Seeking Evidence for Effective Teaching With Variation

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

Abstract

Recent years have witnessed an increase in research focused on studying on perspectives of Chinese mathematics instructions. The sustained interest is partly due to the outstanding performances of Chinese students in international studies such as the Trends in International Mathematics and Science Study (Mullis et al., 2012) and the Programme for International Student Assessment (OECD, 2014); and partly due to the shared interest in comparative studies of instructional practice across different cultural systems (Mok, 2015). Despite the fact that instructional practice can be viewed as a cultural activity (Stigler & Hilbert, 1999), effective implementation of pedagogical theory may have a vibrant feature to meet the needs of different groups of students and different contents of teaching. The Bianshi teaching (e.g. teaching with variation) by Gu has been popular in Mainland China since the 90’s (Experimenting Group of Teaching Reform in maths in Qingpu County, 1991) and many Chinese researchers (Bao, Huang, & Gu, 2003) have developed the application of the pedagogical theory for designing effective learning paths for the students to understand mathematical topics in mathematics classroom instruction. The objectives of this paper are two-fold: to give an example of a lesson applying the pedagogy of variation and to seek for empirical evidences of what the students might have learned.
According to Gu, Huang, and Marton (2004), there are two important types of variation in application, namely the conceptual variation and procedural variation. In brief, conceptual variation refers to understanding concepts from multiple perspectives and procedural variation is progressively unfolding mathematics activities by enhancing the formation of concepts, experiencing problem solving from simple to complex, and establishing a system of mathematics experience that may be internalized. Specific to the teaching of an algebraic formula, the authors of this chapter, based on the work of Gu, used two major categories of variation, namely, variation in the style of examples or questions, and variation in the way of recognizing the formula; with an innovative dimension of a mathematical thinking (discovering, justifying, and applying the formula) in the design of the experimental lesson.
The experimental lessons took place in a middle school in Beijing in 2015. The chosen teacher had 14 years of teaching experience and was well informed by the pedagogy of variation. The teacher taught two 8th grade classes of different abilities. Class 1 had 38 students with average standard and Class 2 had 30 students with slightly poorer standard than Class 1. Students in both classes took a post-lesson test based on the objectives of the lesson. The test consisted of questions about the formula of perfect square. In addition, the students wrote their post-lesson reflections.
The results of the experiment, while demonstrating a vibrant application of the Chinese pedagogy of variation in tandem with a mathematical thinking dimension, provided evidence of students’ learning outcomes for an effective lesson. Further to providing a window for understanding the effective Chinese mathematics instructional culture in practice, the integration of the mathematical thinking dimension adds a transcultural feature to the pedagogical theory.

Authors

• Ida Ah Chee Mok, University of Hong Kong

• Chunxia Qi, Beijing Normal University