Shifts in Forming Solids of Revolution: Characterizing a Student’s Attention Using Paper-and-Pencil Tasks and Manipulatives

In a task-based interview, we examined how a high school student with high spatial visualization ability, Andrea, generated three-dimensional objects by rotating two-dimensional shapes about an axis using paper and pencil and hands-on manipulatives. Initially, Andrea interpreted rotation as planar motion, without extending into three-dimensional space. With the use of hands-on manipulatives, she gradually shifted toward a more integrated understanding of spatial rotation, relying on metaphorical associations and visual cues to support her recognition of dimensional transitions. Afterward, she coordinated spatial elements (e.g., the line of rotation and radius) more precisely, constructing increasingly coherent representations of solids of revolution. Our study offers insights that inform future research and instructional design focused on supporting students’ understanding of dimensional transformations.