We report results of an investigation into physics students' understanding of vector addition, magnitude, and direction for problems presented in graphical form. A seven-item quiz, including free-response problems, was administered in all introductory general physics courses during the 2000-2001 academic year at a large mid-western university; responses were obtained from 2031 students during the first week of class. We found that more than one quarter of students beginning their second

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... of study in the calculusbased general physics course, and more than half of those beginning the second semester of the algebra-based sequence, were unable to carry out two-dimensional vector addition. Although total scores on the seven-item quiz were somewhat better for students in their second semester of physics instruction in comparison to students in their first semester of study (80% vs. 71% for students in the calculus-based course; 62% vs. 47% for students in the algebra-based course), many students retained significant conceptual difficulties regarding vector methods that are heavily employed throughout the physics curriculum. Nguyen and Meltzer, Initial understanding of vector concepts 1