• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.927-941
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• 2013

In this paper, we investigate and analysis high school students' generalization of cosine rule using analogy, and we study teaching and learning methods improving students' analogical thinking ability to improve mathematical thinking process. When students can reproduce what they have learned through inductive reasoning process or analogical thinking process and when they can justify their own mathematical knowledge through logical inference or deductive reasoning process, they can truly internalize what they learn and have an ability to use it in various situations.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.147-166
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• 2007

This study is about the law of cosines. It dealt with its historical origin and the developmental process of the age of Greece, Islam and Modern age. Especially, we tried to find out how the extension of the law of cosines for spherical triangles and tetrahedron from the law of cosines for plane was done. On the basis of this analysis, we investigated how the law of cosines was generated and proved it through the logical demonstration and mathematical induction. This made us find out the mathematical meaning of mathematical concepts.