The research and study paths in the secondary school: the case of the polynomial functions of the second degree

Abstract

This analysis introduces the pedagogy of research and questioning the world within the Math classrooms at secondary schools in Argentina by using Research and Study Paths (RSP). The RSP have been proposed by Chevallard in the Anthropologic Theory of Didactic (ATD) to face the mechanistic model of teaching mathematics in secondary school (Chevallard, 2004). The RSP has been previously conceived as part of this research and could enable to cover the syllabus of the three last years of the secondary level (students aged 14 to 18 years old). The RSP has been carried out in courses intentionally selected by the researcher. Two implementations have been performed once a year during three years; with 163 students participating in the whole research. The results of introducing RSP into the classroom, the characteristics of the Mathematical Organization (MO) and the advantages and disadvantages of teaching mathematics based on the pedagogy of research and questioning the world are described in the present work.