| Mathematics is an objective reflection of the quantitative relationship and spatial form in the real world. Traditional teaching focuses on basic knowledge and methods. The new curriculum pays full attention to mathematical thinking as well as "double base". Symbolic-graphic combination is an important way of thinking throughout the secondary level. Textbook contains a wealth of content which reflects the thinking of symbolic-graphic combination. For students, how do they understand the thinking of symbolic-graphic combination? What are the non-cognitive factors on their understanding? These problems are worth doing in-depth study.Through research and interviews with high school teachers and students, I draw some conclusions as follows:(1) High school students have a narrow understanding about symbolic-graphic combination. They consider it as solving the problem with function images. (2) High school students perform differently in different types of problems when thinking of number from shape. They perform best in the correspondence between function and function shape when thinking of shape from number. Compared with the geometric method and the algebraic method, the geometric method has a higher success rates and less types of error. Few students are able to convert a flexible strategy based on the meaning of problems. (3)Imbalances exist between students when they solving symbolic-graphic combination problems with calculators. Boys are skilled in numerical calculation while girls perform better in the combination of both number and shape. (4) When solving practical problems, most students are able to make intuitive judgments based on graphics, but they felt it was difficult to have a qualitative calculation.In addition, the paper analyzes gender, achievement, reflection, teachers and other non-cognitive factors on students'understanding of symbolic-graphic combination. Finally, the paper provides some suggestions for teaching. |
PDF Full Text Request