Practices of Italian teachers with the derivative concept: a problematic meeting between Algebra and Analysis in secondary school.

This paper reports on a study from a wider project of thesis, whose main focus is investigating, in the secondary school context, the transition between two important mathematics domains: elementary Algebra and Analysis. Following Kuhn (1969), we detect some fundamental paradigm shifts between the two. They represent a change in the way of thinking about and working with functions, so that the related MWSs come to be differently structured. The paper focuses on one of these paradigms, called "paradigm of the generic". Through the analysis of how a teacher manages her students' work on the derivative function, our aim is discussing how the Analysis MWS differs from the Algebra MWS, in terms of cognitive processes and especially with respect to their genesis.