Email this article Exploring Students’ Spatial Ability in Geometry Transformations Based on Cognitive Styles through the APOS Framework
This study aims to analyze the spatial ability of Field Independent (FI) and Field Dependent (FD) students in two-dimensional geometric transformation tasks across three aspects: spatial visualization, mental rotation, and spatial orientation. It also examines students’ cognitive development through APOS stages and identifies thinking patterns across these aspects. This qualitative case study involved six ninth-grade students from a public junior high school in Bandung, Indonesia. Participants were purposively selected based on their Group Embedded Figures Test (GEFT) scores, comprising three FI and three FD students. Data were collected through a spatial ability test and semi-structured interviews. Written responses and interview transcripts were analyzed using APOS-based coding criteria, supported by triangulation between written and verbal data. Students’ spatial ability varied across cognitive styles, spatial aspects, and APOS stages. FI students generally showed higher and more varied achievement than FD students, particularly in spatial visualization. However, this pattern was not entirely consistent, as one FI student did not demonstrate sufficient evidence to be classified at the Action stage, which is the most basic stage in the APOS framework, across all aspects. Mental rotation and spatial orientation were more difficult than spatial visualization; only one FI student met the criteria for each indicator. FD students achieved mainly in spatial visualization, with two students reaching the Schema stage when visual and coordinate-based support was available. However, all FD students failed to achieve the indicators for mental rotation and spatial orientation, and mostly remained at the Action stage. This study indicates that spatial ability in geometric transformations is influenced not only by cognitive style but also by task demands, visual support, and prerequisite understanding. Geometry instruction should provide structured visual support and gradual transitions toward independent mental manipulation, particularly in rotation and orientation tasks.
Keywords: spatial ability, cognitive style, field independent, field dependent, geometry transformation, APOS theory.
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