Understanding the concept of continuity within the framework of Pirie and Kieren’s theory

Authors

  • Rodrigo Antonio Rendón Ramírez University of Antioquia
  • René Alejandro Londoño Cano University of Antioquia

DOI:

https://doi.org/10.17533/udea.unipluri.18631

Keywords:

socratic interview, descriptors, function, understanding, limit, infinitesimal

Abstract

Our objective was to design and implement a semi-structured interview of Socratic nature to describe how the concept of continuity is understood by four students of differential calculus courses in secondary and higher education institutions in the city of Medellín. It was a qualitative type of research including a case study in order to achieve the objective; the Socratic semi-structured interview was strategy to improve the students’ understanding, in accordance with the framework of Pirie and Kieren’s theory, which served as a theoretical support.

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Author Biographies

Rodrigo Antonio Rendón Ramírez, University of Antioquia

Professor at the University of Antioquia. Full-time professor of the Municipality of Medellín.Master in Education from the University of Antioquia. Specialist in Advanced Mathematics at the National University of Colombia, Medellín. Graduate in Mathematics and Physics from the University of Antioquia.

René Alejandro Londoño Cano, University of Antioquia

Master and Doctor in Education, Mathematics Education area of the University of Antioquia.

References

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Jurado, Flor María y Londoño Caro, René Alejandro (2005). Diseño de una entrevista socrática para el concepto de suma de una serie, vía áreas de figuras planas. Tesis de maestría no publicada. Medellín: Universidad de Antioquia.

Meel, David E. (2003). «Modelos y teorías de la comprensión matemática: comparación de los modelos de Pirie y Kieren sobre el crecimiento de la comprensión matemática y la Teoría APoe». En: RELI-ME. Revista Latinoamenricana de Investigación en Matemática Educativa, Vol. 6, N.o 3, pp. 221-278. México: Comité Latinoamericano de Matemática Educativa (CLAME).

Ministerio de Educación Nacional (MEN)(1998). Lineamientos Curriculares. Matemáticas. Bogotá, Colombia. Fecha de consulta: noviembre 21 de 2009 Cf. http://www.mineducacion.gov.co/cvn/1665/article-89869.html

Pirie, Susana y kieren, Thomas (1994). «Growth in mathematical understanding: How can we characterise it and how can we represent it?» En: Educational Studies in Mathematics, Vol. 26, N.os 2-3, pp. 165-190. Holanda: Kluwer Academic Publishers.

Tall, David (1991). «The psychology of advanced mathematical thinking». En: Tall, David (Ed.). Advanced Mathematical Thinking, pp. 3-21. Dordrecht: Springer.

Giasersfeld, Ernst Von (1987). The Construction of knowledge. Contributions of conceptual semantics. Seaside: Intersystems Publications.

Published

2014-02-25

How to Cite

Rendón Ramírez, R. A., & Londoño Cano, R. A. (2014). Understanding the concept of continuity within the framework of Pirie and Kieren’s theory. Uni-Pluriversidad, 13(3), 109–118. https://doi.org/10.17533/udea.unipluri.18631

Issue

Section

RESEARCH REPORTS AND UNPUBLISHED ESSAYS

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