A educação algébrica no contexto de aulas exploratório-investigativas em Matemática nos anos finais do Ensino Fundamental e no Ensino Médio: um estado do conhecimento de teses e dissertações brasileiras

Abstract

The research aimed to understand a state of knowledge of Brazilian research on algebraic education in the Exploratory-Investigative Classes in the final years of basic and secondary education, from theses and dissertations. Methodologically, the theses and dissertations that composed the corpus of the analysis were selected from the Catalogue of Theses and Dissertations of CAPES by means of descriptors, being carried out, subsequently, the description of the regions and research institutions involved, the identification of the most recurring algebraic contents in the research tasks and the analysis of school practices To this objective, specific objectives were listed, including the descriptions of regions and institutions of research involved, identifying the most frequent algebraical content in the investigative tasks, and analysis of the schools practices implemented and the teaching resources used in research. The analysis of the data was carried out from two categories a priori: (a) tasks presented in Exploratory-Investigative classes, which followed a pattern of planning and application to work mathematical concepts; (b) Algebra functions mobilized in Exploration and Investigative Classes, highlighting algebraic contents such as: equations, expressions, functions, remarkable products and progressions; and an emerging category: (c) Organization of the Explorational-Research classes: school practices and didactic resources, emphasizing the structure of the lessons with differentiated dynamics and the use of technology and concrete materials. As a result the research showed that algebraic education mobilized in the corpus analyzed stood out in the bias of algebra that was related to the application of concepts, development of language and thought, problem solving, understanding of the dependency between sizes, the development of writing skills and patterns. In addition, the school practices involved converged in the actions aimed at group work, teacher's oral explanation, exploration of strategies, activities and concepts, use of digital information and communication technologies, tabular, graphical and written records. However, some gaps were present in the research, among them: the need to enhance the prior knowledge of the students, the use of inclusive topics, planning compatible with the application of the activity, educational evaluation for students during application of tasks and the explicitation of difficulties encountered by teachers when implementing the tasks.