This study provides a framework to describe the foundational understandings and reasoning abilities, covariational reasoning and mental actions, and notational aspects involved in understanding the Fundamental Theorem of Calculus (FTC). The results revealed numerous insights into the study's two primary research questions: (a) What does understanding and using the Fundamental Theorem of Calculus entail; and (b) How do students' understandings of the FTC emerge during instruction?; The framework informed the development of activities that were designed to support students' development of an understanding of the FTC. The FTC framework also proved to be useful for analyzing data from one student's understanding of the FTC as he worked through the instructional activities. The results from analyzing the thinking of Joseph also provided novel insights for refining the FTC framework.; The data from this study was collected in the context of a teaching experiment with three first semester calculus students at a large southwestern university. The intervention consisted of pre- and post-interviews with each individual student and five group sessions with the students working through activities to develop the reasoning abilities and mental actions associated with the FTC.
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