• School Mathematics
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• v.10 no.3
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• pp.357-374
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• 2008

The complex number system is supposed to introduce first chapter in the first grade of high school. When number system is expanded to complex numbers, the main aim is to understand preservation of algebraic structure with regard to the flow of curriculum and textbook. This research reviewed overall alternative articulation and treatment of textbooks from a logical viewpoint. Two research questions are developed below. First, in the structure of the current curriculum, when we consider student's 'level', how are the alternative articulation and treatment of textbooks in complex unit on a logical point of view? Second, What are more logical alternative articulation and treatment? What alternative articulation and treatment are suitable for a running goal? and what are the improvement which is definitive?

• Journal of the Korean School Mathematics Society
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• v.8 no.3
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• pp.367-382
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• 2005

In this paper, we deal with various contents relating to the group concept in school mathematics and teaching of algebraic structures indirectly by combining these contents. First, we consider structure of knowledge based on Bruner, and apply these discussions to the teaching of algebraic structure in school algebra. As a result of these analysis, we can verify that the essence of algebraic structure is group concept. So we investigate the previous researches about group concept: Piaget, Freudenthal, Dubinsky. In our school, the contents relating to the group concept have been taught from elementary level indirectly. Tn elementary school, the commutative law and associative law is implicitly taught in the number contexts. And in middle school, various linear equations are taught by the properties of equality which include group concept. But these algebraic contents is not related to the high school. Though we deal with identity and inverse in the binary operations in high school mathematics, we don't relate this algebraic topics with the previous learned contents. In this paper, we discussed algebraic structure focusing to the group concept to obtain a connectivity among school algebra. In conclusion, the group concept can take role in relating these algebraic contents and teaching the algebraic structures in school algebra.