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The Mathematics Curriculum Standard for Full-time Compulsory Education (Revised Draft) (hereinafter referred to as the Standard) is formulated for the mathematics education in China's compulsory education stage. According to the requirements of Compulsory Education Law and Basic Education Curriculum Reform Outline (Trial), this standard aims at comprehensively promoting quality education and cultivating students' innovative spirit and practical ability, clarifying the nature and position of mathematics curriculum, expounding the basic ideas and design ideas of mathematics curriculum, putting forward the objectives and content standards of mathematics curriculum, and making suggestions on curriculum implementation (teaching, evaluation and textbook compilation).

The mathematics curriculum ideas and objectives put forward in "Standards" play a guiding role in mathematics curriculum and teaching in compulsory education, and the selection of teaching content and the organization of teaching activities should follow these basic ideas and objectives. The curriculum objectives and content standards stipulated in the Standards are the basic requirements that students should meet in each compulsory education stage. "Standards" is the basis of textbook compilation, teaching, evaluation and examination proposition. In the process of implementation, we should follow the requirements of the standards, fully consider the development and personality differences of students in the learning process, and teach students in accordance with their aptitude. In order to make teachers better understand and master the relevant objectives and contents, and facilitate the design and organization of teaching activities, the standard provides some targeted cases for teachers to refer to in the implementation process.

Design concept

Mathematics is a science that studies quantitative relations and spatial forms. Mathematics is closely related to human activities, especially with the rapid development of computer technology, mathematics is more widely used in all aspects of social production and daily life. Mathematics, as a scientific language and tool gradually formed by abstracting and generalizing objective phenomena, is not only the foundation of natural science and technical science, but also plays an increasingly important role in social science and humanities. Mathematics is an important part of human culture, and mathematics literacy is the basic literacy that every citizen in modern society must have. As an important part of promoting students' all-round development education, mathematics 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 give full play to the role of mathematics in cultivating people's scientific reasoning and innovative thinking.

Mathematics curriculum in compulsory education has the status of public foundation, so we should focus on improving students' comprehensive quality and promoting their all-round, sustained and harmonious development. Curriculum design should meet the needs of students' future life, work and study, enable students to master the necessary basic knowledge and skills of mathematics, develop students' abstract thinking and reasoning ability, cultivate students' awareness of application and innovation, and develop students' emotions, attitudes and values. It should conform to the characteristics of mathematical science itself and embody the spiritual essence of mathematical science; It should conform to students' cognitive laws and psychological characteristics, which is conducive to stimulating students' interest in learning; While presenting mathematical results as knowledge and skills, we should attach importance to students' existing experience and let students experience the process of abstracting mathematical problems from the actual background, establishing mathematical models, getting results and solving problems.

Therefore, the basic concept and design idea of the standard are formulated.

Basic idea

Mathematics curriculum should be devoted to the realization of the training goal in compulsory education stage, reflecting the foundation, popularization and development. The mathematics curriculum in the compulsory education stage should be geared to all students, meet the needs of students' personality development, so that everyone can get a good mathematics education and different people can get different development in mathematics.

The content of the course should not only reflect the needs of society and the characteristics of mathematics, but also conform to students' cognitive laws. It includes not only the conclusion of mathematics, but also the formation process of mathematical conclusion and mathematical thinking method. The content of the course should be close to students' life, which is conducive to students' experience, thinking and exploration. The organization of content should handle the relationship between process and result, between intuition and abstraction, and between life, situation and knowledge system. The presentation of course content should be hierarchical and diversified to meet students' different learning needs.

Mathematics activity is a process of participation and interaction between teachers and students. Effective mathematics teaching activities are the unity of teachers' teaching and students' learning, students are the main body of mathematics learning, and teachers are the organizers and guides of mathematics learning.

