What is the main difference between the experimental draft and the revised draft of the full-time compulsory education mathematics curriculum standard?

1. Interpretation of mathematics.

Experimental draft: Mathematics is a process in which people qualitatively grasp and quantitatively describe the objective world, gradually abstract and generalize, form methods and theories, and widely apply them.

Revised draft: Mathematics is a science that studies quantitative relations and spatial forms.

Elaboration: At the beginning of the standard experimental draft, a definition was given: "Mathematics is a process in which people qualitatively grasp and quantitatively describe the objective world, gradually abstract and generalize, form methods and theories, and widely apply them".

It is far-fetched to describe mathematics as a process. Mathematics is an understanding, a science and an ideological system. In the above assertion, the word "quantitative characterization" has nothing to do with mathematics except mathematics. It makes sense to replace the first two words "mathematics" with "physics" and "chemistry". Therefore, this description of mathematics is inaccurate. For example, if we want to define a rectangle, I say that the rectangle is a quadrilateral, yes, but the trapezoid is also a quadrilateral. "Quantitative relationship and spatial form" is the object of mathematical research, and it is still the key word to define mathematics, which cannot be bypassed casually.

2. About the value of mathematics education.

Experimental draft: Since the middle of the 20th century, mathematics itself has undergone tremendous changes, especially the combination with computers, which has expanded the research field, research methods and application scope of mathematics. Mathematics can help people better explore the laws of the objective world, make appropriate choices and judgments on a large number of complex information in modern society, and also provide an effective and simple means for people to exchange information. Mathematics, as a universally applicable technology, helps people to collect, sort out and describe information, establish mathematical models, and then solve problems and directly create value for society.

Revised draft: Mathematics education, as an important part of promoting students' all-round development education, on the one hand, should enable students to master the mathematics knowledge and skills needed for modern life and study, on the other hand, it should play an irreplaceable role in cultivating people's logical reasoning and innovative thinking.

Elaboration: The discussion in the experimental draft describes mathematics in the information age. In fact, the value of mathematics includes the value of mathematical civilization, the promotion of mathematics to natural science and social science, the scientific role of mathematical calculation, the contribution of mathematics to a country's prosperity and so on. The revised draft not only outlines the value of mathematics, but also points out the value of mathematics education: on the one hand, students should master the mathematical knowledge and skills needed in modern life and study, on the other hand, mathematics should play an irreplaceable role in cultivating people's logical reasoning and innovative thinking. Mathematics is the gymnastics of thinking, and we can't deviate from this fundamental value orientation.

But be careful not to regard mathematical thinking as omnipotent and perfect. Professor Zheng Yuxin from the Philosophy Department of Nanjing University pointed out that the focus of our teaching is not only to learn mathematical thinking, but more importantly, to learn thinking through mathematics. Mathematical thinking is only one aspect of thinking, and linear thinking in mathematics often hinders people's intuition and imagination. Transformation (apply for fireman). This way of thinking can help us solve many problems. But sometimes it also prevents us from creating new ways and methods. Edison or who? Big hole and small hole.

3. What should be emphasized about "Mathematics Curriculum".

Experimental draft: Mathematics curriculum in compulsory education emphasizes that students should go through the process of abstracting practical problems into mathematical models and explaining and applying them.

Revised draft: While presenting mathematical results as knowledge and skills, curriculum design should attach importance to students' existing experience and let students experience the process of abstracting mathematical problems from the actual background, constructing mathematical models, seeking results and solving problems.

Elaboration: From emphasis to attention, the requirements are obviously different. We know that the source of mathematics, first, comes from the development needs of the real society outside mathematics; The second is the contradiction from the inside of mathematics, that is, the need of the development of mathematics itself. As we all know, people can't experience everything directly. It is a universal cognitive law to acquire a lot of indirect knowledge through receptive learning. Therefore, mathematical learning, including mathematical modeling, can be carried out by creating scenarios, simulating reality, and even using abstract models. In a word, it is inappropriate to emphasize "students' existing life experience" unilaterally, and we should keep a distance from Dewey's pragmatic education thought. This change suggests that we should be moderate in the life of mathematical problems.

4. About "for all students".

Experimental draft: everyone learns valuable mathematics; Everyone can get the necessary mathematics; Different people get different development in mathematics.

Revised draft: Everyone can get a good math education, and different people get different development in math.

Elaboration: The first two sentences, first of all, the value of mathematics content can be large or small, but they all have their own values. Is only the mathematics listed in the standard valuable, and all other mathematics are worthless? Can you name some worthless math? The second sentence says that everyone can get the necessary mathematics, but the "necessity" varies from person to person, from time to time and from place to place. How can it be said that everyone can get it? The characteristic of compulsory education mathematics curriculum is "foundation", that is, to let future citizens acquire the basic mathematics literacy they need.

5. About learning.

Experimental draft: Effective mathematics learning activities cannot rely solely on imitation and memory. Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics.

Revised draft: In addition to learning, hands-on practice, independent exploration and cooperative communication are also important ways to learn mathematics.

