POSSIBILIDADE DE INSERÇÃO DA GEOMETRIA FRACTAL NA LICENCIATURA EM MATEMÁTICA DO IFFAR

• Ano de defesa: 2020
• Autor(a) principal: Lutz, Mauricio Ramos
• Orientador(a): Leivas, José Carlos Pinto
• Banca de defesa: Bulegon, Ana Marli, Costa, Denise Kriedte da, Nehring, Cátia Maria, Velásquez, Osvaldo Jesús Rojas
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Franciscana
• Programa de Pós-Graduação: Programa de Pós-Graduação em Ensino de Ciências e Matemática
• Departamento: Ensino de Ciências e Matemática
• País: Brasil
• Palavras-chave em Português: Geometria Fractal. Registro de Representação Semiótica. Tecnologias Digitais. Geogebra. Ensino Superior.
• Palavras-chave em Inglês: Fractal geometry. Registration of Semiotic Representation. Digital Technologies. Geogebra. Higher Education
• Área do conhecimento CNPq: Ensino de Ciências e Matemática
• Link de acesso: http://www.tede.universidadefranciscana.edu.br:8080/handle/UFN-BDTD/903

This research aims to investigate possibilities of inserting notions of Fractal Geometry in the Mathematics undergraduate courses from Farroupilha Federal Institute of Education, Science and Technology (IFFar) by using Digital Technologies (DTs). The choice to research this subject is due, among other reasons, to the fact that the undergraduate courses in Mathematics of IFFar develop in their curricula only Euclidean Geometry. Moreover, there are few scientific papers with application related to Fractal Geometry and the use of DTs. As a theoretical contribution, Raymond Duval's Register of Semiotic Representation (RSR) is used to analyze the different mobilizations of representation registers that can occur for the apprehension of a mathematical object. The methodology is qualitative. The research subjects are academics from the Mathematics undergraduate course at IFFar – Alegrete Campus. With the intention of obtaining the data, a sequence of activities, in the form of workshops lasting 20 hours, was developed and applied to this public, with DT as a methodological resource. The data collection occurred from three instruments: direct observation and notes of the researcher in his field journal; records written by academics; and figurative records made in GeoGebra. The analysis was based on the qualitative method, seeking to observe the students' resolution procedures in relation to the different types of transformations (treatment or conversions) of the RSR. With the workshops, it was possible to present to the academics involved in the research another Geometry, which is not included in the Pedagogical Course Project. Through the answers presented by the students and the RSR analysis, we concluded that learning process had occurred. As a suggestion for the improvement of the workshops, for further dynamization, we indicated to explore more the spreadsheet and the CAS window of GeoGebra. To this end, we suggested rethinking some activities, guiding students to work with these two tools. We hope that these students, in their future pedagogical practices, will be able to transpose, in Basic Education, the knowledge acquired. Regarding the fact that non-Euclidean geometry discipline is not included in the pedagogical project, we believe it is important to include at least one such discipline, being either mandatory or optional. For future works and investigations, targeted to the teaching and learning of Geometry, we recommend the exploration of other non-Euclidean geometries.