On how to effectively cultivate students' spatial concept 1

Cultivating students' initial concept of space is an important goal of geometry teaching in primary schools, and it is also the basis for further developing students' spatial imagination. In this regard, the "New Curriculum Standard" has a clear statement, "Let students gradually form the appearance of the shape, size and mutual position relationship of simple geometric figures, identify the geometric figures they have learned, summarize the names of geometric figures, reproduce their appearances, and cultivate a preliminary concept of space." Combining with my own teaching practice, I talk about my own experience on how to cultivate the spatial concept of primary school students.

First, the use of physical models to cultivate intuitive understanding

The thinking characteristics of primary school students are mainly concrete image thinking and gradually transition to abstract logical thinking. Therefore, in the whole primary school stage, it is inseparable from intuitive teaching AIDS. Intuitive teaching AIDS include two aspects: object intuition and speech intuition. Physical visualization includes teaching pictures, statistical icons, geometric models and various audio-visual appliances.

The Standard focuses on students' experience of abstracting mathematical models from the actual background and geometric figures from the real life space, and on the process of exploring graphic characteristics and their changing laws. For example, in the first and second phases, through observation, operation, organized thinking, reasoning and communication, students are guided to understand the shape, size, transformation and positional relationship of graphics from multiple angles, and their geometric intuition and spatial concept are developed; In the third stage, students are guided to explore the essence of graphics through various activities such as observation, operation, graphic transformation, unfolding and folding, pattern appreciation and design. To further understand graphics and its essence, enrich the experience and good experience of geometric activities, and develop the concept of space. I remember when I was teaching the lateral area and surface area of a cylinder, I asked my students to expand the side of the cylinder model along a generatrix, and convinced them that the side expansion diagram was a rectangle, so that the lateral area of the cylinder was equal to the area of this rectangle. After the surface area of a cylinder is equal to the side area plus two bottom areas, we can calculate the surface area of a log and the surface area of a cylindrical bucket without a cover. The surface area of a cylindrical chimney is equal to the side area plus the area of several bottom circles. This not only cultivates students' ability to solve practical problems, but also cultivates students' ability to re-create imagination by using the accumulated space concept.

Second, pay attention to students' hands-on operation and let them experience the process of "doing mathematics"

Hands-on operation is closely related to the thinking development of primary school students. Physiological research has proved that "children's wisdom is concentrated at the fingertips". Hands-on operation conforms to the age characteristics of primary school students and enables them to concentrate on conscious teaching activities. In operation, the perception of mathematical knowledge is the strongest, and the representation formed is also the deepest. When primary school students operate, the stimulation generated by fingertip touch can be quickly transmitted to the brain, and under the premise of cerebral cortex excitement, they have the desire to think positively. Therefore, don't miss every opportunity for students to start work in teaching.

Students test their imagination by hands-on operation. First of all, we can design activities such as "jigsaw puzzle", "lace design" and "building blocks" to master the characteristics and formal expression of geometric figures in painting. In addition, let students make models from simple to complex. Finally, it is essential for students to make models of cubes, tetrahedrons and octahedrons, which not only helps students to improve their spatial imagination. Students can look, compare, measure, fold, draw, make models and so on. For example, when teaching the concept of "corner", the teacher can ask students to make learning tools for corners, find two cardboard strips, nail one end of them together, and rotate one of them. On this basis, students can quickly understand acute angles, right angles, right angles and rounded corners. It can also be concluded that an angle can also be regarded as a light rotating around one of its endpoints, and a light rotating along its endpoint can get different angles. For example, in an exercise, several small cubes are used to form a geometry, and its front view and top view are shown in figure 1. Is there only one geometry like (1)? If there is more than one, please draw several different left views. (2) How many cubes do you need to create a geometric figure to meet the requirements of the front view and top view shown? How many cubes at most? This question is an open exercise. After full imagination, let the students revise their imagination constantly in combination with the real thing. Practice has proved that this is effective for cultivating students' concept of space.

Third, use vivid audio-visual means to develop students' spatial imagination.

The appearance of the Internet has caused great changes in all walks of life. Education is no exception. In primary school mathematics teaching, we can also use the network to change the traditional teaching mode. Turn the invisible into the tangible, and turn the limited into the infinite.

Many contents in geometry teaching need to be understood dynamically. Traditional teaching methods are always on the plane, and students can't understand the changing process of graphics without moving. Making simple animation through some software can make static graphics move, thus helping students understand. In the teaching of "angle measurement", audio-visual teaching can be used to reflect the transparent protractor on the screen through the projector (the projector plays an amplification role), so that students can clearly see the angle measurement process demonstrated by the teacher, especially the problems that the center of the protractor coincides with the vertex of the angle, the "0" scale line of the protractor coincides with one side of the angle, and how to use the scale of the inner circle and the outer circle can be solved. In addition, it is more obvious how to measure the angles in different directions by means of audio-visual education. As shown in the figure below, students can see with their own eyes how the teacher rotates in a standard position and turns it into an angle, and then measure it with a protractor, which has practical guidance for students' written practice.

The new mathematics curriculum standard regards "space concept" as an important learning content to cultivate students' initial innovative spirit and ability in compulsory education stage. In teaching, we should constantly explore and innovate. I believe that our students' concept of space will become stronger and stronger, and will eventually become stronger with the imagination of space.