Dialectic on the Problem Solving Approach: Illustrating Hermeneutics as the Ground Theory for Lesson Study in Mathematics Education

Abstract

Lesson study is the major issue in mathematics education for developing and sharing good practice and theorize a theory for teaching and curriculum development. Hermeneutic efforts are the necessary activities for sharing objectives of the lesson study and make them meaningful for further development. This paper illustrates hermeneutic efforts with two examples for understanding the mind set for lesson study. The first example, the internet communication between classrooms in Japan and Australia, demonstrates four types of interpretation activities for hermeneutic effort: Understanding, Getting others’ perspectives, Instruction from experience (self-understanding), and the hermeneutic circle. Using these concepts, we will illustrate the second example with dialectic discussion amongst students in the problem solving classroom engaged in a task involving fractions.