Resolução de problemas e o Arco de Maguerez no ensino da matemática financeira em uma turma da 3ª série do ensino médio sob o olhar do contrato didático

Abstract

This work aims to investigate, from the proposition of a Didactic Sequence using Problem Solving on Financial Mathematics and the handling of the Arch of Maguerez, the negotiations, rules, ruptures and renegotiations of the Didactic Contract, as well as the escape of the perverse effects of the Didactic Contract, and the contributions for the redefinition of knowledge, based on the Communicative Action and the Pedagogical Discourse in a class of the 3rd year of High School. We chose as a reference the Theory of Didactic Situations and the notion of Didactic Contract (BROUSSEAU, 1986), the Theory of Communicative Action (HABERMAS, 1988) and the Theory of Pedagogical Discourse (BERNSTEIN, 1996), Problem Solving (PROENÇA, 2018) and the methodology of problematization with the Arch of Maguerez (BORDENAVE; PEREIRA, 2015). We opted for a qualitative research methodology (LUDKE; ANDRÉ, 2018) through a case study (YIN, 2010), which comprises the analysis of didactic phenomena in the classroom space, considering the contribution of Communicative Action - the from questions asked by the teacher and students –, from the Pedagogical Discourse, from Problem Solving and from Maguerez Arch. As data collection instruments we used participant observation, videography, audio recording, a priori and a posteriori questionnaires and activities contained in the Educational Product originated from this dissertation. In view of the research findings, we noted the contribution of the Arch of Maguerez in Problem Solving, with regard to the relevance of guiding situations arising from reality in proposing problems in Mathematics classes, considering the involvement of students in the creation of questions about the themes dealt with regarding Financial Mathematics, its applicability in society, discussions about the relationships of what was being approached and their personal lives and the search for already constructed knowledge and its resignifications. It was also noticeable that completing the stages of the Arch of Maguerez in problem solving allowed students to read and reread (both the guiding situations and the problems), interpretation, analysis and treatment of data, as well as the implication of each numerical result of the problems about what was being investigated in the application of knowledge.With the points listed being important in the investigation of the Didactic Contract, we emphasize that contract negotiations are not enough for the management of knowledge, with ruptures and renegotiations taking place for teaching and learning to take place. However, we see that for moments of renegotiation of the Didactic Contract in classes that use problem solving with the Maguerez Arch, Communicative Action is of fundamental importance, and can be governed by the types of questions asked by the teacher and can work as a propelling effect. We also emphasize that even though the functions and roles of the student and the teacher have become clear in solving problems with the use of the Arch of Maguerez, at one point it was an effect of the contract that was evidenced, the Topázio effect, and we see it as an ambivalent effect , when the teacher helps the student because he does not have enough knowledge and when the teacher helps when the student does not want to do his homework due to lack of interest. In this regard, we emphasize that the teacher's actions, mediating, leading students to think, questioning them and giving them time to carry out their tasks, is of paramount importance in teaching and learning situations. With this, we understand that the learning situations are not unilateral, but that, when considering the reality and the communicative action in the work with the resolution of problems, the functions of the teacher and the student are highlighted through the negotiations and renegotiations of the Contract Didactic, learning can become autonomous and spontaneous.