臺灣博碩士論文加值系統

直觀規律對K-6年級學童面積概念之探究
中文摘要
本研究的主要目地是先調查K-6年級學童現行知識和錯誤的直觀迷思概念。
樣本來自台北縣兩所國小和宜蘭市一所國小。四個問題是:(一)面積是什麼? (二)面積在哪裡? (三)最大的面積是什麼? 最小的面積是什麼? (四)面積如何測量? 217人被問到現行面積概念，559人測驗的目地是發現直觀規律以及面積的迷思概念。
本研究發現分成二部份:
一、有關面積現行知識部份：
大部份的學童通常使用五種策略來解面積題。
(一)採視覺策略
(二)採工具策略
(三)公式策略
(四)語言策略
(五)狹義面積策略
從以上策略中發現學童在面積現行概念上的面積迷思概念：
1.看不見的東西沒有面積。
2.物體不是規則的或不能被計算就沒有面積(如百格板) 。
3.有規則圖形(長和寬)，其能用公式算出才有面積的存在。
4.面積就是平面圖形中要有大的、小的圖案才有面積的存在。
5.有生命的物體其局部平平的地方才有面積的存在。
6.和長度、體積混淆。
二、有關直觀的部份：
(一) 面積概念在性別方面沒有顯著差異
(二) 面積概念在年級層方面有顯著差異
(三) 面積概念在年級層和性別交互作用方面沒有顯著差異
研究顯示：兒童在面積概念是具有Tirosh & Stavy 等人（1996，1998，1999）所提出的四個直觀規律，此外尚有新的直觀現象。如Linear A Linear B、Different A Different B。
關鍵字:面積、保留、實測、估測、直觀、迷思

Based on Intuition rules to study the area concept for
K-6 graders in Taiwan
Abstract
The purpose of this study was to investigate the informal knowledge and misconceptions consisting of intuitive rules in area for K-6 graders in Taiwan.
Subjects were from two elementary schools in Taipei County and one elementary school in Yilan city. Fours items were given: (一)What is area? (二)Where is the area? (三)What object has the largest area ? What object has the smallest area? (四)How to measure it? 219 pupils were asked to inquire informal knowledge of area , 559 pupils were tested by other self-designed testing to find intuitive rules which caused to the misconceptions of area. The findings are divided by two parts to present:
一、 information knowledge part :
Most pupils used five strategies to process the problem of area.
(一) Visual strategy
(二) Tool strategy
(三) Formula strategy
(四) Language strategy
(五) Narrow sense strategy
So they have the following misconceptions:
1. Invisible object does not have area.
2. Object does not have area if it can’t be covered or can’t be calculated by instructive tools.(such as hundred grids of paper)
3. Object does not have area without length or width.
4. Misunderstanding the definition of terms (area : the size of a plane) only a shape (object) possessing larger part as well as smaller part has area.
5. Only regular plane has area, irregular shape and surface do not have area.
6. Confusing with length and volume.
二、intuitive rules part:
(一) There is no significant difference in gender for the performance of area concept.
(二) There is significant difference in grade for the performance of area concept.
(三) There is no significant interaction between gender and grade in the performance of area.
In addition to 4 intuitive rules proposed by Israel Scholars( Tirosh & Stavy), there are other two kinds of intuition phenomena that are also found: that is Linear A Linear B & Different A Different B.
Keywords : area、conservation、measurement、estimation、intuition 、misconceptions

目　　　錄
第壹章 緒論 1
第一節 研究動機 1
第二節 研究目的 2
第三節 研究問題 3
第四節 名詞解釋 3
第五節 研究範圍與限制 5
第貳章 文獻探討 6
第一節 皮亞傑的認知發展階段論 6
第二節 面積概念發展 6
第三節 面積迷思概念 9
第四節 直觀的意義 13
第五節 直觀認知特性 15
第六節 直觀的分類 16
第七節 直觀規律 17
第參章 研究方法 20
第一節 研究設計 20
第二節 研究對象 22
第三節 研究工具 23
第四節 研究步驟與流程 29
第肆章 研究處理與結果 32
第一節 學童現行面積知識 33
第二節 學童面積概念試題分析 42
第三節 學童其他面積概念 91
第四節 連續細分相關題分析 101
第五節 學童面積保留概念與面積實測相關性 105
第六節 不同屬性學童在面積直觀概念實測相關性 106
第伍章 結論與建議 108
第一節 結論 108
第二節 建議 112
參考資料 114
一、中文部份 114
二、英文部份 116
附 錄 119
附錄一 國小教師對學生在面積方面錯誤概念或想法 120
附錄二 K-3年級學童現行面積試卷 121
附錄三 4-6年級學童現行面積試卷 122
附錄四 甲試卷（K-3年級） 123
附錄五 乙試卷（4-6年級） 131

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