Katie thought she couldn't do it but now she knows she can

The topic of this paper is mathematical identity or self-concept. This elusive construct is explored through two classroom episodes, in the public domain of whole classwork, in a senior high-school class. The structures in the dialogue in both episodes could constitute enhancement of self-concept for some students and mediate against the confidence in mathematics of others, but intersecting effects of students' one-to-one conversations are shown to be important to final outcomes. This revised version was published online in July 2006 with corrections to the Cover Date.