O desafio de argumentar nas aulas de Matemática: uma investigação com estudantes do 1º ano do Ensino Fundamental

• Ano de defesa: 2019
• Autor(a) principal: Azevedo, Simone Aparecida dos Anjos
• Orientador(a): Ag Almouloud, Saddo
• 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: Faculdade de Ciências Exatas e Tecnologia
• País: Brasil
• Palavras-chave em Português: Argumentação em Matemática; Momentos de discussão em aula; Matemática (Ensino fundamental) - Estudo e ensino
• Palavras-chave em Inglês: Argumentation in Mathematics; Moments of discussion in class; Mathematics (Elementary School) - Study and teaching
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/22665

This research deals with the development of argumentative skills by students of the 1st year of elementary school to solve problems of additive field utterance. National and international studies on the topic of argumentation highlight the difficulties to develop works with this theme and the little attention given to the subject, besides the important role of the teacher in the diffusion of this practice. Thus, using the principles of Didactic Engineering as a research methodology, we draw a research course that involved aspects of the processes of both the teaching and the learning of argumentation in Mathematics. Through a questionnaire applied to 81 teachers, who work in the first year of Elementary Education, in different regions of the country, we approached their conceptions and performed a praxeological analysis of the didactic book that most of the members of this group adopted in order to verify how the argumentation is treated in this didactic material. From this perspective, we tried to answer the following research question: does a didactic sequence that articulates the problem solving of additive structures and different moments of discussion in the classroom favor the development of argumentative skills by 1st year students of elementary school? We referred to Brousseau's Theory of Educational Situations (TSD) and Vergnaud's Conceptual Field Theory (TCC) to construct a didactic sequence with six problems of additive structures involving different instances of interaction: the student with the mathematical object, the student with the teacher, the students among themselves and the teacher with the students. For the analyzes, we relied on Toulmin's structural model to qualify arguments. The experiment was carried out in a school in São Paulo by the teacher of a class of 15 students of the 1st year and with the participant observation of the researcher. The analyzes of the activities of the didactic sequence showed that the dialectics involved in didactic situations favored the development of argumentative skills by the students, propitiating the appropriation of knowledge related to the resolution of additive field problems. They also demonstrated the important role of the teacher in both transferring responsibility to the student for the challenge of solving problems as in orchestrating the moments of collective discussion with the class