A atividade algébrica e o significado da igualdade através da exploração e proposição de problemas e o tecer de uma investigação na formação inicial

Abstract

The present work aims to investigate, with a critical eye, what is the understanding that future mathematics teachers have of the equality sign. The study of the literature was carried out in front of an investigation of Algebraic Education, in order to observe how the research on teaching-learning through Exploration, Solving and Posing of Problems has been developed. The literature of the researches instigated the realization of classes with Algebraic Activities through Exploration, Solving and Posing of Problems, to understand the meaning of Equality. The intention was to solve questions in our trajectory and to contribute to the formation of undergraduate students in the area of Algebraic Education. The research, in its practical activities, in the production and analysis of data, is characterized as qualitative. The research was developed in a mathematics undergraduate class, in the subject Algebra Laboratory, in a campus of the state university. The classes took place through remote teaching, mediated by the use of synchronous technology, via web conference, in the context of social isolation in view of the Covid-19 pandemic in Brazil. The data were produced during the course classes through screen recordings of the web conference, through the researcher's and the participants' records in notebooks, and through chat messages. To produce the data, we conducted classes with the following question: "how do Multicontextual Problem Exploration and Posing contribute to the understanding of the equality sign by future mathematics teachers in algebraic activity?". This question aroused the desire to search for evidence and, during the analysis of the results, we could present and discuss the experience of this experimentation by the undergraduates. As results, the understanding of the meaning of equality during the process stood out, evidenced by the presentation of ideas during the work with the problems, and by the participation and engagement in doing mathematics. Thus, when dealing with equality within the Algebraic Activity, it was noticed that the undergraduates were receptive and contributed to the stages of the research process, making their reflections and syntheses, as well as demonstrating such understanding during the exploration. The problem posing proved to be a new practice for the undergraduates, but challenging and instigating when facing the mathematical process in view of the teaching-learning process, building an attitude to do mathematics in the initial training environment. In this sense, the results are directed to the conclusion that there was a contribution of understanding through Exploration, Solving and Posing of Problems with the weaving of the threads of Algebraic Education within the Initial Training, forming a sustainable mathematical fabric in this research.