Organisation and Integration of Procedural and Conceptual Knowledge in Geometric Reasoning across the van Hiele Levels

Abstract

This study analyzes the distribution of procedural fluency and conceptual understanding across the five Van Hiele levels of geometric reasoning and examines their progression and interaction, focusing on the transition between lower and higher levels. Using a descriptive-analytical research design, this study systematically examined tasks aligned with the Van Hiele framework. Data were categorized into procedural fluency, conceptual understanding, or dual-skill requirements based on the properties of each level. Percentages for each skill type were calculated to identify patterns and progression across the levels. Procedural fluency dominated at Level 1, focusing on visual recognition and categorization, while conceptual understanding emerged at Level 2, with tasks emphasizing properties of shapes. Level 3 demonstrated significant integration of both skills, bridging procedural fluency and conceptual reasoning. Levels 4 and 5 relied entirely on conceptual reasoning, emphasizing abstraction and axiomatic comprehension. The findings underscore the developmental nature of geometric reasoning, highlighting transitional stages where skill integration is critical. This provides insights for enhancing instructional strategies in mathematics education. The study advocates for scaffolded instructional strategies, emphasizing dual-skill tasks at transitional levels. Incorporating dynamic tools like GeoGebra can foster alignment between procedural and conceptual understanding, enhancing students’ progression through the Van Hiele levels.