How to explore effectively in the teaching of "space and shape"
-Listening to Feng Chuanzhen's "Ray, Line and Angle" teaching in Longdong Central School in Longmatan District "Mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. Our fourth grade has entered the second phase of primary school. The requirements of the new curriculum standard for the second phase of space and graphics are: "We should pay attention to make students gradually understand the shape, size, positional relationship and transformation of simple geometry and plane graphics through observation, operation and reasoning, and develop students' concept of space"; "Ray, Line and Angle" provides a teaching mode for students to explore independently and construct geometric concepts actively. In teaching, Li Can makes full use of intuitive multimedia to demonstrate, helping students to establish appearances and develop spatial concepts, which is worth learning. So how can we better develop students' concept of space in primary school mathematics classroom teaching? I think Miss Li has achieved the following points in the teaching process: 1, paying attention to the close connection between what she has learned and her daily life. Bring the ray phenomenon that students often see or learn in their daily life into the classroom, let children feel that there is mathematics in life and mathematics is around them, and at the same time arouse their existing knowledge representation, thus stimulating their enthusiasm for learning. By abstracting lines from the Monkey King's golden cudgel, citing the light in life and comparing the lines seen by hands, students get a vivid perceptual knowledge, especially what is finite and infinite. Then, with the help of courseware, the non-essential attributes of line segments and rays are removed, and the line segments and rays in the mathematical sense are presented. On this basis, the introduction of straight lines has a solid practical foundation. 2. Pay attention to let students get intuitive experience in activities such as observation and operation. "Mathematics Curriculum Standards" points out: "Effective mathematics learning activities cannot rely on simple imitation and memory. Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics. " To solve the contradiction between the abstraction of mathematics and the thinking characteristics of primary school students, students should be allowed to do mathematics by hand, instead of listening to mathematics with their ears, and gain a sense of space in the process of doing it by hand. Therefore, in the teaching content of "Space and Graphics", students' hands-on practice is emphasized. For example, to understand the characteristics of line segments, rays and straight lines, the key is to let students observe, operate and compare carefully and communicate the differences and connections between them. Tao Xingzhi once said: "The knower begins to act, and the walker knows his actions." When learning to determine a straight line at two points, the teacher asked the students to try to draw a picture through personal experience, and found that no matter how they draw it, they can draw countless straight lines after one point. The classified query of periodical articles should be carried out in the periodical library, for example, after the introduction of angles, students should learn the teaching materials by themselves and master the expression methods and reading methods of angles. In a pleasant and natural atmosphere, students discovered the connection between knowledge through their own exploration and accumulated energy for the follow-up study. In the usual teaching of Space and Graphics, I have the following experiences: 1, strengthen the teaching of concepts and meanings, and lay a solid foundation. When solving related practical problems, many students often encounter such a situation: whether the length or area of the week is ambiguous in the case of plane graphics, and whether the area (surface area) or volume (volume) is difficult to distinguish in the case of three-dimensional graphics. For example, how many tiles of a specified size need to be laid in a known area? To solve this problem, we must first know the size of the floor and each tile. The size of the floor and tile refers to their area. Many students have vague concepts, which leads to the situation of finding perimeter and side length. How much lime does it take to paint the classroom? You need to find the area of the painted part first, and some students will find the volume. What is the reason for this mistake? First, some students are not careful enough to examine the questions, but the main reason is that these students are vague about the concepts of perimeter, area and volume. Therefore, in the usual teaching, we should pay full attention to the teaching of basic concepts, and let students really understand the essence of solving problems through concrete operation, comparison and communication. 2. Finding the connection point between old and new knowledge and generating new knowledge through migration is a systematic and logical knowledge. The new knowledge that students learn is generally the extension, development and synthesis of the old knowledge, and so is the teaching of space and graphics. This requires teachers to activate the relevant existing knowledge in students' minds, form a trend of assimilation and migration, and then link old and new knowledge to promote the transfer of knowledge and skills. For example, in the teaching of area calculation formula of plane figure, students should first understand the concept of area unit, then deduce the area calculation formula of rectangle by placing a small square, and then deduce the area calculation formula of square, while the area calculation formula of parallelogram is obtained by transformation on the basis of learning the area calculation formula of rectangle, and then further deduce the area calculation formulas of triangle and trapezoid. The same is true for the teaching of volume calculation, which can be compared with the derivation process of area formula. Therefore, when teaching, teachers should fully understand the starting point of students' knowledge and find the connection point between old and new knowledge, so that teaching can get twice the result with half the effort. In a word, I think that when teaching space and graphics knowledge, teachers should effectively organize students' classroom activities and create time and space for students to explore. Don't let the teacher's demonstration or the activities and answers of several students replace each student's hands-on, personal experience and independent thinking. Only in this way can we train students' spatial imagination and thinking ability and develop students' spatial concept. Only in this way can we better embody the new curriculum concept of teacher-oriented, student-centered and activity-oriented.