O conceito de ângulo: reflexões com estudantes ingressantes no curso de Licenciatura em Matemática

• Autor(a) principal: Albuquerque, Ivan Araújo Cordeiro de
• Data de Publicação: 2017
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal de Alagoas (UFAL)
• Texto Completo: http://www.repositorio.ufal.br/handle/riufal/2222
• topic: Matemática – Estudo ensino; Geometria; Ângulos; Professores – Formação; Teach; Geometry; Angle; Formation; Teacher; CNPQ::CIENCIAS HUMANAS::EDUCACAO

This research is a result of my reflections about teaching the concept of angle in mathematics students’ initial formation - future mathematics teachers. From an exploratory study in which five students of ‘Integrating Projects 1’ voluntarily participated, we sought to investigate the definitions of angle in Euclidean elementary plane geometry, identifying the ambiguities and inconsistencies that led us to propose a definition that could best meet the needs of future mathematics teachers. In order to do so, after evaluating the work done in the discipline where the concept of angle was discussed, five semi-structured interviews were recorded in audio and transcribed for later analysis. The interviews were subsidized by Bardin (2011), Fiorentini (2009), Tardif (2011), D'Ambrosio (1996), Shulman (1986), Ponte (2009) and Lorenzato (2010). The definitions analyzed came from Euclides (2009), Hilbert (1996), Barbosa (1985), Muniz Neto (2013) and Gomes & Ralha (2005). The mathematical aspects were guided by the authors: Halmos (1974), Lima (1970), Monteiro (1971) and Dean (1974) and their pillars. To anchor the analyzes under the aspects of mathematics teaching Lorenzato, Fiorentini, Bicudo & Borba (2004) and D'Ambrosio served as reference. The data uncovered how much the concept of angle is complex, both from the mathematical point of view, by the various conceptions in which it is presented, and also by the great amount of definitions in use. Consequently, both understanding and teaching this concept becomes a baffling task. From the analysis of the definitions treated, a definition proposal was found, exempt from the difficulties pointed out in the analysis of the data collected, which is presented in the final considerations. Appendices have been included in order to provide a better understanding, outside of common sense, of what a rotation is as well as a respectful suggestion on how to approach the proposed definition brought by Edwards (1984).