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2011 AAPT Summer Meeting
July 30-August 3, 2011
Omaha, Nebraska

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GF01:

Seeing Through Symbols: Personal and Cultural Semiotic Systems in Algebra
  Location: SS Ballroom DE
  Date: Wednesday, Aug.3
  Time: 1:00 PM -1:30 PM
  Author: Aaron Weinberg, Ithaca College
607-274-7081, aweinberg@ithaca.edu
  Co-Author(s): None
  Abstract: Algebraic symbolism plays a prominent role in mathematics. We try to teach our students to "see through the symbols" to focus on the underlying meaning of variables, functions, systems of equations, and other algebraic notation. Despite our best efforts, students frequently struggle to use algebraic notation meaningfully. The idea of personal and cultural semiotic systems gives us a new way of understanding how students work with algebraic symbols. Previous research on algebraic representation has attempted to describe either the ways students interpret symbols or the ways they produce symbols. In contrast, viewing students' work as part of a semiotic system unifies these perspectives, enabling us to describe the interaction between symbol production and interpretation. This presentation will introduce the idea of semiotic systems and look at examples of student work to illustrate the concept and show how it can be used to understand students' mathematical activity.
  Footnotes: Sponsored by John Thompson
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