Positional System: Pre-service Teachers' Understanding and Representations

This study reports 63 pre-service� teachers'� experiences� of� performing operations in bases other than ten. Identical, ten-item, pre- and post- group� discussion� questions� were� provided.� � Participants'� written� discussion� logs� and� the� instructor's� observation notes were analyzed. The pre-discussions revealed the heavy dependency on base ten, which implied participants'� limited� understanding� of� the� general� concept� of� the� positional� system. In the post-discussions, participants demonstrated improved performance in several ways: increased correct response rate, increased discussion time, increased number of solution strategies, and decreased dependency on base ten. The availability of various modes of representation and the emphasis on the basic math concepts throughout the semester appear to be key factors of this improvement.

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