Title: Using a dynamic geometry system to integrate analytic and synthetic knowledge in the solution of geometry problems

Authors: Carolina Guerrero-Ortiz; Aaron Reyes-Rodríguez; Hugo Espinosa-Pérez

Addresses: Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Blanco Viel, 596, Valparaíso, Chile ' Área Académica de Matemáticas y Física, Universidad Autónoma del Estado de Hidalgo, Carretera Pachuca – Tulancingo, km 4.5, Hidalgo, México ' Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Av. Inst. Pol. Nac., 2508, Delegación Gustavo A. Madero, Col. San Pedro Zacatenco, Ciudad de México, DF, México

Abstract: In this study, we documented how the systematic use of a dynamic geometry system (DGS) during problem solving became a means of integrating synthetic and analytic concepts of geometric knowledge. We analysed solution paths for tasks of geometric construction, developed by participants of a problem-solving seminar during two sessions and identified the limitations of purely analytic approaches and the advantages of integrating synthetic and analytic techniques. The results indicate that solving problems with the support offered by a DGS increases the opportunities that problem solvers have to interpret algebraic procedures from a geometric perspective and to construct meaning of mathematical concepts.

Keywords: problem solving; understanding; connections; dynamic geometry systems; DGS; dynamic analytic knowledge; synthetic knowledge; geometry problems; algebraic procedures; mathematical concepts.

DOI: 10.1504/IJLT.2016.079033

International Journal of Learning Technology, 2016 Vol.11 No.3, pp.179 - 197

Published online: 09 Sep 2016 *

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