A research-based approach to improving student understanding of the vector nature of kinematical concepts

In this paper we describe a long-term, large-scale investigation of the ability of university students to treat velocity and acceleration as vectors in one and two dimensions. Some serious conceptual and reasoning difficulties identified among introductory students also were common among pre-college teachers and physics graduate students. Insights gained from this research guided the development of instructional materials that help improve student learning at the introductory level and beyond. The results have strong implications for the teaching of undergraduate physics, the professional development of teachers, and the preparation of teaching assistants.