Understanding of the straight line from apos theory
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Keywords
Understanding, teaching, learning, APOS theory, linear equation
Abstract
This article reports on the research that aims to establish the mechanisms and mental structures necessary for the understanding of the notion of straight lines by students in the ninth grade of basic education. For this, in the phase of the theoretical analysis of the concept, a genetic decomposition was formulated that guided the teaching, the analysis and the results. According to the performance of the students in the cycle of activities, classes, exercises and in a designed questionnaire, comprehension is characterized as action, when the students calculate the equation of the straight algorithmically and do not infer information from it; as a process, when they represent the line in different registers, they model situations and infer information, and as an object when they establish and apply relationships between straights lines in problem situations. It is concluded that the APOE theoretical and methodological framework allows describing and explaining the understanding of the straights lines and provides tools to analyze, design, implement and evaluate didactic strategies.
References
Arnon, I., Cottrill, J., Dubinsky, E., Oktac, A., Roa Fuentes, S., Trigueros, M., & Weller, K. (2014). APOS Theory, A Framework for Research and Curriculum Development in Mathematics Education. New York: Springer Science.
Bisguerra, R., Dorio, I., Massot, I., & Sabariego, M. (2009). Características Generales de la Metodología Cualitativa. En Metodología de la investigación educativa. Madrid: La Muralla. S.A.
Campeón, M., Aldana, E., & Villa, J. (2018). Ingeniería didáctica para el aprendizaje de la función lineal mediante la modelación de situaciones. Sophia, 116-126.
Chang, C. (1968). Fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 24(1), 182-190.
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. En D. Tall, Advanced mathematical thinking (págs. 95-123). Dordrecht: Kluwer.
George, A., & Veeramani, P. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64, 395-399.
Gómez, N., Sánchez, D., & Sepúlveda, O. (2021). La comprensión del movimiento rectilinea através de las representaciones semióticas. Revista Boletín Redipe, 10(1), 195-204.
Kramosil, J., & Michalek, J. (1975). Fuzzy metric and statistical metric spaces. Kybernetika, 11, 621-633.
Piaget, J. (1985). The Equilibration of Cognitive Structures. (T. T. Brown, Trad.) Cambridge MA (original published 1975). Cambridge: Harvard University Press.
Rodríguez, E. L., & Valdivé, C. (2011). Análisis histórico de la función afín y la ecuación lineal en la economía desde el enfoque ontosemiótico. TEACS, 4(8), 17-29.
Torres, L., & Angulo , O. (2017). La articulación entre situaciones problema de proyectos productivos. Iberoamericana de educación Matemática, UNIÓN(50), 92-110.
Trigueros, M. (2005). La noción de esquema en la investigación en matemática educativa a nivel superior. Educación matemática, 17, 5-31.
Vanegas, D., & Escalona, M. (2010). Representaciones de funciones matemáticas de una variable. Omnia, 16(3), 101-122.
Villa, J. A., Bustamante, C., & Osorio, A. (2009). El proceso de modelación matemática. Una mirada a la práctica del docente. Comité Latinoamericano de Matemática Educativa-Colegio Mexicano de Matemática Educativa, 1443-1451.
Zadeh, L. (1965). Fuzzy sets. Information and Control, 338-353
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Diana Carolina Suárez Gil, Pedagogical and Technological University of Colombia, Colombia
Teacher, Graduate in Mathematics, Specialist in Mathematics Didactics, Master's student in Mathematics Education, Pedagogical and Technological University, Colombia.
Zagalo Enrique Suárez Aguilar, Pedagogical and Technological University of Colombia, Colombia
Research professor, Bachelor of Mathematics, Systems Engineer, Computer Specialist for teaching, Magister in Mathematical Sciences and Doctor of Educational Sciences, Pedagogical and Technological University of Colombia, Tunja, Colombia.
Omaida Sepúlveda Delgado, Universidad Pedagógica y Tecnológica de Colombia, Colombia
Research Professor, Graduate in Mathematics, Systems Engineer, Computer Specialist for Teaching, Magister in Mathematical Sciences and Doctor in Educational Sciences, Pedagogical and Technological University of Colombia, Tunja, Colombia.