Navegando por Assunto "Imagem conceitual"

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Discussões sobre a Relação entre Limite e Continuidade de uma Função: investigando Imagens Conceituais
(Universidade Federal do Pará, 2015-12) MESSIAS, Maria Alice de Vasconcelos Feio; QUARESMA, João Cláudio Brandemberg
This paper presents the results of an investigation that was made with university students enrolled in the 3rd and 4 th semester of graduation in mathematics at two public universities in the state of Pará (Brazil). We aimed to investigate the concept image of these subjects about the relation between limit and continuity of a function, through an exploratory study done in two stages. The results were related to the researches of Tall and Vinner (1981), Vinner (1991) that composed our theoretical framework. Among the evoked concept images, we emphasize the idea that when a function is not defined in one point of the domain implies, necessarily, in the non-existence of the limit of that function in that point. That is, according to them, the limit’s existence depends on the continuity of the function.
Desconhecido
Um estudo exploratório sobre a imagem conceitual de estudantes universitários acerca do conceito de limite de função
(Universidade Federal do Pará, 2013-02-28) MESSIAS, Maria Alice de Vasconcelos Feio; BRANDEMBERG, João Cláudio; http://lattes.cnpq.br/3873561463033176
This is an exploratory research that aimed to investigate the elements that compose university students’ concept image related to the concept of limit of a function of one real variable. It was investigated the knowledge of 25 students of mathematics’ course in two public universities in the state of Pará (Brazil). The data collection was made, at first, through a questionnaire that contained tasks involving limit of one real variable function’s conceptual aspects. The second stage consisted in interviews with six students that were selected because of their evoked concept images in the previous stage, since they were related to the four Discussion Themes (DT) that leaded those interviews. The data analysis was based on the theory of Tall&Vinner (1981) and Vinner (1991), besides the studies of Cottril et al (1996), Jordaan (2005), Juter (2006), Nair (2009), above others, which composed the theoretical framework of this study. Above the results obtained in this research, we emphasize that the students relate the concept of limit of a function of one real variable with static and/or dynamic interpretations that, in some moments, constituted themselves as potential conflict factors, such as described by Vinner (1991). Besides, we’ve also noticed that some evoked concept images weren’t coherent, which influenced them to construct a personal concept definition different from the formal concept definition of limit of a function of one real variable.
Desconhecido
Teorias cognitivas do Pensamento Matemático Avançado e o processo de construção do conhecimento: um estudo envolvendo os conceitos de limite e continuidade
(Universidade Federal do Pará, 2018-12-18) MESSIAS, Maria Alice De Vasconcelos Feio; BRANDEMBERG, João Cláudio; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550
The aim of this thesis was to conjecture about which mental structures and mechanisms need to be built by an individual in order to lead one to comprehend the concepts of limit and continuity of a function. For that, the research was organized in two stages. In the first stage, based on the theory of concept image and concept definition (VINNER, 1991), a preliminary study was developed, by which it was possible to analyze the elements that composed the concept image of mathematics students about such concepts. In the second stage, it was presented a genetic decomposition to limit and continuity, having as reference these mathematical objects, their historical-conceptual development, teaching experiences in the field of Calculus, multiple representations of such concepts and, specially, some assumptions of the APOS theory (DUBINSKY et al., 1984; ARNOON et al., 2014). As principle results, it was observed that various comprehensions about limit and continuity were evoked in the first stage, which led to reflections about the parts of the genetic decomposition that was elaborated from different mathematical objects, such as function, limit‟s definition, relation, relation between lateral and bilateral limits, limit properties, limits involving infinity, continuity at a point and along an interval, among others.