探討在真實情境中幾何量測學習對幾何學習成效、幾何估算能力、空間能力與van Hiele幾何思考的影響

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張筠媛(Yun-Yuan JHANG) 查詢紙本館藏

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論文名稱

探討在真實情境中幾何量測學習對幾何學習成效、幾何估算能力、空間能力與van Hiele幾何思考的影響
(Investigation of the effects of measuring authentic contexts to geometry learning achievement, geometry estimation ability, spatial ability and van Hiele levels)

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摘要(中)

幾何估算能力對於幾何學習是一個重要的影響因素，但過去的研究很少探討其對幾何學習與空間能力的影響。除此之外，很少研究讓學習者將幾何概念應用在解決真實情境的幾何問題，並缺乏探討其對學習成效、空間能力與幾何估算能力的影響。因此，本研究針對國小學童的幾何數學開發了一套Ubiquitous Geometry(UG)學習系統，探討學習者在真實情境中使用UG來量測真實物體，進行幾何量測學習解題，並探討其對幾何估算能力、幾何學習成效、空間能力與Van Hiele幾何思考層次之影響，更進一步探討學習者的幾何量測學習行為與幾何估算能力、幾何學習成效、空間能力與Van Hiele幾何思考層次之相關。
研究對象為國小五年級學生共82位，分成實驗組(使用UG)、傳統量測組(使用量尺)與傳統教學組三組，為期約一個月的實驗時間。實驗結果顯示，在幾何估算能力中的Level2-估算自身到物體的「間距」與Level3-「遠距離」觀看物體的長與寬，實驗組皆顯著優於傳統量測組與傳統教學組。後測的幾何學習成效，實驗組皆顯著優於傳統量測組與傳統教學組。在空間能力中的類比推理，實驗組顯著優於傳統量測組與傳統教學組，而在空間能力的心像旋轉中，實驗組顯著優於傳統量測組。在Van Hiele幾何思考層次，實驗組顯著優於傳統量測組與傳統教學組。
在幾何量測學習行為的影響，結果發現在複合式形狀量測次數與幾何估算能力中Level2-估算自身到物體的「間距」及Level3-「遠距離」觀看物體的長與寬、後測幾何學習成效、空間能力皆呈現顯著正相關。此外，在複合式形狀解題策略中，發現實驗組比傳統量測組與傳統教學組的答對的人數多，而且實驗組會運用較簡單的解題策略計算出複合式面積。最後，多數實驗組的學習者皆認為透過實際量測並結合真實情境的幾何學習是非常有幫助的。

摘要(英)

The geometry estimation ability is an extremely important fact for the geometry learning. However, there is few research that gave students opportunities to apply their geometry concept to solve geometry problems in authentic contexts. And the influence of the geometry concept on the learning achievement of geometry, spatial ability and geometry estimated ability is also ignored. Therefore, we developed an Ubiquitous geometry (UG) system for elementary school students to investigate whether their geometry estimation ability, geometry learning achievement, spatial ability and Van Hiele levels will be affected when they learned using UG. And we also further investigated the correlation between students’ geometry estimation ability, geometry learning achievement, spatial ability and van Hiele levels.
82 fifth grade elementary school students participated in this study for around one month, who were divided into three groups , experiment group (using UG), traditional measurement group (using ruler) and traditional teaching group. The result revealed that experiment group performed significantly better than traditional measurement group and traditional teaching group on Level2- 「distance estimation between students and objects」 and Level3-「long distance estimation the length and width of objects」of the geometry estimation ability. The experiment group also out performed significantly the traditional measurement group and the traditional teaching group in geometry learning achievement of post-test. As for spatial ability, in analogical reasoning, the experimental group performed better than the traditional measurement group and the traditional teaching group, and it also reached a significant level; while in mental rotation, the experimental group only performed significantly better than the traditional measurement group. In Van Hiele levels, the experimental group performed significantly better than the traditional measurement group and the traditional teaching group.
Regarding the influence of geometry measurement learning behavior using UG on learning achievement, it was demonstrated that there was a significant correlation between the amount of area measurement of compound shapes, and Level2-「distance estimation between students and objects」or Level3-「long distance estimation of the length and width of objects」of the geometry estimation ability. And the amount of area measurement of compound shapes also had a positive correlation with geometry learning achievement from post-test, spatial ability.
Besides, we found that the number of the experimental students who got correct answers is higher than those of the traditional measurement group and the traditional teaching group in solving compound area problems. And the experimental students usually employed easier strategies to solve compound area problems. Finally, most students of the experimental group thought that it is helpful geometry learning through the practical measurement in authentic contexts .

關鍵字(中)

★ 幾何學習成效
★ 幾何估算能力
★ 空間能力
★ van Hiele幾何思考層次
★ 單一形狀
★ 複合式形狀

關鍵字(英)

★ Ubiquitous Geometry
★ geometry learning achievement
★ geometry estimation ability
★ spatial ability
★ van Hiele levels
★ single & compound shape problem

