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From the Mathematical Didactics’ viewpoint about teaching Calculus, this paper aims to characterize the knowledge and mathematical work that emerges when high school students solve tasks about the rate of change mediated by GeoGebra. Based on the theory of Mathematical Working Spaces, we analyze the mathematical production of Chilean students (16- 17 years old) and conclude that making sense of the change rate starts from a work based on algorithmic processes and an interpretation/experimentation approach to the idea of variation and change emphasizing the role of the artefact, being particular to establish proof and demonstration processes. [ABSTRACT FROM AUTHOR]