What Is Spatial Attention?

Spatial imagination is the abstract thinking ability of people to observe, analyze, and recognize the spatial form (spatial geometry) of objective things. Cultivating students' spatial imagination is one of the main tasks of middle school mathematics teaching, and it is also one of the difficult points. If the term spatial imagination is only mentioned in teaching, the rational analysis is not enough, and the training law cannot be grasped, it may result in the following: a small number of students with understanding have improved their spatial imagination, and most of them The students did not earn much, and even regarded the study of Solid Geometry as a daunting

Spatial imagination

According to the characteristics of the improvement of spatial imagination, the cultivation of spatial imagination can be subdivided into the following 6 processes:

Process 1 strengthen student pairs

How to improve students' spatial imagination

I. Use computers to draw vivid and vivid three-dimensional graphics so that students can understand abstract theoretical concepts through a thorough observation of intuitive graphics

In the chapter "Volumes of Polyhedron and Rotating Body", the main content is the derivation of the four volume formulas of column, cone, table, and sphere. The key is the analysis and understanding of three-dimensional graphics. In order to help students transition from perceptual knowledge to rational knowledge on the basis of observing graphics, we use our school's computer equipment and work closely with full-time computer programmers to design and compile graphics software to assist teaching. We first design the basic graphics according to the needs of the explanation, and then cooperate with the programmer to draw using the computer's advanced drawing system. In the drawing process, we use the continuous movement of the screen to form an animation to reflect the dynamic actions of cutting, rotating, and moving. When explaining the principle of ancestors, its main content is: if two geometrical bodies of equal height, if the two cross-sectional areas cut by a plane parallel to the base are equal, then the two geometrical bodies have the same volume. In order to reflect the key point: the parallel sections at any position of the two geometries are equal, we have drawn multiple sections of different positions, painted the sections with bright colors, and arranged them in order. The animation effect of movement makes students realize that the parallel sections at different positions are equal everywhere. Another example is when explaining the derivation of the volume formula of the cone, because the triangular prism is divided into three triangular pyramids, the graphics change greatly, and it is not easy for students to understand. Therefore, we will show the cutting process to the students from beginning to end. The two triangular pyramids to be compared gradually return to the state before cutting, and then separated. With the moving process of separation, restoration, and separation, students clearly and naturally came to the conclusions to be inferred, while also making the teacher's explanation easy and logical. With the volume formula of the cone, we further based on the idea of truncating a small cone by a plane that is parallel to the bottom of the large cone to obtain the platform, and use the derived volume formula to derive the volume formula of the platform. We use an animation effect to make a plane move to show the process of dynamically cutting a large cone. That is, let the plane be inserted from somewhere of the large cone in a way parallel to the bottom, and extracted from the other side, leaving traces of cutting, and then intercepting The small cone moves to another position, showing the rest of the platform to the students. The joining of this process has left the connection between the platform and the cone very deeply in the students' minds. It can be said that they have not forgotten it and have received good results.

Second, make full use of the advantages of multi-functional computer graphics, depicting three-dimensional graphics from multiple directions, angles and sides, and solve the visual difference between planar three-dimensional graphics and real three-dimensional graphics.

We need to consider the problem of visual differences when drawing solid graphics on a plane. For example, when drawing a cube on paper, some of its faces must be parallelograms in order to give a sense of "body". In fact, all sides of the cube are square. In order to prevent students from taking the intuitive feeling as a concept, we have designed some rotational deformation actions. When talking about the volume formula of the sphere, using the ancestral principle, a geometry with the same volume as the hemisphere was found, that is, a cone was dug out in the middle of a cylinder of the same height as the hemisphere. The key to the proof was to deduce the parallel sections of the two at the same height. The area is equal. From the figure, these two sections are ellipse and elliptical ring respectively, and the actual shape should be circle and ring. In order to illustrate the problem more vividly, we designed the two sections to move horizontally from the original position, and then rotated horizontally 90 degrees to make it vertical, so that the two sections restored their actual shapes. At the same time, we gradually reduced the small circle in the circular section to a point, so that the ring became a circle the same size as the other section. Through the interchange of the two colors, the students' images intuitively felt that the two areas were equal. Cross-sections, and then theoretically prove that their areas are equal. In this way, the cooperation from intuition to theory has deepened students' understanding and made this difficult problem solved smoothly.

3. Use multimedia to assist teaching to guide students to actively and actively seek solutions to problems by observing graphics

The core of modern teaching theory is to confirm the leading position of teachers in teaching, and to identify the main position of students in learning activities. Therefore, the ultimate goal of teaching is to inspire and motivate students to "learn". In the attempt of multimedia teaching, in order to break the habit of "teachers speaking, students listening" in traditional teaching, we will use the exercises in the class "from a cube, cut off the four triangular pyramids as shown in the figure, and get a regular triangular pyramid. , Find out its volume is a fraction of the volume of the cube? "According to the intent, it is designed into an animated scene. A cube is cut out of the four corners in order, the cut part is placed in the four corners of the screen, and a triangular pyramid is left in the middle. Find the volume of the triangular pyramid. Based on the screen demonstration, the students immediately thought that the rest was cut off by the whole minus. With the idea in mind, it is clearly deduced from the picture that the volume of each corner is 1/6 of the whole, and then the required volume is 1/3 of the whole. In this way, through the demonstration of the screen, without the teacher's explanation, the students can find the solution method by themselves, and at the same time, the concept of indirect volume seeking is established in the middle. Through multimedia teaching, we find that it has incomparable advantages. First of all, multimedia teaching saves effort in class teaching; it can teach intuitively, vividly and vividly, which helps to attract students 'attention, fully motivate students, and greatly reduces the amount of teachers' blackboard writing. Secondly, multimedia teaching increases the capacity of lessons and strengthens the coherence between knowledge. Because multimedia teaching highlights the teaching points intuitively, vividly, and vividly, it eases teaching difficulties, speeds up students' understanding of knowledge, and saves time for teachers to repeatedly explain, saves lesson time, and relatively increases the capacity of the lesson. The continuity of knowledge in each part has achieved better teaching results. ^[1]