In learning scenarios, the main focus should be on knowledge about the learner's strengths and weaknesses. In this context, this article aims to present the results obtained in the previous investigation of the learning styles of teachers in continuing education, in the perspective of the development of strategies that take into account the singularities of the teacher / student. This investigation deals with a case study on teachers in a broad sense in the area of Environmental Education, in a hybrid model, with classroom and virtual environment, offered by a public University. We sought to analyze the responses to promote personalization in the classroom and virtual classroom activities based on pedagogical strategies that included all styles of trainees present. To identify the learning style, an open questionnaire was applied, based on the model by Kolb, where a sample of 57 respondents was obtained, where different learning styles were identified among the course participants. The results indicate that training courses designed for the teaching professional who seek knowledge about the specificities of this professional, using instruments that value and recognize their opinion, favor them to be protagonists of their own training.

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The phenomena related to the mathematical teaching and learning process have a significant and direct influence on the construction of knowledge and studying these issues is of interest to the theory developed by Guy Brousseau, called Theory of Didactical Situations. When dealing with the relations established between student, knowledge and teacher, Brousseau presents those that are specific, explicitly and implicitly, of the relationship between teacher and students, as well as their influences on the teaching and learning process, defining, for this, the Didactic Contract, which consists of the set of behaviors that the teacher expects from the student and the student from the teacher. With this, the following question arose for this work: What is the relevance of the Didactic Contract when designing teaching sequences with input in the Theory of Didactical Situations? The objective was, then, to carry out an integrative review in order to systematize information present in scientific articles about the Didactic Contract in the perspective of the Theory of Didactical Situations. A search for works was carried out in the databases Scielo, Google Scholar and Portal de Periódicos CAPES/MEC through the descriptors "Didactic Contract" and "Theory of Didactical Situations", with the following exclusion criteria: works not related to the theme and book, theses, dissertations and monographs. That is, only papers of the scientific article type were chosen. A total of one hundred and seventy-seven works were obtained as an initial result, of which thirteen were repeated. After reading the abstracts and adopting the exclusion criteria, sixteen articles remained, of which nine responded to the elaborated question. With the research, it was found, in the period consulted, a limitation of publications that deal specifically with the Didactic Contract and, in spite of that, it was concluded that the Didactic Contract is a very important element in a teaching and learning situation, because it can favor or cause an obstacle in the acquisition of new knowledge by the student.