From "exploring the middle zone" to "constructing a bridge": Experimenting in the spiral Bianshi mathematics curriculum

Ngai Ying WONG, Chi Chung LAM, Xuhua SUN, Mei Yan Anna CHAN

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12 Citations (Scopus)


The spiral bianshi curriculum, an improvement on bianshi teaching developed by Gu (2000) and in line with Marton’s theory of variation (Marton & Booth, 1997), was tried out in a primary school in Hong Kong. This improved theoretical framework for the spiral bianshi curriculum comprises four types of bianshi problems—the inductive bianshi, the broadening bianshi, the deepening bianshi, and the applicative bianshi. Based on this framework, the research team developed a set of teaching materials on the three topics of division of fraction, speed, and volume. The materials were tried out in 21 Primary 6 classes (a total of 686 students) in a school. The effect was compared with a reference group using standard textbook materials in Hong Kong. A series of instruments, pre-tests, and post-tests were administered to gauge the effects on students’ performance in solving routine and non-routine problems, as well as the affective outcomes including self-concept, attitude towards learning mathematics, approaches to learning, and conceptions of mathematics. The intervention effects of the experimental design were examined by hierarchical regression analysis. The research reveals that students using spiral bianshi teaching materials performed significantly better than their counterparts using standard textbook materials. However, no significant differences were identified among affective learning outcome variables despite the positive results on cognitive learning outcomes. The findings indicate that spiral bianshi curriculum has high potential in enhancing students’ learning effectiveness. However, further studies are needed to map its strengths in detail. Copyright © 2009 National Science Council, Taiwan.
Original languageEnglish
Pages (from-to)363-382
JournalInternational Journal of Science and Mathematics Education
Issue number2
Publication statusPublished - Apr 2009


Wong, N.-Y., Lam, C.-C., Sun, X., & Chan, A. M. Y. (2009). From "exploring the middle zone" to "constructing a bridge": Experimenting in the spiral Bianshi mathematics curriculum. International Journal of Science and Mathematics Education, 7(2), 363-382.


  • Curriculum evaluation
  • Pedagogy of variation
  • Primary school mathematics
  • Speed
  • Spiral bianshi curriculum


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