PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Emergent Modeling and Riemann Sum
Page: 2-451
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 under the curve 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 from the first task that became a model for reasoning about their next task. In this paper we detail those conceptions and their reasoning that became model for reasoning on the second task.