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<p>This study examines how undergraduate Computer Engineering students at a large Spanish university use and formulate definitions in graph theory. The primary objective is to empirically identify indicators of students’ definition levels in graph theory through the Van Hiele model for graph theory, developed through a theoretical analysis in previous works. Data were collected using a questionnaire comprising five tasks designed to evaluate students’ mastery in using and formulating definitions. Responses were analyzed with an adapted methodology to compute degrees of acquisition of Van Hiele levels, resulting in distinct definition profiles among the students. Our findings give empirical support to the descriptors of the Van Hiele definition levels in graph theory proposed in prior research and align with the essential characteristics of the Van Hiele model: language specificity, hierarchy and sequence, and continuity. Hence, the results&#xa0;showcase the applicability and analytical capacity of the Van Hiele&#xa0;model in the&#xa0;context of graph theory. Notably, 92% of our sample were unable to handle definitions involving complex logical relationships or construct definitions based on necessary and sufficient conditions, which are critical skills for university-level graph theory tasks. These results highlight the importance of addressing students’ definition levels when designing instruction. By refining the understanding of these levels, this study contributes to the broader goal of enhancing pedagogical strategies for teaching graph theory effectively.</p>

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Assessing Graph Theory Students’ Use and Formulation of Definitions through the Van Hiele Model

  • 期刊论文

  • 发表日期：

    2025年2月15日

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

摘要

This study examines how undergraduate Computer Engineering students at a large Spanish university use and formulate definitions in graph theory. The primary objective is to empirically identify indicators of students’ definition levels in graph theory through the Van Hiele model for graph theory, developed through a theoretical analysis in previous works. Data were collected using a questionnaire comprising five tasks designed to evaluate students’ mastery in using and formulating definitions. Responses were analyzed with an adapted methodology to compute degrees of acquisition of Van Hiele levels, resulting in distinct definition profiles among the students. Our findings give empirical support to the descriptors of the Van Hiele definition levels in graph theory proposed in prior research and align with the essential characteristics of the Van Hiele model: language specificity, hierarchy and sequence, and continuity. Hence, the results showcase the applicability and analytical capacity of the Van Hiele model in the context of graph theory. Notably, 92% of our sample were unable to handle definitions involving complex logical relationships or construct definitions based on necessary and sufficient conditions, which are critical skills for university-level graph theory tasks. These results highlight the importance of addressing students’ definition levels when designing instruction. By refining the understanding of these levels, this study contributes to the broader goal of enhancing pedagogical strategies for teaching graph theory effectively.