Polynomial functions resulting from the multiplication of curves in the framework of the Research and Study Paths

Abstract

This paper presents the results of a research which proposes the introduction of the teaching by Research and Study Paths (RSPs) into Argentinean secondary schools within the frame of the Anthropologic Theory of Didactics (ATD). The paths begin with the study of Q0: How to operate with any curves knowing only its graphic representation and the unit of the axes?, which was implemented for two consecutive years by 14-17 year-old students. The results of part of the paths that allows the study of the polynomial functions in the frame of RPS are hereby described. These results justify the introduction of a new pedagogy into schools as proposed by Yves Chevallard in order to study Mathematics in conventional courses of Secondary Education schools in Argentina. The scopes relative to the attitudes of the students which are necessary to face a questions-based education are outlined in this work.