高中生运用极坐标和参数方程解决圆及圆锥曲线问题的影响因素

The influence factors of senior high school students using the polar coordinate and parameter equation to solve the circle and conic problems

选取不同类型学校具有不同数学知识和经验基础的317名高三学生作为研究对象,采用试卷检测的方式研究高中生运用极坐标和参数方程解决圆及圆锥曲线问题的影响因素.结果发现:高三学生运用极坐标和参数方程解决圆及圆锥曲线问题的能力整体上比较薄弱;图形的位置和形状会影响高三学生运用极坐标的准确表征;运用参数方程表征极坐标来解决问题时,具有几何意义的参数方程表征极坐标与学生成功解决问题具有高度的一致性.基于此,建议加强图式表征教学、培养学生知识迁移能力、发展学生几何直观和空间想象素养.

A total of 317 Grade three students from different senior high schools with different mathematical knowledge and experience were selected as the research objects,and the influence factors of senior high school students using polar coordinates and parametric equations to solve circle and conic problems were studied by examination papers.The results show that these students′ability of solving circle and conic problems by using polar coordinates and parametric equations were relatively weak on the whole;the position and shape of the graph will affect the students′accurate representation of polar coordinates;when using parametric equations to characterize polar coordinates to solve problems,the parametric equations with geometrical significance to characterize polar coordinates has a high degree of consistency with students′solving problems successfully.Therefore,it is recommended to strengthen the teaching of schema representation,cultivate students′ability of knowledge transferring,and foster students′geometric intuition and spatial imagination literacy.