By implementing high-impact activities, such as designing a school and a skate park, mathematical thinking can be linked to the engineering design process.
RATIONALE Relating mathematics learned in the classroom to real world situations increases student motivation and enhances learning. We assessed the impact of using applications of calculus to physiology on learning in two courses: Differential Equations (DE) and Calculus I for Biology and Medicine (CIBM). We designed and implemented a project that uses calculus to model volume, flow, and pressure of air inside the lungs of a patient receiving positive pressure ventilation. Students compared mathematical models to a mechanically ventilated high-fidelity breathing simulator and gave feedback on their experience. METHODS Students either construct or observe the mathematical model for volume of a lung during positive pressure ventilation. Calculus is used to obtain functions and graphs for pressure and flow. The class compares their mathematical models with graphs produced by the breathing simulator (ASL 5000) in the Richard A. Henson Simulation Center. Students then develop a written summary of both their mathematics and their conclusions based on the sim center analysis. A short survey about the project was conducted at the end of the course. RESULTS Students obtained and analyzed functions describing volume, pressure and flow during positive pressure ventilation. Student feedback was overwhelmingly positive. Formal data collected in the spring semester of 2018 revealed that 79% of DE students and 41% of CIBM students agreed or strongly agreed that they enjoyed the project and 100% of DE students and 53% of CIBM students answered agreed or strongly agreed to statement regarding connecting the mathematics to the real world. It was obvious from their responses that the project enhanced their understanding of class material and grounded their mathematics in the real world. CONCLUSIONS Seeing the connection to real life and the relevance to their future careers is a significant motivating factor for students learning mathematics. This project of modeling volume, pressure and flow of air in the lungs of a patient under mechanical ventilation has had a positive impact on students in both Differential Equations and Calculus I for Biology and Medicine. Students enjoyed applying calculus concepts to scenarios we could replicate in real time. In addition, they were able to see that applications of mathematics can be found in most facets of life and that calculus plays a role in understanding biology and medicine, even when it is not obvious. Students produced high-quality work demonstrating an understanding of calculus concepts and their connection to medicine and the physiology of the lung.
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