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Abstract
The purpose of this paper is to show and validate a design for a deep understanding of the derivative from its local perspective. Based on a historical and epistemological study of the derivative, we performed an extension of the Sierpinska theoretical framework – Thinking Modes– of the domain of the derivative from its local perspective, and therefore identified three ways of thinking about the derivative, described as the Synthetic-Geometric-Convergent (SGC), Analytic-Operational (AO) and Analytic-Structural (AE, for its name in Spanish), as the components that, along with its articulators comprise a design for deep understanding of its local aspect. Methodologically, hypothetically proposed articulators are compared to data obtained in case studies with two groups of university students, in addition to a semi-structured interview to mathematicians, researchers and scholars, through which the proposed articulators elements were validated and clarified. The result is a design for the understanding of the derivative from its local aspect as a viable tool to cause the rupture from a purely algebraic thinking about this topic, and that benefits its deep understanding, being this, the ability of a student to articulate these thinking modes.
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Article Type: Research Article
INT ELECT J MATH ED, Volume 12, Issue 3, October 2017, 873-898
https://doi.org/10.29333/iejme/654
Publication date: 28 Dec 2017
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Article Downloads: 2401
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