1. The importance of thinking in images in primary school. Thinking in images mainly refers to people's choice of things' appearances in the process of understanding things. It is a thinking method that only uses intuitive images to solve problems. It is a basic thinking form of recognizing, creating and describing images with certain forms, means and tools on the basis of feeling and storing image information, combined with subjective knowledge and emotion. Thinking in images is an important way of thinking to reflect and understand the world and a powerful tool to train and educate people. Even in scientific research, scientists should not only have abstract thinking, but also have image thinking. Primary school is the initial stage for children to learn book knowledge. Pupils can't have much knowledge and must lack abstract thinking. Use image thinking more to understand things. Mathematics generally requires students to have strong abstract thinking ability. However, primary school students cannot have strong abstract thinking ability because of insufficient knowledge storage. Therefore, it is inevitable to use thinking in images in primary school mathematics education. Pupils' understanding of things begins with the appearance of things, begins with thinking in images, and takes thinking in images as the main body to understand and perceive things. In primary school mathematics education, it will only increase the difficulty of students' learning if they only explain the solution to primary school students by abstract thinking instead of using image thinking. 1+ 1=2, this equation is not difficult to understand intuitively, but if students want to understand why 1+ 1 equals 2 in an abstract way, I'm afraid there is no way. How do students understand this equation? You can put a fruit on one side of the table, and then put a fruit on it. You can intuitively find that 1+ 1 really equals 2. When a teaching scene creates a similar image, it is difficult for students to understand 1+ 1=2.
2. Primary school mathematics education needs to transition from thinking in images to rational thinking. However, it is not enough to think in images, but also abstract thinking. Mathematics is also an important subject to cultivate students' abstract thinking. Abstract thinking is a process in which people use concepts, judgments, reasoning and other forms of thinking in cognitive activities to indirectly and generally reflect objective reality. It belongs to the stage of rational cognition. Abstract thinking reflects the essence of things and the far-reaching process of the development of the objective world with scientific abstract concepts, so that people can obtain knowledge far beyond the direct perception of the senses through cognitive activities. Scientific abstraction is to reflect the inherent essence of natural or social material process in concept. Based on the analysis, synthesis and comparison of the essential attributes of things, it extracts the essential attributes of things, puts aside its non-essential attributes, and makes knowledge enter abstract provisions from perceptual concreteness to form concepts. Scientific and logical abstract thinking is formed on the basis of social practice. In primary school mathematics education, when students learn a certain number of concepts, reasoning and judgments, they already have the initial abstract thinking ability. At this time, it is easier for teachers to improve the abstract thinking ability of primary school students by taking appropriate guidance.
3. How to transition from visual thinking to abstract thinking In primary school mathematics teaching, students gain perceptual knowledge through visual demonstrations, and then form appearances. On this basis, abstract generalization, and finally form a new reasoning. Therefore, the transition from image thinking to abstract thinking is a gradual process, which needs to follow the cognitive law and carefully design every link.
3. 1 Gradually increase the steps and slow down the slope. Mathematics teaching in primary schools is based on thinking in images, and insists on intuition, so that students can acquire perceptual knowledge with their brains, mouths and hands. Then through a lot of perceptual knowledge, the representation is formed, and then logical thinking is formed. When teaching concepts such as "average score" and "who is several times more than who", four training levels can be designed.
(1) Let students set up learning tools as required, talk while setting them up, and initially perceive concepts;
(2) Let the students read the pictures, talk while reading, and gradually form the appearance;
3) Let the students draw a line diagram according to the representation to express the quantitative relationship and make a transition to abstraction;
(4) Let students describe the quantitative relationship in concise language, and make students form an image in their minds through objects and charts, so as to further understand the quantitative relationship and achieve the purpose of deeply understanding the concept.
3.2 Strengthen the intuitive purpose to make the appearance more obvious. Representation is a whole. In primary school mathematics teaching, we must pay attention to the intuitive purpose, making it easy to abstract and generalize, with outstanding representation. When learning to multiply one digit by two digits, take Example 4:243 in Book 5 as an example. In teaching, students should be prevented from taking out three 24 sticks and putting them together regardless of the process of completing the task. Instead, let the students arrange three 24 sticks in three rows, then tie 65,438+00 sticks together and finally arrange them in a row. On this basis, the pictures in the book focus on "Why did you roll up a single stick of 10 and draw an arrow to point to a bundle of sticks of 10?" It forms a representation for one-step column calculation, and also lays the foundation for the next calculation. First, calculate one bit, and after reaching 10, enter a dozen.
3.3 Abstract generalization should be based on representation. In teaching, it is necessary to prevent the phenomenon that operation belongs to operation, calculation belongs to calculation, and the number and shape are out of line. Abstract generalization is inseparable from intuition, which forms a representation. After forming the appearance of hands-on operation, students are immediately organized to calculate determinant, from concrete to abstract, and the teaching purpose is successfully achieved.
4. Several common methods to cultivate students' abstract thinking in primary school mathematics education.
4. 1 game. Use some number games, play chess, walk a maze, build blocks, play Rubik's cube, etc. Design different logical endings for each game to help children improve their abstract logical reasoning ability. Through analysis, selection, abandonment and discussion, help children improve their thinking level.
4.2 Draw a map. Inspired by the teacher, students can draw their memories of home or school and the surrounding houses, gardens, shops and so on. And clearly mark the direction, which can also improve their abstract thinking ability.
4.3 Find the shape. The teacher first prepares things with different shapes, so that students can find square things, round things, triangular things, star-shaped things ... Any shape will form an image in students' minds. When these shapes are compared in students' brains, students will have an abstract understanding of different shapes.
4.4 Layout of color patterns. Give the students some beads of different colors and arrange them in different patterns. At first, there can be two colors: purple and green. Let the students exclude: purple-green-purple-green; Green-green-purple-green-green and so on. Then gradually increase the number of colors, so that students' abstract thinking ability can develop with these different colors and patterns.