Teachers' Mathematical Tensions Surfacing During The First Session Of A Problem-Solving Professional Development Workshop

When teachers participating in a professional development workshop discuss their experiences during a problem-solving session, they sometimes express a sense of imbalance or discomfort rooted in the contrast between these experiences and their abilities and previous mathematical self-perceptions, beliefs, and knowledge. These are expressions of what we call mathematical tensions, and it is the purpose of this chapter to classify them and to discuss their appearance as a healthy sign of the effectiveness of the professional development workshop. Our data have been taken from the first of eight sessions of a 30-hour workshop held over the course of 1 year, which included 147 elementary and middle school teachers.