Mathematics teaching activities must stimulate students' interest, arouse their enthusiasm and stimulate their thinking; Attention should be paid to cultivating students' good study habits and mastering effective learning methods. Students' learning should be a lively, active and personalized process. In addition to learning, hands-on practice, independent exploration and cooperative communication are also important ways of mathematics learning. Students should have enough time and space to experience activities such as observation, experiment, guessing, verification, reasoning, calculation and proof. Teachers' teaching should be based on students' cognitive development level and the experience of beneficial friends, face all students, pay attention to heuristics and teach students in accordance with their aptitude, and provide students with sufficient opportunities for mathematics activities. We should properly handle the relationship between teachers' teaching and students' autonomous learning, take effective measures to inspire students to think, guide students to explore independently, and encourage students to cooperate and exchange, so that students can truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods, get necessary mathematical thinking training, and gain rich experience in mathematical activities.

The main purpose of learning evaluation is to fully understand the process and results of students' mathematics learning, stimulate students' learning and improve teachers' teaching. An evaluation system with multiple evaluation objectives and methods should be established. Evaluation should pay attention to students' learning results and learning process; We should pay attention to students' mathematics learning level and their emotions and attitudes in mathematics activities, so as to help students know themselves and try their best to be confident.

The development of information technology has a great influence on the value, goal, content and teaching methods of mathematics education. The design and implementation of mathematics curriculum should use modern information technology reasonably according to the actual situation, and pay attention to the organic combination of information technology and curriculum content. We should fully consider the influence and advantages of calculators and computers on the contents and methods of mathematics learning, vigorously develop and provide students with rich learning resources, take modern information technology as a powerful tool for students to learn mathematics and solve problems, and devote ourselves to changing students' learning methods so that students are willing and have more energy to devote themselves to realistic and exploratory mathematics activities.

Design Concept-About Learning Part

In order to reflect the integrity of compulsory education mathematics curriculum, the standard considers the curriculum content of nine years. At the same time, according to the physiological and psychological characteristics of children's development, the nine-year study time is divided into three sections:

The first phase (1-3), the second phase (4-6) and the third phase (7-9).

Design concept-about goals

"Standard" puts forward the general goal and goal of mathematics curriculum in compulsory education stage, and expounds it from four aspects: knowledge and skills, mathematical thinking, problem solving and emotional attitude.

The standard uses cognitive target verbs such as "know (know), understand, master and use" to express different levels of knowledge and skill goals. As a "basic idea", mathematics learning must pay attention to the process. The Standard uses cognitive process verbs such as "experience (feeling), experience (understanding) and exploration" to express different levels of learning activities. These verbs are used to describe the specific goals of the above four aspects more accurately. In the standard, the specific meanings of these verbs are as follows.

Understanding (cognition): understanding or explaining the relevant characteristics of the object from specific examples; According to the characteristics of the object, identify or explain the object from the specific situation.

Understanding: describe the characteristics and origin of an object, and explain the difference and connection between this object and related objects.

Mastery: On the basis of understanding, apply objects to new situations.

Use: Choose or create appropriate methods with the objects you have mastered.

Experience (feeling): Get some perceptual knowledge in specific mathematical activities.

Experience: Take part in specific mathematical activities, know or verify the characteristics of objects, and gain experience.

Inquiry: participate in specific mathematical activities independently or in cooperation with others, discover the characteristics of the object and its differences and connections with related objects, and gain rational understanding.

Design Ideas —— About One of the Learning Contents: Number and Algebra

In each teaching section, the standard arranges four contents: number and algebra, shape and geometry, statistics and probability, synthesis and practice.

Numbers and algebra

The main contents of Number and Algebra are: understanding, representation, size, operation and estimation of numbers; Letters represent numbers, algebraic expressions and their operations; Equations, equations, inequalities, functions, etc.

In the teaching of "Number and Algebra", students should be helped to establish the concepts of numbers and symbols, develop their computing ability and establish model ideas.

The sense of number mainly refers to the representation of logarithm and quantity, the comparison of quantity, the estimation of quantity and the intuitive feeling of operation results. Establishing "number sense" is helpful for students to understand the meaning of numbers in real life and to understand or express the quantitative relationship in specific situations.

