Go With The Flow: Describing Storm Water Runoff Rates Using The Derivative

This paper presents an innovative teaching approach, how it was implemented, student responses, results of the implementation, and the assessment of impact on student learning. The findings are based on surveys given to the students before and after the lesson taught in partnership with university and community members. The purpose of this lesson was for students to discover how engineers use derivatives to solve real-world engineering problems. Students measured urban, sub-urban, and rural storm water runoff volume to generate three different storm water runoff graphs using Microsoft Excel. Next, students generated the derivative graph to discover differences in rates of change of water runoff within these three watershed scenarios. The class then discussed how to relate their storm water runoff data to watershed characteristics, identified challenges associated with increased runoff rates in a urban setting such as Cincinnati, Ohio and recommended appropriate management practices for its control. This unit concluded with a trip to the award-winning, Sanitation District 1 in Fort Wright, Kentucky where students observed storm water management technologies used in the real-world. Analyses of preand post-assessment performance revealed that students performed statistically significantly higher on post-assessments in both calculus sections, suggesting that this lesson improved student understanding of how derivatives are used to model change within environmental systems. This type of an innovative teaching approach, supported by research on inquiry lessons, provides a more memorable experience for the students – actually experiencing storm water management technologies that they would only read about in textbooks and articles. This paper will provide other instructors with ideas to incorporate into their classes and will showcase both successes and challenges from the teacher’s and students’ perspectives.