PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Opportunities to Develop Understanding of Calculus: A Framework for Analyzing Homework Exercises
Page: 2-570
The purpose of this study was to construct and apply a framework to examine opportunities to understand calculus deeply, as informed by prior research. I applied this framework to analyze opportunities to learn derivatives in two calculus texts: Hughes-Hallett et al. (2009) and Stewart (2012). These tests were chosen to represent different points on a continuum between conventional and reform calculus materials. An analysis of both texts suggests that they are more similar than might be expected with respect to the amount of context given in problems, their attention to position, velocity and acceleration, and opportunities to use multiple representations – algebraic, numeric, graphical, and descriptive. There were differences between graphical and descriptive problems between texts and opportunities to make connections between representations. The framework presented here illuminated degrees of variation and similarity between opportunities to understand calculus in these texts and could have further utility for examining additional calculus texts.