First, the mathematics curriculum in compulsory education should be geared to all students.
Mathematics is closely related to people's lives. People's daily life is inseparable from mathematics, and shopping, estimating calculation time and determining location are all related to mathematics. It can be said that mathematics is ubiquitous in people's lives and it is an indispensable tool in daily life. No matter what occupation people are engaged in, they will use mathematical knowledge and skills and mathematical thinking methods to varying degrees. Especially with the popularization and development of computers, this demand is increasing day by day. Moreover, mathematics, like language, is a tool with international universality. As citizens, it is necessary to master certain mathematical knowledge and skills, and mathematics has become an important part of civic literacy. Especially with the rapid development of science and technology, more and more fields need mathematical knowledge and skills. Because of this, in order to popularize the needs of educational development and improve the quality of citizens, all countries in the world have put forward that "mathematics is for the public, not for a few people", and "popularizing mathematics" has become the common idea and pursuit of global mathematics education. In our country, if we want to turn "popularizing mathematics" into reality, we must start with the mathematics curriculum in the compulsory education stage. The fundamental feature of compulsory education lies in its universality and foundation, and in enabling students to have basic civic literacy. The basic starting point of mathematics curriculum in compulsory education stage is to promote students' all-round, sustained and harmonious development. Therefore, the mathematics curriculum in the compulsory education stage should abandon the previous "elite education" mode, should be geared to all students, provide the basis for lifelong learning for each student, and provide equal learning opportunities for everyone, so as to truly realize the goal of "everyone learns valuable mathematics, everyone can get the necessary mathematics, and different people can get different development in mathematics".
Second, design and realize the most valuable mathematics.
What kind of mathematics should we choose for students in the face of the vast amount of mathematics knowledge? This has always been a difficult problem in the selection of mathematics curriculum content. In fact, what do students have to master? What knowledge is the most valuable? This is a process of value judgment. According to the characteristics of students' mathematics learning and the needs of mathematics discipline and social development, design and implement the "most valuable" mathematics-that is, basic, developmental and realistic knowledge.
Fundamentals-Mathematics, as a discipline, has its unique contents and objectives, such as calculation, graphic understanding and reasoning, data collection, processing and analysis, which are irreplaceable by other disciplines. These contents are of course an important part of mathematics education. However, mathematics education is also an important part of basic education, and it is necessary to complete the task of improving students' general ability and comprehensive quality.
Development-Mathematics education should not only pay attention to students' acquisition of mathematics knowledge, but also pay attention to the development of students' emotion, cognition, thinking and general ability. That is, in addition to basic knowledge and skills, it also includes mathematics as problem solving, mathematics as communication, mathematics as reasoning and the relationship between mathematics, etc. These are not only useful for students to learn mathematics, but also valuable for students to step into society and do anything in the future.
Reality-learning mathematics means doing mathematics: skillfully using mathematical language to solve problems, explore arguments and seek proofs. The most important activity should be to identify or put forward a mathematical concept from a given specific situation, summarize from observed examples, and then form a guess on the basis of intuition through induction and analogy. This is the way of thinking in mathematics. Therefore, the content of mathematics teaching should be mathematics that is closely related to reality and can be applied in practice, that is, "realistic mathematics". If we overemphasize the abstract form of mathematics, ignore the vivid and concrete model, overemphasize the internal logical relationship of mathematics and separate its close connection with external reality, then this kind of mathematics is pathological mathematics, which will only make students lose their interest in learning mathematics and their desire to explore.
Third, pay attention to the cultivation of students' emotional attitudes and values.
Mathematics curriculum should attach importance to cultivating students' emotional attitudes and values and improve students' confidence in learning mathematics. The process of learning mathematics should be positive, enjoyable and imaginative. It should be the goal of mathematics curriculum to make students form a positive emotional experience in teaching and make the process of learning mathematics no longer a daunting process for students. The overall goal of the basic education stage is to cultivate people with all-round development, and the cultivation of students' emotional attitudes and values is the need to realize the training goal of compulsory education. In the past, mathematics courses paid too much attention to the integrity of mathematics subject system and students' understanding and mastery of basic knowledge and skills, and largely ignored the cultivation of students' emotional attitude. At best, they only completed part of the tasks of mathematics education. The teaching of any subject is first and foremost the education of people. Mathematics education that ignores the cultivation of students' emotional attitude and even damages students' self-esteem and self-confidence is definitely not a successful mathematics education. Conversely, paying attention to the cultivation of students' emotional attitude will greatly promote students' learning of mathematics content itself and promote students' active learning and exploration. The cultivation of emotional attitude and values and the acquisition of mathematical knowledge should promote each other.
