The Ability Of Symbolic-graphic Combination Of Senior One Students From Perspective Of Mathematical Representation

This paper does a research of the ability of symbolic-graphic combination of senior one students. The focus on the paper is the use and interaction of algebraic representation and geometric representation.First, the research finds out that the students have some different and unique recognitions for symbolic-graphic combination as following: a. The times of using the geometric representation to solve the algebraic problem are more than the times of using the algebraic representation to solve the geometric problem. b. The role algebraic representation playing in the geometric problem is more important than the role geometric representation playing.Second, allocating various answers, it is found that:a. The distribution of students' score is normal distribution and there isn't distinct difference between the males and females.b. From the perspective of graphical presentation, descending order of student performance is graphic presenting group, graphic missing group, graphic constructing group.there isn't distinct difference between graphic missing group and graphic constructing group both in top students and students with poor study performance.c. From the perspective of study performance, descending order of student performance is top-student group, average-student group, at-risk-student group.there isn't distinct difference between top students and average students in graphic missing group.Third, the research also finds out:a. The times of representations transformed is related to the complexity of the problem.b. The model of representations transformed is "algebraic-geometric representations transformed " in simple problem and is "algebraic-other representations transformed " in complex problem.