Using The Learning Study Grounded On The Variation Theory To Improve Students’ Mathematical Understanding

This paper illustrates how teachers make use of a learning theory, the variation theory, as well as their own professional expertise and collaboration in a learning study (cf. Pang & Marton, 2003) to help students improve their mathematical understanding. A learning study 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 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. The results of the learning study reported here show that students belonging to the learning study group outperformed their counterparts in the comparison group. It seems that the variation theory is a powerful tool for improving student understanding. Furthermore, by engaging in systematic and collective evaluation of their classroom practices, professional dialogue among colleagues on how to best deal with the object of learning, and documentation and dissemination of what they have learned from the study, teachers’ sensitivity towards student learning and their own teaching, towards students’ different ways of understanding an object of learning and their own different ways of handling it, and towards the potential of a learning theory are all simultaneously enhanced. This empowers them to see their own professional practice from both a learning- and learner-centred perspective