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RESEARCH PAPER
Characterizing Levels of Reasoning in Graph Theory
1
Department of Didactics of Mathematics, Universidad de Sevilla, SPAIN
2
Department of Mathematics, Universidad de Almería, SPAIN
Publication date: 2021-06-24
EURASIA J. Math., Sci Tech. Ed 2021;17(8):em1990
KEYWORDS
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.
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