國中資優數學多項式因式分解之解題策略

The Problem-Solving Strategies of Factorizing Polynomial for Gifted Mathematics in Junior High School.

羅詩凱(Shih-Kai Lo)

指導教授 ： 李金城

中原大學/理學院/應用數學研究所/碩士(2015年)

https://doi.org/10.6840/CYCU.2015.00221

摘要

摘要
本研究旨在探討國中資優數學中關於多項式因式分解的重要觀念及題型。故以國中因式分解課程為研究基礎，包含提出公因式、乘法公式、十字交乘法、分組提公因式、公式法等等，並從補充教材及資優相關考題進行分析，並編寫國中資優數學關於多項式因式分解的教材，希望藉以提升國中數學資優生的數學學習能力。讓學生除了能利用舊經驗解題，也能綜合運用解題技巧，增進國中學生對邏輯思考的判斷與想法，了解到數學問題具有多樣性，刺激學生思路活化，並提升學生多元思考的動機。
本研究經文獻探討與試題分析得到如下結論：
一、多項式因式分解中，隨著多項式的變量、次方、項數不同，而會有所不同的因式分解技巧。對於國中課程提到的提出公因式、乘法公式、十字交乘法、配方法、公式法等因式分解技巧之外，運算能力也是重要關鍵，面對複雜的多項式，清晰的因式分解脈絡有助於更有效地解決問題。
二、此外，敏銳的觀察力與足夠的數學技巧能幫助學生做豐富及多元的推測，有足夠的知識連結即能推敲出解題關鍵及技巧，並以此完成因式分解。

關鍵字

數理資優生 ； 多項式因式分解

並列摘要

Abstract
This study aims to investigate the important concepts and questions about Factorizing Polynomial based on the analysis of teaching curriculum in junior high school, especially for mathematically-gifted students. The analysis includes teaching materials on the common factors,multiplication formula,cross method, packet disassembly,formula method, supplementary teaching materials, and tests specifically designed for gifted students. In addition to analysis, compiling teaching materials are used to enhance the ability of mathematically gifted students in mathematics learning.
The results of this study could facilitate students to make use of experiences of solving problems, combine problem-solving skills , and improve junior high school students’judgments and realization of logical thinking. And through these materials, students can learn various forms of Factorizing Polynomial in order to activate and stimulate students’learning motivation , also enhance their thinking in various ways.

It should be concluded, from literature reviews and the analysis of tests, as following.
1.For Factorizing Polynomial, there are corresponding problem-solving skills
from different variables, the power of n and number of items .Except the important concepts based on teaching curriculum in junior high school, operation capacity is also an important key to solving the full, complex calculations. Clearly calculating facilitates students to find out the answers effectively.
2.In addition, good observation and enough mathematical knowledge can help students extensive speculated conjectures, with adequate knowledge links that can associate with solving keys and skills, and help students solve problems.

並列關鍵字

mathematically gifted students ； Factorizing Polynomial

參考文獻

王派峰(2013)。國中資優數學之鴿籠原理的探討。檢索日期2015年6月7日。

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

problems.NJ：Lawrence Erlbaum Associates.

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

參考文獻