Symbol consciousness mainly refers to the ability to understand and use symbols to express numbers, quantitative relations and changing laws; Knowing symbols can be used for general operations and reasoning. Establishing "symbol consciousness" helps students understand that the use of symbols is an important form of mathematical expression and mathematical thinking.

Operation is an important content of Number and Algebra. There are rules to follow in operation, and usually the operation meets certain operation rules. Learning these contents is helpful to understand the law of operation and cultivate the ability of operation.

Model is also an important content of Number and Algebra. Equations, equations, inequalities and functions are all basic mathematical models. Abstracting mathematical problems from real life or specific situations is the starting point of establishing models; It is the process of establishing a model and expressing the quantitative relationship and changing law with symbols; Finding the results of the model and discussing the significance of the results is the process of solving the model. These contents are helpful to cultivate students' interest in learning and application awareness, understand the process of mathematical modeling and establish model ideas.

Design Ideas —— About the Second Learning Content: Graphics and Geometry

Graphics and geometry

The main contents of Graphics and Geometry are: the basic confinement of space and plane, the nature and classification of graphics; Proof of the basic properties of plane graphics; Translation, rotation, axial symmetry, similarity and projection of graphics; Coordinate is used to describe the position and movement of a graph.

In the study of Graphics and Geometry, students should be helped to establish the concept of space. The concept of space refers to abstracting geometric figures according to the characteristics of objects and imagining the actual objects described according to the geometric figures; Can imagine the orientation of space objects and the positional relationship between them; Draw pictures according to language description or imagination.

Intuition and reasoning are two important aspects in the study of Graphics and Geometry. Geometric intuition refers to using graphics to describe geometric or other mathematical problems, explore ways to solve problems, and predict results. In many cases, complex mathematical problems can be made concise and vivid by geometric intuition. Geometric intuition not only plays an irreplaceable role in the study of Graphics and Geometry, but also runs through the whole mathematics study.

Reasoning is a basic way of thinking in mathematics, and it is also a way of thinking that people often use in their study and life. Therefore, reasoning, like intuition, runs through the whole mathematics learning. Thrust generally includes rational reasoning and deductive reasoning. Reasonable reasoning is a process from special to general, which is based on existing facts, experience and intuition, and deduces some results through induction and analogy. Deductive reasoning is a process from the general to the special from the existing facts (including definitions, axioms, theorems, etc.). ) and verify the conclusion according to the specified rules (including logic and operation). In the process of solving problems, sympathetic thrust helps to explore the thinking of solving problems and find conclusions; Deductive reasoning is used to verify the correctness of the conclusion.

Design Ideas —— About Learning Content 3: Statistics and Probability

Statistics and probability

The main contents of Statistics and Probability include: collecting, sorting and describing data, including simple sampling, recording survey data and drawing statistical charts. Processing data, including calculating average, median, mode, range, variance, etc. Extract information from the data and make simple judgments. Simple random events and their occurrence probability.

In Statistics and Probability, it is important to help students gradually establish the concept of data analysis. Data analysis includes: to understand many problems in real life, we must first do investigation and study, collect data, make judgments through analysis, and realize that the data contains information; The empirical data is random and regular. On the one hand, the data collected for the same thing may be different every time. On the other hand, as long as there is enough data, it is possible to find a rule from it. Understand that there are many ways to analyze the same data, and you need to choose the appropriate method according to the background of the problem. In probability learning, the random phenomena involved are based on simple events: all possible results are limited, and the possibility of each result is the same. The content of "Statistics and Probability" is closely related to real life, and teaching must be organized in combination with specific cases.

