__Electronic Proceedings
of the 12 ^{th} Asian Technology Conference in Mathematics__

**Abstract for 12393**

*Using Videotaped Components of Lesson Study
to Build Communities of *

* Practice for Prospective
Mathematics Teachers*

Authors: Jack Carter, Beverly Ferrucci

Affiliations: California State University, East Bay, Keene State

College

Keywords: Undergraduate Level, Equivalence Relations, Lesson Study,

Videos

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.