Teaching through Variation

This book is about variation and invariance in the teaching of mathematics, that is, about what instances, examples, tasks are used and in which order, to make it possible for students to make concepts, principles, methods their own. Although we can find cases of individual teachers and individual textbook authors paying special attention to such aspects of the teaching of mathematics in different places in the world and at different points in time, such focused attention on the pattern of similarities and differences-especially on the latter-between tasks, instances, examples seems have been particularly common in China for a long time. Moreover, this character of Chinese practice of teaching mathematics has been made explicit by Gu (1991) who called it Bianshi (i.e. teaching with variation) and who tried to relate it to theoretical and empirical research on the learning and teaching of mathematics (in the following the acronym “BS” is used to widely refer to the Chinese tradition of systematically using variation and invariance in the teaching of mathematics).