How to cultivate students' spatial concept in primary school mathematics teaching

"Space concept" is one of the ten core concepts put forward in the new curriculum standard, which mainly refers to abstracting geometric figures according to the characteristics of objects, imagining the actual objects described by geometric figures, imagining the orientation and position relationship of objects, describing the movement and change of figures, and drawing figures according to the description of languages. The concept of space is the basic factor needed by the spirit of innovation. Without the concept of space, any invention is almost impossible. Many inventions are presented in the form of objects. Designers first draw design drawings according to their own imagination, then make models, and finally succeed. Spatial concept plays a very important role in this process, so it is very important to cultivate students' spatial concept.

Then, how to cultivate students' spatial concept in primary school mathematics teaching? Below, the author will talk about some methods of cultivating students' spatial concept in teaching with examples:

First, experience and develop students' concept of space.

Freudenthal, a Dutch mathematics educator, said: "Mathematics learning is an activity, which is the same as playing games and riding a bike. Without personal experience, you can't learn from reading, listening to explanations and observing other people's demonstrations. " So is the cultivation of the concept of space. Students' spatial understanding comes from rich realistic prototypes and is closely related to real life. This reminds us that students can gradually establish the concept of space through experience and perception.

For example, when learning the direction and orientation, I take students to the playground early in the morning, let them face the place where the sun rises, and tell them that this is the east, followed by the west, facing the east, with the south on the right and the north on the left. This is to let students experience "the rising direction of the sun is the east", and then know the other three directions after determining the east, thus helping students to establish the concept of space.

Second, develop students' concept of space with the help of experience.

Mathematics comes from life, and the development of students' spatial concept can not be separated from students' life experience. Life experience is a valuable resource for students to learn, so teachers should start with students' life experience in teaching, so that students can connect what they have learned with life experience, so as to better help students establish the concept of space.

For example, when learning graphics and transformation, we should use students' common life phenomena to understand translation and rotation, such as the travel of cable cars and the rise and fall of flags. The rotation of windmill and helicopter propeller are both rotating phenomena. Some beautiful patterns are obtained through the translation and rotation of basic graphics. In this way, it is helpful to develop students' concept of space by expanding their horizons to living space and closely connecting them with real life.

Third, experimental operation to develop students' concept of space.

Piaget, a psychologist, once said: "The formation of the concept of space is not like taking pictures. If we want to establish the concept of space, we must have a hands-on process. " Hands-on operation is a multi-sensory cooperative activity of students, which promotes the internalization of knowledge and enables students to gradually form the concept of space on the basis of understanding mathematical knowledge. Therefore, in the actual teaching process, teachers must guide students to carry out operations, experiments and other activities.

For example, when teaching "Understanding Objects", teachers first let students see, touch and count with learning tools, so that students can initially perceive the characteristics of cuboids, cubes, cylinders and spheres in hands-on operation. Then I prepared several operation activities:

(1) Prepare a bag for each group of students, let the group leader be responsible for it, and the rest of the students will touch out the objects with the specified shape from the bag according to the requirements of the group leader.

(2) Group and organize students to roll these objects to see which objects can't roll and which objects can roll, and compare who can roll the fastest.

(3) In groups, use these shapes of objects to build blocks and talk about what they have built.

The design of each activity actually contains some basic concepts and characteristics of objects, which are infiltrated by students' observation and perceived by experience. Therefore, students use observation and comparative mathematical thinking activities in operation to further perceive the characteristics of various graphics, unify knowledge content and space, enhance students' experience of knowledge, and at the same time strengthen students' concept of space.

Fourth, give full play to imagination and develop students' concept of space.

Spatial imagination is gradually formed on the basis of rich spatial perception, which is a further sublimation of spatial concept. In teaching, students' imagination can often be well developed.

For example, when learning "Understanding of Cuboid", after students have basically mastered the characteristics of cuboid, a three-view cuboid is displayed in the courseware: "Can you imagine what this cuboid looks like without length?" "Delete the width" ... until there is only one group leader, and the width and height intersect at a vertex. "If you remove the other side, can you imagine what this cuboid looks like? Why? " Through a series of imagination, students not only found the key factors that determine the size and shape of a cuboid, but also developed their spatial concept well.

Fifth, draw with a pen to develop students' concept of space.

Students draw a picture by themselves, so that many senses, such as vision, hearing and touch, can participate in the activities in coordination, so that students have more opportunities to explore activities through rich graphic symbol perception and practical operation, which is conducive to the formation and consolidation of the concept of space.

For example, it is not easy for junior children to understand plane graphics and teachers to explain them clearly. Let the students draw a picture by hand. Use a cuboid, lay it flat on the paper, and then draw along the edge. What is drawn on the paper is a rectangle. Students draw a picture by themselves, and initially perceive the relationship between face and body.

Another example is: after learning the orientation, let the students draw the position of the object on the paper according to the description, and let the students draw the physical object of three-dimensional space on the plan according to the description of the language, thus developing the students' concept of space.

The cultivation of spatial concept is not achieved overnight, but a long-term process. The above five strategies do not exist in isolation, but are mutually infiltrated, promoted and comprehensively applied. In short, according to students' cognitive laws, we should adopt various teaching methods and methods to guide students to actively participate in teaching and coordinate activities with various senses, so that the images of specific things can be fully reflected in their minds, thus promoting students' deep understanding of geometric shapes and unconsciously improving the concept of space.