Piaget, a Swiss child psychologist, said: "The important characteristics of the psychological development of primary school students aged 6- 12 are that they are interested in fresh and concrete things and are good at remembering concrete facts, but not abstract contents." Mathematics is an abstract logic subject, and the thinking of primary school students is in the transition stage from concrete thinking in images to abstract thinking in logic. Hands-on activities are a bridge between the abstraction of mathematical knowledge and the visualization of students' thinking.

Hands-on operation plays a very important role in stimulating students' interest in learning mathematics, helping students understand mathematics knowledge, cultivating students' ability to solve problems and cultivating students' innovative ability. As the saying goes, "it is better to pass by once than to pass by a thousand times." In primary school mathematics teaching, it is very beneficial for students to operate properly. Pupils are mainly thinking in images and active in thinking. Let students operate in the classroom, which is a process of hands-on and brains, is an effective means to solve the contradiction between the abstraction of mathematical knowledge and the visualization of primary school students' thinking, and can make teaching achieve twice the result with half the effort.

First, hands-on operation can give full play to students' main role and stimulate students' interest in learning.

Interest is the best teacher. Interest plays a great role in promoting students' learning. With interest, the efficiency of learning will be significantly improved. "Mathematics Curriculum Standard" points out that mathematics learning must start from students' living situations and things of interest, and provide them with opportunities to participate in learning activities, so that they can feel that mathematics is around and have a sense of intimacy with mathematics. Students in the lower grades of primary school have a short time to concentrate. If the whole class is explained by a single teacher, it will be boring and it will be difficult to attract students' attention. Instructing students to operate properly in class can stimulate students' interest in learning, enliven the classroom atmosphere, deepen their understanding and mastery of what they have learned and strengthen their memory. For example, when teaching "Understanding the Circle", students can learn the difference between the circle and other plane figures by giving examples of objects belonging to the circle in real life. As for how to draw a circle, teachers don't need to demonstrate, and students can try their best to make bold attempts. "Can you draw a standard circle? Who has the best way to see it? " This fully mobilized students' curiosity and enthusiasm, and everyone began to explore boldly. Soon, most students know and learn how to draw a circle with compasses and circular objects (such as ink bottles, teacups, coins, etc.). At this time, the teacher praised their active participation and exploration, and then asked, "If you want to build a big round flower bed or pool, can you draw it with compasses?" In this way, students' interest is further stimulated and they are scrambling to do hands-on inquiry. Through the operation experiment, it is finally found that a larger circle can be drawn with columns and ropes. This kind of teaching not only embodies students' dominant position, but also stimulates students' interest from beginning to end, arouses multiple senses to participate at the same time to the maximum extent, and teachers and students enjoy it, which has a multiplier effect on completing teaching objectives and tasks. This greatly stimulated their interest in learning mathematics and developed students' mathematical potential.

Second, hands-on operation visualizes abstract numbers, which helps students understand knowledge.

Operational practice is the source of ability and the starting point of thinking. It concretizes and visualizes abstract things and turns boring words into interesting, happy and thinking games. Make students gradually form correct psychological activities in the process of practice, so as to realize the internalization of knowledge. "Mathematics Curriculum Standard" also points out that students have to go through the formation process of mathematics knowledge. Primary school students' understanding and memory are also based on students' intuitive operation and hands-on practice. Therefore, in the usual teaching, we should combine the teaching content, carefully design the operation activities, and patiently guide the students to feel and think in the hands-on operation, so as to reveal the law and master the knowledge. Only the knowledge acquired by students through their own personal feelings and self-exploration will be deeply rooted in their minds. Primary school students' understanding of numbers is still in the perceptual stage, and they cannot understand simple addition or subtraction. At this time, teachers can use the counting ability of primary school students to teach by counting sticks (or other objects). When teaching fractions in middle schools, teachers can also use origami to deepen students' understanding of fractions. For example, when talking about the meaning of 3/4, students can fold a square piece of paper twice, and then the teacher guides the students to understand by asking questions. This is not only simple and convenient, but also students can easily understand the meanings of natural numbers, addition, subtraction and fractions. And avoid the disadvantages of not being able to use knowledge flexibly because of rote memorization. Therefore, in mathematics teaching, teachers should attach importance to students' hands-on operation. Only by letting them explore and discover themselves in operation can they understand deeply and help them master the internal and essential connection of knowledge.

