Resumen

VALDIVIA SEPULVEDA, Cristóbal  y  PARRAGUEZ GONZALEZ, Marcela. A model for understanding the chain rule. Paradígma [online]. 2015, vol.36, n.2, pp.146-176. ISSN 1011-2251.

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".

Palabras clave : Genetic decomposition; Chain Rule; APOS Theory; Schema levels.

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