The didactic contract from the implementation of a didactic sequence to teach arithmetic progression

Abstract

This paper results from a research that aimed to investigate the dealings between teacher and students in application of a didactic sequence previously established for the teaching of Arithmetic Progression (AP). The survey was conducted in four stages: preparation of the didactic sequence, preliminary analysis of the proposal to the teacher, implementation of the sequence. The didactic sequence sought to accommodate the elaborate steps proposed by Brousseau, the typology of Didactic Situations (action, formulation, validation and institutionalization) in order to allow its application in accordance with a didactic contract type approximation, which is that the active stance of student in constructing knowledge is valued. The results showed that although we have proposed a sequence to be applied as a kind of didactic contract approximate, negotiations, renegotiations and breaks the rules of the didactic contract were made during the development of the sequence. We believe that these breaches of the rules were motivated by previous marks of didactic contract, or implicit and explicit rules by which teacher and students were accustomed.