Students' understanding of vectors in the context of forces

Abstract

A functional understanding of Newton's second law as a vector equation requires that students be able to reason about forces as vectors. In this paper, we present data describing students' conceptual difficulties with forces as vectors. These data suggest that after traditional instruction in introductory physics, some students do not recognize the vector nature of this quantity. Other students do not have the necessary procedural knowledge to determine net force or acceleration, and are therefore unable to reason qualitatively about Newton's second law. We describe some specific procedural and reasoning difficulties we have observed in the students' use of vectors in the context of forces and Newton's second law. In addition, we encourage modifications in the instruction of mechanics that we designed on the basis of our research into student understanding. These modifications are intended to improve the students' understanding of vector addition and subtraction and to promote the students' use of vectors insolving mechanics problems.