• Yu-Ling TsaiEmail author
  • Ching-Kuch Chang


This article reports an alternative approach, called the combinatorial model, to learning multiplicative identities, and investigates the effects of implementing results for this alternative approach. Based on realistic mathematics education theory, the new instructional materials or modules of the new approach were developed by the authors. From the combinatorial activities based on the things around daily life, the teaching modules assisted students to establish their concept of the distributive law, and to generalize it via the process of progressive mathematizing. The subjects were two classes of 8th graders. The experimental group (n = 32) received a combinatorial approach to teaching by the first author using a problem-centered with double-cycles instructional model, while the control group (n = 30) received a geometric approach to teaching, from the textbook by another teacher who uses lecturing. Data analyses were both qualitative and quantitative. The findings indicated that the experimental group had a better performance than the control group in cognition, such as for the inner-school achievement test, mid-term examination, symbol manipulation, and unfamiliar problem-solving: also in affection, such as the tendency to engage in the mathematics activities and enjoy mathematical thinking.

Key words

combinatorial approach distributive law multiplicative identities 


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Copyright information

© National Science Council, Taiwan 2008

Authors and Affiliations

  1. 1.Chongde Junior High SchoolTaichungRepublic of China
  2. 2.Graduate Institute of Science EducationNational Changhua University of EducationTaiwanRepublic of China
  3. 3.Taichung CityRepublic of China

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