Students’ Understanding of the Concepts of Vector Components and Vector Products

Abstract

In this article we investigate students' understanding of: 1) vector components and, 2) vector products. We administered a test to 409 students completing introductory physics courses at a private Mexican university. In the first part, based on the work of Van Deventer [1], we analyze the understanding of components of a vector. We used multiple-choice questions asking for students' reasoning to elaborate on the misconceptions and difficulties of graphical representation of the x-and y-components of a vector. In the rest of this work, we analyze the understanding of the dot and cross products. We designed opened-ended questions to investigate the difficulties on the calculation and the misconceptions in the interpretation of these two products. RESULTS AND DISCUSSIONThis section is divided into three subsections addressing the three objectives of this study.

Test of understanding of vectors: A reliable multiple-choice vector concept test

“…The results of some of our other studies based on open-ended problems have been reported in previous articles [23][24][25][26][27].…”

“…Previous studies of students' understanding of vector concepts can be clustered into three groups: (1) those that analyze their understanding of vector concepts in problems without a physical context [14][15][16][17][18][19][20][21][22][23][24][25][26][27], (2) studies that investigate their understanding in problems with a physical context [16][17][18][19]24,[27][28][29][30][31][32], and (3) studies that compare students' performance on both types of problems, with and without a physical context [17][18][19]24,27,31]. Note that some of these studies pertain to more than one group.…”

“…The studies in the first group [14][15][16][17][18][19][20][21][22][23][24][25][26][27] are closely related to our investigation, since they analyze students' understanding of vector concepts in problems without a physical context. From this group, six studies [14][15][16][17][18][19] (by other researchers) identify frequent errors that university students make when they are learning vector concepts.…”

A Tutorial Worksheet to Help Students Develop the Ability to Interpret the Dot Product as a Projection

“…First, we studied these difficulties in an openended problem that asked students to interpret the dot product of two vectors (Zavala & Barniol, 2010), and then, based on the results, we constructed a multiplechoice option problem and analyzed students' difficulties with it (Zavala & Barniol, 2013). In this latter study, it was found that very few of the students completing the last of three introductory university physics courses had chosen the correct option.…”

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].…”