The current outline of Number and Algebra mainly focuses on the operation of numbers, algebras, equations and functions, which has been greatly reformed in the standard:

1. Pay attention to the meaning of numbers and symbols, as well as the feeling of logarithm, and realize the role of numbers in expression and communication. By exploring the meaning of rich problem scenarios, while maintaining the basic written calculation training, it is emphasized that reasonable and simple operation ways and methods can be sought according to the subject conditions, estimation can be strengthened, calculators can be introduced, and diversification of algorithms can be encouraged.

2. For the application problem: the material selection emphasizes reality, interest and exploration; Diversified theme presentation forms (tables, graphics, cartoons, dialogues, words, etc.). ); Emphasize the selection and judgment of information materials (redundant information, insufficient information ...); Diversified strategy solution; The answer to the question may not be unique; Analysis of types and solutions of artificial application problems in desalination.

3. Make students understand that mathematics can discover, describe and analyze various patterns in the objective world, and grasp the changes of things and the relationship between things; Initially develop students' symbol consciousness, learn to express some basic relations in real problems with symbols, and initially carry out symbol operation.

4. Understanding equations and functions is a powerful tool to describe the real world, effectively express, process, communicate and transmit information, and an important means to explore the good development law of things and predict their development. We should attach importance to the modeling process of simple practical problems, learn to choose effective symbolic operation programs and methods to solve problems, and attach importance to approximate solutions, especially image solutions.

first stage

1.Add "can perform simple elementary arithmetic (two steps).

2. Strengthen the foundation appropriately.

3. Strengthen the cultivation of comprehensive ability.

The second period

1. Add "Feel the meaning of large numbers in combination with the real situation and estimate; Cultivate students' sense of numbers; Strengthen the connection with reality. "

2. Added "Know common multiple and minimum common multiple, know common factor and maximum common factor."

3. Delete "two digits multiplied by one digit within 100" (? Teacher discussion)

4. Change "understanding the properties of equations and solving simple equations by using the properties of equations" to "being able to understand simple equations."

Graphics and geometry

(Formerly known as space and graphics: change "space and graphics" to "graphics and geometry"; Re-emphasize geometric intuition, reasoning ability, calculation ability and logical thinking ability, and use more standardized words, which reflects the seriousness of curriculum standards)

In this part of the current syllabus, primary schools mainly focus on the calculation of length, area and volume, while junior high schools mainly use logical proof and extended axioms to present the nature of plane graphics, which makes students unable to relate their geometry knowledge with real life, and does not reflect the development of modern geometry, which often leads many students to lose interest and confidence in geometry and even the whole mathematics study. On the basis of re-examining the teaching objectives of geometry, the Standard puts forward that the most important goal of geometry learning is to make students better understand their own world, form the concept of space, and make great reforms to the traditional geometry content:

1. Open the field of "space and graphics", broaden the vision of geometry learning to the space of students' life, emphasize the realistic background of space and graphics knowledge, and let students come into contact with the rich geometric world from the first learning period.

2. Through observing, describing, making, observing objects from different angles, knowing the direction, making models and other activities, develop students' spatial concept, graphic design and reasoning ability.

3. Understand the real space and deal with geometric problems through observation, operation, transformation, coordination and reasoning, and experience more applications in real life.

The Standard also points out that the requirements of logical proof are not limited to geometric content, but should be reflected in all fields of mathematics learning, including algebra, statistics and probability. For the teaching of geometric proof, its purpose should not be to pursue the skills, speed and difficulty of proof, but to make students develop the attitude of "showing evidence", the spirit of respecting objective facts and the habit of questioning, form the consciousness of proof, understand the necessity and significance of proof, understand the thought of proof and master the basic methods of proof. Therefore, on the basis of emphasizing the exploration of graphic properties in the standard, it is required to prove the basic properties of basic graphics (triangles and quadrangles), which reduces the requirements for formalization and proof skills in the process of argumentation and omits complex geometric proof questions, so that students can experience the significance and process of logical proof and master the basic proof methods. At the same time, introduce Euclid and geometric elements to students, so that students can realize their important roles in human history and ideological development. All in all, the standards have been greatly strengthened.

< standard > the first section "graphics and geometry" is still divided into four parts, which specifically show changes, (1) understanding of graphics, (2) measurement, (3) movement of graphics, (4) graphics and position,

In the process of exploring, discovering, verifying and proving the essence of graphics, the relationship between two kinds of reasoning (perceptual reasoning and deductive reasoning) is embodied.

Reflect the requirements of enhancing students' ability to "find, ask, analyze and solve problems".

The motion of graphics emphasizes the motion of graphics, which is an effective method to study the properties of graphics.

Exercise is also a basic mathematical idea.

first stage

(1) Put the graphics that can draw simple graphics on the grid paper, and translate horizontally and vertically in the second section.

(2) In the second stage, "Axisymmetric graphics that can draw simple graphics on square paper" was released.

The second period

(1) Delete "two points determine a straight line" and "two straight lines determine a point"

(2) Add "Through operation, we know that the ratio of the circumference to the diameter of a circle is constant." .

