Função: concepções de professores e estudantes dos ensinos médio e superior

• Ano de defesa: 2014
• Autor(a) principal: Pires, Rogério Fernando
• Orientador(a): Silva, Benedito Antonio da
• 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: Educação
• País: BR
• Palavras-chave em Português: Função; Ensino e aprendizagem do conceito; Concepções de professores e de estudantes; Saberes docentes
• Palavras-chave em Inglês: Function; Teaching and learning the concept; Conceptions of teachers and students; Knowledge teachers
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/10984

This study aims to investigate how teachers conceive the concept of function, as this concept is reflected in their work in the classroom in high school and in higher education and how this notion is understood by the students of these two levels of education. Results of external evaluations, our experience as a mathematics teacher in high school , as well as results of other research, pointed to the existence of difficulties for the students to understand this concept. Therefore, our theoretical basis based mainly on Records Representation Semiotics Raymond Duval, the assumptions present in the search The function concept as a prototype for problems in learning Mathematics, Shlomo Vinner and teachers knowledge of Maurice Tardif. However, analysis of the data also relied on studies, such as Sfard (1992), Sierpinska (1992) and Norman (1992). The research was conducted with one hundred twenty-eight students and ten teachers from two public schools and a public university located in São Paulo. Of all students , seventy-three attending the 1st and 3rd grades of high school and the fifty-five attending Higher Education degrees in Mathematics , Physics, Chemistry and Biology. Already teachers, eight were active in high school and two in college. The information that formed the corpus for the analysis were collected through two lists of activities (tests I and II) held at different times by all students, a questionnaire about the profile, also responded by students; creating situations/activities referring to the concept of function and interview with teachers. The research answered the question: "What conceptions of function expressed by teachers high school and higher education and how they reveal themselves in their teaching? Conceptions that this concept emerge at the time these students two levels of education perform activities related to that notion?" The results showed that much of what is done by the student is a reflection of teacher practice, since many of the strategies present in the activities proposed by teachers were identified in student productions. Some teachers showed to believe, according to the classification proposed Sfard, pointed to the operational and pseudoestrutural, and other transiting between operational and structural. In turn, students, those of high school, oscillated between operating and pseudoestrutural, the Higher Education at the end of the study show some consistency in their responses, which indicated that the ideas were not limited to operational aspects, however it was not possible to observe whether there was a reification of the concept. Also it was observed that the majority of participants (teachers and students) saw function as a process, rather than an object