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In a previous study of a traditional, large-lecture algebra-based physics course, we demonstrated that giving students a choice of representational format when they solve quiz problems could have either significantly positive or negative performance effects, depending on the topic and representation used. Further, we see that students are not necessarily aware of the representation with which they are most competent. Here, we extend these results by considering two courses taught by a reform-style instructor. These performance data are substantially different in character, with the students from the reform courses showing much smaller performance variations when given a choice of representation. From these data, we hypothesize that students in the reform courses may be learning a broader set of representational skills than students in the traditional course. We therefore examine major components of the courses (exams, homeworks, lectures) to characterize the use of different representations. We find that the reform courses make use of richer selections of representations, and make more frequent use of multiple representations, suggesting a mechanism by which these students could have learned these broader skills.
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