高中數學不等式與極值之解題策略

The Strategies of Solving of Mathematical Inequality and Extreme Value Problems in Senior High Schools

劉騏瑋(Chi-Wei Liu)

指導教授 ： 李金城

中原大學/理學院/應用數學研究所/碩士(2017年)

https://doi.org/10.6840/cycu201700324

摘要

本研究旨在探討高中數學中關於不等式和極值的重要觀念與題型，目的在於將解題策略做分類統整，編寫高中數學之不等式和極值的教材，讓教師能藉由教材，使學生能體會到數學問題的本質，並提供給學生多樣化的解題方法，培養學生創造思考的能力，以提升學習興趣與解題能力。 編寫高中數學之不等式和極值的教材，能提供學生不同的解題策略且在驗證答案的過程中，培養學生多元思考的精神。研究者對不等式的研究主要涉及絕對不等式及條件不等式以的性質和應用，研究者整理出的解題策略能符合研究目的，對應到不同的題型有不同的解法可分為下列五種：
１.配方法求頂點2.算幾不等式3.柯西不等式4.判別式法:5.基本解題方法

關鍵字

不等式,極值,數學解題

並列摘要

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.

並列關鍵字

inequality,extremum,mathematical,problem solving

參考文獻

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