Developing and Connecting Calculus Students' Notions of Rate-of Change and Accumulation: The Fundamental Theorem of Calculus.

Marilyn P. Carlson Nanci Smith Joni Persson Arizona State University Arizona State University Arizona State University An overview of the conceptual underpinnings, reasoning abilities and notational issues related to learning the Fundamental Theorem of Calculus is provided. Using this theoretical framework, curricular materials were developed to promote these understandings and reasoning abilities in students. Results from a study that investigated the effectiveness of these materials on first semester calculus students’ understandings of the FTC revealed significant advances in their understandings of accumulation and the FTC. Some specific difficulties that were observed in select students provided insights for further refinement of the theoretical framework and for revision of the FTC activities.