A tricotomização entre aritmética, álgebra e geometria nos erros apresentados por estudantes da disciplina de cálculo diferencial integral I

• Autor(a) principal: Dalmolin, Beatriz Alves da Silva
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Universitário da Ânima (RUNA)
• Texto Completo: https://repositorio.animaeducacao.com.br/handle/ANIMA/3489
• topic: Tricotomia entre aritmética, geometria e álgebra; erros; Cálculo Diferencial e Integral I; Teoria Histórico-Cultural

The objective of this present study is to analyze the nature of the errors made by students of the discipline of Differential and Integral Calculus I, in two engineering courses. Data analysis is based on the principles of historical-cultural theory, with focus to the work of Davýdov, whose epistemology is in Dialectical Materialism History, considered as a study method. We developed the following actions: Study of the assumptions of historical-cultural theory to the teaching of mathematics; Analysis of errors presented by the students in the discipline of Differential and Integral Calculus I; Categorization and analysis of the nature of the errors found on the grounds of the Historic-Cultural Theory; Reflection on content and teaching methods that make it possible to overcome the errors detected. The methodology used in this research is a qualitative approach, the study type of case, which had as data collection context a private college network in southern state of Santa Catarina. The research was carried out in a class of Differential and Integral Calculus I students in two engineering courses. The research collaborators are seven students, who were followed individually by the researcher. During data collection, written records, photographs and audio recordings of conversations of the students with the teacher or with the researcher were made and the mistakes were photographed. The organization of data was performed using the following analysis unit: Trichotomy between arithmetic, geometry and algebra. After data analysis, we present the contributions of historical-cultural theory with a view to understanding the errors detected. At this stage of research, we concluded that the nature of the errors made by students of the discipline of Differential and Integral Calculus I is related to the trichotomy of the mentioned areas. We see as a possibility for overcoming the Davýdov proposal which provides for an interconnection of such mathematical meanings, from the first school year, with the study of quantities.