Students' thinking activities always start from "problems" and develop in solving problems. Students' learning is a process of constantly discovering and solving problems. Therefore, in mathematics teaching, teachers should carefully design questions and put forward some enlightening questions to stimulate the waves of thinking and arouse students' enthusiasm and initiative to the maximum extent. In classroom teaching, teachers' questioning is very important, because the process of asking and solving problems is an important way to develop students' thinking.

1. Design enlightening questions for knowledge growth points.

Any knowledge is not isolated, but developed from old knowledge. In the teaching process, teachers should carefully design thinking questions according to the internal relationship between old and new knowledge, and inspire students to actively find answers through their own positive thinking. For example, when learning the knowledge of carry-free addition and abdication subtraction of a decimal, students can do some integer addition and subtraction problems first, such as 457+522=? 375+23=? 987-877=? 435-3 1=? Ask the students to calculate vertically, but ask how to calculate the integer addition and subtraction. In this way, the decimal addition and subtraction are integrated into the students' existing experience of integer addition and subtraction, so that students can learn new knowledge by means of knowledge transfer and feel that the learning of new knowledge is not carried out in isolation. Students go from shallow to deep on the ladder of knowledge, thus developing their thinking ability.

2. According to the key knowledge points, the design difficulty is moderate.

Teachers should put forward thoughtful and moderate questions according to the focus of teaching materials and the reality of students. The setting of questions should focus on the key points, from simple to complex, so as to effectively mobilize students' ideological enthusiasm. For example, after learning the meaning of decimals in the context of "yuan", "angle" and "fen", students can design some contrast questions according to the weight and difficulty of knowledge and design them according to a certain gradient. (1)5 yuan 6 jiao 3 fen = () yuan, 3 yuan 5 jiao = () yuan, 3 yuan 5 fen = () yuan, 10 yuan 5 fen = () yuan. (2) Write decimals with four numbers of 0, 0, 4 and 5 and decimal points. ① Don't read all zeros; ② Read a 0 with two decimal places; ③ Read two and three decimal places of 0. In this way, by creating a good thinking environment for students, students can be promoted to think actively, and their understanding of knowledge can be deepened through thinking, analysis and comparison.

3. In view of the deepening of knowledge and the flexibility of design.

Psychological research has proved that strengthening the understanding of knowledge can develop students' thinking ability. Mathematical knowledge is abstract. Let students really understand and consciously master the basic knowledge of mathematics, and the key to forming ability is to let students master the knowledge of mathematics on the basis of understanding. Only when students understand knowledge can they firmly grasp knowledge and make it freely used. For example, after students learn the calculation method of dividing one digit by three digits, they can consolidate their knowledge in the form of the following questions: 425÷□= (). When the quotient is three digits, the divisor can be filled at least (), and when the quotient is two digits, the divisor can be filled at most (). 634 ÷□ = () ...5. In this case, the minimum divisor should be filled in (). Through various forms of practice, students can think from different angles, deepen their understanding of knowledge and promote the further development of thinking ability.

4. Design guiding questions according to actual operation.

In order to help students establish the concept of space when learning the abstract basic knowledge of geometry, I try to let students measure, compare, fold, cut and spell, guide them to participate in some practical activities, and then guide them to abstract the properties and calculation formulas of geometric shapes. For example, when learning "Calculation Method of Rectangular Perimeter", let the students feel which part the rectangular perimeter refers to, then let the students measure and calculate with the help of a ruler, and finally let the students choose the optimal algorithm to get the calculation formula of rectangular perimeter. After learning the length unit "Calculation Method of Rectangular Perimeter", students can be arranged to calculate the perimeter of the school's class desktop, blackboard and basketball court, and such calculation needs to measure the length and width of each object before calculation can be made. When solving this kind of problems, students not only consolidate new knowledge, but also make students comprehensively use what they have learned before to solve practical problems around them, thus cultivating students' innovative spirit and laying the foundation for solving practical problems in the future. Through such practical activities, students are provided with rich perceptual materials, which can promote them to abstract and summarize, so that they can gradually understand the nature and laws of things. Students use a variety of sensory learning activities to deepen their understanding of knowledge, not only know what it is, but also know why, thus activating their thinking and stimulating their enthusiasm for learning.

Second, change the angle of thinking and train the thinking of finding the opposite sex.

To cultivate and develop primary school students' abstract thinking ability, we must pay great attention to the cultivation of heterosexual thinking, so that students can gradually form multi-angle and multi-directional thinking methods and abilities in training. This requires teachers to create a space for students to think and present some problem situations with thinking value to students.

