| Summary: | 碩士 === 中原大學 === 應用數學研究所 === 105 === The purpose of this study was to find out the important concepts and categories in senior high schools in Taiwan.This research examined and integrated the mathematical problem solving strategies and compiled inequality and extremum teaching materials into textbooks of mathematics.By using the teaching materials, it is able to help students to realize the essence of mathematical and furthermore provided various methods of problem-solving. Therefore, the methods were beneficial for students to develop creative thinking and motivated interests of solving problems. The teaching materials of inequality and extremum from senior high school can provide different strategies. In addition, it is useful to cultivate diverse thinking during the process of verifying solutions.It contained the nature and application of absolute inequality and conditional inequality.It is concluded that the strategies of problem-solving were able to achieve the research purpose and gave a variety of solutions. There were five solutions shown below,
1.Find vertex by using completing squares
2.Inequality of arithmetic and geometric means
3.Cauchy–Schwarz inequality
4.Discriminant method
5.Basic problem-solving solutions.
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