Characterizing Levels of Reasoning in Graph Theory
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, SPAIN
2 Department of Mathematics, Universidad de Almería, SPAIN
* Corresponding Author


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.


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Article Type: Research Article

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

Publication date: 24 Jun 2021

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