Statistics and probability

In the current syllabus, algebra in the upper and lower grades of primary schools only sets a chapter to introduce the preliminary content of statistics, and hardly involves probability content. At the same time, the system of "definition-formula-example-exercise" is still used to present the preliminary knowledge of string counting, which makes it difficult for students to understand the connection between this part of content and reality and the role of statistics and probability in decision-making. Therefore, the content of "statistics and probability" has been greatly increased in the standard. According to students' cognitive characteristics, corresponding contents are set in three learning periods, which embodies the basic idea of combining statistics and probability with practical problems: 1, which reflects the whole process of data statistics: collecting and sorting out data, representing data, analyzing data, making decisions and communicating; 2. Take the concept of population randomness and the preliminary idea of estimating the population with samples as a powerful means of decision-making; 3, based on data.

unified plan

Encourage students to show the results of sorting out data in their own way.

(1) (the first phase) does not require students to learn "regular" statistical charts (one bar represents one unit) and averages (the second phase).

There are three reasons for this change:

① Highlight students' data analysis experience and encourage students to analyze data in their own way.

The diversification of early experience can lay a solid foundation for future study: regular statistical charts and statistics.

(3) Make the requirements of the first and second statistical contents more clear.

⑵ Strengthen the cultivation of chart analysis ability.

The Cultivation of Improving the Ability of Reading Pictures

(3) Strengthen the experience of inspection and other activities. (mainly small surveys)

In terms of data collection methods, considering the age characteristics of students, students are required to understand simple methods such as measurement and investigation, and students are not required to collect data from newspapers, magazines and television.

(4) Compared with the standard, the second period only requires students to understand the meaning of the average, and does not require students to learn the median and the mode (these contents are placed in the third period). The average is easily influenced by the extreme values (maximum and minimum).

In addition, the requirement of "knowing the possible misleading of data" is deleted.

Probability (possibility, attaching importance to "random phenomena")

Requirements for this content in the first issue of the Standard: In the second issue, students are only required to experience random phenomena and describe the possibility of random phenomena qualitatively.

Synthesis and practice

"Comprehensive practice" is a kind of learning activity with problems as the carrier and students actively participating. It is an important way to help students accumulate experience in mathematics activities and cultivate their sense of application and innovation.

In view of the problem scenario, students integrate their knowledge and life experience, think independently or cooperate with others, experience the whole process of finding, asking, analyzing and solving problems, and feel the connection between various parts of mathematics \ between mathematics and real life \ between mathematics and other disciplines, so as to deepen their understanding of the content of mathematics taught.

The purpose of adding "connection and synthesis" in the standard is to make students consciously understand the connection between mathematics and its life experience, the real society and other disciplines, and the role of mathematics in the development and progress of human civilization in the learning process of various knowledge fields. Understand the internal relationship of mathematical knowledge. At the same time, students have adopted the new learning form of "comprehensive practical activities". Through independent exploration and cooperative communication, they have gained the ability to comprehensively apply mathematical knowledge and methods to solve practical problems and explore mathematical laws, and gradually developed their overall understanding of mathematics.

The new mathematics curriculum and new technology put forward new requirements for mathematics curriculum, pointing out that new technology has great influence on the purpose of mathematics curriculum, the content of mathematics learning and the way of teaching and learning. Therefore, the standard proposes to introduce calculators in the second learning stage, and encourages the use of calculators and computers as powerful tools for studying and solving problems. This can prevent students from doing a lot of complicated and repetitive operations, so as to devote more energy to exploratory and creative mathematics activities and solve problems.

At the same time, in the course implementation plan, it is emphasized that areas with conditions should use modern educational technology as much as possible in the teaching process, increase the technical content of mathematics courses, make full use of the advantages of modern educational technology in increasing teacher-student interaction, visualizing mathematics content, effectively handling complex mathematical operations, etc., improve students' mathematics learning methods, enhance students' understanding of mathematics, and finally improve the quality of mathematics teaching.

Understanding of synthesis and practice-practicality, comprehensiveness and exploration.

"Synthesis and Practice" is guaranteed at least once every semester, which can be carried out in class, or combined outside class or in class.

The core of "synthesis and practice" is to find and put forward problems, analyze and solve problems, and different students have different characteristics.

The first issue: the content arrangement emphasizes practicality and interest.

The second period:

Through application, exploration and reflection, we can deepen our understanding of what we have learned, stimulate students' interest in learning and cultivate the habit of thinking, and cultivate the cooperative spirit of understanding others, unity and mutual assistance through communication.

Revelation:

Enlightenment 1: Adhere to the three-dimensional overall goal of mathematics curriculum

Promoting students' all-round development is embodied in the new teaching curriculum standard, which has formed three basic goals: knowledge and skills, thinking and ability, emotion and attitude.

Enlightenment 2: Developing students' mathematical thinking is one of the key points in curriculum and teaching.

Under the guidance of teachers, learn to study and explore problems independently, and learn to judge and adjust themselves in the process of learning and solving problems.

Let students organize their knowledge systematically.

Initially learn to question the existing knowledge and experience and analyze the problems in many aspects, and be able to think divergently and put forward their own opinions (diversified algorithms and strategic thinking).

Master a variety of mathematical thinking methods of observation, operation, comparison, analysis, analogy and induction, as well as the methods of sorting out data and obtaining information by using charts.

He has the experience of grasping the essence of real life and abstractly summarizing mathematics.

Know the thinking strategy from special to general, from general to special and transformation.

Revelation 3: Put problem solving at the core of mathematics curriculum.

In the revised standard, it not only embodies the basic idea of solving problems, but also forms its own characteristics in the implementation process (the process of exploration and practice).

Revelation 4: We should unify the promotion of innovation with the implementation of basic knowledge.

Innovative activities in mathematics learning mainly focus on the process of finding, asking, analyzing and solving problems.

In the above activities, students' existing knowledge base plays an important role.