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Master's Dissertation
DOI
10.11606/D.45.2016.tde-21012016-211144
Document
Author
Full name
Caio Moura Quina
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Abdounur, Oscar Joao (President)
Bianconi, Ricardo
Prado, Esther Pacheco de Almeida
Title in Portuguese
Sequências e séries: uma proposta duvaliana para a educação básica
Keywords in Portuguese
Ensino médio
Infinito
Representação semiótica
Sequências
Séries
Abstract in Portuguese
Esta dissertação versa sobre o ensino de Sequências e Séries na educação básica. A questão é entender em que medida o uso da Teoria dos Registros de Representação Semiótica se mostra favorável à criação de atividades que sejam propícias à aprendizagem dos alunos. Foram elaboradas dez atividades sobre Sequências e Séries e foi feita uma aplicação de quatro destas atividades com alunos de 1a série do ensino médio. Com esta aplicação, procurou-se buscar evidências de que o uso de diversos registros de representação semiótica favorecem a aprendizagem dos alunos em Matemática. Como escopo secundário, buscamos também investigar a concepção de infinito que os alunos manifestaram durante a aplicação das atividades. Antes, porém, buscamos na história da Matemática diferentes maneiras de como filósofos e matemáticos concebiam e utilizavam o infinito. Visto que Sequências e Séries também são assunto tratados no ensino superior, foram abordadas algumas dificuldades de transição ensino básico/ensino superior tendo em vista diferenças culturais entre os dois níveis de ensino. Concluímos que o uso de materiais concretos para representação de objetos matemáticos se mostrou favorável à compreensão dos alunos e a concepção de infinito dos alunos está predominantemente ligada a ideia de infinito potencial.
Title in English
Sequences and series: a Duvalian proposal for primary school
Keywords in English
Infinity
Secondary school
Semiotic representation
Sequences
Series
Abstract in English
The subject of this research is about teaching and learning sequences and series in primary education. The research question is to understand how favorable is the use of the theory of semiotic representation registers to create activities that help students to learn. Were created ten activities about sequences and series and four of these were chosen to be used in a classroom with 1st year students of a secondary school. By observing these activities being used in classroom, evidences were searched to evaluate if including different semiotic representation registers facilitates student's learning on mathematics. As a secondary aim, the student's infinity conception is investigated in the classroom. We also researched mathematics' history to find different conceptions adopted by philosophers and mathematicians on infinity. As sequences and series are also studied in college, some transition difficulties (from High School to College) were discussed considering cultural differences between the two educational levels. It was concluded that concrete teaching materials to the students' comprehension and the students' concept of infinity is mainly linked to potential infinity.
 
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Publishing Date
2016-01-22
 
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