Problem-solving is regarded as an important curriculum goal in the Curriculum Standard of Mathematics for Full-time Compulsory Education (Experimental Draft) (hereinafter referred to as the Standard), and it is pointed out that students should actively try to use the knowledge and methods they have learned to seek strategies to solve problems from the perspective of mathematics. Drawing strategy is the most basic and important strategy among many problem-solving strategies. It helps students to concretize and visualize abstract problems through various graphics, so that students can understand the meaning of problems from graphics and analyze the quantitative relationship, find a breakthrough to solve problems, thus forming a solution to problems. Therefore, people like to use drawing strategy when solving problems. Why do you need to draw? How to make students learn to draw? It is not to show students ready-made pictures, nor to tell them how to draw directly, but to let students have the need to draw in the process of thinking, experience methods, feel strategies, develop thinking and gain ideas in their own painting activities. What runs through the learning process should be to guide students to embark on the journey of mathematical thinking. In this sense, drawing ability also embodies problem-solving ability and thinking ability. Therefore, in the process of problem-solving teaching, we should pay attention to cultivating students' ability to analyze and solve problems by using drawing strategies.

Second, how to cultivate students' painting strategies in teaching.

1. Help students understand the value and function of painting strategies.

The understanding of drawing strategy should be gradually infiltrated from low to high. It is difficult for children in the primary stage to understand the abstract quantitative relationship. If children are allowed to draw a picture on paper in time, it can help students analyze and understand the abstract quantitative relationship, so as to find a solution to the problem. Therefore, in the teaching of lower grades, teachers should consciously teach students to analyze and understand the quantitative relationship with the help of charts.

For example, the number of application problems has always been a difficult point for students to learn. Students always can't tell who is better than who, who is more and who is less, which leads to the wrong logic of watching more and adding less and reducing less. If from the beginning of teaching, teachers teach students to analyze the quantitative relationship by using the method of drawing (of course, drawing should be based on physical drawing at this time), the teaching effect will be greatly improved.

2. Encourage students to analyze and solve problems in the form of various charts.

In the traditional application teaching, it was mentioned that the drawing teacher paid more attention to line drawing. At that time, line drawing also had clear requirements in drawing method, such as: the unit "1" should be marked on the top of the drawing, the drawing must be accurate, and a ruler should be used. It can be said that traditional teaching is more about teaching drawing as a knowledge, rather than as a strategy to help students solve problems, so students. The new textbook teaches students drawing as a strategy, and the form of drawing is not limited to line drawing. Students can draw different diagrams according to their own needs to help analyze and understand the quantitative relationship and solve practical problems. Therefore, teachers should encourage students to analyze and solve problems in the form of various charts. In this process, we should follow the principle that the graph that can display the quantitative relationship most clearly and directly is our best choice. It is in the constant encouragement and respect of teachers that students boldly put forward their different opinions and use more pictures to help them analyze and solve problems.

3. Grasp the important content of cultivating students' painting strategies.

Teaching should really cultivate students' ability to solve problems by drawing strategies, not by deepening the difficulty of the problems, but by focusing on cultivating students' drawing strategies through representative and easily accepted topics, so that even if they encounter some unsolved problems, they can find solutions through their own drawing and analysis. For example, comparison, multiplication, division with remainder, travel problems, understanding of application problems with hundreds of digits, and some special problems such as collocation, chicken and rabbit in the same cage, planting trees and so on. It is an important content to cultivate students' painting strategies.

4. Pay attention to the guidance of problem-solving strategies and make the "hidden" strategies "explicit"

In the past application problem teaching, teachers paid more attention to knowledge teaching and problem solving, but not to the summary and induction of problem-solving strategies. In teaching, teachers should pay attention to the guidance of students' problem-solving strategies and make the "hidden" problem-solving strategies "explicit". This will help students realize the value of strategies in solving problems and improve their ability to solve problems. For example, before solving problems, teachers can encourage students to think about which problem-solving strategies need to be used; In the process of solving problems, teachers can let students pay attention to whether to adjust the problem-solving strategies according to specific conditions; After solving problems, teachers should encourage students to reflect on the strategies they use and organize exchanges. At an appropriate time, teachers can summarize some problem-solving strategies and ask students to collect typical examples of using these strategies. In short, teachers should take problem-solving strategies as an important goal and consciously guide and teach them.

In practical teaching, we should help students master the process of solving problems by using drawing strategies and promote students to experience the role of drawing strategies. You can guide it like this:

A. Reading questions: Ask students to be familiar with the questions and clarify the conditions and problems in the questions;

B. Drawing: Inspire students to draw corresponding figures according to the conditions and problems in the questions;

C, display: display the information of the question intuitively, which is convenient for students to analyze and think (conditions and questions can be marked in the diagram);

D, analysis: after drawing, guide students to analyze with the help of intuitive graphics, think about what to ask for first, and find out the solution to the problem;

E. solution: determine what should be calculated before solving the problem, solve the problem by yourself and complete the solution.

