How to Cultivate Primary School Students' Geometrical Intuitive Ability
The new curriculum standard clearly points out: "Geometric intuition mainly refers to describing and analyzing problems with graphics. With the help of geometric intuition, complex mathematical problems can be made concise and vivid, which is helpful to explore the solution ideas and predict the results. Geometric intuition can help students understand mathematics intuitively and play an important role in the whole mathematics learning process. " Therefore, geometric intuition should be emphasized in mathematics teaching, and the ability of geometric intuition should be cultivated throughout mathematics teaching. Let students better perceive and understand mathematics, and let mathematical logic and mathematical intuition be intertwined, with logic in intuition and intuition in logic. So, how to cultivate students' geometric intuitive ability? Combined with my teaching practice, talk about some experiences.
First, hands-on operation, intuitive perception of geometry
Teachers should gradually cultivate students' concept of space in teaching, require students to feel the characteristics of various geometric shapes through hands-on operation, let students "play, see, touch, spell and draw pictures" and other specific practical operations, guide students to touch, observe and make by themselves, combine vision, touch and cooperation, and enable students to master the characteristics of graphics and form initial geometric intuition.
For example, when teaching the course "Understanding Graphics", I focus on hands-on operation to cultivate students' geometric intuitive ability.
(1) Understanding graphics-taking activities as the learning carrier.
Activity 1: Touch the object game.
Teacher: We invited some friends to class. They hid in their pockets. Before class, they whispered to the teacher that you had to play a game first. The rules of the game are like this. Please reach into your bag and touch an object at will, and then tell everyone what the object you touch is like. In your own words.
Sheng 1: Fang Ersu ...
Student 2: Cubes.
One student touched the "cuboid" and another student came forward to look for such an object. ...
(2) Draw a plan.
Teacher: They are happy to make friends with you when they see that everyone is living so well. Look, here they come.
Show courseware: cube, cuboid, cylinder, triangular prism. Ask the students to say their names. )
(1) Looking for footprints
Teacher: I also brought a photo of them playing Snow Painter to share with you.
Teacher: There are many beautiful footprints in the snow. Guess whose footprints these are?
Teacher: What about the footprints of the cuboid?
② Draw footprints
Teacher: Then how can we write such footprints on paper?
The deskmate discussed: How are you going to move such a flat surface to paper?
Health 1: I want to use inkpad ...
Health 2: I use the one that draws strokes. ...
Health 3: I covered it with paper and folded the corner marks. ……
③ Move it.
Teacher: The children are amazing. They came up with so many good ideas. The teacher prepared a piece of paper for everyone. Please move one side of the three-dimensional figure in your hand to the paper in your favorite way. After moving, cut it open and cut off the footprints.
Students do it by hand. Pay attention to the students' homework during the patrol. ) Ask three children to come up for a haircut.
Teacher: I want to ask some students to show you your work. Can you tell me from which object you moved this portrait to where?
1: I moved this figure away from this side of the cuboid.
Health 2: I moved this figure away from this side of the cube. ……
It can be seen that hands-on practice and autonomous participation are very effective learning methods for learners, and it is true that "wisdom often comes from the fingertips." The process of students' learning is the process of dynamic knowledge generation, re-creation and re-practice, and they gain the experience of learning spatial graphics. Teachers give full play to students' initiative in learning, let students actively acquire new knowledge, let students experience in a happy mood, master knowledge in deep experience, feel mathematics personally and enhance their interest in mathematics.
Second, the combination of numbers and shapes turns abstraction into concreteness.
Hua, a famous mathematician in China, once said: "If there are few shapes, it is less intuitive, and if there are few shapes, it is difficult to be nuanced;" The combination of numbers and shapes is good in all aspects, and everything will be combined. "The idea of combining numbers and shapes can make some abstract mathematical problems intuitive and vivid, change abstract thinking into thinking in images, and help to grasp the essence of mathematical problems, which is easy to solve and simple to solve. ?
For example, when guiding students to learn the application problem of "how many times is a number", the concept of "times" is the most difficult for students to understand. How to teach students the mathematical concept of "time" in simple terms, so that they can have their own understanding of "time" and internalize it into their own things? Graphic demonstration is the simplest and most effective method.
3 for the first discharge and 4 for the second discharge.
With the demonstration, let the students observe and compare the quantitative characteristics of sticks in the first row and the second row. Inspired by the teacher, students discuss and communicate in groups, so that students can clearly understand:
There are 1 in the first row and 4 in the second row. Take one stick as one, and the second row of sticks as four.
Then describe it in mathematical language:
Compared with the first row of rods, the number of rods in the second row is 1 times, and the number of rods in the second row is four times that in the first row.
Let students see from "number" to "number of copies" in the demonstration diagram, and then lead out the multiple, so that they can quickly touch the essence of the concept, give full play to the pillar role of intuition in abstraction, reveal the internal relationship between number and shape, make abstract mathematical knowledge clear, exercise students' thinking quality and add value to classroom teaching.
Third, the use of multimedia to cultivate the concept of space
For abstract mathematical problems in textbooks, we should adopt a visual teaching method-the effect of multimedia intuitive demonstration. Teaching is from abstract to intuitive, illustrated and vivid, which makes mathematics no longer boring. Dynamic demonstration is carried out in classroom teaching, which reveals the generation process of knowledge, turns abstraction into concreteness and rationality into sensibility.
For example, when teaching the knowledge of cuboids, we can skillfully use my multimedia to make a dynamic demonstration, so that students can feel that cuboids have six faces, and the opposite faces are represented by the same color. Dynamic demonstration, the opposite sides are completely coincident, and the opposite sides are exactly the same. Then, hide six faces and expose 12 edges. Through the movement of the edge, the demonstration is assembled and accompanied by sound. Color dynamics is used for comparison, and a cuboid is obtained. In this way, all the features of the cuboid are presented to the students.
Multimedia courseware demonstration can fully display the characteristics of cuboid, reduce the difficulty of observation, highlight the key points of observation, not only give students a sense of beauty, but also effectively activate their thinking and interest, which greatly improves the teaching efficiency. Let students learn this knowledge easily and happily, and at the same time cultivate their spatial concept.
In short, it is not a one-off event to cultivate students' geometric intuition ability. It requires teachers to take classroom teaching as a link, pursue constantly, study hard and improve constantly, so as to find an innovative way to develop students' spatial concept and geometric intuition in geometric intuitive teaching.