拖曳對國小生理解四邊形包含關係之研究

A study of Dragging in Dynamic Geometry Environment in Developing Elementary School Students´ Understanding of Inclusive Relationships among Quadrilaterals

本研究旨在探討動態幾何環境之拖曳行為如何影響學生理解不同四邊形間的包含關係。從三位五年級學生個案資料分析得知：第一，即使學生能在紙筆測驗正確回答四邊形定義，動態幾何環境圖形的呈現方式仍會改變他們對於定義的想法。第二，從分析學生在動態幾何環境拖曳，區別出六種不同認知行為和思維類別：（1）認為拖曳無法窮盡各種圖形；（2）關注圖形外觀；（3）微幅調度；（4）以特定性質為目標；（5）結合表格分析策略；（6）從一般例到特例。不同拖曳行會影響學生後續是否成功建構四邊形的包含關係。第三，研究提出學生不同判定四邊形關係的思維模式，包括分類思維、交集思維和包含思維。依據研究結果，本文進一步提出動態幾何環境拖曳和包含關係的研究和教學相關建議。

This study investigated how dragging in a Dynamic geometryenvironment(DGE) influences fifth graders in understanding inclusive relationships among quadrilaterals.We selected studentswho correctly recalled quadrilateral definitions but did not understand inclusive relationships. An analysis revealed that the diagrams in the DGE influenced students' responses to quadrilateral definitions, indicating that their concept definitions of the quadrilaterals are not stable. Six types of student cognitive behaviors associated with dragging in the DGEwere identified. First, students could not understand that draggingcan help them find all diagram examples constructed based on certain geometric properties. Second, students may only focus on diagramoutlooks when dragging.Third, students may slightly drag vertices or segments to avoid big diagram changes. Fourth, students may focus on what diagrams they intended to drag without noticing the dragging process. Fifth, students may only use data shown in table to evaluate inclusive relationships. Sixth, students can notice generalization and specification in various dynamic examples. Additionally, the types of student evaluations on relationships between quadrilaterals were recognized. They were evaluations based on classification, intersection, and inclusive relationship. Implications and suggestions for research and practices about the use of dragging to learn inclusive relationships are proposed.