Estado do conhecimento da abordagem dada às disciplinas dos ramos de análise matemática, álgebra e geometria nos cursos de licenciatura em Matemática (2001-2019)

• Autor(a) principal: Lopes, Lailson dos Reis Pereira
• Data de Publicação: 2020
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://tede2.pucsp.br/handle/handle/23490
• topic: Professores - Formação profissional; Análise matemática; Álgebra; Geometria; Teachers - Occupational training; Mathematical analysis; Algebra; Geometry; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The present study aims to identify, in Brazilian research, the approaches to the content to be worked on in basic education, at the heartwood of the disciplines of the branches of: Mathematical Analysis, Algebra and Geometry. This is a study of a bibliographic nature that fits into the State of Knowledge research modality, guided by the question: what are the contributions of specific disciplines, of the branches of: Mathematical Analysis, Algebra and Geometry, of undergraduate courses, in Mathematics, in the formation of the future teacher, in the approach of the mathematical contents to be taught in basic education? For data collection, we performed a time frame from 2001 to 2019, subdivided into two others, 2001 - 2012, which had as source dissertations and theses that address the initial training of mathematics teachers. And, the other time frame from 2013 to 2019, which counted as a source for data collection Brazilian academic magazines in the teaching area, evaluated with Qualis A1 or A2. Among the evidenced results, in relation to the presence of the contents of Mathematics within the disciplines of Analysis, Algebra and Geometry, we highlight: notes of excess of rigor and formalism, problems in relation to teaching and learning marked by reproduction and memorization, regarding the Analysis area. As for the area of Algebra, there is a lack of consensus on the scope and the objects studied in the discipline, especially on which Algebra to be studied in the degree. Consequently, problems have been identified in relation to the learning that is present in basic education and persist in higher education. Thus, it evidenced in the researches the formalism and rigor in the disciplines entitled, such as Linear Algebra, Algebraic Structures or Algebra and dichotomy between academic Algebra and School Algebra. In relation to Geometry, for a long time the discipline was little present in the curricula of basic education, for several reasons, among them, the teachers' formative deficiency and the influences of textbooks. Nowadays, it is known that there are still significant advances, but it is necessary to go further to obtain better results. Thus, it identified the incorporation of new technologies in classes, an increase in the number of hours and the number of Geometry subjects, experiences that relate to the inclusion of this non-Euclidean subject and changes in relation to textbooks. Although the researches has found that much of the foreseen content for undergraduate courses represents an extension of those covered in basic education, these are marked by the axiomatic and advanced approach