Students’ instrumental understanding in solving spatial mathematical problems across levels of mathematical ability

Abstract

This study explores students’ instrumental understanding of spatial geometry problems, accounting for differences in initial mathematical ability. Many students tend to solve geometry problems procedurally without sufficient conceptual understanding, while research that examines explicitly instrumental understanding in spatial contexts remains limited. A qualitative case study design was employed involving 25 eighth-grade students from a public junior high school in Pagar Alam City, South Sumatra. Data were collected through written tests and in-depth interviews with six students representing high, medium, and low levels of mathematical ability. The analysis was guided by four indicators of instrumental understanding: recalling concepts, identifying concepts, selecting appropriate solution strategies, and representing concepts visually and in written form. The findings indicate apparent differences across ability levels. Students with high initial mathematical ability consistently fulfilled all four indicators across various spatial geometry problems. In contrast, students with medium and low ability demonstrated partial fulfilment of the indicators, particularly in topics such as cylinder volume and triangular prisms. These results suggest that students’ initial mathematical ability plays a crucial role in the development of instrumental understanding. Therefore, differentiated instructional strategies aligned with students' ability levels are recommended to support balanced procedural and conceptual learning in spatial geometry.