Piagetian Abstraction Processes of a Field Independent Male Student in Reconstructing the Cuboid Concept

Abstract

This study aims to describe how a masculine junior high school boy with a field independent cognitive style abstracts step by step the concept of a cuboid while reconstructing it. The research adopted a qualitative descriptive approach focused on a single Grade IX student, coded AF, who met two criteria: a high score on the Group Embedded Figures Test indicating field independence and a masculine profile on the Bem Sex Role Inventory. Data were gathered through task based interviews and direct observation as AF classified concrete objects, interpreted two dimensional drawings, and attempted to create a formal definition of a cuboid. All sessions were recorded, transcribed, and processed through the phases of reduction, display, and conclusion drawing in order to align each episode with Piaget’s sequence of empirical, semi empirical, and reflective abstraction. Analysis revealed a clear three step progression. In the empirical phase AF decided whether a solid was a cuboid by listing six rectangular faces, twelve edges, and eight vertices, presenting these facts as separate items without explaining relationships among them. During the semi empirical phase, accuracy improved when he handled drawings: he corrected earlier edge counts, insisted on rectangular faces, and dismissed colour and scale as irrelevant. Reflective abstraction emerged when he produced a concise definition, identified the cube as a special cuboid, supplied a numerical example measuring ten by five by five centimetres, and linked the concept to familiar objects such as cardboard boxes and cupboards. Throughout the sessions his field independent style marked by selective attention, systematic counting, and self monitoring helped him move quickly from perceptual sorting to conceptual reasoning. The study offers detailed evidence that field independence supports smooth movement through Piaget’s abstraction hierarchy by enabling learners to impose internal structure on external stimuli. It strengthens the theoretical claim that mathematical understanding grows gradually from concrete observation toward formal reasoning and provides practical insight for geometry teaching: tasks that highlight structural invariants can capitalise on analytic strengths in field independent students while also serving as scaffolds for peers who depend more heavily on contextual cues.