Uma sequência didática para o ensino de recorrências lineares homogêneas de segunda ordem, com coeficientes constantes, utilizando a metodologia da engenharia didática

Abstract

RESUMO EM OUTRO IDIOMA OPCIONAL E NÃO REPETITIVO – Inglês: Abstract (dc.description.abstract); Francês: Résumé (dc.description.resume); Espanhol: Resumen (dc.description.resumen); Italiano: Riassunto (dc.description.riassunto); Alemão: Zusammenfassung (dc.description.zusammenfassung); Resumo Indígena (dc.description.). Fonte: PDF/ Catálogo Teses Capes This work systematically presents the use of a didactic sequence, based on the methodology of didactic engineering, in the teaching of recursively defined sequences, recurrences, especially those of the linear, homogeneous, second order type with constant coefficients for students in the first year of high school, and the application was developed at a suggestively appropriate time, after or in line with the students' contact with the teaching of arithmetic and geometric progressions, content that is already part of the mathematics teaching curriculum for this grade. In this work, concepts related to the methodology of didactic engineering are presented, such as conception and a priori analyses, experimentation, a posteriori analysis and validation, as well as data related to the application of these concepts in the teaching of recurrences. The work brings an analysis based on graphics on the answers presented by the students during the execution of a questionnaire that was answered during and after the experimentation of the proposed didactic sequence, in which this questionnaire has the objective of a self-evaluation of each student about their learning, of the concepts presented in the classroom about recurrences. The results obtained and presented in this work, with the analysis of graphs and the perception of the development and understanding of the students on the subject, prove to be positive and satisfactory, since it was understood that a greater number of students were successful in understanding the theoretical part about recurrences and most understood the resolution of the proposed exercises