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

Background:When we administered the Test of Understanding of Vectors (TUV) to students who were completing a physics university remedial course (which covers subjects of a traditional high school physics course), we observed that they had considerable difficulties in interpreting the dot product as a projection. As a result of this, we decided to design a tutorial worksheet to guide students through the development of this skill. The worksheet was implemented with 288 students of the same course in another semester.Material and methods:A test was administered to all the participants before the beginning of the course. It is a multiple-choice test that evaluates students’ knowledge of the main topics of a traditional high school mechanics course. We used the test to validate that both groups were comparable. To evaluate the participants’ understanding of vector concepts once the course had ended, we used the TUV. We had 313 students in the control group and 288 in the experimental.Results:Upon using the TUV to evaluate the students’ understanding, we confirmed that the tutorial worksheet facilitated their learning.Conclusions:This tutorial worksheet is presented in the Appendix and might be used by other physics instructors teaching this material in high schools, colleges or universities.