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Recent work has uncovered a consistent set of student difficulties with graphs of position, velocity, and acceleration versus time. These include misinterpreting graphs as pictures, slope/height confusion, problems finding the slopes of lines not passing through the origin, and the inability to interpret the meaning of the area under various graph curves. For this particular study, data from 895 students at the high school and college level was collected and analyzed. The test used to collect the data is included at the end of the article and should prove useful for other researchers studying kinematics learning as well as instructors teaching the material. The process of developing and analyzing the test is fully documented and is suggested as a model for similar assessment projects.

The Brief Electricity and Magnetism Assessment ͑BEMA͒, developed by Chabay and Sherwood, was designed to assess student understanding of basic electricity and magnetism concepts covered in college-level calculus-based introductory physics courses. To evaluate the reliability and discriminatory power of this assessment tool, we performed statistical tests focusing both on item analyses ͑item difficulty index, item discrimination index, and item point biserial coefficient͒ and on the entire test ͑test reliability and Ferguson's delta͒. The results indicate that BEMA is a reliable assessment tool.

Both high school and university students' reasoning regarding direct current resistive electric circuits often differ from the accepted explanations. At present, there are no standard diagnostic tests on electric circuits. Two versions of a diagnostic instrument were developed, each consisting of 29 questions. The information provided by this test can provide instructors with a way of evaluating the progress and conceptual difficulties of their students. The analysis indicates that students, especially females, tend to hold multiple misconceptions, even after instruction. During interviews, the idea that the battery is a constant source of current was used most often in answering the questions. Students tended to focus on the current in solving problems and to confuse terms, often assigning the properties of current to voltage and/or resistance.2

This paper introduces five commonly used approaches to analyzing multiple-choice test data. They are classical test theory, factor analysis, cluster analysis, item response theory, and model analysis. Brief descriptions of the goals and algorithms of these approaches are provided, together with examples illustrating their applications in physics education research. We minimize mathematics, instead placing emphasis on data interpretation using these approaches