Um estudo sobre a convergência de seqüências numéricas com alunos que já tiveram contato com a noção de limite

• Ano de defesa: 2005
• Autor(a) principal: Santos, Milena Gonçalves
• Orientador(a): Silva, Benedito Antonio da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Pontifícia Universidade Católica de São Paulo
• Programa de Pós-Graduação: Programa de Estudos Pós-Graduados em Educação Matemática
• Departamento: Educação
• País: BR
• Palavras-chave em Português: seqüência numérica; limite; convergência; concepções; infinito; Educação matemática; Matemática - Estudo e ensino
• Palavras-chave em Inglês: numerical sequencies; limit; convergence; conceptions and infinite
• Área do conhecimento CNPq: CNPQ::CIENCIAS HUMANAS::PSICOLOGIA::PSICOLOGIA DO ENSINO E DA APRENDIZAGEM::ENSINO E APRENDIZAGEM NA SALA DE AULA
• Link de acesso: https://tede2.pucsp.br/handle/handle/10892

This term deals with an investigation about students conceptions of a math course taking into accont concepts related to the convergence of the numerical sequencies. The individuals in this research had already had contact with the limit notion, but they hadn´t studied numerical sequencies yet. The goal is to investigate the student s resistency in disassociate the limit conception of a physic movement, of an approximation, once its definition is static. It s also intender to discuss the conceptions presented by the students concerned with: have a limit and being limited , numerical sequencies, sequencies convergence and the difference between the representation of a set with n elements and of another with infinite arouse by Caraça are discussed. In order to get to investigate such conceptions, a sequency of five activities was developed to be given to these students. The study was based on a term about the epistemological obstacles related to the concept of limit carried out by Anka Sierpinska and on the research of Aline Robert, whose theme is related to the matter of infinite presented by Bento de Jesus Caraça in his book entitled: Fundamental concepts of Mathematics . With the analisys of the results it was possible to realize that even discussing different kinds of convergence and non-convergence sequencies, monotonous and non-monotonous, the students, many times, resist in disassociate the convergency concept of a physic movement, that is translated by the descriptions that appeal to the fact that the students have written with their own words, the explanation of their understanding both in algorithms, and in the definition represented in algebraic language and geometrical representations, sowed that the procedure adopted was effective to rise to the surface multiple reactions facing the dealed concepts.