Third, hands-on operation brings mathematical problems into life, which is conducive to cultivating problem-solving ability.

Dutch mathematics educator Frandenthal believes that "mathematics comes from reality and must also be rooted in reality and applied to reality." Active is a child's nature. Children are full of curiosity about things in life. They all want to see, move and test. Strengthening hands-on operation is a way for junior students to acquire knowledge and solve practical problems. By doing this, students learn more interesting; Only by doing it can students solve practical problems better. The new textbook provides students with many operational opportunities in this field. For junior students, second is a very abstract unit of time. The teacher's single explanation can't make students really understand. Hands-on operation and personal experience are important ways to learn mathematics. In the teaching of this course, I designed a variety of activities, such as clapping, stamping, counting to feel the length of 1 second, how many numbers can be written at most in 10 second, memorizing multiplication formulas, doing oral calculations, writing new words, reading texts and skipping rope for 30 seconds, so that students can really feel "seconds" in these operating activities. On the basis of students' understanding of the concept of "second", let them estimate how many seconds it takes to walk from the front to the back of the classroom. Guess 1 sec what you can do and so on. After teaching "Measuring Length", ask students to measure the length of some objects in the classroom, and measure the length of their sleeves, trousers, waist circumference and height. Apply what you have learned and cultivate students' ability to solve problems. Hands-on operation is also conducive to solving multi-solution application problems. In the review, the students encountered an exercise: "Turn a rectangular paper roll with a length of 18.84 cm and a width of 9.42 cm into a cylinder and find the volume of the cylinder". After the students answered the questions, I visited. Not ideal. I'll ask them to take out a paper roll right away. Students accidentally found that there are two volume methods, there should be two solutions, and then there is no solution behind. Although the result is different, it is also correct. After such a long training, the students' brains are much more flexible. My thinking is also broadened, my ability to solve problems independently is gradually enhanced, and I am very interested in learning mathematics. The practice in recent years shows that through practical activities such as hands-on operation, students can experience the pleasure of actively exploring and acquiring knowledge, enhance their motivation and confidence in learning, change their passive acceptance of knowledge into active exploration and research, change their passive situation, and cultivate their exploration and innovation abilities.

Fourth, hands-on operation comes from practice, which is conducive to promoting students' innovation.

Suhomlinski said: "There are some special, active and creative areas in the human brain. By combining abstract thinking with delicate and dexterous movements of hands, these areas can be activated. Without this combination, these areas of the brain are asleep. " Facts have proved that effective operation activities are the source of cultivating students' innovative spirit. Only when students begin to operate, many areas of the cerebral cortex can be trained, which is conducive to mobilizing the activity of creative areas, thus igniting students' innovation sparks. For example, after the teaching of "angle measurement", let students master the general method of measuring and drawing angles with protractor, and then provide students with the opportunity to operate and promote innovation. Drawing the angle of 120 is usually done by students with the help of a protractor and a triangular ruler. On this basis, the teacher asked the question again: "Can you draw this angle accurately without using a protractor?" With questions, the students entered a pleasant hands-on operation and experimental exploration. Soon, the students found two kinds of drawing methods: draw the angle of 120 with the right angle and 30 angle of a triangular ruler; Put two triangular rulers together at an angle of 60 degrees and draw an angle of 120. Students have innovated their methods through their own experiments, which have been recognized by everyone and praised by teachers, and they have enjoyed the joy of success. At this point, the teacher flashed a question: "There is a new painting method, who can find it first?" In this way, the students are more enthusiastic, scrambling to explore the operation, and finally find and learn another method: draw an angle of120 (that is, a right angle MINUS 60) with one side (or ruler) of a triangular ruler and another angle of 60. Such innovative methods are constantly emerging, and it is difficult to have such a result without hands-on operation. Therefore, in classroom teaching, students are provided with more operation opportunities and encouraged to seek novelty and difference. Through practical operation, students not only have a strong interest in the connection and transformation between graphics, but also cultivate their spatial concept and ability to understand things dynamically. It is conducive to stimulating students' exploration and attempt with individuality, stimulating students' divergent thinking and cultivating students' innovative ability.

