Abstract: 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.

Key words: Positional system; Place value; Representations; Pre-service teachers’ understanding