A learning trajectory for the fundamental theorem of calculus using digital tools

This study sets for itself the task of constructing a learning trajectory for the fundamental theorem of calculus (FTC) that takes into account the interaction with an educational digital tool. Students were asked to explain the connections between interactive and multiple-linked representations in an educational digital tool, and to conjecture about the mathematical relationships embedded in it. The study was guided by the theory of knowledge objectification. We included two rounds of analysis: one, to detect ‘learning focuses’ involved in learning the FTC and to identify the relationship between them; the other, to identify the ways in which students used the tool to become aware of each focus. Data analysis identified nine focuses in the process of learning the FTC. We described these focuses, the relationships between them, and the ways in which students interacted with the tool to characterize the learning trajectory of the FTC.