A tutorial worksheet to help students develop the ability to interpret the dot product as a projection

Abstract

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. Upon using the TUV to evaluate the students' understanding, we confirmed that the tutorial worksheet facilitated their learning. 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.