Abstract:

Ordinary Differential Equations (ODE) is one of most widely taught undergraduate mathematics subjects. It is a core course for mathematics, physics and many engineering majors. A traditional ODE course largely covers a collection of recipes for solving various classes of differential equations, such as separable, linear, homogeneous, Bernoulli, exact equations etc. The mode of assessment in a traditional ODE course is usually a written exam.

We believe that knowing various classes of differential equations and the ability to solve exercises purposely set to test a student’s understanding of basic concepts is less important for students today than modelling real life phenomena, communication and teamwork. Indeed, modern computer algebra systems are better and more efficient in solving differential equations symbolically and numerically than any human could ever be. However, understanding how to translate a real life phenomenon into the language of differential equations and how to do qualitative analysis of the model is what computers are not yet capable of.

We engaged in a several-year transformation of the ODE course, a core subject for mathematics majors at a large research university in South East Asia. The number of students is about 200.

The transformation underwent the following stages:
- Year 1: course curriculum was changed to put less emphasis on methods of solving various classes of differential equations and more emphasis on qualitative analysis and mathematical modelling.
- Year 2: a team project was introduced as a second main assessment component, together with the final exam.
- Year 3: the course was flipped. All lectures were recorded and uploaded on YouTube. Lectures and tutorials in class were replaced with team-based learning (TBL) sessions. Final exam was completely replaced with a team project on modelling a real life scenario with a system of differential equations.
- Years 4-5: the TBL implementation and assessment criteria for the team project were fine-tuned.

We have faced a number of organizational and logistic challenges. The biggest of them was assessment system. On the one hand, students were anxious about how their individual contribution to teamwork would be graded. On the other hand, the school management imposed certain rules on assessment that, to put it plainly, prevented us from being too generous in grading. We needed a method of assessing individual contribution to teamwork that is powerful enough to give a realistic distribution of grades, transparent to students, and not too demanding for the course instructor as compared to written exams.

In the end, the course was a success. It was well-received by students (student feedback on teaching changed from below 80 before the transformation to 93.6 in the 5th year of the transformation). We have also developed a powerful method of grading students’ individual contribution to teamwork that can be of interest to educators working in a wide range of disciplines. A by-product of our method is a collection of peer reviews that our students get. Students can (and do) use these reviews for future job applications.

Keywords:

Flipped classroom, project-based learning, team-based learning, undergraduate mathematics, assessment.