This study explores the use of video clips from teachers' own classrooms as a resource for investigating student mathematical thinking. Three dimensions for characterizing video clips of student mathematical thinking are introduced: the extent to which a clip provides "windows" into student thinking, the "depth" of thinking shown, and the "clarity" of the thinking. Twenty-six video clips were rated as being low, medium, or high on each dimension. Corresponding teacher discussions of each video were then examined to identify the ways in which clip dimensions served as catalysts for more and less productive teacher conversations of student mathematical thinking. Findings include first, that, under certain circumstances, both low-and high-depth clips lead to productive discussions. Second, high-depth clips in which student thinking is sustained only briefly do not typically lead to productive discussions. Third, in cases where windows and depth are both high, clips that are either low or high in clarity resulted in productive conversations of student thinking on the part of teachers. (Contains 6 tables and 7 notes.)