. The target group is advanced undergraduate Engineering students, with a few graduate students also, who take a special section of this course taught on North Campus. The students will be divided into teams of size three or four for interactive learning in class and preparation of homework outside of class, with team assignments changed twice during the term. Assigned reading outside of class will be enhanced by supplementary explanatory materials prepared by the instructor, and existing materials already used by the instructor for in-class interactive team work will be upgraded for better learning and more efficient use of time. Lecture was de-emphasized in a preliminary experiment with this format in this class, and an experiment with podcasting is planned to see whether further de-emphasis is possible and helpful.
Final Report Fields
Project Objectives:

The main objective is to reduce greatly the amount of time spent lecturing in a traditional STEM course, flipping it so the students receive the standard lecture information outside of class, as described in the original abstract. This has been accomplished.

Project Achievements:

The project's main achievements have been to engage students more strongly during class time by having them absorb material generally presented in lecture through other means. The other means have included supplemental written materials to be used in parallel with the course text, as if I were looking over their shoulder pointing out material that could be misunderstood or not understood at all, and offering asides and further explanations; targeted activities beyond the reading to help them prepare for further engagement in class (including analyzing a YouTube video that explains the harmonics of a vibrating drum better than I ever could with formulas at a blackboard; and having them study and work in groups outside class to dispel the isolated learner syndrome that can happen when too much reliance is placed on single people doing reading alone. I also heard an exceptionally interesting idea at the last Provost's seminar from a colleague, that I implemented, namely, having students do brief presentations of their own at the beginning of every other class to set the stage for the rest of the class session. I have been impressed with their professionalism, and will make this a regular feature of my classes in the future. This has impacted my own teaching greatly, since these methods are now going to be my preferred ones for engaging students actively in their own education.

Yes. First of all, every time I teach this course, I will continue using the materials and techniques I piloted this semester. And I am going to find ways to insert the techniques into other courses I teach.
Though my main target has been engineers with this course, and thus it has been taught on North Campus (where my colleagues rarely venture, unfortunately), I am seeking to teach it on Central Campus to a different audience, and I am going to invite colleagues to come take a look at what is happening. I will also speak about lessons learned from it in a future mathematics education seminar in my department, and am convinced enough that it is a better way to do things that I will look for opportunities to talk about the project at meetings of mathematics professional societies. In particular, I believe this would make an ideal talk at an annual meeting of the Michigan Chapter of the Mathematical Association of America, and will seek to make that happen.
Advice to your Colleagues:
Factors facilitating the success of the project were, first and foremost, student flexibility in learning in a STEM course in a way that may have seemed highly unconventional to them. There has been essentially no resistance on their part. I did tell the students at the beginning of the term that there were some changes being made, but I never used the word "experiment", and I highly recommend not doing so; students hate to be experimented upon. The biggest challenges were: (1) The room. 107 GFL is, unfortunately, one of the most challenging classrooms in which I have ever tried to have the students engaged in their own learning. There are bolted down strip tables with narrow lanes between them, almost designed to thwart active learning and instructor and student mobility. I had tried to change the room for this project, but was unsuccessful. (2) My own underappreciation of what can happen to a carefully laid out class plan dependent on technology when that technology collapses on you. I fought the digital projector and document camera in the room from day 1, and one or the other would end up failing on me more often than not. CAEN tried exceptionally hard to deal with the issues, including replacing the document camera (but then also conceding that the particular model with which Engineering has cast its lot was inherently flawed, and they had had many problems with it). The class has fared better now that I always have some backup plan in case the technology goes south at some crucial point.