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Abstract Title: Faculty Discourse in the Classroom: Meaning in the Math
Abstract: The distinction between physics concept and mathematical formalism often seems arbitrary to the physicist. As one faculty colleague put it, "the concepts are the math and the math are the concepts." We interpret faculty lectures in the context of frames, defined by Tannen as the contextual surrounding of communication.  But where "normal" dialogue requires both parties to agree to the particular frame, the unidirectional nature of lecture can result in an important mismatch between faculty and student expectation, particularly about the underlying reasons behind a mathematical manipulation.  In this work we link classroom frame with symbolic forms, a structure proposed to explain how physicists embed conceptual meaning in mathematics. These forms reveal a multi-faceted view of equations and derivations, with simple mathematical operations resulting in profound shifts in meaning. We find faculty using these to move seamlessly between frames, switching, for example, between the conceptual and mathematical. These changes in frame can be explicit, as is the case with a deliberate re-writing of an equation, or implicit, and, as a consequence, students may not detect a frame change and therefore answer inappropriately or erroneously. These analyses lead discussion of pedagogy in a new direction, one that strikes at the heart of what it means to understand a mathematical representation.
Abstract Type: Contributed Poster Presentation

Author/Organizer Information

Primary Contact: Scott Franklin
Rochester Institute of Technology
Dept. of Physics/RIT
1 Lomb Memorial Drive
Rochester, NY 14623
Phone: 5854752536
and Co-Presenter(s)
Jonathan Lindine

Contributed Poster

Contributed Poster: Download the Contributed Poster