Compreensões de conceitos de cálculo diferencial no primeiro ano de matemática: uma abordagem integrando oralidade, escrita e informática
Carregando...
Data
2006-03-13
Autores
Olimpio Junior, Antonio [UNESP]
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Estadual Paulista (Unesp)
Resumo
A partir da integração oralidade-escrita-CAS/MAPLE, eu investiguei compreensões emergentes sobre os conceitos de função, limite, continuidade e derivada, produzidas por ingressantes em um curso de Matemática oferecido por uma universidade pública do estado de São Paulo. A investigação, sob o balizamento do paradigma interpretativo e caracterizado pela metodologia qualitativa, desenvolveu-se com a realização de experimentos com oito voluntário(a)s. Os dados para a análise inicial constituíram-se de respostas individuais escritas em linguagem natural e de videotapes das interações entre duplas de participantes e o MAPLE. Esta análise produziu quatro episódios tematizando conflitos emergentes sobre o conceito de derivabilidade, a definição de derivada, o conceito de limite e a comparação entre os gráficos de uma função e de sua derivada. Cinco categorias de interação entre duplas de participantes e o MAPLE foram descritas. Três níveis de compatibilidade entre compreensões materializadas a priori pela escrita e as emergentes da interação participantes-MAPLE foram identificados. A análise inicial sugere que abordagem é apropriada à materialização de tais compreensões. A análise final sugere que os conflitos emergentes poderiam ter suas raízes numa limitada compreensão do conceito de função. A pesquisa também sugere uma maior e mais intensiva exploração da natureza dinâmica do Cálculo Diferencial.
From the integration of orality, writing and the CAS-MAPLE, I investigated understandings that emerge about the concepts of function, limit, continuity and derivative produced by full-time first-year students of mathematics from a public university in the state of São Paulo, Brazil. The research, implemented under the guidelines of the interpretive paradigm and of the qualitative methodology, was characterized by experiments, which were conducted with eight volunteer participants. The data consisted of individual written answers in natural language and videotapes of the interactions between pairs of participants and the MAPLE. The initial analysis is on four episodes focusing on emerging conflicts on the concept of differentiability, the definition of derivative, the concept of limit, and the comparison between the graph of a function f and the graph of its derivative. Five interaction categories between pairs of participants and the MAPLE were described. In addition, three levels of compatibilities between a priori participants' writings and the mentioned interactions were identified. The initial analysis suggests that the chosen approach is appropriate to the materialization of such understandings. The final analysis suggests that the conflicts that emerged from the experiments could have their roots in a limited understanding of the concept of function. The research also suggests a more intensive exploration of the dynamical nature of the differential calculus.
From the integration of orality, writing and the CAS-MAPLE, I investigated understandings that emerge about the concepts of function, limit, continuity and derivative produced by full-time first-year students of mathematics from a public university in the state of São Paulo, Brazil. The research, implemented under the guidelines of the interpretive paradigm and of the qualitative methodology, was characterized by experiments, which were conducted with eight volunteer participants. The data consisted of individual written answers in natural language and videotapes of the interactions between pairs of participants and the MAPLE. The initial analysis is on four episodes focusing on emerging conflicts on the concept of differentiability, the definition of derivative, the concept of limit, and the comparison between the graph of a function f and the graph of its derivative. Five interaction categories between pairs of participants and the MAPLE were described. In addition, three levels of compatibilities between a priori participants' writings and the mentioned interactions were identified. The initial analysis suggests that the chosen approach is appropriate to the materialization of such understandings. The final analysis suggests that the conflicts that emerged from the experiments could have their roots in a limited understanding of the concept of function. The research also suggests a more intensive exploration of the dynamical nature of the differential calculus.
Descrição
Palavras-chave
Cálculo, Escrita, Oralidade, Compreensão conceitual, Maple, Writing, Orality, Conceptual understanding, Calculus
Como citar
OLIMPIO JUNIOR, Antonio. Compreensões de conceitos de cálculo diferencial no primeiro ano de matemática: uma abordagem integrando oralidade, escrita e informática. 2006. 263 f. Tese (doutorado) - Universidade Estadual Paulista, Instituto de Geociências e Ciências Exatas, 2006.