1. Introduction

The preface of the original curriculum standard is not quite like the preface. Our math group just does it ourselves, regardless of others. Anyway, we did it according to our own ideas. We think the curriculum standard should be said to be for what. Very good. This compulsory education law is also written in the curriculum standards, so the preface is easy to write. The preface has been completely changed, and the basic orientation is: "The curriculum ideas and objectives put forward by the standards have a guiding role in the mathematics curriculum and teaching in the compulsory education stage. The prescribed curriculum objectives and content standards are the basic requirements that every student should meet in the compulsory education stage, and the standards are the basis for the compilation, teaching, evaluation, examination and proposition of teaching materials." We changed it slightly according to the compulsory education law.

2. Basic ideas

Introduce past mathematical standards into basic concepts. This has changed a lot. We have redefined mathematics. We expounded mathematics in relatively short language. Then it expounds mathematics education. Mathematics is like this, so what is mathematics education like? The mathematics education in the compulsory education stage is expounded in great length. According to this idea, the previous paragraph "hat" has been rewritten, which is bigger than the past. I hope to be more clear.

We have also made great changes in basic concepts, and this issue is still controversial. The basic idea of the past said: "Everyone learns valuable mathematics, everyone gets the necessary mathematics, and different people get different development in mathematics." The reason for the argument is: what is valuable mathematics and what is necessary mathematics for everyone. We have a standard from the beginning: write clearly, clearly and regularly. It needs to be tested and it is difficult to explain clearly. Is the mathematics we study valuable, and is it valuable to study Goldbach's conjecture? And the necessary math. How do you know what is necessary and what is not? Later, we changed this sentence: "Everyone can get a good math education, and different people get different development in math education." This year, the Prime Minister said, "Everyone gets an education, and everyone gets a good education". We wrote it before the Prime Minister.

And we explained it in the later teaching suggestions. What is a good math education? It means that you not only know the knowledge, but also know the basic ideas, which are honed in the learning process.

There is also a lecture in the concept. I totally understand this matter. At that time, the standard was written to break through the past, so it was written with emphasis on students' autonomous learning. Emphasis on activities, so the teacher hardly mentions a word in the lecture, which is too biased. What is good teaching? First, in addition to imparting knowledge, we should also mobilize students' learning enthusiasm and inspire their thinking; Second, it can not only cultivate students' good study habits, but also enable students to master effective learning methods. As for what form and how to teach, every teacher should have his own style. Teachers' teaching style is fixed, so they can't attend classes. Teachers have their own personality. It cannot be emphasized that every class is introduced from life, with 20 minutes of study and discussion and 30 minutes of end. Some knowledge suits this. Some knowledge is suitable. It is different and can't be rigidly stipulated, but there must be a criterion and principle to make these things clear in the place of concept.

There is also the use of multimedia educational technology. Of course, it is very important, but it is still very important. Teaching students face to face instead of using multimedia in every class will make them think.

3. Design concept

We defined the design idea. The past standard design ideas were not clearly written. In the design thinking of mathematics, it is mainly the explanation of several target verbs, which must be clearly explained in the design thinking. There are three aspects of knowledge in mathematics: quantitative relationship, geometric relationship and random relationship, so the main names are number and algebra, figure and geometry, and the word eternal geometry should also appear. In the United States, plane geometry is no longer talked about, but it is still called geometry. There are also four aspects: statistics and probability, synthesis and practice. It's hard to give it a name. "Comprehensive Practice" was put together with "Mathematics and Algebra" and was later named "Four Courses"? Because modeling will also be taught as a course in universities. The four courses are elaborated carefully, and it is very difficult to explain. We made a very serious exposition. If you want to make numbers and algebra clear, you must make figures and geometry clear.

We have also made a principle that we have talked about all the most important things and made it clear. It is impossible to cover everything. So our course has made it clear how to design these four aspects. For compiling teaching materials and teachers to master.

A main line in the content must be very clear. What is "number and algebra"? Then unify its core ideas. After repeated screening, Number and Algebra involves four core ideas, one is "number sense", which is the primary school stage. The second is "symbol consciousness", knowing that the use of symbols is very important in mathematics and an abstraction of real life, knowing that the results obtained by operation and reasoning with symbols are general. We put all this in. When we are writing, we always think about talking to teachers in rural primary and secondary schools. I'm sure what I wrote will make him understand and understand. I believe that most middle school math teachers can know this.

What is geometry? First of all, we should cultivate geometric concepts, immerse ourselves in geometric intuition and cultivate reasoning ability.

What are statistics and probability? Cultivate knowledge, speak with data, and draw conclusions through investigation and research. He also knows that the data is random, and this survey will get these things, and the next survey will find other things. However, through a large number of investigations, we can find some regular things.

What is synthesis and practice? It is an important carrier to cultivate students' process experience. It is very important to systematize knowledge and solve some practical problems through integration and practice. But in this class, we suggest not too much. The course of integration and practice may not be completed in one class, but it may be completed in one week. Let the students investigate and think, and then let the children often explain their views together. We think the explanation is relatively clear. I am very happy to show it to some primary and secondary school teachers. It wasn't clear before, but it is clear now.

4. Objectives

Fourth, the object has changed a lot. In the past, mathematics emphasized two foundations: "basic knowledge and basic skills". It has been the core of Chinese mathematics education since it was put forward in 53 years and written in 56 years. Basic knowledge and skills are indispensable, which makes the basic mathematics education in China have great influence in the world. Our children have a solid grasp of basic knowledge and skills. But we lack creative things. We added two, one is the basic idea and the other is the basic activity experience. Become fourth base.

