I the principle of combining abstraction with concreteness

High abstraction is one of the basic characteristics of mathematical theory. Mathematics takes the spatial form and quantitative relationship of the real world as the research object, so mathematics abandons all other characteristics of the objective object and only conducts systematic and theoretical research on its spatial form and quantitative relationship. So mathematics is more abstract than other disciplines. This abstraction is also manifested in a high degree of universality. Generally speaking, the higher the abstraction of mathematics, the stronger its universality.

Second, the principle of combining rigor with ability.

Stiffness is one of the basic characteristics of mathematics. Its significance mainly refers to the rigor of mathematical logic and the accuracy of conclusions. In the theoretical system of middle school mathematics, it is mainly manifested in the following two aspects: first, it is necessary to define concepts (except original concepts) and prove propositions (except axioms); Secondly, the arrangement of mathematics content should conform to the inherent logical structure of the discipline.

Third, cultivate the principle of combining "two basics" with strategic innovation.

Mathematics "double basics" refers to the basic knowledge and skills of mathematics. The basic knowledge of mathematics, that is, the "nodes" in the mathematical knowledge network, includes concepts, theorems, formulas, rules and methods in middle school mathematics. Basic skills refer to the operation methods related to the basic knowledge of mathematics according to certain procedures and steps, including mental activities such as operation, reasoning, data processing, drawing and table drawing. A correct understanding of mathematical concepts is the premise of mastering mathematical knowledge, while a firm grasp of mathematical laws such as definitions, properties, axioms, theorems, formulas, rules and proof methods for solving problems is a necessary condition for learning mathematics well.

Fourth, strengthen the principle of combining teaching with self-construction.

Intensive teaching and more practice is the main method of mathematics classroom teaching at present. Intensive teaching is put forward for teachers' explanation, which requires teachers to choose typical problems to explain and explain the key points in mathematical concepts and theorems incisively. Explanations should be few but precise, targeted, representative and universal, and individual problems should be taught separately. More practice requires students to practice solving problems in a certain amount.

Extended data:

Mathematics originated from the early production activities of human beings, and the ancient Babylonians had accumulated some mathematical knowledge, which could be applied to practical problems. As far as mathematics itself is concerned, their mathematical knowledge is only obtained through observation and experience, and there is no comprehensive conclusion and proof, but their contribution to mathematics should also be fully affirmed.

The knowledge and application of basic mathematics is an indispensable part of individual and group life. The refinement of its basic concepts can be found in ancient mathematical documents of ancient Egypt, Mesopotamia and ancient India. Since then, its development has continued to make small progress. But algebra and geometry at that time were still independent for a long time.

Algebra can be said to be the most widely accepted "mathematics". It can be said that the first mathematics he came into contact with was algebra since everyone began to learn to count when he was a child. Mathematics is a subject that studies numbers, and algebra is also one of the most important parts of mathematics. Geometry is the earliest branch of mathematics studied by people.

Until the Renaissance in16th century, Descartes founded analytic geometry, which linked algebra and geometry which were completely separated at that time. From then on, we can finally prove the theorem of geometry through calculation; At the same time, abstract algebraic equations and trigonometric functions can also be graphically represented. Then more subtle calculus was developed.

References:

Baidu Encyclopedia-Mathematics (Subject)