“Variation problems” and their roles in the topic of fraction division in Chinese mathematics textbook examples

摘要

This article deals with the roles of variation problems (“one problem multiple solution” and “one problem multiple changes”) as used in Chinese textbooks. It is argued that variation problems as an “indigenous” Chinese practice aim to discern and to compare the invariant feature of the relationship among concepts and solutions. This practice also aims to provide opportunities for making connections, since comparison is considered the pre-condition to perceive the structures, dependencies, and relationships that may lead to mathematical abstraction. In the first part of the article, the “indigenous” practice is discussed against its philosophical Daoism and Confucianism backgrounds. To grasp its distinctiveness, a comparison between Chinese and American textbooks is carried out. In the second part of the article, the focus is on the manner in which fraction division is articulated in an important Chinese textbook. A framework to understand variation practice is introduced and some educational implications are suggested.