Fostering Mathematical Curiosity: Using Real-Life Modeling to Teach Differential Equations
0Presented by:
Brittany Oletti, US Military Academy, West Point NY USA
https://qubeshub.org/community/groups/simiode/expo
Abstract: Imagine a paradigm shift in higher education: where instead of tossing mathematically apt and advanced students into Calculus II or III as their first college class, suppose that we put them into Differential Equations instead. Furthermore, what if we made that Differential Equations class a modeling class as well, where students would have to simultaneously learn how to model as they learned various techniques including variation of parameters, integrating factor, Euler’s Method and more? What if I told you that we are doing just that? The framework we’ve developed for teaching our advanced population of students involves a parallel learning schematic of mathematical modeling and differential equations. As we scaffold the techniques of solving first-order, second-order, and systems of ODEs; we also introduce modeling at its basic levels of transforming the variables, through the solve step and ultimately interpreting meaningful solutions. We do this as a three-part process: by engaging in in-class lectures and associated practice problems; with smaller, engaging modeling application days where students focus on parameters in ODEs; and finally with a large scale project and presentation at the end of the course on a differential equation modeling problem of their choice. During this talk, we will discuss how we facilitate this innovative educational journey, where students don’t just learn mathematics; they become mathematical explorers.