The purpose of this study is to analyze 5th graders’ Understandings of the meaning of Symmetric Figure for a Point and the types of problems or errors while constructing and to develop student’s Understandings using the New Educational Method. By the literature I arranged the complex meaning of ‘Symmetry’ in the sight of transformation, analyzed curriculums of Korea and other countries about ‘Point Symmetry’, and found out the cause of students’ difficulties while constructing the Symmetric Figure for a Point. For solving this problem I made the ‘Bilateral Symmetric Ruler’ and ‘Problems without the grid’. And students had the lessons of construction of Symmetric Figure for a Point using them. After the lesson, I analyzed the effectiveness of the new educational method using the questionnaire and the interview.