| 摘要: | 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。
;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 . |
