"Everything is established in advance, and if it is not planned, it will be abolished." Teaching without presupposition is blind, inefficient and even worthless. Teaching content is the flesh and blood and backbone of classroom teaching. Only by careful preparation before class can we stand the test of students within 40 minutes, have effective guidance and dynamic generation in class, and be comfortable in class. Otherwise, the teacher will be at a loss and in a hurry. For example, in the teaching of "understanding the circle", teachers should know whether students have a direct or indirect understanding of the circle before class and whether students can draw a circle with compasses. Therefore, in my teaching design, the teacher did not focus on drawing a circle with compasses, but appropriately led to a higher level-how to draw a circle with a specified size.

The beautiful generation in the classroom needs some space. Therefore, we should be broad and flexible in the design of classroom teaching. The so-called "rough" refers to defining the three-dimensional goals to be achieved, describing the general outline of the classroom situation, and leaving enough interactive space for students in each link. The so-called "fine" is to foresee what problems may occur in each link and what different thinking students may have, so that teachers can know fairly well. For example, when I was teaching the meaning of decimals, in order to realize that 0.2 is equal to 0.20, I showed a square paper with an average score of 100, in which 20 squares were colored. The teacher asked a question, "Which decimal can be used to represent it?" Ask the students to make it clear that 0.2=0.20 in reasoning, but the meaning is different. This presupposition makes students' thinking more open, and students acquire new knowledge through their own observation, imagination and thinking. Isn't this kind of study more effective?

Secondly, it is an important way to organize and mobilize students' enthusiasm for independent inquiry.

In teaching, we should change the current situation of overemphasizing learning, rote learning and mechanical training, establish a brand-new sense of curriculum objectives, give full play to the curriculum function of textbooks, meet the needs of students in learning mathematics, and let each student construct his own knowledge system in his own construction and develop in his own construction.

For example, when teaching the judgment question "The side of a cylinder must be rectangular when it is unfolded", I give this question to the students for discussion, so that they can find enough evidence for their conclusions. After reading the book and discussing it in a low voice, the students naturally divided into two opposing groups. The debate began, and the proposal of the students who thought it was correct said: "Expand the edge of the cylinder and you can get a rectangle." Students who think it is wrong suggest that the side of the cylinder may also be square, and there are such questions in the workbook. The students who think it is correct retort that the square is a special rectangle, so it is still a rectangle after expansion. Everyone began to agree that this sentence was correct. At this time, a classmate expressed a different view. He thinks that the side of the cylinder may be a parallelogram when it is unfolded. At the same time, he showed the side of the cylinder he made of paper, which was indeed a parallelogram. Inspired by him, some students suggested that the side of the cylinder may be irregular after being unfolded.

In fact, every student's judgment has some truth, because everyone looks at the problem from different angles, so they have different views. If the side of the cylinder is unfolded along the height, it will become a rectangle; If it is not spread along the height, but along the diagonal or curve, it is a parallelogram or irregular figure. I don't think the right or wrong of this question is the most important question. It is important to highlight the three-dimensional goal of teaching.

Thirdly, it is an effective means of classroom teaching to pay attention to incentive evaluation and promote students' active development.

Because traditional education has always been to check students' mastery of knowledge and skills through written tests and exams, in the long run, students' curiosity has been intentionally or unintentionally extinguished, and students' thirst for knowledge and creativity have been suppressed and stifled. With the deepening of curriculum reform, we are increasingly using a variety of ways to comprehensively evaluate the changes and progress of students in knowledge and skills, innovation and practice, emotional attitudes and values. In teaching, we should make correct and positive evaluations from all aspects, mobilize students' subjective initiative, and let students feel the "continuous success of mathematics learning", so as to taste the pleasure of "success is the mother of success".

For example, when teaching "circumference", students actively explore the relationship between circumference and its diameter with their brains and hands, laying the foundation for calculating circumference. The teacher encouraged: "As early as 1000 years ago, China mathematician Zu Chongzhi discovered this relationship and calculated pi. Students also discovered this rule through research. You are really a contemporary Zu Chongzhi. " This evaluation is actually a good communication with students in mathematical language, which is conducive to developing students' personality and promoting their active development.

In short, in classroom teaching, teachers should treat each class seriously and solidly with full enthusiasm, accurately grasp the new curriculum standards, strengthen the sense of goal, and actively and consciously promote the change of their own ideas, so as to achieve the purpose of organizing effective mathematics classroom teaching, better improve the efficiency of 40 minutes and promote the all-round development of students.