國中代數數學解題之探討

The Study of Algebra Problem Solving in the Mathematic Courses of Junior High School

洪榆茜(Yu-Chien Hung)

指導教授 ： 王牧民

中原大學/理學院/應用數學研究所/碩士(2016年)

https://doi.org/10.6840/cycu201600174

摘要

本研究旨在探討國中數學中關於代數的重要觀念及題型。故以國中數學領域課綱範圍為基礎，編寫國中數學之代數的教材，包含一元一次方程式、一元一次不等式、二元一次方程式、一元二次方程式、多元方程式等，希望透過此教材使學生體會到數學問題的本質，並提供給學生多樣化的解題方法，以提升數學學習興趣與解題能力。研究結果如下：
國中數學之代數教材，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。
研究者所編製的國中數學之代數教材，最後研發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，簡列如下：
解代數相關方程式及不等式必須熟悉基本運算規則。
較複雜之題型或多次方程式可善用代換或乘法公式簡化問題。
理解方程式與坐標圖形的相關性。
針對代數之應用問題，要能將文字敘述轉換成方程式或不等式，因此了解題意是首要解題能力。

關鍵字

代數 ； 方程式 ； 不等式

並列摘要

The purpose of this study is to investigate the important concepts and questions of algebra.Based on the analysis of teaching curriculum in Grade7-9,the analysis includes teaching materials on the one-degree equation with one variable, the one-degree inequation with one variable, the one-degree equation with two variables, the two-degree equation with one variable, the one-degree equation with multiple variables. Teaching materials on the inequality for students were designed to make them understand the essence of mathematics questions.In addition, the teaching materials provided the students with various ways to solve mathematics questions, increased their interest in learning mathematics,and enhanced the ability of students in mathematics learning.
The results are as follows:
1. The teaching materials in the present study provided students with different strategies and techniques to solve mathematics questions. Furthermore, in the process of answer validation, students’ diversified thoughts were built.
2. The teaching materials were summarized by the researcher and the solving techniques in them met the purpose of the present study. Problem-solving techniques is detailed in the concluding portion of Chapter Five.The techniques are listed below:
(1) Solving algebraic equations and inequalities must be familiar with the basic rules of operation.
(2) In regard to the more complex questions or more equations,we can simplify the problem by using
the substitution or multiplication formula.
(3) Understand the correlation between equations and coordinate graphics.
(4) For questions of algebra,we have to convert statements into equations.Hence,the statements is the
first priority of solving problems.

並列關鍵字

algebra ； equation ； inequality

參考文獻

顏德琮（2004）。探討以概念改變策略促進代數符號理解對代數成就表現及學習興趣之影響－以一元一次方程式為例。國立師範大學科學教育研究所碩士論文。

謝佳叡（2001）。國中生配方法學習歷程中之數學思維研究，國立台灣師大數學研究所碩士論文。

陳盈言（2000）。國二學生變數概念的成熟度對其函數概念發展的影響。台灣師範大學數學系碩士論文。

Clement, J.,Lochhead, J.,＆Monk, G.(1981). Translation difficulties in learning mathematics.American Mathematical Monthly,88,286-290.

Wanger,S.(1981). Conservation of equation and function under transformation of variable.Journal for Research in Mathematics Education,12,107-118.