Dottorato in MODELLI MATEMATICI PER L'INGEGNERIA, ELETTROMAGNETISMO E
NANOSCIENZE

Titolo della tesi: Graphical recognition of the properties of derivatives and anti-derivatives: analysis of different strategies using an eye-tracker

We present a qualitative analysis based on data collected by means of an eye-tracker instrument, concerning the outcome of a mathematical analysis test based on the concept of derivative and anti-derivative and administered to a group of candidates at university level or above. One of the aims of the research is to highlight the similarities and differences in the visual observation of the questions between candidates who are considered experts and novices. Analysing the way in which a mathematical text is read can provide a significant amount of information about the way a problem is approached and the underlying cognitive processes for dealing with it. This can be a useful research tool in the field of mathematics education, even at university level. In particular, using an eye tracker tool, it is possible to observe a candidate's ability to switch between registers in the various semiotic representations of the same mathematical object. One of the main difficulties in this process is highlighted by the fact that the novice candidate tends to collect more information on both the input and the alternative answers but has a reduced ability to select the useful ones from the superfluous ones. This also allowed us to provide some suggestions that, in our opinion, could improve the teaching of mathematics in the first years of academic studies, in the delicate period that accompanies the student in the transition from secondary to tertiary education.