THE TEACHING CONTRACT IN A 3rd GRADE CLASS OF HIGH SCHOOL: CONTRIBUTIONS OF PROBLEM SOLVING, THE MAGUEREZ ARCH AND COMMUNICATIVE ACTION IN WORKING WITH FINANCIAL MATHEMATICS
Keywords: Didactic Contract; Problem solving; Arch of Maguerez; Communicative Action; Pedagogical Discourse; Financial math.
This work aimed to investigate, from the proposition of a type of mathematical task using Problem Solving on Financial Mathematics and the handling of the Maguerez Arc, the negotiations, rules, ruptures and renegotiations of the Didactic Contract, as well as the escape of the perverse effects of the Didactic Contract, and contributions to the construction of new knowledge, based on Communicative Action and Pedagogical Discourse in a class of the 3rd grade of High School. We chose as reference the Theory of Didactic Situations and the notion of Didactic Contract (BROUSSEAU, 1986), the Theory of Communicative Action (HABERMAS, 1988), 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 included 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 the Arch of Maguerez. 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 general, we identified that the Didactic Contract negotiations are not enough in the management of knowledge, with ruptures and renegotiations happening so that teaching and learning can take place. As a contributor to the renegotiation of the Didactic Contract, we point out the teacher's mediation, through the types of questions considering the Communicative Action and the ideas of rhythm and sequencing of the Pedagogical Discourse Theory. With regard to problem solving, we point out the contribution of the work with guiding situations that consider reality as a starting point and application in it (Arco de Maguerez), allowing reading, interpretation, analysis, data processing, results and the implications of the numerical results about what is being investigated. However, although the functions and roles of the student and the teacher have become clear in the development of the problem-type task, at times it was evidenced that possible effects of the Didactic Contract could happen, but that the teacher's action, making the intermediation, taking the students to think, questioning them and giving them time to carry out their tasks, was decisive for the escape from these effects. 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, being in evidence the functions of the teacher and the student through the negotiations and renegotiations of the Contract Didactic, learning can become autonomous and spontaneous. Therefore, we believe that the development of the study contributed to the development of learning skills (critical thinking, creativity, collaboration and communication), literacy skills (informational) and life skills (flexibility, leadership, initiative and productivity).