七年級學生的等號概念與其對代數學習之影響研究

Abstract

本研究主要在探究七年級學生的等號概念，並分析不同等號概念的七年級學生在一元一次代數式學習上的影響。本研究的主要目的有四項：（一）探討七年級新生的等號概念以及對於等號意義的理解；（二）瞭解不同等號概念的七年級新生對典型等式與非典型等式的判讀與解題策略；（三）瞭解「運算型」學生在學習等量公理後，其等號概念的拓展情形；（四）瞭解不同等號概念的七年級學生在一元一次代數式中解題策略與其學習成效。 本研究採問卷調查法，以國中七年級學生為調查與研究對象，由研究者自編前後測以及一元一次代數式學習成就測驗分析得到以下研究結論： 一、七年級學生在尚未正式接觸代數課程前，只有近五成的學生可以理解等號除「運算」意涵外，還有更深一層的等量「關係型」概念。 二、七年級學生多數能夠正確判讀非典型等式問題，唯獨「等號自反性」的題型僅有三成學生能夠理解。 三、七年級的關係型學生比運算型學生更能理解等號的特性，但擁有關係型概念不代表完全擁有解決非典型等式問題的能力。 四、七年級的運算型學生在處理典型或非典型等式時，所採用的解題策略傾向於「求得一個結果」，無法跳出計算的思考框架。 五、七年級的關係型學生在處理典型或非典型等式時，能運用「等號的替代意義與等價意義」進行解題，同時展現較多元的解題策略。 六、七年級的運算型學生在化簡一元一次式時往往會忽略要維持等號兩邊等價的關係，並固著於計算出一個最後的數值。 七、部份運算型學生認為等號是一種計算過程的連結，因此習慣在所有解題步驟中加入等號，而忽略了等號兩邊必須等價的概念。 八、七年級關係型學生在一元一次代數式的學習成效優於運算型學生。 最後，本研究根據研究結果，提出具體建議，以做為未來相關研究、教材設計與等號概念教學的參考。

This study aimed to explore the concept of seventh graders’ equal sign , and how does it affect student’s learning of algebra. There are four main purpose of this study：1. To realize the seventh graders' understanding of the equal sign concept；2. To analysis of seventh graders' who have different equal concept problem solving strategies on standard or nonstandard equation；3.To analysis the operational students how to change the concept of the equal sign by learning through equality axioms；4. To analysis of seventh graders' who have different equal concept problem solving strategies on algebra and how does it affect student’s learning of algebra. The study used questionnaire survey to analysis of seventh graders' equal concept. Through some test designed by the researcher can get the following conclusions： 1. Before learning algebra, there is only 50% of seventh-graders can really understand the relational meaning of equal sign. 2. Most of seventh-graders can distinguish the nonstandard equation, but only 30% of them can understand the equal sign reflexive Quiz. 3. In understanding the concept of equal sign, the relational seventh-graders are better than operational ones. But has a relation concept is not the same as having the ability to solve problems. 4. When the operational-seventh graders solve the nonstandard equation, they are used to calculate a result or to do something. 5. When the relational seventh-graders solve the nonstandard equation, they have a variety of problem-solving ability. 6. The operational seventh-graders always ignore the equivalence equal significance when they solve algebra problems. 7. A part of operational seventh-graders consider the equal sign is a link of calculation process. 8. In the effect of learning algebra, the relational seventh-graders are better than the operational ones. In conclusion, the findings of this study show that specific proposals are offered to be used in the design of instructional materials and the equal sign concept as reference.