運用幾何軟體Cabri 3D 與實體積木教具教學對國小二年級學童學習空間旋轉概念之影響

Based on Cabri 3D and physical manipulatives to study the effect of learning on the spatial rotation concept for second graders

本研究旨在探討二年級學生以Cabri 3D幾何軟體與實體積木融入空間旋轉概念教學之後，學生的學習成效以及解題策略和錯誤類型。研究法係採用準實驗不等組前後測研究設計，以六十一位二年級學童為研究對象。實驗組進行Cabri 3D幾何軟體搭配實體積木操作進行教學，而控制組僅以實體積木操作進行教學。研究發現結果如下：一、兩組學童在空間旋轉能力測驗的後測成績均有進步，顯示空間旋轉能力的教學對二年級學童是有效的。二、接受不同教學模式之兩組學童其學習成效並沒有顯著差異。於延後測後以訪談的方式探究二年級學童在空間旋轉能力的解題策略及錯誤類型，進行質性研究的分析。結果發現多數學生先以直觀方式做選項的判斷，先找出整體結構類似的立方塊，接下來欲確認答案的方式則大多會使用心像旋轉的解題策略，並再以整體或是切割立方連塊、進行分析比對來做確認。也有部分學生以直觀方式做形體的判別後，並未做旋轉而是直接選擇答案，此類學生容易出現鏡射形體迷思。最後綜合上述研究結果，分別從教學與未來研究等，提出具體建議。

For teaching spatial rotation concepts, this study investigated the learning effectiveness, problem-solving strategies, and error types produced by different teaching methods that used physical manipulatives with and without Cabri 3D geometry software. The study adopted a quasiexperimental, nonequivalent group design, and 61 second graders participated. The experimental group comprised 31 students who used physical manipulatives with Cabri 3D geometry software. The control group comprised 30 students who used only physical manipulatives without the software. The research revealed the following findings: Both the experimental and the control group exhibited considerable improvement following the posttest and showed that these methods of teaching spatial rotation concepts were effective for second graders; however, there was no significant difference in learning effectiveness between the groups. In addition, qualitative analysis was performed on interviews conducted after a relay test. The results indicated the following problem-solving strategies and error types: Most students first used intuition to make spatial judgements, before finding overall similarities between objects, checking for possible alternatives, and confirming their spatial judgement by using mental rotation strategies that employed all or part of the objects. After using their intuition, some students directly chose without rotating the objects; these second graders were apt to make an error involving a mirror misconception. Finally, some suggestions for future research and teacher development are offered as a reference to researchers and teachers, respectively.