Lo sviluppo delle competenze di modellizzazione matematica nella scuola secondaria di secondo grado. Concezioni iniziali e processi di intervento didattico.

The present work investigates both the mathematical modelling competencies that high school students develop and the instructional design that teachers consider suitable to promote competencies. The research relies on the constructivist paradigm; the specific version elaborated at UC Berkeley from the group of work directed by A. di Sessa is used. In the dissertation, mathematical modelling is seen as a competence, in this way the link between “constructivism” and “competence“ is show. The investigation is exploratory and divided in two paths: In stage 1, through the use of Clinical Interviewing the modelling competency of the students is investigated. Particularly the basic elements of knowledge are investigated (phenomenological primitives or p-prims) of mathematical modelling in real phenomena and the complex shapes of the competence, are investigated through three different activities: the Taxi, the Statue and the Travel. The phenomenological primitives are the basis elements of knowledge, on which the more complex mathematical competence are constructed. In the analysis the p-prims that the students had presented during the activities are identified; in order to understand which points mathematical competence gets stuck. The students were mainly analyzed by interview about real situations, proving to counteract their representations and their behavior in everyday life. Furthermore, students were asked to express their conceptions about learning mathematics, their motivation to learn and their perception of their self-efficacy. In stage 2 of the research some semi-structured interviews with high school mathematical teachers are conducted. Through an initial reflection on scraps from the first stage, each interview inquires what are the obstacles faced by the students in the modeling processes and which are the possible ways to overcome such obstacles in the classroom, in order to develop in class, modelling as a competence. The qualitative analysis of content has generated nine categories for interpreting ...