Other
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aas...20914507w&link_type=abstract
2007 AAS/AAPT Joint Meeting, American Astronomical Society Meeting 209, #145.07; Bulletin of the American Astronomical Society,
Other
Scientific paper
We find that students solving a variety of first order linear differential equations in a sophomore level mechanics class emphasize certain reasoning resources over others. Contrary to informal commentary by many observers, students can often do the math, but they stick to purely mathematical reasoning paths when physical insight can simplify the problem for them. For example, they emphasize the indefinite integral rather than using physically meaningful limits of integration when solving integrals after separation of variables. Also, they often leave solutions mathematically complete while not paying attention to the unique physical solution. We observe a context dependence based on the formalism used to ask the question. We also observe consistent results in both small group "mini interviews" and on examination questions. Even on identical questions asked months apar, students show little consistency in their solution methods. We give specific examples in this talk. (Sponsored in part by NSF grants REC-0633951 and DUE-0442388.)
Black Katrina E.
Wittmann Michael C.
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