本研究的主要目的是在探討我國國小中年級學童點對稱概念之發展、認知情況、以及差異性，並觀察其思考類型及分析可能錯誤，藉以提供小學教師教學及課程編訂之參考。研究對象及就台中市忠孝國小，選取中年級學童，設計面談工具，以進行個別訪談。 　　研究進行以「質」為主，經由學童的反應觀察，發現中年級辨別具點對稱特徵，仍需借助圖卡操作判斷，多數學童將具點對稱圖形視為線對稱圖形，而呈現所謂二元逆轉（binary reversion）現象。由學童外顯之操弄過程，研究者特別注意揣摹其視覺導引程序，以了解學童概念發展情況，其結果顯示：中年級學童大都仍停留於van Hiele的識別層次，少部份四年級學童已知利用點對稱的特性操弄圖形，而達到分析層次。

　　　　　 The major purpose of this study is to discuss the development of the Chinese children's concept of point-symmetry. This study includes probing the children's state of cognition which related to symmetric concept, comparing the conceptual differences among children, observing children's types of thinking, and analysing children's possible error. It is the goal of this study, providing elementary school teachers with reference, when they teach and revise the mathematics curriculum. The subjects were chosen from the middle graders of Chung-hsiao Elementary School in Taichung city, the materials of task were especially designed, and interviews were taken individually. The important data were collected mainly by the "quality analysis". Through observing these children's reaction, while the middle graders were recognizing the characters of point-symmetry-figures, it is found that they still need to rely upon operating picture card. Furthermore, the majority of these children dealed with the point-symmetry-figure as same as the line-symmetry-figure, it reveals that this type of response is similar to the phenomenon of binary reversion. The researchers have paid more attention upon observing each child's visually-moderated sequences, in order to trace the state of the development of the concept. It is revealed from the result: most of the middle graders stay at the recognition level, according to van Hiele Level; a few of the forth graders have known to apply the character of symmetry for operating figures, and they reached to the analysis level.