It was the spring of 2015 when I was in my junior year when I had to finish an elective course requirement and was forced to take a course called Nonlinear oscillations. The only reason I took the course is that I didn’t have pre-requisites for any of the options available, and the instructor of this course was not very stringent on the pre-requisite criteria. Nonlinear oscillations course was a theoretical course with advanced calculus, and throughout the course, the instructor took us on a journey of solving several complicated differential equations that describe different incredible (satisfying) phenomena.
The instructor had provided me a brief idea of what the course entails, and I was not looking forward to taking the course – way too much math. However, the course has transformed my perspective towards complicated math, as now I had understood that why an equation is they it is more important what it is or how huge it is; and motivated me to pursue graduate studies. Furthermore, I still used some of the ideas taught in that course and have used them in six out of seven journal papers that I have published. For the reasons mentioned above, I believe that the Nonlinear Oscillations course is the most valuable and impactful in my student journey.
As mentioned earlier, just like in most of the classes, the instructor started with basic concepts and introduced different case studies (equations), which became more and more complicated as the semester progressed. The crux of the course was teaching students to use a perturbation toolbox that can be used to gain useful insights into nonlinear differential equations. The instructor not only provided detailed analysis for every case study but also explained it’s importance and application. Further, the instructor went above and beyond what is required by providing us with relevant research articles and notes of experts in the field. Due to the nature of the course content, I don’t think it is possible to utilize the material taught in the course to a new problem. However, I believe that the instructor was successful as some of the students who took the course still use the toolbox in our research.
Since the instructor used pieces of already existing solutions to teach the toolbox, this type of teaching is case-based teaching . I think this approach is ideal for a course where a novel project component is not realistic and would implement a similar strategy in my teaching. Since I have some personal experience, I will share my experiences, in particular, the problems that I solved and the reasoning behind why I did what I did to enhance the learning experience to my future students.
 Janet L. Kolodner, Paul J. Camp, David Crismond, Barbara Fasse, Jackie Gray, Jennifer Holbrook, Sadhana Puntambekar & Mike Ryan (2003) Problem-Based Learning Meets Case-Based Reasoning in the Middle-School Science Classroom: Putting Learning by Design (TM) Into Practice, The Journal of the Learning Sciences, 12:4, 495-547, DOI: 10.1207/S15327809JLS1204_2