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In this paper we present reflections on challenges faced in the use of an alternative writing model in our doctoral thesis, showing its relevance as a coherent and insubordinate model. The model mobilized was the questions-answers map, developed within the framework of the anthropological theory of the didactic. Due to the limits of the exhibition, we present some clippings of our investigation, whose objective was to answer the following generative question: What teaching proposal for Z is possible to build through the interaction with a study group of teachers in the perspective of the paradigm of questioning of the world (PQW)? The heart answer was divided in two, one referring to the study group constituted during the research and the other referring to the other studies of the thesis. We built a reference epistemological model (REM) that allowed us to analyze the dominant model of the relative integers, which, in turn, was complemented with analyses of previous research data. We mobilized aspects of the PQW, more specifically, conditions and constraints, identified from the conclusions related to continuing education with the group of teachers and from the studies on the study and research path, analyzed through the dialectics question/answers, media/milieu, and collective/individual. These analyses also helped us to finalize the reference epistemological model and the teaching proposal initiated together with the members of the study group. [ABSTRACT FROM AUTHOR]

This paper aimed to analyze proposals of teaching 2nd degree Equations developed in research's postgraduate with a focus on problem solving and the conceptions of Algebra. We developed bibliographic research in which we obtained two dissertations that underwent a meta-analysis. The results show that both are interested in teaching approaches to 2nd degree Equations related to Problem Solving. However, misunderstandings between theory and practice are evident regard to limitations and potential of each approach to Problem Solving, in addition to the recurrence of exercises related to the systematization of techniques through repetition, reinforcing a fundamentalist-analytical view of Algebra. It is necessary to consider the importance of expanding studies that present sequential proposals for teaching 2nd degree Equations in the midst of Problem Solving, consistently employing the different approaches (about, for and via), and the conceptions of Algebra that are linked to this teaching. [ABSTRACT FROM AUTHOR]