Improving Teaching Through Variation: A Japanese Perspective

• In Event: 29.082 - Roundtable Session 9
  In Roundtable Session: 29.082-4 - Teaching and Learning Mathematics Through Variations: An International Perspective

Abstract

This paper examines the Japanese problem-solving approach to teaching mathematics from the perspective of variation. The research question is, “What types of variation are strategically used in the forms of structured problem solving that are commonly used to organize a lesson in the Japanese problem-solving approach?”
Teaching mathematics through problem solving is a widely preferred method within the community of mathematics education in Japan. A unique aspect of this method is the ways of organizing a lesson, which is called structured problem solving (Stigler & Hiebert, 1999). Based on the well-illustrated features of structured problem-solving lessons, from the perspective of variation (BT and VT) (e.g., Gu et al., 2004; Lo & Marton, 2012; Marton & Booth, 1997), this paper presents three viewpoints to show how teachers use variations strategically to create a rich space for learning in the lesson. They are: (1) presenting problems with variation; (2) providing opportunities for students to construct variation themselves; and (3) promoting student reflection on variation toward the intended object of learning.
The analysed lessons are two fifth-grade lessons on comparing fractions. They were conducted in 2010 in a university-affiliated primary school in Tokyo as part of the Learner’s Perspective Study-Primary (LPS-P) (Fujii, 2013). The LPS-P collected data from the lessons and from interviews with the teacher and four focus students (c.f., Clarke, 2006). The transcribed data of the lessons were sectioned according to the activities in the structured problem-solving and then examined by making references to the types of variation.
Lesson analysis showed that although the number of problems was small, the teacher incorporated variation into the problems. In the lesson, the teacher provided opportunities for the students to construct variations through their reasoning and explanations. The teacher also promoted and regulated the students’ reflection on the variations by making different reactions such as questioning, probing, or asking for elaboration. These findings demonstrate how a structured problem-solving lesson provides possible learning opportunities from the perspective of variation.
Moreover, the paper makes several implications on teaching with variation. First, some types of variation will promote students’ mathematical thinking and problem-solving ability. They include procedural variation (Gu et al., 2004), as it was especially rich in the analysed classroom in which the teacher emphasized process. Second, students’ autonomy in the activity of variation is an important condition for learning. By engaging in both constructing and reflecting on the variation, students can be involved in the activity of changing their ways of seeing and experiencing the critical features. Third, the three viewpoints and the lesson analysis call attention to the importance of examining the students’ actual experience of and engagement in variation with their peers and the teacher.
The paper makes connections between the pedagogy of variation, which has been proven effective in practice in China, and a well-recognized structured problem-solving model in Japan by providing three viewpoints of variations. It will contribute to a systematic examination and use of the pedagogy of variations cross-culturally.

Author

• Keiko Hino, Utsunomiya University