Data-infused model of sprinting in an introductory ODE course for STEM students A Work in Progress
Year: 2024
Type: conference-paper
Abstract: After Calculus 2, many cadets at the United States Air Force Academy (USAFA) take a first course in Ordinary Differential Equations (ODEs).ODEs as mathematical tools are fundamental for modelling and analyzing dynamical systems which are prevalent in many areas of STEM education: electrical circuits, chemical reactions, mechanical systems, fluid dynamics, and many others.Unfortunately, many courses in ODEs are still presented in a traditional lecture approach, where there is significant emphasis on algebraic manipulations of differential equations or applying formulaic Calculus results.At the Air Force Academy, we recognize the importance of incorporating active learning teaching strategies in order to enhance student engagement and to strengthen course relevance.In particular, we integrated data-infused real-life modeling scenarios and some data-fitting classroom activities in order to better prepare students for the challenges they may encounter in their future military duties.In this Work-in-Progress, we share curricular material towards this effort.We believe that providing a classroom experience in a data-fitting technique on a real-life problem that is relatable to the 21 st -century student (sprinting) equips our students with skills on analyzing experimental data, creating predictive models, and making informed decisions based on data and underlying theories. Introduction.In a compelling MAA address in 1997 (transcribed and available widely online), famous Italian mathematician Gian-Carlo Rota laments that "Most of the material now taught in an introductory differential equations course is hopelessly obsolete [1]."Some of the techniques in solving ODEs that he labelled as "disconnected tricks" and "preposterous" are exact equations, integrating factors, and substitution-based techniques to solve homogeneous differential equations.In recent years, fortunately, there has been an increasing emphasis on applying active learning strategies in many STEM classes.At the Air Force Academy, our ODE course is in the process of being modernized with intentional curricular efforts that include the use of computational software, mathematical modeling from interdisciplinary applications, and data-analysis techniques.Here, we will share a classroom activity that we implement on the first day of classes in our ODE course. Course Description.The introductory course is called Math 245 and every student in this course has been provided access to the full MATLAB learning suite.MATLAB is the chosen computational tool because it is student-friendly, has many intuitive syntax and built-in commands, has extensive documentations and online learning resources, and powerful numerical solvers and visualization tools.Moreover, MATLAB is a common tool in Air and Space Force labs and research units.We adopted a modeling-based textbook called, "Differential Equations: A Toolbox for Modeling the World" published by Kurt Bryan, Rose-Hulman Institute of Technology, and published by SIMIODE (Systemic Initiative for Modeling Investigations & Opportunities with Differential Equations) [2]. Lesson Description. The lesson objectives on the first day are
Authors: Maila Hallare, Beth Schaubroeck, Kevin Treat
Institution: United States Air Force Academy
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
SDG: Quality education
Open Access status: gold
OpenAlex ID: W4404106571