A Calculus Graphing Schema

In this study, we analyzed students' understanding of a complex calculus graphing problem. Students were asked to sketch the graph of a function, given its analytic properties (1st and 2nd derivatives, limits, and continuity) on specific intervals of the domain. The triad of schema development in the context of APOS theory was utilized to study students' responses. Two dimensions of understanding emerged, 1 involving properties and the other involving intervals. A student's coordination of the 2 dimensions is referred to as that student's overall calculus graphing schema . Additionally, a number of conceptual problems were consistently demonstrated by students throughout the study, and these difficulties are discussed in some detail.