PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Model-of to Model-for in the context of Riemann sum
Page: 471
This research focuses on the cognitive 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 ten interviews. They were given three contextual problems related to Riemann sums but were not informed of this relationship. The intent was to observes students' transitioning from "model-of" to “model-for” reasoning based on Gravemeijer and Stephan (2010). Findings indicate that it was not the end results but records of their ways of acting and reasoning about their contextual problem through multiple representations along with real life intervention that served as tools for supporting their transition from “model-of” informal activities to “model-for” more formal mathematical reasoning.