Correlating Common Errors in Statics Problem Solving with Spatial Ability

Solving engineering problems is more than simply solving equations. It requires a clear visual representation of the problem, e.g. a schematic or diagram, before analysis is possible. In statics, for example, generating an appropriate free-body diagram is a critical step in the process. Spatial visualization skills (SVS) may play a critical role in developing these free-body diagrams properly. Many concepts in statics rely on the ability to visualize the effects of various force vectors on the equilibrium of an object. Understanding the direction of force and moment vectors is key to mastering these concepts. Without strong SVS, students may rely on other tactics such as identifying superficial patterns to help solve the problem without a good understanding of the underlying concept. When confronted with a new situation, they are unable to properly “extrapolate” the memorized examples, so their misconceptions are revealed. Students with strong SVS may be able to more easily interpret graphical representations (such as vector addition) leading to a stronger understanding of the underlying concepts. However, high visualizers are not guaranteed to grasp the concepts if they do not spend the effort to connect with the material. In this study, we studied the potential correlation between a student's spatial ability and the types of errors made in solving fundamental statics problems. The two exam problems selected for the study focus on calculating resultant force and resultant moment in 2D. If certain types of errors are indicative of low spatial ability, identifying these types of errors will be the first step in developing activities to help correct these misconceptions. We performed statistical analyses on the datasets and found that the error prevalence rates for higher in students with low and medium SVS skills compared to the high-level mastery students. We also performed one-way ANOVA and looked at the correlation between two problems sets. Our results indicate that there is a correlation between the SVS skill levels and the problem outcomes, i.e., low visualizers master concepts at a lower rate than high visualizers. Based on our findings, we infer that activities involving physical manipulatives and/or virtual 3D models may improve conceptual understanding for low visualizers, including the development of hands-on lab experiments.