Exploring problem solving strategies in integral calculus with GeoGebra: a collaborative approach

The present study aims to identify strategies that university students put into play when solving a problem involving notions of integral calculus and GeoGebra mediation. Problem solving is considered as a theoretical approach aimed at characterizing resolution processes through the use of digital technologies. A mathematical problem involving two cyclists is designed and presented to 20 calculus students enrolled at a university in Lima (Peru). The results show that tasks performed in pairs allow identifying the need to graphically represent the speeds of two cyclists in GeoGebra to compare them. Antiderivatives, areas, and a defined integral are also used to find and compared the distances traveled. Discussions between pairs allow comparing resolution strategies, recognizing errors, and rectifying them, while improving learning in a collaborative way. It is concluded that GeoGebra enables various forms of reasoning to occur, which are transformed into problemsolving strategies by students.