Congruência e equações Diofantinas: uma proposta para o ensino básico

• Ano de defesa: 2013
• Autor(a) principal: Santos, Paulo Sergio de Almeida
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Alagoas; Brasil; Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional - PROFMAT; UFAL
• Palavras-chave em Português: Matemática – Estudo e ensino; Sequência didática; Equações diofantinas; Algoritmo de Euclides; Didactic sequences; Congruence modulo n; Diophantine linear equations; Teaching; Euclidian division; Euclid algorithm; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://www.repositorio.ufal.br/handle/riufal/2425

The principal objective of this work was the development of didactic sequences that could to help teacher and students in the teaching-learning process of concepts, some topics of Arithmetic in Basic Education. Will be see congruence modulo n and diophantine equations linear with two unknowns; also, to show the Euclidean division of a manner more mature, of equal manner to present the Euclidean algorithm to obtain the MDC of two integer numbers or natural numbers. So also make a short analysis is displayer how the division of natural numbers and obtaining MDC in textbooks. Throughout this work are exposed justification of why is being proposed the teaching of congruence modulo n and linear diophantine equations in Basic Education, observing oneside, the students of the ability to solve problems of cyclical character found in Math Olympics and otherwise, to make a natural transition between Arithmetic and Algebra. So, in the last chapters are presented didactic sequences, that representing the final product of this dissertation work.