Student use of vectors in introductory mechanics

Abstract

Most students’ initial exposure to physics is in the context of kinematics and dynamics. An understanding of how these topics relate to each other requires the ability to reason about vectors that represent forces and kinematic quantities. We present data that suggest that after traditional instruction in mechanics many students lack this ability. Modifications to instruction can significantly improve student performance on questions about vector addition and subtraction and increase the likelihood that students employ vectors in their attempt to solve mechanics problems. However, an increased emphasis on these topics has so far been only moderately successful in promoting the level of proficiency required to understand the connection between force and acceleration as vector quantities. We describe some of the procedural and reasoning difficulties we have observed in students’ use of vectors.

Testing Students’ Understanding of Vector Concepts

“…In designing the open-ended problems, we took into account the results of the previous studies mentioned earlier [3][4][5][6][7]. Note that the results of some of our other studies based on open-ended problems have been reported in previous articles [8][9][10][11][12].…”

“…Six studies [3][4][5][6][7] (from other researchers) identified frequent errors that university students make regarding vector concepts in problems without physical context. The methods used in these studies are individual interviews or tests that use open-ended problems.…”

Student Understanding of Superposition: Vectors and Wave Functions

“…Past research has shown that many introductory physics students have difficulty with concepts such as superposition and addition of vectors in a wide variety of contexts [1][2][3][4][5]. Instruction on topics such as classical waves (e.g., waves on a string or EM waves) and quantum mechanics also rely on superposition.…”

Student Ideas around Vector Decomposition in the Upper Division

“…To this end, a number of studies at the introductory level have investigated students' ability to add and subtract vectors (e.g. [3][4][5]), and students' understanding and execution of vector decomposition and vector products [6,7].…”