論文目次

目錄
中文摘要 i
Abstract ii
目錄 iv
圖目錄 vi
表目錄 vii
第一章　緒論 1
1.1 研究背景與動機 1
1.2 研究目的與待答問題 3
1.3名詞釋義 4
1.4 研究限制 5
第二章　文獻探討 6
2.1幾何能力的重要性 6
2.2空間能力對幾何能力的關聯與影響 8
2.3估算能力對幾何學習的重要性 9
第三章　系統設計與實作 11
3.1 系統設計概念 11
3.1.1 基本幾何概念 12
3.1.2 單一形狀量測 13
3.1.3 複合式形狀量測 17
第四章　研究方法 20
4.1 研究架構 20
4.2 研究對象 21
4.3 實驗設計 22
4.4 研究工具 26
4.5 資料蒐集與資料分析 31
第五章　結果分析與討論 33
5.1 學習成效分析 33
5.1.1 幾何估算能力分析 33
5.1.2 Van Hiele幾何思考層次分析 35
5.1.3 幾何學習成效分析 36
5.1.4 空間能力分析 38
5.2 幾何估算能力、幾何學習成效、空間能力與Van Hiele幾何思考層次之間的關係 40
5.3學習成效與學習行為之間的關係 41
5.3.1學習成效與實際量測行為之相關分析 41
5.3.2幾何估算能力向度與實際量測行為之相關分析 42
5.3.3幾何學習成效向度與實際量測行為之相關分析 43
5.3.4空間能力向度與實際量測行為之相關分析 43
5.4幾何解題策略 44
5.5 問卷分析 46
5.5.1科技接受模式(TAM)問卷分析 46
5.5.2凱勒學習動機(ARCS)問卷分析 48
第六章　結論與建議 51
6.1 結論 51
6.1.1 探討實驗組在幾何估算能力、幾何學習成效、空間能力與Van Hiele幾何思考層次上是否顯著優於傳統量測組和傳統教學組？ 51
6.1.2 探討學習者在「單一形狀量測次數」、「複合式物體量測次數」與幾何估算能力、幾何學習成效、空間能力與Van Hiele幾何思考層次之相關性為何 52
6.1.3 探討學習者的幾何估算能力、幾何學習成效、空間能力與Van Hiele幾何思考層次之相關性為何？ 53
6.1.4 實驗組、傳統量測組與傳統教學組在複合式的解題上是否有差異與其解題策略為何？ 53
6.1.5 學習者對於使用UG學習系統的看法與其動機為何？ 53
6.2未來工作與建議 54
第七章　參考文獻 55
附錄一前測試卷-幾何學習成效 64
附錄二後測試卷-幾何學習成效 68
附錄三前測試卷-幾何估算能力 72
附錄四後測試卷-幾何估算能力 73
附錄五科技接受模型問卷 74
附錄六凱勒學習動機問卷 75
附錄七控制組幾何概念學習單 76
附錄八控制組單一物體量測學習單 77
附錄九控制組複合式物體量測學習單 78

圖目錄
圖1 推測數值的位置 10
圖2 給予正確的回饋 10
圖3系統設計架構圖 11
圖4三角形幾何概念 12
圖5單一形狀量測的步驟 13
圖6選擇物體所在位置 14
圖7拍照物體 14
圖8裁切照片 14
圖9物體的距離越近 15
圖10物體的距離越遠 15
圖11物體的高度越短 15
圖12物體的高度越長 15
圖13測量物體的寬度 16
圖14計算物體面積 16
圖15複合式形狀量測的步驟 17
圖16拍攝複合式物體 18
圖17裁切複合式物體 18
圖18觀看複合式物體 18
圖19拼出複合式物體 18
圖20選擇物件的所在位置 18
圖21計算複合式物體面積 19
圖22研究架構圖 20
圖23參與者人數統計表 21
圖24學習活動期程表 22
圖25實驗組的平板學習教材 23
圖26傳統量測的數位學習教材 24
圖27實驗組計算面積與練習紀錄 24
圖28組合複合式形狀 25
圖29計算複合式形狀的總面積 25
圖30複合式形狀練習紀錄 25

表目錄
表1單一形狀量測的操作流程介紹 14
表2複合式形狀量測的操作流程介紹 18
表3幾何估算能力向度說明 26
表4幾何估算能力評分方式 27
表5幾何學習成效評分方式 27
表6空間能力評分方式 28
表7 Van Hiele幾何思考層次說明 28
表8 Van Hiele幾何思考層次評分方式 29
表9 TAM評分方式 29
表10 TAM問卷信度檢驗表 29
表11 ARCS評分方式 30
表12 ARCS問卷信度檢驗表 30
表13資料蒐集 31
表15幾何估算能力(後測)及幾何估算能力向度之各組描述性統計及單因子變異數分析 35
表20 Van Hiele能力(後測) 36
表16幾何學習成效(前測)之各組描述性統計及變異數分析 37
表17幾何學習成效(後測)與幾何學習成效向度之各組描述性統計及單因子變異數分析 38
表18空間能力及空間能力向度之各組描述性統計及單因子變異數分析 39
表21幾何估算能力、幾何學習成效、空間能力與Van Hiele幾何思考層次之Pearson相關分析 41
表23幾何估算能力向度與學習行為之Pearson相關分析 42
表24幾何學習成效向度與學習行為之Pearson相關分析 43
表25空間能力向度與學習行為之相關分析 44
表26學習者解題複合式面積的策略方式 44
表27 TAM-系統易用性統計資料表 47
表28 TAM-系統有用性統計資料表 47
表29 TAM-估算有用性統計資料表 47
表30 TAM-使用意圖統計資料表 48
表31 ARCS-注意統計資料表 48
表32 ARCS-相關統計資料表 49
表33 ARCS-信心統計資料表 49
表34 ARCS-滿足統計資料表 49

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指導教授

黃武元(Wu-Yuan Hwang)

審核日期

2016-7-26

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