First, the computing power and its characteristics

Computing power has two basic characteristics:

1, the hierarchy of computing power

In the history of mathematics development, different types of operations are gradually formed and developed from simple to complex, from concrete to abstract, and from low to advanced. Therefore, the understanding and mastery of operation must be gradual, and it is impossible to master the calculation of real numbers without mastering the calculation of rational numbers. Without the calculation of algebraic expressions, it is impossible to master the calculation of fractions. If you don't master finite calculation, you can't master infinite calculation. Without the foundation of concrete operation, abstract operation is difficult to realize. It can be seen that the computing power is gradually developed with the gradual broadening of knowledge, the deepening of content and the continuous improvement of abstract programs. If the development of mathematics content is infinite, the improvement of computing power will be endless.

The requirements for middle school mathematics operation ability can be roughly divided into two levels: ① Accuracy of calculation-basic requirements ② Rationality, simplicity and rapidity of calculation-higher requirements ③ Skill and flexibility of calculation-high standard requirements. Ideologically, we should fully understand the importance of improving computing ability, raise computing skills to the level of ability, and integrate computing skills with developing thinking.

2, comprehensive computing power

Computing ability can neither exist in isolation from specific mathematical knowledge nor develop independently from other abilities. Computing ability permeates memory ability, observation ability, understanding ability, association ability and expression ability, and is also supported by mathematical ability such as logical thinking ability. Mathematical operation ability in senior high school refers to the collective name of mathematical ability such as memory ability, calculation ability, observation ability, understanding ability, association ability, expression ability and logical thinking ability. Therefore, the problem of improving computing power is a comprehensive problem. In the teaching process of various subjects in middle schools, we should strive to cultivate the computing ability, constantly guide it, and gradually accumulate and improve it.

Second, the factors affecting students' computing ability

1. Ignorance of ideology: Under the guidance of the new curriculum standards, the requirements for calculation methods and skills in mathematics are reduced, and complicated, difficult or skillful contents and methods are not required. Some teachers and students ignore the cultivation of computing ability and lack sufficient attention to improving computing ability. They always use "carelessness" and "carelessness" as excuses to ignore the accuracy of slightly required operations, and even have a fear of avoidance.

2. Reasons for current textbooks: The current mathematics textbook for senior high schools in China is a new textbook for nine-year compulsory education under the new curriculum standard, which deletes some complicated, difficult, dead and old knowledge, and the teaching content is not as difficult as in previous years. The purpose is to transition from the previous "talent education" to "mass education" and improve the mathematics quality of the whole nation. Such as algebraic operations, factorization, equations, quadratic functions, inequalities, etc., have greatly reduced the requirements. However, many contents of algebra and analytic geometry in the current high school mathematics textbooks are based on these contents, and the requirements of these contents greatly exceed those of junior high school, and some contents have never been learned in junior high school, so the contents of the textbooks are greatly out of touch. If high school teachers don't study junior high school textbooks, there will be problems.

3, the use of calculators: Now students from primary school to high school have calculators, and many simple numerical calculations are done with calculators, which weakens the computing power and cannot form a sense of numbers. The sense of number makes the world seen in people's eyes have quantitative significance. When we encounter specific problems that may be related to mathematics, we can naturally and consciously relate to mathematics, or try to further deal with and explain them with mathematical viewpoints and methods. It can be seen that the sense of number is an attitude and consciousness to solve and use numbers actively, consciously or automatically. Sense of number is a basic mathematical quality of human beings. It is the basis of establishing a clear concept of number and effectively carrying out mathematical activities such as calculation, and it is a bridge connecting mathematics with practical problems. Long-term use of calculators can not form a sense of numbers, which seriously affects the calculation ability and can not learn mathematics and related science and engineering knowledge well.

4. thinking set method: thinking set method has both positive and negative effects in operation. When students master a certain knowledge (method) and think with old knowledge (method) with similar habits, thinking inertia will inevitably appear, which will affect the operation speed and make the operation process cumbersome.

5. Lack of comparative awareness: Comparative awareness is an important direction to solve problems. When solving problems, there are often many ways to solve them, which requires us to be good at choosing the best and following them. Some students lack comparative consciousness. When doing problems, they often try to do it with death. Even if it is boring, they don't care. They just thought it was the right thing to do. When commenting on the test questions, the teacher ignored the priority of simple methods in various solutions.

1, pay attention to the cultivation and improvement of computing ability ideologically: it is necessary to realize that the reduction of computing ability required by the new curriculum standard is appropriate, not to avoid computing, but to delete and adjust some complex, difficult, outdated and technical contents appropriately. Mathematics is a subject based on quantitative relations. If there is a quantitative relationship, there must be operations. If there is operation, there will be a requirement for computing power, and computing power is one of the major capacity requirements of mathematics.

2. Reasonable arrangement of teaching materials. Besides compiling textbooks, we should also have our own school-based mathematics textbooks. The current junior high school mathematics textbook is a new textbook for nine-year compulsory education under the new curriculum standard, which deletes some complicated, difficult, dead and old knowledge and increases the new knowledge needed by modern society. In order to make all students learn mathematics well and improve their mathematical ability, the difficulty of some contents is greatly reduced. But now the high school textbooks are more difficult than before. The students in our school have a good foundation in mathematics from primary school to this junior high school, and junior high school mathematics has enough time every Saturday. Therefore, it is necessary to develop school-based teaching materials suitable for the actual situation of our school, solve the problem of the connection between senior high school and junior high school mathematics knowledge, and lay a solid foundation for senior high school mathematics teaching.

In short, students should pay attention to the cultivation of computing ability in their usual study and training, use calculators as little as possible, strengthen the training of oral calculation, mental calculation, written calculation and quick calculation, and do not forget to analyze and explain the calculation methods and skills in classroom teaching, so as to gradually cultivate students' sense of number, thus improving their computing ability and laying a solid foundation for students to learn mathematics well and improve their quality.