Force, velocity, and work: The effects of different contexts on students’ understanding of vector concepts using isomorphic problems

In this article we compare students’ understanding of vector concepts in problems with no physical context, and with three mechanics contexts: force, velocity, and work. Based on our “Test of Understanding of Vectors,” a multiple-choice test presented elsewhere, we designed two isomorphic shorter versions of 12 items each: a test with no physical context, and a test with mechanics contexts. For this study, we administered the items twice to students who were finishing an introductory mechanics course at a large private university in Mexico. The first time, we administered the two 12-item tests to 608 students. In the second, we only tested the items for which we had found differences in students’ performances that were difficult to explain, and in this case, we asked them to show their reasoning in written form. In the first administration, we detected no significant difference between the medians obtained in the tests; however, we did identify significant differences in some of the items. For each item we analyze the type of difference found between the tests in the selection of the correct answer, the most common error on each of the tests, and the differences in the selection of incorrect answers. We also investigate the causes of the different context effects. Based on these analyses, we establish specific recommendations for the instruction of vector concepts in an introductory mechanics course. In the Supplemental Material we include both tests for other researchers studying vector learning, and for physics teachers who teach this material.

Figure 1

Item 2 of the TUV-12 items no context and the TUV-12 items mechanics that evaluate the geometric interpretation of the dot product as a projection in both contexts used in the first administration. Note that in the second administration we also included at the end of these items the question “Explain your reasoning.”