Geometrical Abstraction on VAN Hiele Levels Among Mathematics Undergraduates

Abstract

This research aims to analyze the geometrical abstraction on van Hiele levels among Mathematics Undergraduates at The State University of Makassar by utilizing an explanatory sequential mixed methods approach. Research subjects are selected by using a purposive sampling method from each van Hiele level to analyze their geometrical abstractions through geometrical abstraction tests and interviews. Data analysis includes: 1) statistical analysis, 2) qualitative data collection, 3) thematic analysis, 4) result interpretation, and 5) source triangulation. NVivo 12 software assists in coding qualitative data. Results indicate 27.7% of undergraduates are at the visualization level, 37.2% at the analysis level, 14.1% at the informal deduction level, 1.0% at the formal deduction level, and 2.6% at the rigor level. On the visualization level, abstraction involves understanding geometry concepts contextually. On the analysis level, it involves using concepts in complex contexts. On the informal deduction level, students connect geometry concepts, while on the formal deduction level, they deepen understanding through mathematical concepts. Furthermore, on the rigor level, students construct and connect various mathematical concepts broadly. This study also found higher van Hiele levels lead to more comprehensive geometrical abstraction. Future studies are recommended to explore the relationship between van Hiele levels and geometrical abstraction.