臺灣博碩士論文加值系統

摘 要
本研究主要是利用概念心像和概念定義的互動歷程來探究國小六年級學童對於四邊形幾何概念的瞭解情形。本研究基於欲瞭解學生概念心像和概念定義的互動情形之前，必先瞭解學生擁有怎樣的概念心像和概念定義，因此將研究分成兩個部分。研究一是探究學生對於四邊形幾何概念概念心像和概念定義的瞭解情形，對象為研究者所任教的班級學生共計30人；首先利用自編之測驗進行概念調查，其次再以測驗上所呈現的各類迷思概念為依據，選取12位學生進行個別的訪談，其研究結果作為研究第二部分的重要依據。研究二則是探究學生概念發展過程中概念心像和概念定義的互動方式，對象是自研究一30位學生中立意取樣選取三名學生進行個別晤談，研究資料的分析來源是對三位受訪者訪談錄影帶轉譯和編輯而成的訪談原稿。
研究發現，學生在四邊形幾何圖形的概念心像上普遍有包含性不足的情況，也就是有些圖例被錯誤地排除（如：以為斜擺的正方形是菱形，但不是正方形），此一現象應與學生接觸的通常是典型圖例所致，且會影響更高層次的幾何推理之發展，例如無法理解正方形與菱形的包含關係。另外也有部分概念出現相反的現象，也就是概念心像中混淆了錯誤的圖例在內（如：以為鳶形也是菱形的一種）。對於上述概念心像的問題，研究者嘗試以增加非典型例、特例，或宣告反例的方式處理，發現不只可以修正概念心像，也可以進一步改變概念定義。以Vinner（1991）的問題解決歷程模式圖為參考，研究者也以模式圖說明上述這些修正的歷程。
至於概念定義的部分，學生已經逐漸發展出以圖形特徵加以描述的能力，不過受到語彙能力的影響，對於一些邏輯性的語詞較不易瞭解，因而對於概念產生迷思。學生四邊形幾何圖形概念定義的建立和修正是藉由概念心像來進行，不過概念心像的調整又常常必須藉由概念定義的幫助，但學生對概念心像和概念定義間存在著不一致現象，不一定會覺察，如果被指出時，學生對於概念的詮釋會比較依賴概念心像。
在研究概念心像的瞭解過程中發現，學生透過選圖方式所呈現的答案優於透過繪圖方式所得到的答案，研究者推測這和學生解題思考的歷程有所不同所致，這也可以用研究者的概念發展模式圖加以說明。

Abstract
This study tries to realize grade 6th students’ understanding about quadrilaterals, through the interaction between the concept image and the concept definition. Before we get to the interaction between concept image and the concept definition, first we need to understand what ideas student have about concept image and the concept definition. Therefore, this study will be divided into two parts. First part is to understand what ideas students have on concept image and concept definition regard to quadrilaterals. Research target is 30 students in my class. First, I did a concept test with these students. Then base on the myth that shows on the test result, I’d chose 12 students, and did the individual interview. Base on the content of these individual interviews, move on to part II of this study. The second part of this study is to understand during the development of concept, how the interaction takes place between concept image and the concept definition. 3 target students are chose from the 30 students, and did individual interview. The analysis data for part II study is base on the interview videos of these 3 target students。
Research found, generally speaking, students’ concept image is not fully covered about quadrilaterals. That is to say, some graph is excluded wrongly. For example：students took oblique square is rhombi, not square. This phenomenon probably caused by they see the typical shape all the time, which will impact the development of the higher level reasoning. Say, students might not be able to understand the inclusion relationship between square and rhombi. In addition, some of the concepts show just the opposite phenomenon. That is the concept image mix the mistaken shapes. For example:：Students thought kite is part of the rhombi. Regard to above issues, I try to handle them by adding the non-typical types、exceptions, or announce the opposite examples. I found it not only can fix students’ concept image, but also can change their concept definition. Take Vinner’s（1991）problem solving process model graph for reference, I also tries to explain these fixing process with the model graph.
As to the concept definition, students have gradually developing the ability to describe the shapes. However, their language ability is limited, so some logical terms are not easy to be understood to students, and caused some myth. Through the concept image, students build up and fix the concept definition of quadrilaterals; nevertheless, the adjustment of concept image often needs help from the concept definition. However, students might not aware of their concept image and concept definition are not consistent, when point that out students tend to rely on the concept image more.
In the process of study the concept image, I found answer by picking is better than drawing. I assume it has to do with students’ problem solving process, this can also be explain with research’s concept develop model graph.

內 容 目 次
第一章 緒論…… …….…………………...…………………..1
第一節 研究動機與目的………………………………….1
第二節 待答的問題……………………………………….3
第二章 文獻探討………………..………..…...………………4
第一節 學童幾何概念之理論…………………………….4
第二節 概念心像和概念定義之探究..………………….19
第三節 定義和圖例間不一致性的探討………………...27
第四節 國小學生幾何圖形概念的探究………………...32
第三章 研究一：幾何概念知識的調查…………….……….40
第一節 研究對象……………….………………………..40
第二節 研究工具………………………………………...40
第三節 實施步驟………………………………………...44
第四節 結果與討論……………………………………...45
第四章 研究二：個案的研究……………………….……….56
第一節 受試者………………………………………...…57
第二節 訪談問題與程序……………………...…………57
第三節 訪談的實施及反思記錄………………………...60
第四節 資料的整理與分析……………………………...61
第五節 結果與討論……………………………………...61
第五章 結論與建議…………………………………..….…95
第一節 結論……………………………………………...95
第二節 建議…………………………………………….105
參考文獻…………………………………………………….108
附錄一………………………………………….………...….116
附錄二……………………………………………………….123
附錄三……………………………………………………….124

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