Um estudo exploratório das relações funcionais e suas representações no terceiro ciclo do ensino fundamental

• Ano de defesa: 2011
• Autor(a) principal: Castro, Edson Eduardo
• Orientador(a): Bianchini, Barbara Lutaif
• 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: Educação algébrica; Álgebra; Variável; Relação funcional; Registros de representação semiótica
• Palavras-chave em Inglês: Education algebra; Algebra; Variable; Functional relationship; Registers of semiotic representationq
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/10871

This study is a qualitative research whose focus is the introduction to algebra in the third cycle of elementary school. One of the great difficulties encountered by students when they come into contact with the learning of algebra due to the rupture between the ways of thinking and representing existing so far and those that become necessary in algebraic contexts.There are several possible approaches to the introduction to the study of algebra, such as generalization of patterns, modeling, equations etc. This study has chosen to explore the variation between magnitudes or the functional relationships in different representations with ten Year 7 students from elementary school to a public school in the eastern zone of Sao Paulo. The goal is to investigate how the functional relationships in different representations contribute to the introduction to the thought and language of algebra. With this purpose, we developed, implemented and evaluated a didactic sequence developed according to the research methodology called didactic engineering proposed by Michèle Artigue (1995). Faced with the approach chosen for initiation into algebra used to Representation Theory of Semiotics records of Raymond Duval as a theoretical framework to support the development and analysis of students' production. Through didactic sequence applied, we found the feasibility of working with students from the 7th year of elementary school with the functional relationships in different representations in order to develop thinking and language of algebra. However, one should take into consideration that this approach is a study that requires a longitudinal design, since, according to the references adopted, "learning mathematics is the simultaneous mobilization of at least two registers of representation." The products of the students showed that despite mistakes in his writings algebraic most students could think broadly and write symbolically an expression involving two quantities. Thus, finishing this thesis contained a separate product (digital and print versions) and can serve as a support to teachers as it has been tested and results showed that in fact should be taken into consideration in the introduction to Algebra