Abstract

SALINAS, Patricia Rojas  and  TRIGUEROS GAISMAN, María. El Esquema del Cálculo Diferencial e Integral para ser enseñado en simultáneo. Rev. electrón. investig. educ. cienc. [online]. 2020, vol.15, n.2, pp.12-26. ISSN 1850-6666.

A solution to the problem of learning and teaching of Differential and Integral Calculus at the university level is presented, introducing, from the beginning, an emphasis on the relationship between the fundamental concepts of this discipline; the derivative and the integral. It starts from a cognitive look that allows generating a Genetic Decomposition (DG) in pursuit of the construction of a Scheme that describes relationships between concepts, to be used as a model for the construction of Differential and Integral Calculus (CDI) from a perspective that intends to work these two mathematical objects simultaneously. From the APOE theory (acronym for: Actions, Processes, Objects and Schemes), we appreciate how students show evidence of the theory's structures as they learn, and with it of the reflexive abstraction mechanisms, which reveals the construction of their own scheme. The didactic proposal is evaluated, through an exploratory study, in a course consisting of 17 students, during a semester. At the end of the course, an interview was applied providing the characterization of each student, the type of relationship exhibited through the analysis based on each of the levels of the Scheme and indicating if the students are at an Intra-CDI, Inter- CDI or Trans-CDI as appropriate.

Keywords : Scheme; Calculus; Derivative; Integral; APOE Theory.

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