Fourth, provide a realistic and attractive learning background.
Students' learning mathematics is the systematization of students' common sense of life, and it is inseparable from students' real life experience. For students, mathematics knowledge is not "new knowledge", but "old knowledge" to some extent. In their lives, they have had a lot of experience in mathematics knowledge. Mathematics learning in the classroom is the summary and sublimation of mathematical phenomena and experiences in their lives. Every student starts from his real mathematical world, interacts with the textbook content and constructs his own mathematical knowledge. Therefore, in teaching, teachers should create realistic and attractive learning background according to students' specific situation, teaching content and teaching environment, stimulate students' interest and motivation in learning mathematics, and let students "do mathematics" by themselves with the help of teachers in natural situations, and collect information by observing, imitating, experimenting and guessing, so as to gain experience and learn to use mathematics to solve problems in life.
Five, mathematics teaching should pay attention to independent exploration and cooperation.
Mathematics learning is the process of students' own activities, and students use their own activities to establish their understanding of human existing mathematics knowledge. Mathematics teaching is the teaching of mathematics activities, and mathematics learning is not simply accepting knowledge, but a student-centered mathematics activity. Therefore, in the mathematics classroom, to change the traditional mode of teachers teaching and students learning, we should consciously embody the contents and methods of exploration in every link of the design, arrangement and organization of the teaching process, so that students can have space and opportunities for independent exploration, cooperative communication, positive thinking and operation of experiments, and learn and explore in activities with realistic background, thus cultivating students' spirit of exploration and innovation, and using mathematics to find problems, solve problems, communicate and deal with them. Therefore, realistic, interesting and exploratory mathematics learning activities should become an organic part of mathematics learning content.
6. Diversification of evaluation objectives and methods in mathematics learning.
The traditional view of educational evaluation is static and utilitarian, which limits students' all-round development to mastering knowledge and skills, simplifies the complete educational evaluation system into a single "summative evaluation" and simplifies rich evaluation methods into a single paper-and-pencil test. This kind of evaluation is "yesterday"-oriented, looking for differences and rankings only from how much knowledge and skills students have mastered, and emphasizing the appraisal and selection functions of evaluation. As a guide, this evaluation has seriously affected the teaching of teachers and the development of students.
In the future mathematics curriculum reform, we should attach importance to the developmental evaluation view. The purpose of evaluation is to fully understand the process of students' mathematics learning, stimulate students' learning and improve teachers' teaching. An evaluation system with multiple evaluation objectives and methods should be established. In the evaluation goal, we not only pay attention to students' mastery of knowledge and skills, but also pay attention to students' ability to find and solve problems, as well as their emotional attitude and values towards mathematics. In terms of evaluation methods, students are evaluated by combining self-evaluation, students' mutual evaluation, teachers' evaluation, parents' evaluation and social related personnel's evaluation, and students are evaluated in various forms, such as written examination, oral examination, homework analysis, classroom observation, after-class interview, big homework, establishment of growth record bag, essay analysis and activity report.
Seven, pay full attention to the role of modern information technology in mathematics curriculum.
The symbol of the information society is the information revolution centered on computers, which affects society, economy, culture and other aspects. Computers have had a profound influence on mathematics. The development of modern information technology, including computer technology, will undoubtedly greatly affect the present situation of students' mathematics learning. Mathematics teaching conditions in schools will be further improved, and mathematics teaching will begin to enter the information age.
In recent years, all countries and regions in the world have applied information technology to mathematics education in primary and secondary schools, and attached great importance to computer-aided teaching and the research and implementation of mathematics experiments using computers. However, many math educators in our country are always worried that once calculators or computers are used in math teaching, students' computing ability will be weakened. In fact, this kind of worry is unnecessary. Calculators and computers are powerful tools for students to explore mathematical knowledge. The cockcroft report pointed out: "There is enough evidence to show that using calculators has no negative effect on basic computing ability, and it is wise for children to learn to use simple calculators from an early age." We should strive to improve the application level of computer technology in mathematics teaching, vigorously develop and provide more abundant learning resources for students, take modern information technology as a powerful tool for students to learn mathematics and solve problems, increase the technical content of mathematics classroom in China, and improve students' learning.