This paper puts forward my own ideas on the teaching of space and graphics, mainly including the understanding of graphics, graphics and position, graphics and transformation, graphics measurement, and finally the concept of space, so as to have further communication with you. It should be emphasized that these views are the result of collective discussion by this project team and have our own ideas. Of course, there must be something immature, but I hope it can cause more discussion.

First, the understanding of graphics

In this part, I will share with you my understanding of graphics and the clues presented by the whole content.

The main clues of content presentation

(1) From Stereo to Plane to Stereo

Why does the new curriculum advocate understanding three-dimensional first, then plane, and vice versa?

A. First of all, according to children's cognitive rules, in children's real life, the first thing they come into contact with should be three-dimensional, such as their pencil boxes, such as blackboards, desks and chairs they see every day. The plane figure is attached to the solid. Students' mathematics learning should naturally follow children's cognitive laws and reflect the process from whole to part and then to whole.

B then from three-dimensional to plane and then to three-dimensional, if further refined, it should be from three-dimensional to plane to basic elements, then to plane and then to three-dimensional, and the two planes are different. First, students intuitively understand three-dimensional graphics and plane graphics, and then they try to master the characteristics of these plane graphics and three-dimensional graphics. For example, just like when we go to see a person, you first get to know him as a whole, and then you will pay attention to his eyebrows, nose and eyes; Conversely, when you pay attention to eyebrows, nose and eyes, you will get to know this person as a whole, and you will have a newer understanding.

There is another reason. The new curriculum emphasizes the concept of space, which has an important aspect: the transformation of three-dimensional and two-dimensional, that is, from three-dimensional to plane, and vice versa. Of course, this can be reflected by observing objects and other substances, but in the process of students' learning, it can also reflect such a process: finding plane graphics from three-dimensional graphics and restoring three-dimensional graphics from them.

Let's go back to the first case discussed earlier, that is, two teaching processes of intuitive understanding of plane graphics in senior one. According to the above discussion, the process of 1 gives students more space to operate and explore, so that they can feel the process from three-dimensional to plane. From this perspective, the process of 1 is still very valuable.

(2) Abstracting graphics from life and applying them to life.

The second clue is the process of abstracting graphics from life, then learning graphics and their characteristics, and then applying them to life. Let's go back to the process 2 of the first case discussed earlier, which embodies this process and is also very valuable. Some teachers may say, do you like process 1 or process 2? In fact, there is no conclusion. The key is what the teacher has set for this class. Some teachers think that both processes are very good, so they need the idea of preparing lessons in units. These two processes can't be completed in one class.

I also want to emphasize that teachers nowadays pay more attention to the process of abstracting graphics from life, and conversely, teachers seem to dig less when applying graphics and their characteristics to life. This requires teachers and students to think together. After learning the characteristics of rectangle, square and triangle, can they use these characteristics in their lives? Give an example of a middle school, hoping to give you some inspiration.

[Case]: When building a cuboid base for a repair shop, the builder needs to judge whether the surface of the base is rectangular. Can you design a judgment method for him? If he only has a tape measure, can he finish the task?

When students try to solve this practical problem, they need to make full use of the relevant graphic features they have learned, which not only promotes their understanding of these features, but also cultivates their ability to solve problems. Students can explore different methods. In the case of only tape measure, the length of all sides and diagonal lines on the base surface can be measured, so as to judge; You can also measure the length of some basic surfaces, and then use the inverse theorem of Pythagorean theorem to judge.