How to guide students to preview primary school mathematics and geometry?

On the Application of Teaching Strategies of Mathematical Geometry in Primary Schools

This paper is included in 60050 1: Mathematics Discipline Group (2023).

On the Application of Teaching Strategies of Mathematical Geometry in Primary Schools

The knowledge points of geometry are closely related. Of course, primary school geometry is not a strict axiomatic system, but also belongs to the category of empirical geometry or experimental geometry. Its main contents include the understanding of simple geometric figures, transformation (translation, rotation, symmetry), position, direction, perimeter, area, volume and preliminary understanding of coordinates. In this regard, based on these properties of geometric figures, how to cultivate students' spatial concept, geometric intuition, graphic design and reasoning ability is worth discussing. This paper talks about my own practices and strategies based on some personal experiences.

In my opinion, in teaching, teachers should use various methods to help students understand the characteristics, size, positional relationship and transformation of geometric figures in life, so that students can better understand and describe living space and communicate effectively with geometric figures. Teachers can guide students to understand simple geometric figures, feel translation, transformation, symmetry and other phenomena, learn some methods to describe the relative position of objects, and guide students to carry out simple measurement activities. On this basis, they can further understand the basic characteristics of some geometric figures.

Teachers organize students to gradually understand simple geometry knowledge through observation, operation and reasoning. Students develop their spatial concepts in various learning activities. In the process of learning, teachers should also organize and guide students to express and communicate. At the same time, we should also avoid complicated calculations such as perimeter and area. Generally speaking, I think geometry teaching should be carried out from the following aspects.

First, the material of life experience, truly implement the idea that mathematics comes from life.

Make full use of students' life experience and attract people to teach from things familiar to primary school students, and the effect is remarkable. When the students were learning triangles, I took the triangle paper they usually played with and asked, "What shape is this?" "What other triangles have you seen?" At this time, students will immediately talk about their triangle, the red scarf around their necks, the roof truss of the house and so on. Direct and effective from the perspective of life. For another example, when I introduce the concept of "circle", I can ask the students such a question first: "Have you ever seen a wheel? What shape is the wheel? " In fact, the geometric figures that students learn have prototypes in their lives, and students can also see many geometric phenomena in their lives. So make full use of these life foundations in teaching, and then abstract these life prototypes into our geometric knowledge for teaching.

Second, a variety of observation activities, really learn the characteristics of geometric figures.

Observation is the activity of primary school students to understand the outside world through their senses. Students can't learn geometry without observation activities, and organizing various observation activities is the main way for students to further develop the concept of space. After entering primary school, pupils' observation of graphics will enter a new stage. How can teachers guide students to observe effectively? In fact, the effect of students' observation has a lot to do with the way teachers provide graphics. Provide standard geometric figures, and use the "stability" of standard geometric figures to let students know some characteristics of the figures. Providing some variant graphics can help students think in observation and further master geometric concepts. Of course, in the observation activities, it is necessary to cultivate students' comprehensive and serious observation habits, so that students' observation ability can be effectively improved and improved. When I was talking about "understanding cylinders", I took out several cylinder models for everyone to observe and asked, "What are the characteristics of cylinders?" Most students can say that the top and bottom are round, and the areas of the circles are equal. The students' observation is really careful. Students' initiative naturally rises at once.

Third, simple geometric reasoning can really realize the development of spatial concepts.

Guiding students to make geometric reasoning is an important teaching link. Geometric reasoning in teaching is mainly reflected in the following activities:

First: think through observation. For example, knowing triangles can show triangles with different shapes (right triangle, acute triangle and obtuse triangle), different sizes, different orientations and even different colors and materials. Then students realize through observation that a closed figure surrounded by three sides like this is called a triangle, which has nothing to do with other factors.

Second: judge by comparison. This way can help students accurately identify the essence of graphics from similar graphics, and the impression is clearer. For example, when teaching triangles and quadrangles, we can show such figures for comparison and judgment, and finally summarize the concepts and characteristics of triangles and quadrangles.

Third: imaginary reasoning. Sometimes, we create more time and space for students' imagination, and apply the art of sketching to math classes. For example, some situations can be created for students to talk about what they see, and students can use this time to use spatial imagination for geometric reasoning in such situations.

Fourth: think in the activity. When I was listening to Left and Right, the teacher organized students to carry out simulation activities well and really realized the relativity of left and right. For another example, when teaching the activity of "Interesting Tangram", the teacher first asked the students to choose two pieces of Tangram to make a square, and guided the students to observe that two identical triangles can be made into squares, and the two sides (the longest sides) of the triangle should be put together. Let the students think again: What other figures can be put together with two identical triangles? Students find one or more answers through independent operation, and then organize students to cooperate and exchange, share the ideas of their peers, learn from each other and inspire each other. Finally, while the iron is hot, the teacher asked, "Can you spell squares, triangles and parallelograms at once in an orderly way? With your friends, think about any good ideas? " The students took action at once. During the trial run and group discussion, they found that just hold down 1 triangle and let the other triangle move (translate or rotate). In the cooperation and communication, students really deepened their understanding of graphic transformation and learned the method of orderly thinking, and the concept of space naturally developed further.

Fourthly, effective experimental operation really goes through the process of mathematical deduction and demonstration.

Students' hands-on experiments are the most effective, which can make students participate in vision, hearing and touch, and truly form and consolidate the concept of space geometry. In the operation of the experiment, students have a preliminary deduction and demonstration through rich graphics and symbols perception, operation and participation in inquiry activities. For example, when teaching the knowledge of the sum of the internal angles of a triangle, the dose method can be used. But there are errors in the process of quantity, so why not guide students to carry out inquiry experiments? You can put the three inner corners of a triangle together, and the students will come to life at once. Students will start to pick up scissors to cut off three corners and put them together, and naturally get a mathematical conclusion. For another example, when teaching the concept of volume, I put two glasses with the same size of water into two stones with different sizes, so that students can observe the change of water level; When the stone is taken out and compared with water, students will vividly and concretely realize the meaning and concept of volume. Of course, in the operation of the experiment, students can also be guided to understand through experimental activities such as swinging, folding, cutting, making, drawing and field operation.

Fifth, interesting graphic variants really avoid the limitations of students' understanding.

In order to overcome the limitations of students' understanding, the materials we provide should be changed. For example, when teaching isosceles triangle, let students observe the standard isosceles triangle figure first, and then show several variants of isosceles triangle figure. In the process of teaching, there is an argument. How do students grasp the essence of graphics in such variant graphics?

Students quickly summed up the concept of isosceles triangle in comparison. Then show the non-isosceles triangle and isosceles triangle at the same time, and then let the students judge and distinguish. Using such interesting variant figures, we can grasp the essence and attributes of geometric figures.

In terms of students' learning style, I advocate independent cooperation and exploration, gradually understand the shape, size and mutual position relationship of simple graphics, understand the characteristics and properties of some special graphics, and develop students' spatial concept and graphic design ability in simple geometric reasoning.

In short, the relationship between geometry and life is closely related, so we should broaden our horizons to life space and pay attention to the problems related to graphics and space in the real world. Through independent exploration, we gradually understand the knowledge of geometric figures. In this process, students' spatial concept, geometric intuition and graphic design reasoning ability are truly developed by observing objects from different angles, knowing the direction and making models.

Other people's opinions, I hope to help you.