國中資優數學之方程式的探討

The Study of Gifted Mathematics in Some Courses of Equations in Junior High School

莊馥毓(Fu-Yu Chuang)

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/CYCU.2013.00019

摘要

摘要
本研究旨在探討國中資優數學中關於方程式的重要觀念及題型。故以國中方程式課程為研究基礎，包含一元一次方程式、二元一次方程式、一元二次方程式、多元方程式等，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方程式的教材，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，也能建構新觀念，使數學資優生能針對題目作有系統的分析，建構有效的解題策略並有能力呈現邏輯清晰的解題歷程。亦希望能給予中學教師在教學上得以旁徵博引，滿足數學資優生在學習上的需求，並提升數學資優生多元思考的動機。
本研究經由文獻探討與試題分析後獲得以下結論：
(一)方程式的解題中，對於題意的了解為解題之第一要務。要能將文字敘述轉換成數學文字符號的過程中，閱讀能力也就非常重要。
(二) 此外，足夠的數學知識能幫助學生做豐富及隨機的推測，有了足夠的知識連結即能聯想到解題關鍵，並能以此列出方程式。
(三) 運算能力亦是在完整解題中重要的關鍵，面對複雜的運算，清晰的計算脈絡有助於找出答案。

關鍵字

方程式 ； 數學資優生

並列摘要

Abstract
This study aims to investigate the important concepts and questions of equations based on the analysis of teaching curriculum in Grade7-9, especially for mathematically-gifted students. The analysis includes teaching materials on the one-degree equation with one variable, the one-degree equation with two variables, the two-degree equation with one variable, the one-degree equation with multiple variables, 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 to solve problems and to construct new ideas, make mathematically gifted students analyze systematically for the statement of questions, construct effective problem-solving strategies, and complete the logical clarity of problem- solving process. The results can be given more pedagogic application to junior high school teachers in order to meet the needs of mathematically gifted students in learning and to enhance the motivation of multivariate thinking in various ways.

It should be concluded, from literature reviews and the analysis of tests, as following.
1.For solving equations, understanding the statements is the first priority of solving problems. For being able to convert statements into mathematical symbols, reading skills are very important.
2. In addition, Getting enough mathematical knowledge can help students extensive and randomly speculated conjectures, with adequate knowledge links that can associate with solving keys, and help students list the equations.
3. Operation capacity is also an important key to solving the full, complex calculations. Clearly calculating facilitates students to find out the answers.

並列關鍵字

Equation ； mathematically gifted students

參考文獻

7.財團法人九九文教基金會出版(2011)。JHMC國中數學競賽2003~2008試題暨詳解。台北市：博凱。

8.財團法人九九文教基金會出版(2011)。JHMC國中數學競賽2009~試題暨詳解。台北市：博凱。

20.蔡莉莉(2011)。國小高年級資優生與一般生數學解題表現之比較。國立臺北教育大學數學暨資訊教育學系研究所論文。

Coleman. M. R. 2003. Four variables for success. Gifted child today. 26:22~24

參考文獻