Teaching Algebra Through Variations: Contrast, Generalization, Fusion, and Separation

Teaching with variation is recently identified to be an important feature of Chinese mathematics lessons, contributing to a factor conducive for learning. The theoretical stance promoted within the Variation Theory of Learning is that learning involves experiencing by which the learners develop a way of seeing or experiencing. Hence, it is very important for learners to discern the critical features of the object of learning, which can be referred to as the topic of the lesson. Further application of the ideas to learning experiences in lessons, discernment is made possible when variation concerning the critical aspects of the object of learning is embedded in the design of the instructional tasks or in the interaction between teacher and students and between peers. Within this paper we provide empirical examples from algebra lessons in Hong Kong and Shanghai, to illustrate key skills in creating useful patterns of variation in the teaching and learning namely contrast, generalization, fusion and separatio