By using drawing strategy to solve problems, students can experience the effectiveness of drawing strategy, feel the role of intuitive graphics in solving problems, and form interest and consciousness in applying drawing strategy. In addition, teachers should pay attention to the infiltration, summary and arrangement of drawing strategies in different stages in the process of guiding students to use drawing strategies to solve problems. For example, lower grades can infiltrate painting strategies from actual demonstrations and operational activities; Middle and senior grades can embody painting strategies from simulation demonstration, sketch drawing and abstract line drawing. Grasp the drawing strategy as a whole and guide the teaching systematically.

5. The connection between painting strategy and other strategies

"Forming some basic problem-solving strategies, experiencing the diversity of problem-solving strategies, and developing practical ability and innovative spirit" is one of the curriculum objectives set by mathematics curriculum standards.

Students' knowledge background and thinking angle are different, and the differences exist objectively. For the same problem, because students' cognitive level and cognitive style are different, there are often different methods to solve the problem, which is the embodiment of students' different personalities. In teaching, teachers should encourage students to use their existing experience to think boldly, go through the process of exploring mathematical knowledge and seek solutions to problems. Drawing strategy is an important problem-solving strategy, but it should be used flexibly in solving practical problems, and sometimes it needs to be combined with other strategies to give full play to its role and improve students' problem-solving ability.

For example, there is such a problem of meeting: Xiaoping and Xiaohong walk from A to B at the same time, and Xiaoping walks 20 meters more than Xiaohong every minute. After 30 minutes, Xiaoping arrived at B, and then immediately went back the same way. He met Xiaohong at a distance of 350 meters. How many meters does Xiaohong walk every minute? In order to make students understand the meaning of the problem, students can perform a simulation performance and remember the demonstration so as to draw a picture to solve it. The simulation performance is more and more in place in the continuous revision of students, which shows that students' understanding of the content of the topic is more and more clear. On this basis, draw the simulated situation with lines, so that the quantitative relationship in the topic is clear at a glance, and it will certainly be much easier for students to analyze.

6. Pay attention to the infiltration of mathematical ideas in the teaching of painting strategies.

The basic idea of primary school mathematics refers to the essential idea that permeates the knowledge and methods of primary school mathematics and has universality and strong adaptability. As far as its specific content is concerned, it can be divided into transformation thinking, corresponding thinking, inductive thinking, transformation thinking, analogy thinking and so on. These thoughts are the cornerstone of mathematics in the whole primary school and the bridge from mathematics to science hall. Therefore, in the process of cultivating students to solve practical problems by drawing strategies, teachers should consciously infiltrate mathematical ideas, so as to cultivate and develop students' mathematical ability.

The idea of (1) combination of numbers and shapes

Number and shape are two aspects of the research object in mathematics teaching. Combining the relationship between numbers and spatial forms to analyze and solve problems is the idea of combining numbers with shapes. The combination of numbers and shapes, with the help of simple illustrations made by figures, symbols and words, can promote the coordinated development of students' thinking in images and abstract thinking, communicate the connection between mathematical knowledge, and highlight the most essential characteristics from the complex quantitative relationship.

(2) the corresponding ideas

It is an extremely important method to solve fractional application problems with corresponding thinking methods. The correspondence of fractional application problems refers to the correspondence of quantity and rate. Simple fractional application problems directly correspond to quantity and rate, while in complex application problems, the corresponding relationship between quantity and rate is indirect. Sometimes quantity is a hidden condition, sometimes rate is a hidden condition, and sometimes both quantity and rate are hidden conditions. Therefore, the formation of problem-solving methods is based on the clear correspondence between quantity and rate, which is an important link to solve more complicated fractional application problems. Drawing strategy plays an important role in helping us to clarify the corresponding relationship.

(3) the idea of transformation

Transforming thinking is one of the basic ideas of mathematics. In primary school mathematics teaching, we should combine the specific teaching content, infiltrate the transformation thinking of mathematics, and consciously cultivate students to learn to solve problems with transformation thinking, so as to improve students' mathematical ability.

Some application questions are more complicated to answer according to the conditions of the original question. If we think in a different way according to the internal relationship between knowledge and properly use intuitive graphics to transform the quantitative relationship in the problem, then the original problem will be transformed into another problem that is easy to solve, thus opening the way to solve the problem and solving it smoothly. For example, the conversion of conditions, the conversion of unit "1", the conversion between travel problem, score problem and proportion application problem, and so on.

In the process of using drawing strategy to solve problems, in addition to the above mathematical thinking methods, we can also infiltrate hypothetical thinking methods, comparative thinking methods, classified thinking methods, analogy thinking methods and so on. Infiltrating and applying these teaching ideas and methods in teaching can not only enhance students' interest in learning and arouse their enthusiasm, but also develop students' thinking flexibility and mathematical intelligence, which is conducive to the overall improvement of students' mathematical literacy.

Of course, how teachers grasp the drawing strategy in the textbook as a whole and gradually make it explicit, so that students can consciously use the drawing strategy in the process of solving practical problems needs further in-depth study. But in the end, I think it should be summed up by xu teacher at the end of the conference: only when students are confused and have needs, under the exploration and inspiration, to experience and refine the strategies to solve problems and realize the internalization of learning, can our teachers succeed!