Students' Application of Concavity and Inflection Points to Real-World Contexts

The calculus concepts of concavity and inflection points are critical for a complete understanding of quantities' behavior, making them important topics of research for those interested in the intersections of STEM disciplines. This study seeks to provide insight into this area by reporting on trends in students' concept projections of these concepts in a range of real-world contexts, including temperature, economics, human height, and the universe's expansion. While the students mostly thought of concavity and inflection points in pure mathematics as shapes associated with graphs, the projections with the real-world contexts were based much more on changing rates of change. Pedagogically important student confusions were also evident in their attempts at applying concavity and inflection points to the real-world contexts, and this paper uses the concept projection perspective to identify possible sources of these confusions.