==== Geometric and Harmonic Reasoning ====
We have begun to study how students use their understanding of the geometry of a problem to make progress in problem solving. We are also looking at the extent to which students go from geometric understanding to algebraic symbols or go from a mathematical expression to geometric understanding. Students who go fluidly back and forth between the geometry and the symbols are referred to as thinking "harmonically".
=== PhD Dissertation in Progress regarding Geometric and Harmonic Reasoning in E&M Problems ===
A Science Education PhD student is working on a dissertation related to geometric and harmonic reasoning in the context of solving E&M problems in groups. This work will include written materials, as well as video clips of students using different types of reasoning. Link to [[Dissertation]]
=== Video of a group of students translating algebraic symbols to a geometric picture===
In this one-minute video clip, students have already been working in a group of three for about 15 minutes trying to find the magnetic vector potential in all space for a spinning ring of charge. This activity is described in <html> <a href="http://www.physics.oregonstate.edu/portfolioswiki/doku.php?id=activities:main&file=vfaring">MagneticVectorPotential</a> </html> Activity. They have already determined the current and other aspects of the problem and are now trying to work on the denominator of the integral which is | r - r' |. They are creating a geometric understanding of what this means.
{{:whitepapers:harmonic:rrprime071026grp1.wmv|SeeVideo}}
{{:whitepapers:harmonic:rrprime071026grp1trans.doc|VideoTranscript}}