PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2013
Denver, Colorado
Challenges While Modeling Using Riemann Sum
Page: 1-146
This research focuses on mental challenges that students face and how they resolve these challenges while transitioning from intuitive reasoning to constructing a more formal mathematical structure of Riemann sum while modeling “real life” contexts. A pair of Calculus I students who had just received instruction on definite integral defined using Riemann sums and illustrated as area participated in multiple interview sessions. They were given contextual problems related to Riemann sums but were not informed of this relationship. Our intent was to observe students’ transitioning from model of to model for reasoning while modeling these problem situations. Results indicate that students conceived of five major conceptions during their first task and their reasoning about their task from one form of representation became a model for reasoning into another form of representation within a task. Also, their ways of reasoning from their first task served as referential tools to reason about their next task. In this paper we detail those conceptions and their reasoning from their first task that became model for reasoning within and across subsequent tasks.