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      Un modelo cognitivo para la comprensión profunda de la regla de la cadena Translated title: A model for understanding the chain rule

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          Abstract

          Se propone un modelo, denominado Descomposición Genética (DG), para el aprendizaje del concepto Regla de la Cadena, el cual indaga en la manera como los estudiantes pueden construir, mentalmente, la derivada de la composición de funciones. La investigación se sustenta en la teoría APOE (Acción, Proceso, Objeto y Esquema) (Dubinsky, 1991) como marco teórico y metodológico. La estructura general del estudio pasa por tres etapas, primero se realizó un análisis teórico del concepto en estudio, que permitió elaborar la DG (hipotética). Luego, se diseñó y aplicó (a once estudiantes de una universidad chilena) un cuestionario y una entrevista semiestructurada. En la tercera etapa se analizaron los datos a la luz de la DG. Estas fases permitieron dejar en evidencia las estructuras necesarias para la construcción del esquema Regla de la Cadena, y las características que conforman su evolución a través de la tríada de Piaget y García (1989): Intra, Inter y Trans. Un resultado relevante es que los conceptos de función y composición de funciones quedan separados de la Regla de la Cadena misma, mediante un algoritmo que absorbe dicha regla y que hemos llamado "de afuera hacia adentro"

          Translated abstract

          Our proposal is related to a model called Genetic Decomposition (GD). This is considered to be viable for the learning process of the concept "Chain Rule", which looks for the way in which students can mentally build the derivative of the composite function. The research is sustained, in its theoretical and methodological framework, by the theory of APOS (action, process, object, and schema) (Dubinsky, 1991). The overall structure of the research is divided into three stages: In the first place, a theoretical analysis, of the concept in question, to allow the GD to be developed (hypothetically). Secondly, a questionnaire was designed to be used in a semi-structured interview of eleven (11) Chilean university students. In the third and final stage, the data was analyzed in the light of the GD. The result of these steps showed the necessary structures for the construction of the Chain Rule, as well as a description of the characteristics that make use of the triad mechanism of the Schema theory (Piaget and Garcia, 1989): Intra, Inter y Trans. A meaningful result is that the concepts of function and the function composition remain separate from the chain rule in itself, using an algorithm that absorbs the selfsame rule and which we have named "outside/inside method".

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          Investigación con estudio de casos

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            La noción de esquema en la investigación en matemática educativa a nivel superior

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              Advanced mathematical thinking

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                Author and article information

                Contributors
                Role: ND
                Role: ND
                Journal
                pdg
                Paradígma
                Paradígma
                Universidad Pedagogica Experimental Libertador
                1011-2251
                December 2015
                : 36
                : 2
                : 146-176
                Affiliations
                [1 ] Universidad Austral de Chile
                Article
                S1011-22512015000200008
                00106526-8b10-45d9-94ec-6c4fc8f8e5cf

                http://creativecommons.org/licenses/by/4.0/

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                Product

                SciELO Venezuela

                Self URI (journal page): http://www.scielo.org.ve/scielo.php?script=sci_serial&pid=1011-2251&lng=en
                Categories
                EDUCATION & EDUCATIONAL RESEARCH

                Educational research & Statistics
                Descomposición genética,Regla de la Cadena,Teoría APOE,niveles de Esquema,Genetic decomposition,Chain Rule,APOS Theory,Schema levels

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