The Investigation And Research Of The Students In Senior One Using The Combination Of Number And Shape To Solve Problems

Mathematical thoughts is the essence of mathematical knowledge.Both the curriculum standards issued by the state and the requirements related to the core quality of mathematics have raised the penetration of mathematical thought to a very high position.As one of the commonly used mathematical thoughts in senior high school,the thought of combination of number and shape permeates almost all stages and modules of mathematical learning in senior high school.The essence of the thought of combination of number and shape lies in the organic combination of "number" and "shape".This paper analyzes the theoretical basis and educational significance of the idea of symbolic-graphic combination.By studying high school mathematics textbooks,the author summarizes and analyzes the main application of the symbolic-graphic combination in high school mathematics problem solving.And on the basis of summarizing the previous research results,by means of questinaaire survey and interviews with teachers and students,this paper investigated,studied and analyzed the current situation of the students in senior one applying the idea of symbolic-graphic combination,especially the differences between the students with learning difficulties in senior one and the students with learning excellence in senior one applying the idea of symbolic-graphic combination were analyzed in detail.On the basis of the research results,this paper discusses the strategies to improve the students' ability to solve problems in symbolic-grahic combination from the two aspects of teachers and students,and puts forward some reasonable opinions and suggestions.The results show that:(1)Students think that teachers often refer to the symbolic-graphic combination in recitation class.In combination with specific situations,the symbolic-graphic combination is taken as a problem-solving tool with exercises as the carrier.(2)Students' understanding of the combination of number and application is not comprehensive and narrow.(3)Students don't have a strong sense of solving problems with the combination of number and shape,and their ability of "thinking of number by shape" is stronger than "thinking of shape by number".(4)Students' mathematics foundation isn't solid enough,and there are problems in the transformation of number and shape.(5)Students' normative answering ability still needs to be strengthened.(6)In the first grade of senior high school,excellent students and poor students apply the idea of combining number and shape to solve problems,and there is a significant difference between the two.And in the correct rate,there is a big difference between the gifted students and the poor students.Based on the above research,the author puts forward some suggestions to the students and teachers on how to improve the students' ability to solve problems with the combination of number and shape.As far as students are concerned,(1)Students should lay a solid foundation and attach importance to basic skills training.(2)Students should attach importance to the reflection after solving the problem and make timely induction and summary.As far as teachers are concerned,(1)Teachers should enhance students' interest in learning and cultivate their thinking of combining number and shape.(2)Teachers should dig deeply into the teaching materials and explore the idea of combining number and shape.(3)Teachers should guide students to develop their own thinking and strengthen the cultivation of their ability to choose and judge.(4)Teachers should pay attention to students' problem solving norms.(5)Teachers should pay more attention to students with learning difficulties.