The training of mathematics teachers in universities in Colombia has as a transversal axis the
resolution of problems based on their social and cognitive mission pillars. In this sense, this study
relates to the re-signification and construction of the concept of definite integral (DI) (integral
calculus) through socio-epistemological studies, action researches, and the typology of didactic
situations. The results are obtained through content analysis, didactic sequences (GeoGebra), and
a discussion group. The above allows us to conclude that the validation of meanings, historical
contexts, and associated social practices leads to the construction of the concept of DI as a model
of mathematical analysis. This structuring of knowledge from its epistemological framework
enables the exploration of mathematical objects from the basic notions that emerge in the history
of humanity and didactic processes that reconstruct the evolution of the concept in society.
REFERENCES(19)
1.
Aldana, E. (2011). Comprensión del concepto de integral definida en el marco de la teoría APOE [Understanding of the concept of definite integral within the framework of APOE theory] [Doctoral dissertation, Universidad de Salamanca].
Aldana, E., González, M. T., & López-Leyton, C. (2020). El desarrollo del esquema de integral definida [The development of the definite integral scheme]. Revista Espacios, 41(2), Article 4.
Azcárate Gimenez, C., & Camacho-Machín, M. (2003). Sobre la investigación en didáctica del análisis matemático [On research in the didactics of mathematical analysis]. Bolet´ın de la Asociaci´ on Matematica Venezolana, X(2), 135-149.
Cantoral, R. (2013). Teoría socioepistemológica de la matemática educativa. Estudios sobre construcción social del conocimiento [Socio-epistemological theory of educational mathematics. Studies on social construction of knowledge] (2nd ed.). Editorial Gedisa SA.
Cantoral, R., Reyes-Gasperini, D., & Montiel, G. (2014). Socioepistemología, matemáticas y realidad [Socioepistemology, mathematics and reality]. Revista Latinoamericana de Etnomatemática, 7(3), 91-116.
Chevallard, Y. (1991). La transposición didáctica: Del saber sabio al saber enseñado [The didactic transposition: From knowledge to taught knowledge]. Aique.
Godino, J., Batanero, C., Rivas, E., & Arteaga, P. (2013). Componentes e indicadores de idoneidad de programas de formación de profesores en didáctica de las matemáticas [Components and indicators of suitability of teacher training programs in mathematics education]. Revista Electrónica de Educación Matemática, 8(1), 46-74. https://doi.org/10.5007/1981-1....
Gómez, B. (2005). Aprendizaje basado en problemas (ABP): Una innovación didáctica para la enseñanza universitaria [Problem-based learning (PBL): A didactic innovation for university teaching]. Educación y Educadores, (8), 9-20.
Gray, E., & Tall, D. (1994). Duality, ambiguity, and flexibility: A “proceptual” view of simple arithmetic. Journal for research in Mathematics Education, 25(2), 116-140. https://doi.org/10.5951/jresem....
Jiménez, R., & Cerón, J. M. (1992). Paradigmas de investigación en educación. Hacia una concepción crítico-constructiva [Paradigms of research in education. Towards a critical-constructive conception]. Tavira: Revista de Ciencias de la Educación, 9, 105-128.
Latorre, A. (2007). La investigación- acción. Conocer y cambiar la práctica educativa educativa [Action research. Knowing and changing educational practice]. Grao.
López-Leyton, C., Aldana, E., & Erazo, J. (2018). Concepciones de los profesores sobre la resolución de problemas en cálculo diferencial e integral [Teachers’ conceptions of problem solving in differential and integral calculus]. Revista Logos Ciencia & Tecnología, 10(1), 145-157. https://doi.org/10.22335/rlct.....
López-Leyton, C., Aldana, E., & Erazo, J. (2019). El papel de la resolución de problemas para la enseñanza del cálculo integral [The role of problem solving for the teaching of integral calculus]. Revista Espacios, 40(17), Article 12.
Serrano, R. (2010). Pensamientos del profesor: Un acercamiento a las creencias y concepciones sobre el proceso de enseñanza-aprendizaje en la educación superior [Teacher’s thoughts: An approach to beliefs and conceptions about the teaching-learning process in higher education]. Revista de Educación, 352, 267-287.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36. https://doi.org/10.1007/BF0030....
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169. https://doi.org/10.1007/BF0030....
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