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A Calculus Graphing Schema

Bernadette Baker, Laurel Cooley, Marma Trigueros 

November 2000, Volume 31, Issue 5, Page 557

Abstract:
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.  

Keywords:
Quantitative
Article
Research
Experienced Teachers
Calculus and Higher Level Mathematics
Conceptual Development
Math Coordinator / Coach
Higher Education
Problems
Problem Solving / Problem Posing
Professional Development / Teacher Education
Representation
Theory