文章基本信息

标题：Characterizing Levels of Reasoning in Graph Theory
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作者：Antonio González ; Inés Gallego-Sánchez ; José María Gavilán-Izquierdo 等
期刊名称：Eurasia Journal of Mathematics, Science & Technology Education
印刷版ISSN：1305-8223
电子版ISSN：1305-8223
出版年度：2021
卷号：17
期号：8
页码：em1990
DOI：10.29333/ejmste/11020
出版社：Pamukkale Univ Dept Sci Education
摘要：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.
其他关键词：levels of reasoning, van Hiele model, processes of reasoning, graph theory