1. research background: mathematics is a science that studies the relationship between spatial form and quantity in the objective world. Number is an abstract generalization of shape, and shape is an intuitive expression of number. Mr. Hua pointed out that the combination of numbers and shapes is not only an important mathematical thought, but also a commonly used mathematical method. The combination of numbers and shapes has important guiding significance in solving mathematical problems. This "number" and "shape" information. That is, quantitative problems and visualization can be transformed into each other, which can not only make the solution of some problems simple and vivid, but also greatly broaden our thinking of solving problems and open up an important way for studying and exploring mathematical problems. For a long time, mathematics knowledge has always been a bright line in teaching, which has been valued by mathematics teachers. Mathematical thinking method is a dark line, which is easily ignored by teachers. In our primary school mathematics teaching, if teachers can consciously use the idea of combining numbers and shapes to design teaching, it will be very beneficial for students to deepen their understanding and understanding of problems from different aspects, provide solutions to problems, and also help to cultivate students' ability to transform practical problems into mathematical problems. "Combination of numbers and shapes" is a teaching method and teaching strategy for teachers. It is a learning method for students. If it is infiltrated for a long time and used properly, it can make students form good mathematics consciousness and thought and play a long-term and stable role in their mathematics learning career. As a front-line teacher, how to systematically apply the idea of combining numbers and shapes to mathematics teaching is an important topic with great practical value. Second, research value: 1. By organizing and implementing the research of this topic, teachers can improve their understanding of the combination of numbers and shapes and deepen their analytical ability of the combination of numbers and shapes in teaching materials. They can always pay attention to the combination of numbers and shapes in their usual teaching to improve the professional quality of teachers. 2. By organizing and implementing the research of this topic, students' thinking level can be improved and their ability to solve practical problems can be improved. To meet the needs of future social development. Iii. Research objective: 1. Teachers consciously use the idea of combining numbers and shapes to design teaching, turn abstraction into images, creatively develop curriculum resources and effectively improve the quality of classroom teaching. Second, study the application of "combination of numbers and shapes" in the field of mathematics in the fourth to sixth grades of primary schools. Infiltrate the idea of combining numbers and shapes in stages and at different levels. 3. Effectively improve students' interest in learning mathematics through the combination of numbers and shapes, make the combination of numbers and shapes an important learning method for students, and creatively use the combination of numbers and shapes to solve abstract mathematical problems. Through constant "exploration" and "creation", personal mathematical thoughts are constructed. 4. Concept definition: 1, combination of number and shape: "shape" mainly refers to geometric figures, which belongs to the category of thinking in images and is the product of brain thinking. They are both opposite and unified, and each geometric figure contains a quantitative relationship closely related to its shape, size and position. On the contrary, quantitative relations can often be intuitively reflected and described by geometric figures. The essence of the combination of numbers and shapes is to combine abstract mathematical language with intuitive graphics, so that abstract thinking and image thinking can be combined, making it difficult to be easy and abstract to be intuitive. People can make full use of the interdependent and stimulating thinking functions of the left and right brains to develop people's thinking ability in an all-round, coordinated and in-depth way. Its essence is to combine abstract mathematical language with intuitive images, that is, to solve mathematical problems through the mutual transformation between numbers and shapes according to the corresponding relationship between numbers and shapes. It is a common mathematical thinking method, which can simplify complex problems and concretize abstract problems. There are mainly the following solutions: (1) changing "number" into "shape"; (2) changing "number" into "shape"; (3) "Shape" and "number" are mutual changes. 3. "Infiltration" refers to the gradual infiltration and application of certain thinking methods in a certain practical process. This mainly refers to the combination of numbers and shapes gradually infiltrated in primary school mathematics classroom teaching. V. Research content: 1, the application of the combination of number and shape in the knowledge field of "number and algebra". Second, the application of the combination of numbers and shapes in the knowledge field of "space and graphics". Third, the application of the combination of numbers and shapes in the knowledge field of "Statistics and Probability". 2. Teachers of different grades began specific research; 3. Further improve the research contents and measures in concrete practice; 4. Finally, the research effect is improved to form the project achievement report. 7. Research methods: 1. Investigation method: to investigate the current primary school mathematics teachers' understanding of infiltrating the idea of combining numbers with shapes in teaching, and to investigate the current students' understanding of solving problems by combining numbers with shapes. 2. Literature research method: collect, study, sort out and analyze the relevant literature materials about the infiltration of mathematical thinking methods and the combination of numbers and shapes. Used in experimental research. 3. Case study method: Select materials from different fields (number and algebra, space and graphics, statistics and probability, practice and comprehensive application) as cases to analyze and study, and seek ways and modes to effectively infiltrate the idea of combining number and shape in different mathematics learning fields. 4. Experience summary method: summarize the experience accumulated in the experiment and demonstrate it during the experiment.