Physics
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aas...20913503b&link_type=abstract
2007 AAS/AAPT Joint Meeting, American Astronomical Society Meeting 209, #135.03; Bulletin of the American Astronomical Society,
Physics
Scientific paper
Many upper level physics classes are concerned with abstract vector spaces. Building a wavefunction from eigenfunctions of the Schrodinger equation and decomposing a wave on a string into normal modes are two prominent examples. When physics students first encounter these abstract vector spaces, they are relatively familiar with Cartesian vector spaces and the use of functions in graphical, algebraic, and simple calculus contexts. Constructing a notion of an abstract vector space involves a complicated combination of these relatively familiar ideas. Not only does something new emerge from this combination, but the original conceptions of, for example, Cartesian vectors are often modified as well. We analyze the thinking of second and third year physics majors as they work on Cartesian and string wave problems concurrently. Several analysis frameworks, including cognitive blending, will be used in an attempt to understand the dynamics of this construction of understanding for abstract vector spaces.
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