5. Hands-on operation based on appearance is conducive to the development of students' spatial concept and spatial thinking.

The concept of space refers to the visual representation of geometric shapes in the human brain, which is the necessary thinking and ability to learn geometry. Primary school students' spatial concept is very weak, so we should gradually cultivate their spatial concept in teaching. This requires hands-on operation, so that students can personally feel the characteristics of various geometric shapes and form various representations in their brains, thus cultivating students' initial concept of space. For example, in teaching & gt middle school, teachers teach around certain parts of students' bodies (such as left hand, right hand, left eye, right eye, left ear, right ear, left foot, right foot, etc.). ) and guide students to better understand the left and right directions; Discuss the seating relationship between students, so that students can understand that the positional relationship between objects is relative. This kind of teaching is practical and operational, which enables students to understand and master the relative position relationship between left and right in a relaxed and pleasant learning atmosphere, experience the close relationship between mathematics and life, and gradually develop the concept of space. For example, when teaching length, area and unit of volume, students can draw, cut and make various units of paper or cartons by themselves and feel their size. In the hands-on operation, students not only learned knowledge, but also cultivated and developed spatial concepts and spatial thinking. In addition, guiding students to operate in practice can help students understand the meaning of the problem, deepen their understanding and help develop their spatial imagination. This is particularly prominent in students' practice of geometric shapes. Once, in a practical class, a student asked such a question: "There is an iron piece, which is 20 decimeters long and 15 decimeter wide. Cut a square with a side length of 5 decimeters at four corners, then make it into a cuboid container, and find out the volume. At first, no matter how I explained it, even if I drew the grass on the blackboard, some students couldn't understand it. I can't figure out which parts of this iron are equivalent to the length, width and height of the made cuboid. When the language is difficult to explain clearly, I ask students to do it. Make a cuboid with white paper, and soon students will get that the length of cuboid is 20? -5× 2 = 10 decimeter, width L5-5× 2 = 5 decimeter, and calculated volume is 250 cubic meters. After students begin to operate, they form the concept of space, develop their thinking and cultivate their ability to think carefully and solve problems with their hands and brains.

6. Persistence is the key to hands-on operation, which is conducive to cultivating students' rigorous scientific attitude.

Long-term hands-on operation also cultivates students' hands-on ability invisibly. We have higher and higher requirements for students' hands-on operation, and primary school students themselves have a desire for beauty and a desire for expression, and they will also ask themselves to complete each operation seriously. In this way, after long-term operation and training, we gradually developed a serious and rigorous scientific attitude.

Hands-on operation plays an important role in mathematics classroom. Starr, a famous Dutch scholar, said: "The only correct way to learn mathematics is to' re-create', that is, students discover or create what they want to learn by themselves. The teacher's task is to guide and help students to carry out this kind of re-creation, and the potential of students' active development is enormous. "

"I think it's an armchair strategist. I don't know if it must be done." In mathematics teaching, teachers should provide students with sufficient opportunities to engage in mathematics activities, let students experience the fun of mathematics in hands-on operation, deepen their understanding of knowledge in hands-on operation, improve their ability to solve problems and develop creative thinking.