Gender differences and didactic contract: analysis of two INVALSI tasks on powers properties

The results of standardized tests such as PISA and the Italian INVALSI, point out the existence of a gender gap in mathematics. This gap is deeply studied in mathematics educations literature. In this paper we analyse two INVALSI items of grade 10 in which male and female answers have distinctly different behaviour. Our aim is to observe if this different trend of male and female answers is influenced in particular by effects of didactic contract. In this analysis we integrate quantitative and qualitative methods. The quantitative analysis is based on IRT models and it allow us to highlight the trend of the correct and wrong answers, distinguishing between male and female. The qualitative analysis involves interviews to students and confirm that the choice of a particular response is influenced by didactic contract effects.