Design Concept —— About Learning Content IV: Synthesis and Practice

Synthesis and practice

"Synthesis and Practice" is a kind of learning activity with a class of problems as the carrier, in which students actively participate, and it is an important way to help students accumulate experience in mathematics activities. In view of the problem scenario, with the help of the knowledge learned and life experience, students can think independently or cooperate with others to experience the whole process of finding, asking, analyzing and solving problems, so as to realize the relationship between mathematics content, mathematics and real life, and other disciplines, stimulate students' interest in learning mathematics and deepen their understanding of what they have learned. This type of course is conducive to cultivating students' abstract ability and logical thinking ability, innovative consciousness and application ability, and cooperative spirit. Reasonable design of teaching content and teaching methods is the key to realize teaching objectives. We should not only consider students' direct experience to inspire students to think, but also consider the mathematical nature of the problem and cultivate students' mathematical literacy. This kind of course is a challenge for teachers. Teachers should try their best to grasp the essence of the problem and guide students to think. At the same time, teachers should try their best to help students sort out their own ideas and guide students to show their achievements or report their work in different forms.

This type of course should implement the principle of "fewer but better" and be guaranteed at least once every semester. You can do it in class or combine it inside and outside class.

Design ideas-suggestions for implementation

In order to ensure the smooth implementation of the standard, the standard puts forward some suggestions on teaching activities, learning evaluation, textbook compilation and curriculum resources development and utilization. At the same time, in order to better explain the course content, the standard provides some cases in the relevant part. The above contents are for the reference of relevant personnel.

Revised Draft Curriculum Standards-Overall Objectives (1)

Through mathematics study in compulsory education, students can:

1. Get the basic knowledge, skills, thoughts and activities of mathematics necessary for adapting to social life and further development.

2. Understand the relationship between mathematics knowledge, mathematics and other disciplines, mathematics and life, and use mathematical thinking mode to think, thus enhancing the ability to find, ask, analyze and solve problems.

3, understand the value of mathematics, improve interest in learning mathematics, enhance confidence in learning mathematics well, develop good study habits, and have a preliminary sense of innovation and a scientific attitude of seeking truth from facts.

Revised Draft of Curriculum Standards-Overall Objectives (2)

The "overall goal" is defined as follows:

know

know

skill

Can * experience the abstract operation and modeling of numbers and algebra, and master the basic knowledge and skills of numbers and algebra.

* Master the basic knowledge and skills of graphics and geometry through the process of abstraction, classification, nature discussion, movement and position determination of graphics.

* Experience the process of collecting and processing data in practical problems, analyzing problems with data and obtaining information, and master the basic knowledge and skills of statistics and probability.

* Participate in comprehensive practical activities, solve simple practical problems by comprehensively applying mathematical knowledge, skills and methods, and accumulate experience in mathematical activities.

count

study

think

Understand the function of algebraic representation operation and geometric intuition, initially establish a sense of number, symbol and space, and develop image thinking and abstract thinking.

* Understand data and stochastic phenomena, understand the significance of statistical methods, and develop data analysis and stochastic concepts.

* In participating in observation, experiment, Cai Xiang, Zheng Ming, comprehensive practice and other mathematical activities, cultivate the ability of rational reasoning and deductive reasoning, and clearly express their ideas.

* Learn to think independently and understand the basic ideas and ways of thinking of mathematics.

ask

title

solve

Affirmation * Initially learn to find and ask questions from the perspective of mathematics, comprehensively apply mathematical knowledge and other knowledge to solve simple mathematical problems, and cultivate application awareness and practical ability.

* Get some basic methods to analyze and solve problems, experience the diversity of problem-solving methods, and cultivate innovative consciousness.

* Learn to cooperate and communicate with others.

* Initially form a sense of evaluation and reflection.

feel

feel

form

Degree * Take an active part in mathematics activities, and have curiosity and thirst for knowledge about mathematics.

* Experience the pleasure of success, exercise the will to overcome difficulties and build self-confidence in learning mathematics well.

* Understand the characteristics and value of mathematics.

* Develop the habit of questioning and form a realistic attitude.

