Middle School Students’ Geometric Reasoning About the Right Circular Cylinder

This study investigates eighth-grade students’ geometric reasoning regarding right circular cylinders, focusing on the interaction between figural and conceptual components within Fischbein’s Figural Concept Theory. Twenty-five students from public middle schools participated in a case study using the Reasoning Assessment Instrument (RAI) and semi-structured interviews. The RAI included tasks on recognizing, defining, and constructing cylinder developments, while interviews provided deeper insights into students’ reasoning processes. Qualitative analysis revealed that geometric reasoning was predominantly figural. Sixteen students (64%) were figure-dominant, relying primarily on visual cues rather than conceptual properties, while only four students (16%) demonstrated potentially harmonic reasoning, integrating figural images with conceptual understanding. Five students (20%) provided insufficient data for classification. None exhibited fully harmonic reasoning. Figure-dominant students struggled to define cylinders correctly, justify classifications, and produce conceptually accurate drawings, often relying on image-based or procedural explanations. Potentially harmonic students performed better in recognition and justification tasks but still showed limitations in spatial reasoning. Notably, prototypical reasoning was less pronounced than in prior studies, suggesting flexible figural representations without full conceptual integration. This deviation from traditional literature on 2D shapes could be attributed to students' frequent daily-life exposure to 3D cylindrical objects, which potentially enhances the flexibility of their figural representations. These findings highlight that middle school students’ geometric reasoning remains predominantly under perceptual control and does not spontaneously develop conceptual understanding. Instructional implications include designing learning environments that explicitly emphasize critical properties of geometric objects while integrating visual representations to support, rather than replace, conceptual reasoning. Guided use of manipulatives and dynamic visualizations may foster harmony between figural and conceptual components, enhancing students’ ability to reason accurately about three-dimensional geometry.