2026 ASEE Annual Conference & Exposition

Understanding fundamental concepts in statics, such as force vectors and moments of forces, requires varying levels of spatial visualization skills (SVS). To resolve a force vector, for example, students must visualize the right triangle formed by the X and Y components of that force vector. To determine moment arm, students must visualize the force line of action and the perpendicular distance to the pivot.
In addition, basic geometry skills are a pre-requisite to calculating the necessary force components and moment arm distances, specifically angle properties and trigonometric functions. If students lacking these skills can be identified early, they can be provided with supplemental resources and encouraged to complete targeted activities that help build these prerequisite skills as soon as possible to give them the best chance to succeed in the course.
Visualization skills and math (geometry) skills are both necessary to solve statics problems completely. A growing body of literature suggests that strong SVS play a critical role in the mastery of statics concepts. In a prior study, we observed similar trends where strong SVS led to higher mastery rates for force vectors and moments of forces in basic problems. In problems involving slightly more complex geometric configurations, however, we observed that mastery of moments of forces declined, across all SVS levels. Since there is a significant visualization component in solving geometry problems, we hypothesize that geometry skills may be a better predictor of student success in mastering fundamental statics concepts than general spatial visualization skills.
In this study, we investigate the importance of geometric ability for the mastery of two fundamental statics concepts: force vectors and moments of forces. We assess geometric ability using a 20-item test on basic skills related to trigonometry, right triangles, and angle properties. Mastery of statics concepts is assessed using two problems from the first exam.
Results suggest that strong geometry skills are less critical for problem solving with force vectors only and are more highly correlated with problems involving moments of forces, especially when structural members that are not strictly horizontal or vertical are included. We also observed a significant increase in geometry skills over the first six weeks of the semester.