Evoked Concept Images of the concept of Continuity of a Function
DOI:
10.23926/RPD.2025.v10.e25003.id1012Keywords:
Concept Image, Concept Definition, Continuity of a FunctionAbstract
The study described in this paper has the aim of presenting an analysis of Evoked Concept Images of college students about the concept of continuity of a function. A diagnostic study was developed with fifteen students in a mathematics course at a public university located in Belém (Pará). The students answered a group of tasks involving the concept of continuity of a function; Their answers were analyzed according to the assumptions of the Theory of Concept Image and Concept Definition (Vinner, 1991). It was verified that the concept image of the investigated students was based on the comprehension of continuity as connectivity, wholeness, fluidity, absence of jumps and/or holes in their graphic representations. Most students experienced cognitive conflict when attempting to understand the relationship between domain, limit, and continuity.
Downloads
Metrics
References
AMATANGELO, Miriam Lynne. Student understanding of limit and continuity at a point: a look at four potentially problematic conceptions. 2013. 112f. Dissertação (Mestrado em Artes), Bringham Young University (Utah/USA), 2013.
BRANDEMBERG, João Cláudio. ; MESSIAS, Maria Alice de Vasconcelos Feio. Imagem Conceitual e Definição Conceitual: uma reflexão sobre a aprendizagem de conceitos matemáticos. In: Francisco Regis Vieira Alves; Ana Carolina Costa Pereira. (Org.). Ciências e Matemática: investigações no ensino. 1ed.Curitiba: CRV, 2016, p. 15-28.
CINVESTAV, Fernando Hitt; LARA-CHAVEZ, Hector. Limits, continuity and discontinuity of functions from two points of view: that of the teachers and that of the students. In: BILLS, L (ED). Proceedings of the British Society for Research into Learning Mathematics, v. 19, p. 49 – 54, jun.1999.
CORNU, Bernard. Limits. In: Advanced Mathematical Thinking (ed. David Tall). Kluwer publications, 1991.
DENBEL, Dejene Girma. Students misconceptions of the limit concept in a first Calculus course. Journal of Education and Practice, v.5, nº34, 2014.
FREITAS, Wesley; JABBOUR, Charbel. Utilizando estudo de caso(s) como estratégia de pesquisa qualitativa: boas práticas e sugestões. ESTUDO & DEBATE, Lajeado, v. 18, n. 2, p. 7 – 22, 2011.
GIL, Antônio Carlos. Métodos e técnicas de pesquisa social. São Paulo: Atlas, 2008.
JAYAKODY, Gaya. University first year students’ discourse on continuous functions: A commognitive interpretation. 2015. 276f. Tese (Doutorado em filosofia) – Programa de Educação Matemática, Simon Fraser University, 2015.
JAYAKODY,Gaya; ZAZKIS, Rina. Continuous problem of function continuity. For the Learning of Mathematics, New Brunswick (Canada), v. 35, p. 8 – 14, março, 2015.
KARATAS et al. A cross-age study of students’ understanding of limit and continuity concepts. BOLEMA, Rio Claro (SP), v. 24, nº 38, p. 245 a 264, abril, 2011.
MESSIAS, Maria Alice de Vasconcelos Feio. Um estudo exploratório sobre a imagem conceitual de estudantes universitários acerca do conceito de limite de função. 2013. 133f. Dissertação (Mestrado em Educação em Ciências e Matemáticas) – Instituto de Educação Matemática e Científica, Universidade Federal do Pará, Belém, 2013.
MESSIAS, Maria Alice de Vasconcelos Feio. Teorias Cognitivas do Pensamento Matemático Avançado e o processo de construção do conhecimento: um estudo envolvendo os conceitos de limite e continuidade. 2018. 186f. Tese (Doutorado em Educação em Ciências e Matemáticas), Programa de Pós-Graduação em Educação em Ciências e Matemáticas, UFPA, 2018.
MESSIAS, Maria Alice de Vasconcelos Feio; BRANDEMBERG, João Cláudio. Discussões sobre a relação entre limite e continuidade de uma função: investigando imagens conceituais. BOLEMA, Rio Claro (SP), v. 29, n.53, p. 1224 – 1241, dez., 2015.
NÚÑEZ et al. Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, Netherlands, v. 39, p. 45 – 65, 1999.
PONTE, João Pedro Mendes da. Estudos de caso em educação matemática. BOLEMA, Rio Claro (SP), v. 19, n.25, p. 1 – 23, 2006.
STRAUSS, Anselm; CORBIN, Juliet. Pesquisa qualitativa: técnicas e procedimentos para o desenvolvimento de teoria fundamentada. Porto Alegre (RS): Artmed, 2008.
TALL, David; VINNER, Shlomo. Concept image and concept definition with particular reference to limits and continuity. Educational Studies in Mathematics, n. 12, 1981, p. 151 – 169.
VINNER, Shlomo. Continuous functions and reasoning in college students. In Bergeron, J. (ED) Proceedings of the international conference on the psychology of mathematics education (PME), 1987, vol. 1, pp. 177 – 183.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 A Revista Prática Docente tem o direito de primeira publicação
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Authors who publish in this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication, with the paper simultaneously licensed under the Licença Creative Commons Attribution allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
- Authors are authorized to take additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (e.g. publish in institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
