Abstract ▼ AI-Helper

The purposes of this thesis are to 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 jus...

The purposes of this thesis are to 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. By using ‘Extension of Cosine Rule’, problems students’ may have will be identified and instruction models and solution plan will be introduced. So this study presents two questions as follows. 1. When students guess a generalized cosine rule, what similarity of elementary questions are used to infer the rule? 2. What activities affect to infer a generalized cosine rule? This study comes to results as follows. First, To give lessons which generalize and extend mathematics law by using analogical thinking process, teachers need to explain the rule considering the meaning of the rule, connection structure and comparability rather than using simple extension. Second, Teachers should let students think about the characteristics of polygon itself rather than divide the polygon into several triangles. Also, teachers should let students think about specific examples in verifying their own rules. Third, in fact many students have no prior knowledge of proving Cosine Rule of triangle. However, the number of students who could prove Cosine Rule of quadrangle was increased, when they learned how to prove Cosine Rule of triangle. If students have prior knowledge on Cosine Rule of triangle should be identified before the main class. Fourth, Teachers need to make students do considerable practice of complex theorem and help students to widen their perspective by practicing vertical extension.