Relation of Spatial Skills to Calculus Proficiency: A Brief Report

Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM majors and careers. We gathered data on paper-and-pencil measures of spatial skills (mental rotation, paper folding, and hidden figures); calculus proficiency (conceptual knowledge and released Advanced Placement [AP] calculus items); coordinating graph, table, and algebraic representations (coordinating multiple representations); and basic graph/table skills. Regression analyses suggest that mental rotation is the best of the spatial predictors for scores on released AP calculus exam questions (β = 0.21), but that spatial skills are not a significant predictor of calculus conceptual knowledge. Proficiency in coordinating multiple representations is also a significant predictor of both released AP calculus questions (β = 0.37) and calculus conceptual knowledge (β = 0.47). The spatial skills tapped by the measure for mental rotation may be similar to those required to engage in mental animation of typical explanations in AP textbooks and in AP class teaching as tested on the AP exam questions. Our measure for calculus conceptual knowledge, by contrast, did not require coordinating representations.