How to cultivate pupils' geometric intuition

Hua, a famous mathematician, said: "The lack of form is difficult to be nuanced, and it is even less intuitive." Geometric intuition refers to a mathematical ability to think and perceive with the help of intuitive graphics. In primary school mathematics teaching, geometric intuition runs through the teaching and is the core content of developing students' intelligence. In teaching, how to play the role of geometric intuition in the classroom and build the geometric intuition ability of primary school students?

Firstly, based on the drawing strategy, mathematical representation is used.

In primary school mathematics learning, it is difficult for most students to form an intuitive geometric model in their minds, which leads to confusion in solving problems. The reason is inseparable from students' lack of painting strategies. Based on this, teachers should cultivate students' ability to look at pictures, read pictures and draw pictures, help students to construct drawing strategies, make them learn to analyze and solve problems by mathematical representation, and gradually improve their geometric intuitive ability. For example, in the teaching of "problem-solving strategy-pushing back", the teacher showed the following examples: two cups of juice ***400 ml. Pour 40 ml into cup A and 40 ml into cup B. Now there are as many as two cups of juice. How many milliliters are there in two cups of juice? In teaching, teachers use geometric intuition and drawing methods to help students describe mathematical problems and understand the changing relationship between the capacity of two cups of juice. Two glasses of juice, the original capacity is unknown. After pouring from a cup to b cup, the amount of juice changed. Let the students clearly see the amount of B cup through intuitive graphics. Then extract the relevant information from the list, and students can easily find the original capacity of two cups of juice. In the above links, students can fully reproduce the problem situation, deeply understand the meaning of the problem, and grasp the internal relationship of mathematical information in the event. Graphics provide strong support for students to solve problems, enable students to quickly find the core of the problem, have a full experience of the two core issues "why do you want to push backwards" and "how to push backwards", and realize the development of geometric intuitive ability.

Second, based on the concept of space, cultivate imagination.

In teaching, teachers can use geometry to intuitively develop students' spatial concepts and cultivate students' mathematical imagination. For example, when teaching "cuboid and cube's volume and surface area", the teaching activity of spatial imagination is designed: first draw six sides of cuboid on the blackboard, then erase the sides, and then erase a few sides, so that students can determine the shape of cuboid according to the remaining three sides. Students imagine the corresponding surface through the information of the edge, so as to determine the shape of the cuboid. By erasing surfaces and edges, from line to surface to body, from one-dimensional to two-dimensional to three-dimensional, teachers help students to establish the characteristics of surfaces, so that students can have a deep understanding of cuboids by extracting and analyzing representations. Students not only gradually construct the concept of space in imagination, but also greatly improve their ability of spatial imagination.

Third, based on the combination of numbers and shapes, it promotes intuitive perception.

The combination of numbers and shapes is not only widely used in mathematics, but also plays a great role in daily life. In teaching, teachers should not only make abstract mathematical concepts intuitive and simple with the help of graphics, but also transform graphic problems into algebraic problems to make the expression of problems more accurate. The mutual penetration of "number" and "shape" not only makes the problem solving concise and clear, but also helps students to form geometric intuitive ability. For example, in the "multiplication formula" exercise, a small triangle represents the number 5, so what does this big triangle represent? Please calculate in the form of formula. The students were completely at a loss at first and didn't know how to solve it. At this time, the teacher guides the students around numbers and shapes, and lets them observe how many small triangles there are in the big triangle. Students quickly concluded that * * * has four triangles. Question: "What numbers can four small triangles represent? Why? " According to the meaning of multiplication, students think that this means the addition of four fives, and the formula "4× 5 = 20" can be listed through multiplication calculation. Through this teaching design, students realize that numbers are tangible and there are numbers in form, which effectively breaks through the boundary between numbers and shapes and promotes students' intuitive perception of logarithms and shapes.

In short, the cultivation of students' geometric intuitive ability can not be completed overnight. Only by visualizing abstract problems and clarifying hidden problems can teachers effectively help students deepen the essence of mathematics and develop their geometric intuitive ability by leaps and bounds.