Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática

• Ano de defesa: 2021
• Autor(a) principal: Mota, Janine Freitas
• Orientador(a): Abar, Celina Aparecida Almeida Pereira
• Tipo de documento: Tese
• 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: Matemática - Estudo e ensino (Superior); Licenciatura em Matemática; Integral definida
• Palavras-chave em Inglês: Mathematics - Study and teaching (Higher Education); Licenciate degree in Mathematics; Definite integral
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/23641

This research aims to analyze the way a group of licenciate in Mathematics students mobilizes competencies and develop didactic-mathematical knowledge during the implementation of a didactic proposal that approaches the meanings of the Definite Integral, involving digital technologies. The theoretical contribution lies in the Ontossemiotic Approach to Knowledge and Mathematical Instruction (OAK) and in the Didactic-Mathematical Knowledge of the teacher (DMK). Using the methodological aspects of Didactic Engineering interpreted according to the OAK, through the epistemic-ecological, cognitive-affective and instructional facets, we conducted the Preliminary Study, Design, Implementation of the Didactic Trajectory and Evaluation phases which enabled the systematic analysis of the development and implementation of the didactic proposal. The Preliminary Study phase highlighted the contributions of investigations that approached cognitive, didactic, epistemological aspects related to Definite Integral. In the Design phase, we planned the activities that compose the didactic proposal, starting from problem situations developed in intra and extra-mathematical contexts, assisted by GeoGebra. In the Implementation Phase of the Didactic Trajectory, the activities were applied to students of the third semester of the Licentiate degree in Mathematics at the State University of Montes Claros (Unimontes) in two face-to-face meetings and one remote meeting. The data were collected through recordings of the research participants’ dialogues, written and digital records containing the development of the activities, in addition to observation notes written during the activities. The tools and notions of mathematical object and OAK process configuration used in the Evaluation Phase enabled to identify the didactic configurations identification that permitted to determine how much the students institutionalized the knowledge about the studied mathematical objects. The analysis of the data showed that the didactic proposal in experimentation contributed to the didactic-mathematical knowledge of students in relation to the Definite Integral in the aspects: connections between theory and practice using intra and extra-mathematical contexts; formalization, generalization and institutionalization of knowledge; mobilization of skills; development of autonomy; use of interdisciplinarity; use of different types of representation records and mobilization of cognitive processes. The educational process in the perspective of the Didactic Analysis model proposed by OAK obtained a satisfactory level of didactic adequacy. We concluded that a didactic proposal referenced in the categories of OAK in which an adequate digital resource is used can enhance the construction of personal meanings and once the activities involve contexts that bring meaning and meaning to the knowledge about the mathematical object under study, students tend to understand it better