Vector Addition: Effect of the Context and Position of the Vectors

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.…”

Vector Addition in Different Contexts

“…Finally, it is worth re-iterating that this sensitivity to context (of the particular vector quantity being added) appears both in a graphical context [4], where a continuum of answers are available (i.e. the resultant vector could assume any possible length), and in an algebraic context, where a discrete number of answers are available (see Figure 2).…”

“…It is very different from other vectors such as force." Barniol and Zavala [4] show that student responses do indeed exhibit context sensitivity depending on whether the vectors to be added are displacements or forces. Barniol demonstrates this sensitivity in a graphical context (students are given two arrows drawn on graph paper and required to draw the resultant vector) while this paper describes an algebraic context (see below).…”