The rapid development of science and technology, especially the rapid development of computer technology, has greatly expanded the application field of mathematics. Mathematics is applied to all walks of life. Just like literacy and reading today, mathematics has become a necessary cultural accomplishment for citizens, and popularizing mathematics education has become a requirement of the times. All these constitute the basis of the current international mathematics education reform.

1989, the National Research Council (NRC) published "Unity and * * *-Report on the Failure of Mathematics Education to the Whole Country", proposing that the mathematics curriculum must be reformed greatly. The National Association of Mathematics Teachers (NCTM), as an advocate of the reform of mathematics education in the United States, has successively formulated three standards: teaching, teachers and evaluation, which has made great contributions to the improvement of mathematics curriculum.

NCTM standard holds that with the development of the times, the purpose of mathematics education has changed greatly. In the information society, mathematics education has four social purposes: one is to train students to become laborers with mathematical literacy; Second, make students have the ability of lifelong learning; Third, let all students have the opportunity to learn mathematics; Fourth, make students have the ability to process information. Its core is to cultivate all students' mathematical literacy.

According to the NCTM standard, mathematics education should cultivate citizens with mathematics literacy, and put forward five specific goals: (1) to understand the value of mathematics, that is, to understand its position in culture and its role in social life; (2) Self-confidence in one's mathematical ability; (3) Ability to solve practical mathematical problems; (4) Learn math communication, math reading, writing and discussion; (5) The thinking method of learning mathematics.

Correspondingly, other countries have also carried out curriculum reform first and then. From the perspective of curriculum objectives, although they are different in expression, they also show some similarities: First, mathematics curriculum objectives pay more attention to the development of people and the improvement of students' mathematical literacy; Second, the goal of mathematics curriculum is to face all students, from elite to public; Third, the goal of mathematics curriculum pays attention to the individual differences of students, rather than the unified model; Fourthly, the goal of mathematics curriculum pays more attention to the connection with real life and society.

The Development Trend of Mathematics Education in China

Under the background of worldwide basic education reform, China's basic education curriculum reform also started in 200 1 year, and showed a good development trend. In recent years, all primary and secondary schools in China are discussing quality education. The following trends have emerged in the field of mathematics teaching reform in primary and secondary schools in China:

1. Attach importance to cultivating students' awareness of mathematics application.

One of the greatest advances in mathematics in the second half of the 20th century was its wide application. Cultivating students' consciousness and ability of applying mathematics can help students understand the contents, ideas and methods of mathematics more intuitively and deeply. It is helpful for students to correctly understand the development path of mathematics and even science, understand the thinking mode used in mathematical analysis and problem solving, and let students really understand what mathematics is.

2. Pay attention to cultivating students' mathematical thinking.

The contribution of mathematics to the country lies not only in enriching the country, but also in strengthening the people. Mathematics provides us with some universal and powerful ways of thinking, including intuitive judgment, induction and analogy, abstraction, logical analysis, modeling, systematization (axiomatization) of complex phenomena, reasoning with data, optimization and so on. Thinking in these ways can make people better understand the world around them; Make people have scientific spirit, rational thinking and innovative ability; It is full of confidence and tenacity.

3. The choice of mathematics curriculum content emphasizes the needs of the times.

More and more attention has been paid to data processing.

Pay attention to the understanding, application and expression of logarithms and symbols, and weaken the tedious calculation.

Give full play to the intuitive function of graphics.

4. "Back to nature", moderately "informal"

Practice has always been a rich source of mathematics development, and mathematics will become "passive water" and "wood without roots" if it is divorced from reality. Modern mathematics education advocates connecting with students' daily life, increasing the interest of mathematics problems and presenting mathematics as an "educational form" that students can easily accept.

In a word, we should establish a kind of mathematics education that conforms to the essence and trend of modern mathematics development, the law of students' physical and mental development and the future needs. We should not only attach importance to the background and application of mathematics, but also attach importance to the abstract process and proof process of mathematics.

The deficiency of extracurricular mathematics education in China

The goal of mathematics education is to let students master knowledge and improve their ability. However, in order to achieve the educational goal with high quality, it is not enough to complete the teaching progress only by relying on the usual classroom teaching. In order to make up for the limitations of traditional classroom teaching, a variety of extracurricular mathematics training has been actively carried out in some conditional areas. With the continuous reform of the education system, especially the college entrance examination system, and the extensive development of mathematics extracurricular activities, mathematics extracurricular activities will play an increasingly important role in cultivating talents.

According to a survey, more than half of the primary school students in Beijing took part in the Olympic math study on weekends. In recent years, the training enthusiasm of "Olympic Mathematics" and "Chinese Mathematics" in the whole country is also very high, which shows that parents and students have a strong sense of identity with extracurricular mathematics training and can also see huge market potential. However, at present, there are still the following problems in extracurricular mathematics education in China:

The single learning goal is difficult to meet the development needs of students.

Mathematics learning is divorced from social reality.

Excessive pursuit of system formalization makes it difficult to learn content

Learning style is mainly passive acceptance.

The Necessity of Mathematical Thinking Training

In mathematics teaching, we should not only enrich students' mathematical knowledge and improve their mathematical problem-solving ability, but also pay attention to the improvement of their mathematical ability. Therefore, in mathematics teaching and training, we should strengthen the training of students' mathematical thinking and promote the all-round development of students' quality.

Mathematics itself is not only the result of mathematical thinking, but also a tool of scientific thinking. European geometry and other traditional mathematics courses have a great influence on the formation of early thinking modes of many great scientists such as Einstein and Yang Zhenning. Not only some natural or experimental sciences such as physics, chemistry and biology have long regarded mathematical concepts, formulas, methods, equations and models as tools of thinking activities, but also contemporary social sciences such as political economy and management science have increasingly borrowed mathematical methods such as mathematical models, mathematical statistics and functional analysis as tools of thinking, and achieved great scientific achievements and social benefits.

Japanese mathematician Mi Shan Kunsan believes that for students, mathematics as knowledge is usually forgotten within one or two years after leaving school. However, no matter what kind of work they are engaged in, the spirit, thinking ability, research methods, reasoning methods and key points of mathematics deeply engraved in their minds (if they cultivate this quality) will play a role anytime and anywhere and benefit them for life.