Designing Instruction to Promote a Riemann Sum-Based Understanding of the Definite Integral

A robust understanding of the definite integral concept is essential to a variety of applications in STEM fields. However, research has shown that successful students regularly emerge from calculus unsure or even unaware of the underlying structure of the definite integral. Investigations into student learning of the limit and definite integral have revealed potentially powerful ways of teaching these concepts. In this paper I describe how I structured a first-semester calculus course around these novel teaching techniques. I then discuss my experience teaching one section of this course and provide some preliminary findings. Finally, I preview my plans to investigate how this teaching approach has affected students' understanding of the definite integral through surveys and follow-up interviews.