Using the learning study grounded on the variation theory to improve students’ mathematical understanding

Abstract

This paper illustrates how teachers make use of a learning theory, the variation theory, as well as their own professional expertise and collaboration to help students improve their mathematical understanding. A learning study (cf. Pang & Marton, 2003) involves a group of teachers who undertake theoretically grounded collaborative action research on their own practice. Unlike design experiments, a learning study emphasises teachers’ involvement in and ownership of the innovative practices that echo the spirit of the lesson study. The primary role of the researcher(s) in a learning study is to have a professional dialogue with the teachers and to provide professional support when necessary. Furthermore, the major focus of a learning study is on the objects of learning, i.e., on what students are expected to learn, rather than on the teaching arrangements. According to the variation theory, to help students appropriate certain objects of learning, certain patterns of variation and invariance that are co-constituted by the learners and the teacher are necessary. To exemplify this, this paper presents two learning studies conducted in mathematics in Hong Kong. The results show that there was a marked improvement in students’ mathematical understanding after learning studies grounded in the variation theory were introduced.