Modeling students' conceptual understanding of force, velocity, and acceleration

We have developed a multiple choice test designed to probe students' conceptual understanding of the relationships among the directions of force, velocity, and acceleration. The test was administered to more than 800 students enrolled in standard or honors introductory physics courses or a second-year physics majors course. The test was found to be reasonably statistically reliable, and correlations of test score with grade, course level, and the Force Concept Inventory were moderate to strong. Further analysis revealed that in addition to the common incorrect response that velocity must be in the direction of the acceleration or net force, up to 30% of students gave "partially correct" responses, for example that velocity can he either opposite to or in the direction of the acceleration or net force but not zero. The data also suggests that for some students their evolution of understanding may progress through this kind of partially incorrect understanding.