Analysis of the final comments provided by a knowledgeable other in lesson study.

Lesson study has been implemented in schools around the world as a method of professional development for teachers. Lesson study consists of five steps, among which the "Research Lesson" and "Post-lesson Discussion" are central. During the Post-lesson Discussion, after the teacher has commented on the lesson, all of the observers discuss the lesson, and the "knowledgeable other" (koshi), a specially invited expert, provides final comments. The quality of these final comments is critical to the learning of the lesson-study participants, and, consequently, the koshi plays an extremely important role. However, few studies have examined the nature and structure of the final comments that koshis provide. This study analyzed the final comments made in three elementary-school research lessons in Japan by a highly distinguished university mathematics educator with considerable teaching experience and an outstanding reputation as a koshi. We found that his final comments clustered into seven categories, which we named: (1) considering the didactical value of mathematical content; (2) use of representations; (3) fostering positive attitudes to learning; (4) incorporating students' ideas into whole-class discussions; (5) giving attention to what students write down; (6) giving attention to the content of the board-work; and (7) teacher growth through reflection. These categories provide insight into the nature of final comments that are regarded as being particularly useful and may form the basis for less-experienced koshis to structure their final comments in lesson study. [ABSTRACT FROM AUTHOR]