1. Select the content and cultivate the thinking of "seeking the opposite sex"

For primary school students, it is necessary to cultivate their qualities of not blindly following, like questioning, breaking the rules and expressing their opinions boldly, and to cultivate their courage to seek differences, develop their thinking of seeking differences, and then develop the habit of solving problems independently. For example, when a teacher was teaching the application of "the meaning of multiplication" to a class, he showed such an addition problem: 9+9+9+5+9=? Let the students calculate in a simple way. One student put forward the method of 9×4+5, and another student put forward a new scheme and suggested using the method of 9×5-4. The student's idea is very original. He discovered the scheme himself. In his thinking activities, he saw a 9 that didn't actually exist. He first assumed that the topic was 9×5, and then his thinking participated in the argument: 9-4 is the actual 5 in the original title. Therefore, teachers should cherish and cherish this flash of creative thinking. For another example, when teaching four simple mixed decimal operations, a teacher made a line for students to practice: 3.5×0.98+0.07=? Some students soon found the method: 3.5× 1-3.5×0.02+0.07. However, a classmate found a new method. He said that 0.07 can be converted into 3.5×0.02, and then a simple operation can be performed by multiplication and division: 3.5×(0.98+0.02). Although the first type of students can do some simple operations, in fact, their thinking has formed a certain formula. It is the latter type of students who really use this problem, innovate and think differently, and realize the value of this problem. Through the training of these questions, students can have the content, level and space of thinking training and improve their thinking ability.

2. Multiple solutions to one question, variant extension and broad thinking training.

Broadness of thinking is another feature of divergent thinking. The narrowness of thinking is manifested in knowing only one and not the other. A slight change will make you feel at a loss. Repeated training with multiple solutions to one problem and drawing inferences from one example is an effective way to help students overcome the narrowness of thinking. Teachers can inspire students' thinking through discussion and develop ideas to solve problems. On this basis, students can not only increase their knowledge, but also cultivate their thinking ability through repeated training. If two rectangles with a length of 3cm and a width of 2cm are spelled into a big rectangle, how many spellings are there? What's their circumference? Method 1: Two rectangles are 6cm long, 2cm wide and 16cm in circumference. Method 2: The length, width and circumference of two rectangles are 4cm, 3cm and 14cm respectively. Designing some exercises with multiple solutions to one problem can not only stimulate students' strong desire for discovery and creation, deepen their deep understanding of what they have learned, but also expand their cognitive space, stimulate inspiration, explore creativity and promote the improvement of problem-solving ability.

3. Change the angle of thinking and cultivate the flexibility of students' thinking.

Some mathematical problems, especially thinking problems, have certain differences in conditions and methods, and students often can't grasp the essence of the problem through language when thinking. At this time, the teacher may wish to guide students to change their thinking angle and look at the problem from another angle, which will solve some difficult problems. For example, there are internal relations among the four operations: subtraction is the inverse operation of addition; Division is the inverse operation of multiplication; Addition and multiplication have a conversion relationship. When the addends are the same, addition is converted into multiplication, and all multiplication can be converted into addition. There is an internal relationship between addition, subtraction, multiplication and division. For example, 189-7, how many 7s can be reduced in a row? Students should be asked to change their perspectives and think from the relationship between subtraction and division. This problem can be regarded as 189, which contains several 7s. The problem is easy. Another example is a thinking question: A and B are running on a 400-meter circular track. They started from the same place and walked in the same direction at the same time. A runs 280 meters per minute, and B runs 240 meters per minute. How many minutes does it take for A to catch up with B? It is difficult for students to understand what this question means. Teachers can guide students to think from different angles. When A catches up with B, it actually means that A runs one lap more than B, which means A runs 400 meters more than B. By changing the thinking angle, students can easily list the formula of 400(280-240). This kind of training not only prevents one-sided, isolated and static view of problems, but also enables students to sublimate what they have learned, from which they can further understand and master the internal relationship between mathematical knowledge, and also carries out training in thinking differently.

Third, enlarge mistakes and deepen thinking ability.

Dewey, an American educator, pointed out: "People who really think learn more from mistakes than from achievements. Only by combining mistakes with exploration can we breed truth. " In teaching, teachers can use wrong examples to enlarge them in time, or design corresponding multiple-choice questions and judgment questions, so that students can know their mistakes and why they are wrong in the exploration of right and wrong. Only by rationally reflecting on "misjudged cases", distinguishing similarities and differences, and exploring the "root causes" can we prescribe the right medicine and put an end to the recurrence of old diseases. In classroom teaching, once students form good thinking quality, they can promote the combination of cognitive structure, promote the deepening of thinking level and lay the foundation for their good thinking.

In short, the development of students' mathematical thinking is not formed overnight. In practical work, only by respecting students' ideas, starting from students' existing thinking, creating a space for them to explore, practice and create freely, and truly returning the dominant position in the classroom to students, can teachers cultivate students with thinking ability, innovative spirit and practical consciousness.