Using Videotaped Components of Lesson Study to Build Communities of Practice for Prospective Mathematics Teachers

Two tiers of pre-service mathematics teachers participated in an exploratory investigation in which components of lesson study were used to develop, teach, refine, revise, re-teach, and evaluate a unit on mathematical relations. Twelve fourth-year prospective mathematics teachers served as the instructional developers, planners, analyzers, and instructors for the unit, and twenty-five, second-year future elementary school mathematics teachers participated as students. Videotapes of the lesson study and the instruction showed that the fourth-year pre-service teachers were modestly successful in developing their second-year peers’ understanding of the properties of a mathematical relation, primarily by using arrow diagrams and relations on sets of people to give meaning to the properties. Analysis of the videotapes and written lessons showed that the participants who taught the lessons were prone to tell their students about relations without providing tasks for the students to conjecture and construct their own relations. The fourth-year pre-service mathematics teachers prepared a final paper reflecting on their experiences with the lesson study. A review of the final papers showed that these participants valued: (1) the opportunity to experience the lesson study process within the setting of an academic classroom, (2) the opportunity to work in a group to develop and improve a lesson, and (3) the experience of observing, and in some cases teaching, a lesson that incorporated the joint efforts of other participants. In retrospect, most of the participants also indicated that they would include more examples in the instructional unit, more examples of equivalence relations, more mathematical examples, and more examples generated and constructed by the students. Increasing class participation was also a concern expressed by most participants.