Revised Draft of Curriculum Standards —— Overall Objectives (III)

The four aspects of the overall goal are not independent and separated from each other, but an organic whole that is closely linked and blended with each other. In the course organization and teaching activities, four objectives should be considered at the same time. The realization of these goals marks students' good mathematics education and is of great significance to their comprehensive, sustained and harmonious development. The development of mathematical thinking, problem solving and emotional attitude can not be separated from the learning of knowledge and skills, which must be conducive to the realization of the other three goals.

Revised Curriculum Standards-Stage 1 Objectives (1-3 grade)

Knowledge and skills

1, experience the process of abstracting numbers from daily life and understand common quantities; Understand the meaning of four operations and master the necessary operation skills. Understand the estimate.

2. Experience the process of abstracting simple geometry and plane graphics from actual objects, and learn some simple geometry and common plane graphics; Feel translation, rotation and axial symmetry, and know the relative position of objects. Master the skills of preliminary measurement, reading and drawing.

3. Understand simple data processing methods through the process of data collection and sorting.

Mathematical thinking

1, can understand the information about numbers around you, and can describe simple phenomena in real life with numbers (appropriate dimensions). Develop a sense of numbers.

2. Develop the concept of space in the process of discussing the properties of simple objects.

3. Under the guidance of teachers, simple survey data can be classified.

4. I can think and express my thoughts; In the process of discussing the problem, we can initially distinguish the similarities and differences of the conclusions.

problem solving

1, under the guidance of teachers, can find and put forward simple math problems from daily life.

2. Get some basic methods to analyze and solve problems, and know that the same problem can have different solutions.

3. Experience the process of cooperation, communication and problem solving with others.

4. Initially learn to sort out the process and results of solving problems.

Emotional attitude

1, curious about things (phenomena) related to mathematics around him, able to participate in mathematical activities.

2. With the help of others, experience the process of overcoming difficulties in mathematics activities.

3. Understanding mathematics can describe some phenomena in life and feel that mathematics is closely related to life.

4. In the process of solving problems, get into the habit of asking "why".

Revised Curriculum Standards-Stage Objectives of the Second Stage (Grade 4-6)

Knowledge and skills

1, experience the process of abstracting numbers from specific situations; Understand the meaning of fractions and percentages, understand negative numbers, and master the necessary operation skills; Understand the meaning of estimation; Master the expression method of simple quantitative relationship and the method of solving simple equations with equations.

2. Explore the relationship between the shape, size and position of some graphics, and understand the basic characteristics of some geometric bodies and plane graphics; Experience the simple movement of graphics, understand the method of determining the position of objects, and master the basic methods of measurement, map recognition and drawing.

3, through the process of data collection, sorting and analysis, master some simple data processing skills; Experience the equal possibility of an event and master the simple method of calculating the equal possibility.

Mathematical thinking

1, which can reasonably explain the digital information in life, and can describe simple problems in life with numbers (appropriate dimensions), letters and charts; Initially form a sense of numbers and develop a sense of symbols.

2. In the process of exploring the essence and movement phenomenon of simple graphics, the concept of space was initially formed.

3. According to the needs of solving problems, collect and represent data and summarize useful information.

4. Be able to think methodically and clearly express the process and result of thinking; In the process of communicating with others, I can have a simple debate.

problem solving

1, can find and put forward simple mathematical problems from social life.

2. Be able to explore effective methods to analyze and solve problems and understand the diversity of problem-solving methods.

3. Can solve simple calculation problems with the help of digital calculator.

4. Initially learn to cooperate with others to solve problems and try to explain your own thinking process.

5. Be able to preliminarily judge the rationality of the results and experience the activities of reviewing and analyzing the problem-solving process.

Emotional attitude

1. Willing to know the information related to mathematics in social life and actively participate in mathematics learning activities.

2. Under the encouragement and guidance of others, try to overcome the difficulties encountered in mathematics activities and believe that you can learn mathematics well.

3. Experience the value of mathematics in the process of solving problems with mathematics.

4. Initially develop good qualities such as being willing to think, seeking truth from facts and being brave in questioning. Agree 5| Comment