Pre-service teachers' mathematical reasoning - how can it be developed?

The focus of this study is the mathematical reasoning of pre-service teachers. The author of this paper was the instructor of a class of pre-service teachers preparing to teach in lower secondary school. The instructor divided the class in small groups and gave each group some mathematical exercises to work on. The unit of analysis of this study is the video and audio-recorded dialogue of each group. The aim of this study is to characterize different aspects of pre-service teachers' mathematical reasoning, as well as to indicate ways to develop their reasoning further. The basic idea of the study is that rote learning reasoning is imitative, and the opposite kind of reasoning is creative. However, the study indicates that the reasoning of the participating students sometimes could be neither imitative nor creative. Thus, some of the reasoning was in a grey zone somewhere between imitative and creative reasoning.