Our Approach: Mathematical Conversations

The core part of each lesson is delivered through mathematical conversations shown on the first page of each lesson. The conversations, presented by the program's cast of characters and acted out by students, model a way of thinking and learning mathematics that may be new to low-achieving students. They also offer a unique way to get students to talk about mathematical ideas and concepts.

Ms. Park's students express their ideas about mathematics. Some of these ideas are not entirely correct or not correctly expressed. These mistakes and misconceptions are discussed in the conversation or in the lesson support. We realize that this may be considered unusual. However, research from cross-national studies suggests that classroom discussion of incorrect ideas is valuable for student learning.

Studies of elementary classrooms in East Asian countries and the United States reveal different classroom practices. Consistent with the practices described in The Learning Gap,¹ James Stigler, Clea Fernandez, and Makoto Yoshida note that in contrast with Japanese teachers, "American teachers go to great lengths to keep errors out of the mathematics classroom, and especially out of the public discourse." In contrast, Japanese teachers "see errors as a natural part of the learning process and as important sources of information about children's mathematical thinking."² It may be for cultural reasons such as fear of damaging students' self-esteem that U.S. teachers do not discuss students' errors. Ms. Park's students reveal common understandings and errors in order that the real students reading the conversations can discuss them and understand why the errors are errors.

Our Approach: Organization of the Mathematics