Analyzing and designing cross-section inference problems: a 20-variable framework

Cross-section inference, determining the shape produced when a plane cuts a three-dimensional object, is foundational in STEM, yet no framework specifies which problem features govern its difficulty. We introduce the cross-section problem analysis and design matrix, a 20-variable framework spanning object structure, plane-to-object relations, and cross-section properties, for analyzing and generating problems of controlled difficulty. A 29-problem instrument built with the matrix was administered to 865 fifth and sixth graders. Five matrix features predicted item difficulty, each linked to a hypothesized cognitive mechanism, such as penetrative thinking or interference control. The matrix offers a principled basis for designing spatial assessments.