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## Representation Issues: Using Mathematics in Upper-Division Physics

Corinne Manogue and John Thompson

### Submitted Abstract to PERC 2011

Upper-division students must learn to apply sophisticated mathematics from algebra, limits, calculus, multi-variable and vector calculus, linear algebra, complex variables, and ordinary and partial differential equations. The presenters in this session will discuss how the representations that we choose may affect whether students are able to use this mathematics spontaneously and correctly, whether they can move smoothly between representations, and the extent to which their understanding of the mathematics enhances their understanding of the physics. The discussant will incorporate the perspective of research in undergraduate mathematics education as it applies to the representations that have been presented.

- Mastering new mathematics/representations
- When teachers have a choice of representation, how do we choose?
- Cueing of inappropriate representations based on superficial geometric features
- (line integrals vs. area under curve)

- Geometry

People that John has invited to AAPT from RUME:

- Fr. Joseph Wagner, Xavier University: transfer in pieces
- Michael Oehrtmann, University of Northern Colorado: limits, sums, integrals
- Timothy Fukawa-Connelly, University of New Hampshire: “•Describing the beliefs, goals and knowledge that shape mathematician’s teaching of proof-based undergraduate mathematics courses as a means to understand why lecture-teaching persists.”
- Aaron Weinberg, Ithaca College: “I am interested in the way the words and symbols we use while doing mathematics shape the way we participate in mathematical activity.”

Due Dates:

- Get drafts to Joe Wagner by July 22
- Peer-review deadline: July 7
- Invited paper deadline: August 8
- AAPT: Saturday, 7/30
- PERC: Thursday, 8/4