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

In this article we discuss the findings of our research on students' understanding of vector concepts in problems without physical context. first,we develop a complete taxonomy of the most frequent errors made by university students when learning vector concepts. this study is based on the results of several test administrations of open-ended problems in which a total of 2067 students participated. using this taxonomy,we then designed a 20-item multiple-choice test [test of understanding of vectors (tuv)] and administered it in english to 423 students who were completing the required sequence of introductory physics courses at a large private mexican university. we evaluated the test's content validity,reliability,and discriminatory power. the results indicate that the tuv is a reliable assessment tool. we also conducted a detailed analysis of the students' understanding of the vector concepts evaluated in the test. the tuv is included in the supplemental material as a resource for other researchers studying vector learning,as well as instructors teaching the material. © published by the american physical society.