國中資優數學之鴿籠原理的探討

The Study of Gifted Mathematics in Some Courses of Pigeonhole Principle in Junior High School

王派峰(Pai-Feng Wang)

指導教授 ： 王牧民

中原大學/理學院/應用數學研究所/碩士(2013年)

https://doi.org/10.6840/cycu201300192

摘要

本研究旨在探討國中資優數學教育之鴿籠原理的問題與原理，增進國中學生對邏輯思考的判斷與想法。研究主要以蒐集、整理、分類、解析相關試題，藉由教材讓學生對數學問題有另一層的思維，了解到其本質上具多樣性，活化並刺激學生的學習。

本研究經文獻探討與試題分析得到如下結論：
一、國中資優數學教育之鴿籠原理的教材，能使學生獲致不同層面的解題技巧，進而培
養國中學生多元思考的能力。
二、研究者所提出的解題技法整理如下：
(1) 以「最不利原則」作反向思考
(2) 建構適當鴿籠，解決圖形分割、整數分組、同餘等問題
(3) 利用鴿籠原理討論不同狀態的正確性

關鍵字

鴿籠原理 ； 資優數學

並列摘要

This research is aimed to discuss questions and principles of gifted mathematics in some courses of Pigeonhole Principle in junior high school in order to improve junior high school students’ judgments and realization of logical thinking. In this research, related questions are collected, organized, classified, and analyzed. And through these materials, students can contemplate more deeply what is under the surface questions and learn various forms of Pigeonhole Principle. Thus, students’ learning can be activated and stimulated.
After demonstrated literature review and item analysis, the researcher has come to the following conclusions:
A. Materials of Pigeonhole Principle in gifted mathematics in junior high school can lead students to acquire different strategies and techniques to solve mathematics questions.
Meanwhile, students’ diversified thoughts were developed.
B. Strategies and techniques that the researcher proposed are showed below:
1. Think in the opposite way by considering “the worst situation.”
2. Set an appropriate “drawer” to solve geometry, number theory, and congruent.
3. Discuss the rightness of the answers to different forms of questions by Pigeonhole Principle.

並列關鍵字

pigeonhole principle ； mathematically gifted students

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。顏啟麟(2011)。JHMC國中數學競賽2009~試題暨詳解。台北市：博凱。

NJ：Lawrence Erlbaum Associates.

Renzulli,J S.(1978).What makes giftedness：Reexamining a definition.Phi Delta Kappan,60,180-184.

中文部分

AOSHU奧數網試題。網址：http://www.aoshu.com/tk/aszsd/zt/ctyl/