Variational study of the pendulum's angular motion in a differential equations course

The objective of this research is to get students to mean the mathematical objects related to the second order differential equation through the context of a physical phenomenon. With the support of the physical system of the simple pendulum, the behavior of the angular position is studied in a modelling process with the help of simulators. From variational thought and language as a line of research of socio-epistemology in mathematics education, activities that promote a modelling process in a differential equations course for students in initial training for teaching mathematics are designed, implemented, and analyzed. The results of the process experienced by the students are presented, such as: familiarization of the phenomenon, use and interpretation of the simulations, construction of the mathematical model and its predictive role for decision making. It was identified that the students' experiences, as well as the physical context, were determining elements for success in the resolution of the design.