Elaboration: The elaboration of the experimental draft once made us afraid to explain in math class. After the practice and reflection of curriculum reform, Mathematics Curriculum Standard (Revised Edition) attaches equal importance to traditional learning methods and modern learning methods, and clearly puts forward that "besides accepting learning, hands-on practice, independent exploration and cooperative communication are also important ways to learn mathematics." From the perspective of learning psychology, it can be divided into meaningful learning and mechanical learning according to the depth of learning, and it can be divided into discovery learning and acceptance learning according to the way of learning. These two classifications are independent of each other and become orthogonal (see the figure below).

Meaningful learning, meaningful acceptance learning, meaningful discovery learning.

Mechanical learning, mechanical acceptance, mechanical discovery and learning.

Accept learning and find learning.

Psychologist Ausubel believes that receptive learning is not equal to passive learning. As long as it is handled properly, receptive learning can also become meaningful learning. In mathematics teaching, meaningful receptive learning is a common and effective way for students to learn mathematics. Traditional receptive learning is not equal to mechanical learning. On the contrary, hands-on practice, independent exploration and cooperative communication under the guidance of teachers may also be mechanical. Therefore, it is necessary to break the concept of "what the teacher says is poor, and what the students find is good".

Some people say that memory is a sign of intelligence. A person's high memory is not equal to good intelligence, but a well-managed person must have a high memory. What we advocate is that memory imitation should lead to understanding. On the basis of memory imitation, students are encouraged to actively carry out mathematical activities such as observation, experiment, guess, verification, reasoning and communication, and then discover.

6. About the role of teachers.

Experimental draft: Students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning.

Revised draft: Effective mathematics teaching activities are the unity of students' learning and teachers' teaching. Students are the main body of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning. Teachers should play a leading role and handle the relationship between teaching and students' autonomous learning.

Elaboration: Education is to transfer the essence of knowledge accumulated by human beings for thousands of years to future generations in a very short time, and efficiency is very important. Let students grope in the dark and experience the process of discovery and creation, only a small amount. The progress of students must follow the experience of predecessors and climb on the shoulders of "teachers" Most of them are meaningful receptive learning, and teachers will inevitably play a leading role. Teach boldly. But at the same time, the teaching here is by no means encouraging full-time irrigation.

7. About process and result, knowledge and emotion.

Experimental draft: the evaluation of mathematics learning should pay attention to the results of students' learning, and pay more attention to their learning process; We should pay attention to students' mathematics learning level, and pay more attention to students' emotions and attitudes in mathematics activities, so as to help students know themselves and build up confidence.

Revised draft: evaluation should pay attention to students' learning results and learning process; We should pay attention to students' mathematics learning level, as well as their emotions and attitudes in mathematics activities, so as to help students know themselves and build up confidence.

Elaboration: By analyzing related words in Chinese, we can realize that, more importantly, it is a progressive relationship, the latter is more important, and if it is a parallel relationship, it is equally important. The word difference tells us not to ignore the process and result, knowledge and emotion.

8. About double-base teaching.

Experimental draft: not mentioned.

Revised draft: In the implementation of the proposal, mathematics teaching should enable students to acquire basic knowledge, skills, thoughts and activities of mathematics.

Expounding: The double-base teaching of mathematics is a fine tradition of Chinese mathematics education, and the standard should inherit the fine tradition of traditional mathematics education in China. In addition to double-base teaching, heuristic teaching, intensive teaching and more practice, refining mathematical thinking methods and so on. The speed of operation keeps the efficiency of thinking, and repeated drills depend on the development of "variants", which is also worthy of attention.

This revision changed from "two basics" to "four basics", further put forward the basic experience of mathematical activities and basic mathematical ideas, and achieved both tradition and modernity. Clarify the implied requirements.

(2) Revision of design ideas.

1. Overall changes in the content field.

In each section, the standard arranges four courses: number and algebra, graphics and geometry, statistics and probability, synthesis and practice. "Graphics and geometry" is space and graphics, and "synthesis and practice" is practice and comprehensive application. Restored the traditional names of geometry and algebra.

2. Numbers and Algebra

Clearly put forward the development of computing power. The new definition of computing power in the revised draft is: it mainly refers to the ability to correctly perform operations according to laws and operational laws. Cultivating students' computing ability is also helpful for students to understand the operation principle and seek reasonable and concise operation methods to solve problems.

3. Graphics and geometry

(1) clearly put forward to cultivate students' geometric intuition ability. The new definition of geometric intuition in the revised draft is that geometric intuition mainly refers to describing and analyzing mathematical 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 not only plays an irreplaceable role in the learning of Graphics and Geometry, but also runs through the whole process of mathematics learning. There is infiltration in primary schools, such as the calculation of++in the second volume of the sixth grade "Combination of Numbers and Shapes". If you look at the formula, you can't see the result and development trend, but it is easy to see the last score less than 1 when you convert it into a graph.

(2) Explain the meanings of perceptual reasoning and deductive reasoning. For example, this year's annual income is 65438+ million, and next year it may still be 65438+ million or more. This cannot be said to be deductive reasoning. Relying on experience and intuition should be reasonable reasoning.

4. Statistics and probability.

Add the concept of data analysis and understand random phenomena. Among them, the concept of data analysis is the original statistical concept, but it is clearer.