Applying clustering to statistical analysis of student reasoning about two-dimensional kinematics

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14. Normally an unweighted, normalized Euclidian distance would imply that each element of the vectors represents the scalar component of the vector along a unique orthogonal dimension. Since our data are binary and the result of nonexclusionary student responses, neither of these assumptions can safely be made.
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19. We have carried out preliminary interviews on the question. We have one interview in which a student did start with this response and explained why it was made. The student, however, changed the answer partway through the interview so we remain unsure if this student’s reasons for using a curve following response are representative of the group as a whole, or just that particular student’s idiosyncrasies.
20. We do not claim that all cases are expected and understood, based on correct and tangent, whose response pattern we cannot explain. We believe that continued research in this subject area will allow us to explain the logic that students with this response pattern are using and thus to strengthen our claim that the groups found by cluster analysis all have an element of logic in their makeup.