Why add "basic ideas"? Let's sum up the basic ideas of mathematics education in China in the past 50 years, not only mathematics, but also other sciences. Just two: one is deduction and the other is induction. The idea of deduction comes from Aristotle, his instrumental "syllogism". He has two basic views. The first is to have a starting point, that is, to have a recognized premise when arguing about things, and then it evolved into an axiomatic system. Second, its reasoning logic has a major premise and a minor premise. A typical example is: "All prisoners have to die, Socrates is a man, and Gonggradi has to die." For fifty years, we have seldom studied this idea. Know A, and prove that B. A is also a definite proposition, and B is also a definite proposition.

There is another important thought: inductive thought. The idea of induction began after the Renaissance, especially after the new industry. The summary of this idea was given by Bacon in The Theory of New Tools. Later, someone studied causality, and Maier gave it a good organization. Translated by Yan Fu of China. The idea of induction is this: many objects of this kind have this conclusion, so can we speculate? There is an analogy in induction: everything with properties of A, B and C has properties of D. I found a new thing with properties of A, B and C, so can it imagine that it has properties of D? Einstein said: our science can get such great development now, thanks to two things. One is the deductive method created by the ancient Greeks, and the other is the discussion of causality, which is essentially the idea of returning to the outline. Inductive thinking needs deduction to prove its correctness. In any case, inductive thinking can be used to discover new results, which has hardly been taught in our fifty years of mathematics education.

For example, the problem of chickens and rabbits in the same cage. We think this problem is too difficult. They were missing two legs, so we changed chairs with four legs and stools with three legs. Try according to the law, and finally try to get the desired result. Mathematics used to be reasonable from the beginning. How about three-legged and four-legged ones? The equation will be given in a minute. In fact, we should pay attention to such things. Teachers are too smart and students should be stupid. Teachers should not be too clever in their lectures. The teacher knows the result. To arouse students' thinking, you should give it to them at once. What else do students discuss? Thinking method is very important.

In addition to the core idea I said, there is also the idea of combining numbers with shapes and replacing ideas by equal amounts. Very important. Therefore, it is impossible for us not to pay attention to our past thoughts in mathematics education. Teachers must form ideas in their minds, and ideas that should be infiltrated must be infiltrated in the teaching process. How else can we cultivate creativity? There is nothing wrong with creative thinking.

Recently, a problem was discovered. Our school investigated the quality of migrant workers and farmers and designed some questionnaires for migrant workers. They will be willing to answer a question for ten dollars. We investigated 10 thousand copies. The difference is not mathematics or physics, but Chinese. Chinese is the worst. I just can't read an article. I don't know what this means. He can't say and write what he thinks. I don't know if he has thought it over. There is something wrong with our Chinese teaching. Anyway, you can let our children understand the article, think things over clearly and express them. It was the same when we took the postgraduate exam. In fact, we got all the math scores, but we couldn't write well.

I don't believe that there was no way to speak Chinese in the past. Chinese should have a way of thinking, and help children to clear their minds, clear their minds and explain clearly before and after. So I think the Chinese syllabus should also be improved. Really, no matter what, we should teach our children to make things clear. This is the result of my investigation, which surprised me. I also blame them for being lazy and not studying hard, but the sum of the inner angles of their triangles is equal to 180 degrees. We really need to work hard to make our children have basic civic qualities. I mean, other subjects have similar problems.

There is also basic operating experience. As I said just now, the process is very important. Help students to think about the accumulation of experience, ask questions, accumulate experience and accumulate innovative activities. Only in this way can our country become the future of innovative tourists and an innovative country.

The past two abilities: the ability to analyze and solve problems, have been changed to: the ability to find and solve problems, the ability to find and ask problems, and then the ability to analyze problems. It is difficult to put it forward mathematically, and it is even more difficult to express it with mathematical symbols after it is put forward.

5. The content has been deleted.

Geometry just mentioned to be "precise and deep" and cut off knowledge points. We really cut them off. Including the application of unary inequality, we think it is too difficult.

6. Cases

A large number of cases have been added, and the cases have been explained in greater space, so that teachers can understand what the thinking of curriculum standards is and what the purpose of putting forward knowledge points is. Some of these cases were compiled by me. When I was sorting them out, my mind was talking to teachers in rural primary and secondary schools. I'm telling them what it is and how to teach them more clearly. The case is very important, and the effort is almost more time-consuming than the text. It is very important to think about examples and explain the problem.

Spiral rise is not necessarily the knowledge point itself, but also the thing itself from different angles. What we do is the curriculum standard from primary school to grade three, and such problems can appear constantly from primary school to grade three. However, with the increase of their knowledge and horizons, the depth of analyzing problems is also increasing. We gave such an example to illustrate our idea.

7. Implementation of recommendations

The implementation has been completely rewritten. In the past, suggestions on writing, teaching and evaluation were all written according to learning paragraphs. When we found them inappropriate, we removed them. We write according to the basic ideas and stick to them. For example, first, the problem of getting a good math education is basically written according to the concept. The second thing is to attach importance to students' dominant position in learning. Third, pay attention to students' mastery of basic knowledge. Then the fourth question, how to help students accumulate experience in mathematical activities and understand mathematical ideas. Whenever you want to write something new, you have to make a long speech and give many examples.

The traditional things that everyone knows are few, but they should be written. Then, pay attention to how to pay attention to the change, development and cultivation of students' emotional attitude in teaching. Sixth, several problems should be paid attention to in teaching, such as preparation and generation, how to prepare lessons in advance, and how to deal with the situations encountered in class. Also, how to face the relationship between all students and individual students. How to deal with the relationship between in-class and out-of-class, and how to use teaching techniques and relationships. We write completely according to the core idea, not according to the learning paragraphs as in the past. Write according to the paragraph, or you will repeat it.

Mainly these seven aspects.