Teachers' professional knowledge and tasks on geometric transformations: establishing relationships with teaching practice
This dissertation was conceived as a continuation of scientific initiation research, in which theoretical foundations, curriculum documents and tasks related to teaching the mathematical content of geometric transformations were explored. Aiming to approach how the teacher organizes and materializes such aspects in the classroom, the objectives are: to identify and understand how the teacher's knowledge impacts on his professional practice in relation to the content of geometric transformations, and to identify and discuss what the teacher's knowledge emerge in the interaction with tasks on the mathematical content of geometric transformations. Through the qualitative nature of the research, it consisted of three axes, the first being a literature review on the concepts to be addressed in the other axes. The second axis addressed the teacher's professional knowledge that emerges when approaching the content of geometric transformations in the classroom, using the Knowledge Quartet tool, in the analysis of a teacher's professional practice on geometric transformations. The third axis dealt with the analysis of the teacher's professional knowledge that emerges in the (re) elaboration of an investigative task on geometric transformations, by teachers during a study group. The results identified the need to advance in investigative and reflective living spaces, involving the approach and discussion of the content of geometric transformations through different types of tasks of different natures, in order to favor the mitigation of gaps in professional teaching practice.