The 2011 edition of the Mathematics Curriculum Standards defines mathematics as a science

Mathematics is the science that studies quantitative relationships and spatial forms in the real world. To put it simply, it is the science of numbers and shapes. Due to the demands of life and labor, even the most primitive peoples knew simple counting, and developed from counting with fingers or objects to counting with numbers.

The knowledge and application of basic mathematics is always an indispensable part of individual and group life. The refinement of its basic concepts can be seen in ancient mathematical texts in ancient Egypt, Mesopotamia, and ancient India. From then on, there was a steady stream of progress until the Renaissance in the 16th century, when mathematical innovations in response to new scientific discoveries led to an acceleration of knowledge to the present day.

1] Mathematics is used in different fields around the world, including science, engineering, medicine, and economics. The application of mathematics to these areas is often referred to as applied mathematics and sometimes provokes new mathematical discoveries and leads to the development of entirely new disciplines. Mathematicians also study pure mathematics that has no practical application, even if its application is often discovered later.

Founded in the thirties of the twentieth century, the Bourbaki school in France believes that mathematics, at least pure mathematics, is the study of abstract structures. Structure is a deductive system based on initial concepts and axioms.

According to the Cloth School, there are three basic abstract structures: algebraic structures (groups, rings, fields......Sequence structure (partial order, full order......Topology (neighborhood, limits, connectivity, dimensionality......）

Mathematics is a transformation, an abstract model, a system of symbols, the real world is transformed into a mathematical model, described in mathematical language, and after the calculation, the result can be returned and interpreted into a concrete science in the real world.

The name of "Axioms of Mathematics" was changed to "Fundamental Facts of Mathematics", which is as follows:

1. Determine a straight line at two points

2. Between two points, the line segment is the shortest.

3. There is only one straight line perpendicular to this straight line.

4. Two straight lines are truncated by the third straight line, if the same angle is located.

equal, then the two lines are parallel.

5. There is only one state foot thick straight line parallel to the straight line.

6. Congruent triangles.

The corresponding sides and corresponding angles are equal respectively.

7. The edge edge axiom (SSS) has three sides corresponding to two equal triangle congruence

8. The two straight lines are parallel and the isotope angles are equal.

9. Three points that are not collinear determine a circle.

It is as follows:

At the primary school level, the core literacy is mainly manifested as: number sense, quantity sense, symbol awareness, arithmetic ability, geometric intuition, spatial concept, reasoning awareness, data awareness, model awareness, application awareness, and innovation awareness.

In junior high school, the core literacy is mainly manifested in: abstract ability, computing ability, geometric intuition, spatial concept, reasoning ability, data concept, model concept, application awareness, and innovation consciousness.

The specific performance requirements of core literacy in each school stage are differentiated, and the core literacy performance of high school, junior high school, and primary school is compared as follows: consciousness and concept are both the understanding of things, consciousness is based on intuitive feelings, and concepts are based on clear concepts, among which there are application consciousness and innovation consciousness in junior high school and primary school.

Observe the real world with a mathematical eye

Mathematics provides a way for people to understand and observe the real world. Through the perspective of mathematics, we can discover the quantitative relationship and spatial form from the objective phenomena in the real world, and put forward meaningful mathematical problems.

Be able to abstract the research objects and properties of mathematics, and form concepts, relationships and structures; Be able to understand the mathematical principles behind natural phenomena and appreciate the aesthetic value of mathematics; Form curiosity and imagination about mathematics, take the initiative to participate in mathematics activities, and develop a sense of innovation.

The Curriculum Standards put forward six basic concepts, which mainly reflect the overall goal of mathematics education to focus on student development, and the two basic strategies to achieve this goal.

Specifically, it is manifested in the following aspects:

1) Mathematics curriculum objectives with a focus on human development.

1.Everyone learns valuable mathematics.

2.Everyone has access to the necessary mathematics.

3.Different shouters develop mathematically differently.

2. Hail learned) to change the structure and presentation of mathematics curriculum content.

1 Mathematics education for all students should be what students need in the future, have a realistic background, be interesting and provocative.

3) Improve the way mathematics is learned and evaluated.

1. Advocate meaningful learning: independent exploration, hands-on practice, cooperation and communication, and innovation.

2. Implement a pluralistic and diversified evaluation method.