This study undertakes a new attempt in theory and practice in curriculum design in mathematics, which includes an operational model, its theoretical interpretation and experimentation.
The operational model, called Spiral bianshi (literally means variation) Curriculum, is extracted from the use of connecting problem clusters, one of the prominent features in current practice in mathematics instruction in Mainland China, the origin of which can be traced back to the Qingpu experience in Shanghai in the 1980s. Such a long history of practice was conceptualized according to the nature of mathematics and mathematics learning. The Spiral bianshi Curriculum comprises four components: The inductive bianshi which abstract mathematics notions from realistic situations, the deepening bianshi which lead one to new concepts and rules from already established one, the broadening bianshi which connects various concepts which are already acquired and the applicative bianshi which helps learners applying concepts and rules to more realistic situations.
Division of fraction was taken as the topic for experimentation. The corresponding bianshi curriculum was designed and experimented in 14 classes in three Primary schools in Hong Kong. The other 13 classes in three comparable schools were taken as control group.
The students' cognitive learning outcomes and self-efficacy were measured before and after the experimentation by means of a pre-test and a post-test. The students' approach to learning and other affective variables were measured too.
Significant positive results were obtained by the spiral bianshi curriculum. The post-test scores of learning outcomes in the experimental group were significantly higher than those in the control group while all these scores indicated no significant differences in the pre-tests among these two groups. The students in the experimental group reflected that they have clearer relevant concepts than their counterparts. They also understood