Characterizing Levels of Reasoning in Graph Theory

Antonio González; Inés Gallego-Sánchez; José María Gavilán-Izquierdo; María Luz Puertas

doi:10.29333/ejmste/11020

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Antonio González ¹ ^* , Inés Gallego-Sánchez ¹ , José María Gavilán-Izquierdo ¹ , María Luz Puertas ²

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¹ Department of Didactics of Mathematics, Universidad de Sevilla, SPAIN² Department of Mathematics, Universidad de Almería, SPAIN^* Corresponding Author

Abstract

This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We thus obtain four levels of reasoning: an initial level of visual character in which students perceive graphs as a whole; a second level, analytical in nature in which students distinguish parts and properties of graphs; a pre-formal level in which students can interrelate properties; and a formal level in which graphs are handled as abstract mathematical objects. Our results, which are supported by a review of the literature on the teaching and learning of graph theory, might be very helpful to design efficient data collection instruments for empirical studies aiming to analyze students’ thinking in this field of mathematics.

Keywords

levels of reasoning
van Hiele model
processes of reasoning
graph theory

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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

EURASIA J Math Sci Tech Ed, Volume 17, Issue 8, August 2021, Article No: em1990

https://doi.org/10.29333/ejmste/11020

Publication date: 24 Jun 2021

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

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How to cite this article

APA

González, A., Gallego-Sánchez, I., Gavilán-Izquierdo, J. M., & Puertas, M. L. (2021). Characterizing Levels of Reasoning in Graph Theory. Eurasia Journal of Mathematics, Science and Technology Education, 17(8), em1990. https://doi.org/10.29333/ejmste/11020

Vancouver

González A, Gallego-Sánchez I, Gavilán-Izquierdo JM, Puertas ML. Characterizing Levels of Reasoning in Graph Theory. EURASIA J Math Sci Tech Ed. 2021;17(8):em1990. https://doi.org/10.29333/ejmste/11020

AMA

González A, Gallego-Sánchez I, Gavilán-Izquierdo JM, Puertas ML. Characterizing Levels of Reasoning in Graph Theory. EURASIA J Math Sci Tech Ed. 2021;17(8), em1990. https://doi.org/10.29333/ejmste/11020

Chicago

González, Antonio, Inés Gallego-Sánchez, José María Gavilán-Izquierdo, and María Luz Puertas. "Characterizing Levels of Reasoning in Graph Theory". Eurasia Journal of Mathematics, Science and Technology Education 2021 17 no. 8 (2021): em1990. https://doi.org/10.29333/ejmste/11020

Harvard

González, A., Gallego-Sánchez, I., Gavilán-Izquierdo, J. M., and Puertas, M. L. (2021). Characterizing Levels of Reasoning in Graph Theory. Eurasia Journal of Mathematics, Science and Technology Education, 17(8), em1990. https://doi.org/10.29333/ejmste/11020

MLA

González, Antonio et al. "Characterizing Levels of Reasoning in Graph Theory". Eurasia Journal of Mathematics, Science and Technology Education, vol. 17, no. 8, 2021, em1990. https://doi.org/10.29333/ejmste/11020