Spatial Orientation Reasoning Demands: Theory-Informed Patterns and Pedagogical Insights for Mathematics Teacher Education

This study uses a theory-informed design to examine the reasoning-demand patterns underlying preservice mathematics teachers’ spatial orientation (SO) in orthographic view (OV) construction and to clarify how these demands shape task performance. Forty-four participants each produced 36 OVs (six structures × six labeled viewpoints) and completed task-based interviews. The design and interpretation were guided by spatial reference-frame theory and geometrical reasoning about OVs, enabling participants’ drawings, verbal explanations, and gestures to be analyzed as evidence of specific reasoning processes and demands. Multimodal analysis yielded thirteen reasoning-demand patterns grouped into five clusters: Perceptual-Appearance-Based Misconceptions and Misconstructions (M), Incomplete Geometric Reasoning (I), Egocentrism (E), Deviations and Instability of Observer-Based Reference-Frame Use (Cbj), and Limited Adoption of Object-Based Reference Frame (Cjj). Quantitative associations among codes were modest and dispersed, and no cluster-level associations remained significant after Bonferroni correction, providing no evidence of broad cluster-level association in this sample. Implications for teacher education point to a modular repertoire of instructional supports for spatio-geometric tasks, aligned with these reasoning demands: perceptual–appearance distinctions, geometric abstraction, proportional and spatial structuring, perspective-taking with sustained observer-viewpoint use, and coordination of observer- and object-based reference frames.