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## IMPACT Plus - Mathematical Modeling in Differential Equations and Student Confidence

#### By Vinodh Kumar Chellamuthu posted 09-20-2021 09:31:30

Differential equations is an important component of mathematics curricula for STEM majors. Students at my institution often find Differential Equations class as a "capstone" course of the first two years of college mathematics that they complete as part of their STEM degrees such as engineering. I believe that it is important to learn to think creatively and logically and see the connection of real-world context in mathematics curriculum. This is particularly important for opening doors to STEM majors, and retaining STEM students. I try to connect the class material to real world scenarios that encompass the course curriculum's conceptual understanding. Engaging students in contextualized context through modeling can provide rich and motivating learning experiences for students.

My SoTL inquiry focused on exploring how connecting differential equations concepts to real-world scenarios through mathematical modeling impacts student confidence in their mathematical abilities for STEM majors. I gave a pretest and posttest survey and an end-of-semester interview to check the impact of incorporating mathematical modeling in the class activities. Both tests had questions about understanding first-order differential questions and how mathematical modeling incorporation had impacted their learning. Assessment results (n=20) indicated that there is an improvement in students' confidence and in their mathematical abilities.

To further explore the ways student experience with real-world scenarios through mathematical modeling impacted their perception of their mathematical abilities, eight students were interviewed after the course concluded. Seven of  the survey participants indicated the mathematical modeling activities pushed their thinking beyond the textbook problems and connected real-world scenarios to the class material. For instance, students were asked to identify at least one real-world scenario and how it related to differential equations. Six participants immediately identified the spread of COVID-19 as a real-world scenario and how to model it through differential equations. Importantly, these students were able to explain the parameters in the differential equation and its physical significance. A majority of comments praised all the mathematical modeling activities. Many stated the hands-on activities helped them see differential equations in a real-world context and better gauge their learning process. Furthermore, they all indicated that mathematical modeling activities helped them see the value and positive perspectives towards STEM disciplines.

This SoTL experience has provided me an opportunity to ask an important question, add to the field, and reflect on the findings. It has allowed me to think more deeply about the student learning process and identify issues within the delivery and course curriculum structure. Through this experience, I have found that when mathematical modeling of real-world scenarios is emphasized in the classroom, students can make important connections among the mathematics and other STEM fields, and this can positively impact their interest and confidence in doing mathematics. This study is vital because Differential Equations is a critical point where STEM students choose their interests and proceed with their mathematical adventures. Although the findings of this study indicate a positive effect on student perspectives of STEM fields, the dataset consisted mostly of engineering students during the unique context of Covid-impacted learning. In a future study, I would like to extend the study to more STEM majors. I also would like to explore the impacts of authentic mathematical modeling activities across the calculus curriculum.