An Analysis of Students' Mathematical Reasoning in Solving Geometry Problems in Terms of Spatial Ability at SMP Islam Klojen Lumajang

Abstract

Students' mathematical reasoning in solving geometry problems is significantly influenced by their spatial ability; however, an in-depth qualitative description of the relationship between these two variables remains scarce at the junior high school level. This study aims to describe the mathematical reasoning of junior high school students in solving flat-faced three-dimensional geometry problems, categorized by their spatial ability (high, moderate, and low). Employing a descriptive qualitative approach, the research involved eight ninth-grade students from SMP Islam Klojen Lumajang as subjects. Participants were selected using spatial ability and mathematical reasoning tests, followed by observations, in-depth interviews, and documentation. Data analysis was conducted through data reduction, data display, and conclusion drawing, with validity established via technique and source triangulation. The findings revealed a tiered pattern: students with low spatial ability exhibited mechanical-procedural reasoning; those with moderate ability demonstrated situational reasoning (proficient in concrete contexts but deficient in abstract problems); and students with high spatial ability displayed reflective and consistent reasoning across all indicators. In conclusion, a higher degree of spatial ability corresponds to a more mature mathematical reasoning profile. Consequently, geometry instruction should be hierarchically designed to accommodate students' varying levels of spatial ability.