Students’ Proportional Reasoning in Solving Geometry Problems: A Qualitative Analysis Based on Van Hiele Levels
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Abstract
Purpose - Proportional reasoning is a fundamental component of mathematical thinking and plays an important role in students’ understanding of geometry. However, empirical evidence remains limited on how students’ proportional reasoning develops qualitatively across different levels of geometric thinking. This study aims to explore students’ proportional reasoning in solving geometry problems through the lens of Van Hiele’s theory.
Methodology - This study employed a qualitative descriptive design with undergraduate students. Data were collected from written responses to geometry tasks involving proportional relationships. The analysis used an integrated framework combining Van Hiele levels of geometric thinking and indicators of proportional reasoning, including multiplicative relationships, coordination of quantities, ratios, and logical justification.
Findings - The findings show a progressive development of proportional reasoning across Van Hiele levels, from perceptual and additive reasoning to coordinated multiplicative reasoning and formal proportional justification. However, persistent difficulties, such as additive bias and fixed-number reasoning, were observed across levels, indicating ongoing challenges in developing consistent proportional reasoning.
Novelty - This study conceptualises proportional reasoning as a developmental cognitive process shaped by levels of geometric thinking through an integrated analytical framework.
Significance - The findings are useful for educators, curriculum developers, and researchers in designing instruction that supports students’ proportional reasoning through level-appropriate, justification-focused activities.
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References
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