Situações didáticas olímpicas para o ensino de sequências numéricas: um contributo da engenharia didática

Abstract

The Mathematics Olympiads aim to improve the quality of mathematics teaching and present problems that require the student to have a lot of creativity, logical reasoning and interpretation skills. With the implementation of the Brazilian Mathematics Olympiad of Public Schools (OBMEP) in 2005, the dissemination of this kind of competition has increased considerably and, to encourage students, especially those who do not like or have difficulties in Mathematics, to study Olympic Problems, it is important that they often have access to these problems through situations that motivate them to develop the necessary skills. The present work has as general objective to structure and propose Olympic Didactic Situations (SDO) of the content Numerical Sequences, in the context of OBMEP, with Geogebra software as an auxiliary resource for the teacher and for the student. Analyzing the dissertations available in the repository of the Professional Master in Mathematics in National Network (PROFMAT) and in the Thesis and Dissertations Bank of the Coordination of Improvement of Higher Education Personnel (CAPES), we identified that there is no in-depth discussion about specific teaching methodologies for (POs). We also noticed that there is a small amount of research using SDO. Therefore, we used as a research methodology the first two phases of Didactic Engineering (ED), namely preliminary analyzes and a priori analysis in complementarity with the Theory of Educational Situations (TSD) to elaborate ten SDO referring to the content Number Sequences using the four stages of TSD, namely, action, formulation, validation and institutionalization and having as technological resource auxiliary Geogebra software. The SDOs are elaborated in advance by the teacher, favoring the investigation and development of intuitive thinking of the student, so that the teacher is a mediator. With this research, we aim to offer teachers of High School Mathematics an alternative approach to POs in an environment where the active participation of the student in the construction of his knowledge is privileged. The elaborated SDO compose a workbook, which is the educational product of the research.