高中數學問題新思維之研究

The research of the innovative thinking of the high school mathematics problems

莊志宏(Chih-Hung Chuang)

指導教授 ： 王牧民

中原大學/理學院/應用數學研究所/碩士(2014年)

https://doi.org/10.6840/cycu201400577

摘要

本研究是為了釐清解決高中數學問題過程中所隱含的數學思維，並藉由此次研究能夠討論出一般的解題程序作為培養學生數學能力的觀念與原則。高中數學原就延續國中數學的課程，並為將來進入高等教育的養成教育。故以高中數學領域課綱範圍為基礎，編寫高中數學之內容的教材，讓教師能藉由教材的研究，讓學生能體會到數學問題的本質，並提供給學生可依循的解題方法，培養學生作獨立研究思考應有的原則與習慣，提昇學習興趣。研究結果如下：
一、 高中數學的教材，並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。
二、 研究者所編製的高中數學之教材，最後整理出的解題技法，能符合研究目的。解題技法詳述於第五章的結論部分。

關鍵字

高中數學

並列摘要

This research is aimed to clarify certain mathematic notions implied in the process of working on mathematic problems of senior high school level. By doing so, It is hoped that general problem-solving methods can be offered to help develop students’ abilities in mathematics.
Mathematics in senior high school is the continuation of that in junior high school and the preparation for higher education. Accordingly, this research is proceeded based on the schema of mathematics of senior high school level in order to be done as a project. With this project, teachers can help students see the nature of mathematics problems, provide them with possible solutions, and form certain principles and habits students are supposed to have during the process of developing their independent thinking, and raise their interests in learning as well. The results of the research are as follows:

I. This project offers students various strategies of solving problems. Besides, it helps diversify students’ thinking through the process of testing and verifying answers.
This project finds out methods for solving problems which tally with the purpose of the research. The methods are dilated on in the conclusion part in Chapter Five.

並列關鍵字

innovative thinking

參考文獻

劉貞宜(2000)。數學資優生的解題歷程分析。國立臺灣師範大學特殊教育研究所論文。

Groen, G & Resnick, L.B.(1977).Can preschool children invent addition algorithms? Journal of educational psychology,69,645-652.

Renzulli,J S.,Resi,S.M., & Smith, L.H.(1981).The Revolving Door Identification Model.

參考文獻

中文部分