Graphical Recognition of Antiderivatives: Analysis of Different Strategies Reflecting Level of Expertise Using Eye-Tracker Tool

The aim of this research is to identify the difficulties of the students with Calculus tasks. This study is a qualitative analysis carried out using the eye-tracker tool. The data collected allowed us to study the differences and analogies between the experts and novices in their cognitive processes. The way of reading a text can provide a lot of information about cognitive and resolution processes. Through the eye tracker instrument, it is possible to observe the ability of the subject to switch between different registers of representation. Calculus tasks concern the concept of derivative and antiderivative; in particular, students were asked to recognise the graph of an antiderivative function. Finally, this allowed us to put forward some suggestions that, in our opinion, could improve the Didactics of Mathematics at the level of the first years of academic studies, in the delicate period that accompanies the student in the transition from secondary school to university.