Some people say that the classroom used to be full-time irrigation, but now it is full-time questioning, which reduces the time for students to think independently. To this end, teachers should be good at asking more "big" questions with thinking value, reducing the "small" questions of table tennis, and guiding in-depth thinking around the main problems. For example, when students know the percentage, they should screen out important questions such as "Why do you want to learn the percentage", "What is the significance and function of the percentage" and "What is the difference between the percentage and the score" from many questions, so that students can think about the necessity, significance, function and knowledge connection of learning the percentage.

Similarly, for students' answers, teachers can't simply ask "Do you understand?" . Teachers should learn to delay judgment. The research shows that when teachers increase the waiting time from 3 seconds to 5 seconds, the following results will appear: the time for students to answer questions increases, the situation of not answering questions decreases, students ask more questions, the situation of actively answering questions increases, and students' self-confidence improves. Teachers should also be good at adding questions and asking questions, leading questions to the depths, and letting students realize the value of thinking. For example, when teaching "the size of possibility", when students realize that there are more yellow balls and fewer blue balls, the possibility of touching the yellow ball is greater than the possibility of the blue ball, the teacher immediately asks: "Can you touch the yellow ball at will or not?" In this way, students can think more deeply, that is, events with high possibility may not necessarily happen, and events with low possibility may not necessarily happen.

Second, open the space for students to think independently.

In teaching, the author found that when there are multiple solutions to a problem, students often have more thinking impulses and higher learning emotions. The reason is that open questions open the space for students to think independently. By analogy, students are required to think independently, and teachers should first try to be open in teaching methods. Classroom must not be "centralized", otherwise students' independent thinking is passive water. The teacher's explanation should not be too detailed, and students should be given room for thinking, exploration and self-development. Otherwise, it seems thorough, but it is difficult to internalize it into students' views, and students' independent thinking ability cannot be formed.

Teachers strive to cultivate students' ability to ask questions independently. Can ask questions, indicating that students are thinking independently; The problem of quantity and harmony just shows the breadth and depth of thinking. For example, senior three students look at the statistical chart, and some students can ask a single question, such as who is more and who is less, and the sum is poor; Some students can ask questions that reflect a slightly complicated relationship, such as finding the total and comparing two quantities. A few students can also ask questions that reflect trends and forecasts. Therefore, teachers should encourage students to improve their quality.

Opening the space for students to think independently also requires teachers to respect students' differences. For higher-level students, we should adopt the way of "letting go" and provide them with broader time and space for independent thinking; For middle school students, we should take the "exciting" way, provide them with appropriate questions, and gradually develop the habit of independent thinking; For underachievers, we should adopt the way of "induction", give more encouragement and inspiration, and form the consciousness of independent thinking. In classroom teaching, teachers can put forward different requirements for different students after asking "big questions", respect differences and teach at different levels.

Third, teach students the basic methods of independent thinking.

Mathematical problem solving in primary schools is closely related to mathematical thinking. In problem-solving teaching, teachers can't just pay attention to whether the problem is solved (the result), because the basic strategies and experiences formed in the process of problem-solving are necessary for subsequent learning.

For example, according to Paulia's How to Solve Problems, we can ask students the following questions: (1) What does this question tell us? What is the problem to be solved? What is the connection between information and problems? What is the difference? (2) What questions do you know about this topic? Can you reiterate this question? Can you think of an easier problem to solve? More general questions? A similar problem? (3) Can a solution be found and implemented? Students often go through this process of independent thinking and gradually learn how to seek solutions to problems. When reviewing and solving problems, you can also ask students: (1) Can you test your grades? Can you tell me about the bay road you took in the process of solving problems? Can you sum up the main experience in solving the problem? (2) Can we get the result by other methods? (3) Can this result or method be used to solve other problems? Such a list of questions is a framework to guide students to think independently and an external form of independent thinking. Once students form the habit of asking and answering questions, their ability to think independently will be greatly improved.

In addition, the basic thinking methods emphasized in the new curriculum are: transformation, combination of numbers and shapes, model and so on. Emphasis on problem-solving strategies are: drawing, listing, examples and so on. The learning methods advocated are: independent exploration, hands-on operation, cooperation and communication, etc. The above different levels can be considered in combination with the goal of cultivating students' independent thinking ability, so that students can solve problems, understand methods and improve their independent thinking ability in good learning methods.

Fourth, cultivate students' good habit of thinking about a problem for a long time.

Teacher Zhang Dan, editor-in-chief of "Mathematics Textbook for Primary School Teachers" published by Beijing Normal University, said that primary school mathematics teachers should try to learn to think about a problem for a long time. The deeper they think, the better they are at their major, and it will also change a person's way of thinking. For primary school students, the length of thinking time may not be very important, but whether they can continue to pay attention to and think about a problem can be gradually cultivated.

For example, students may face a math problem for a short time, but it is the epitome of thinking about a problem for a long time. For example, in the "Figure and Position" part of the "Space and Figure" field, students in the first and second grades learn the surrounding, east and west, north and south, students in the third and fourth grades learn the number pairs and polar coordinates, and then they learn the plane rectangular coordinate system in the seventh grade. The internal relationship between these mathematical knowledge is networked, and the understanding of the context of knowledge tests a student's habit and ability to think about a problem for a long time.

In short, as a teacher, we should consciously guide students to think about a problem completely and encourage students to communicate their new knowledge with their previous knowledge in their own way. In this process, students' thinking will jump out of the concern about one problem and one solution, and gain a focused thinking experience and good thinking habits.