International Electronic Journal of Mathematics Education

Articulators for Thinking Modes of the Derivative from a Local Perspective
  • Article Type: Research Article
  • International Electronic Journal of Mathematics Education, 2017 - Volume 12 Issue 3, pp. 873-898
  • Published Online: 28 Dec 2017
  • Article Views: 434 | Article Download: 327
  • Open Access Full Text (PDF)
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Pinto-Rojas IE, Parraguez M. Articulators for Thinking Modes of the Derivative from a Local Perspective. Int Elect J Math Ed. 2017;12(3), 873-898.
APA 6th edition
In-text citation: (Pinto-Rojas & Parraguez, 2017)
Reference: Pinto-Rojas, I. E., & Parraguez, M. (2017). Articulators for Thinking Modes of the Derivative from a Local Perspective. International Electronic Journal of Mathematics Education, 12(3), 873-898.
Chicago
In-text citation: (Pinto-Rojas and Parraguez, 2017)
Reference: Pinto-Rojas, Irma Ercira, and Marcela Parraguez. "Articulators for Thinking Modes of the Derivative from a Local Perspective". International Electronic Journal of Mathematics Education 2017 12 no. 3 (2017): 873-898.
Harvard
In-text citation: (Pinto-Rojas and Parraguez, 2017)
Reference: Pinto-Rojas, I. E., and Parraguez, M. (2017). Articulators for Thinking Modes of the Derivative from a Local Perspective. International Electronic Journal of Mathematics Education, 12(3), pp. 873-898.
MLA
In-text citation: (Pinto-Rojas and Parraguez, 2017)
Reference: Pinto-Rojas, Irma Ercira et al. "Articulators for Thinking Modes of the Derivative from a Local Perspective". International Electronic Journal of Mathematics Education, vol. 12, no. 3, 2017, pp. 873-898.
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Pinto-Rojas IE, Parraguez M. Articulators for Thinking Modes of the Derivative from a Local Perspective. Int Elect J Math Ed. 2017;12(3):873-98.

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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