关键词: 彝族学生, 表征, 表征水平, 数学理解, 数学问题解决

Abstract: In this paper,survey and test, homework analysis, verbal protocol, and comparative analysis are adopted to study the mathematics learning situation of seven-grade Yi students and understands their status of mathematical representation level in solving mathematical problems from the perspective of representation. The investigation suggests that for seven-grade Yi students, there is an imbalanced mathematical representation regarding to solving different math problems. Some have reach the level 4, and some merely stay at the level 1. In the process of solving math problems, a marked difference can not be seen between the mathematical representation level of Yi and Han students that are from grade seven ,nor does it appears between minority students and Yi students. In addition, no obvious difference of representation can be found between the girl and boy Yi students either. More significantly,the mathematical representation level of working out math problems that seven-grade Yi students possess is significantly and positively correlated with their math scores,in other words,the higher the representations level is , the better math score they achieve. According to this study, three corresponding advice can be provided:laying emphasis on the development of students’ thinking habits in teaching progress; combining specific teaching activities with multiple representations; making rational use of multimedia-assisted teaching and integrating the mathematical resources of Yi culture in class.

Key words: Yi ethnic minority students, representation, representation level, mathematical understanding, capability of mathematics problem solving