The overgeneralization of linear models among university students´ mathematical productions: a long-term study

Abstract

Over the last several years, we have been exploring and researching on a phenomenon that occurs among undergraduate students which we called extension of linear models to non-linear contexts or overgeneralization of linear models. This phenomenon appears when some students use linear representations in situations that are non-linear. In a first phase, we recognized and characterized the overgeneralization among agronomy majors while working with different kind of problems. This process let us raise some conjectures about the statement of the problems that were studied in a second phase. In a third phase we conducted some interviews in order to deep our understanding. The study allowed us to discuss: a) the robustness and broadness of the linear models as tacit models among university students, b) the emergence of a tension between unrealistic tasks posed by the teacher/researcher and the students? realistic interpretation of it, and c) some considerations about the teaching environment at university level.