Re-significando a disciplina teoria dos números na formação do professor de matemática na licenciatura

• Autor(a) principal: Resende, Marilene Ribeiro
• Data de Publicação: 2007
• 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/11207
• topic: Educação Matemática; Formação de Professores; Educação Algébrica; Ensino de Teoria dos Números; Números inteiros; Educacao matematica; Matematica -- Estudo e ensino; Teoria dos numeros; Professores de matematica -- Formacao profissional; Mathematics Education; Teacher Development; Algebraic Education; Teaching of the Theory of Numbers; Integer Numbers; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

This study is part of the issue that questions which algebra should be taught in the different levels of schooling, especially in the development of mathematics teachers for basic education. In this context, this study was guided by the question: Which Number Theory is or should be understood as a piece of knowledge to be taught in mathematics teacher development courses, aiming at teacher s practice in basic education? The purpose is to understand the Theory of Numbers from the point of view of knowledge to be taught, and find elements to give it a new meaning in the mathematics teacher development courses. The theoretical references were based on Chevallard, Chervel, Tardif, Macedo and Lopes in the discussion of the scientific knowledge and the knowledge to be taught; on Shulman when discussing teachers knowledge and on Campbell & Zazkis to discuss the Theory of Numbers in teaching. The research takes on a qualitative approach, thus analyzing the curricular proposals of the subjects which deal with the Theory of Numbers in twelve Brazilian universities; ten school books, chosen from among those which are most mentioned in the programmes of the subjects under scrutiny, were analyzed, and seven semi-structured questionnaires were carried out with teachers and researchers of the Theory of Numbers or Mathematics Education. For the data treatment, the content analysis as described by Lüdke & André, Laville & Dionne and Bardin were used. It was possible to conclude that the Theory of Numbers, as worked in the majority of the universities under study, does not have any preoccupation with the development of teachers for basic education, as the content approach is axiomatic, using a predominantly symbolic-formal language, with emphasis on demonstrations, which allows for fitting this teaching into the classical formalistic tendency. On the other hand, it was possible to perceive elements and possibilities for giving a new meaning to it, considering that: topics of the Theory of Numbers are present in basic education, as the natural and integer numbers occupy a great part of the mathematics curriculums at this level, involving special issues in their teaching, which can not be left out in teacher development; the Theory of Numbers is a favourable space for the development of relevant mathematical ideas related to natural numbers and some also extended to the integers, present in school mathematics, such as recurrence, mathematical induction and divisibility; the Theory of Numbers is a favourable field for a wider approach on the issue of proof, because it offers rich opportunities for the exploration of the different types of proofs, allowing the teacher-student to understand that the proof has different functions, and that, in teaching, it can not be understood in the same manner as in mathematical research; the Theory of Numbers is a favourable field for mathematical investigation, because it allows for exploration of patterns and numerical relations, the use of recursion and mathematical induction, offering the opportunity for development of the abilities of conjecturing, generalizing, testing and validating the conjectures. These potentialities sustain the conception of a subject which is being called Elementary Theory of Numbers, which has as its source the scientific knowledge, but also the school knowledge and the demands which such teaching puts on the teacher. These constitute essential topics for discussion: the integer numbers and historical, epistemological and procedural aspects; divisibility, prime numbers and lineal diophantine equations. Their aims and approaches should take into consideration that the content and the pedagogic knowledge on the content, theory and practice, should be present in its constitution