First, mathematics teaching has changed from being keen on numerous routine exercises to developing a broad-based mathematical ability. Students' mathematical ability should be able to distinguish relationships, make logical reasoning, and use various mathematical methods to solve a wide range of unconventional problems.

Second, students are required to perform mental arithmetic and effective estimation;

Fourth, know what kind of mathematical operation is suitable under certain conditions;

Fifth, some special problems can be formed from vague practical problems;

Sixth, we will choose effective strategies to solve the problem.

2) In 2000, the American Association of Mathematics Teachers issued the Mathematics Curriculum Standard, which mentioned six abilities:

First, the numerical operation ability;

Second, the ability to solve problems;

Third, the ability of logical reasoning;

Fourth, the ability of mathematical contact;

Fifth, mathematical communication ability;

Sixth, mathematical expression ability. 3) In 2003, the Mathematics Curriculum Standard for Ordinary Senior High Schools (Experiment) formulated by the People's Republic of China defined the mathematical thinking ability, which includes intuitive perception, observation and discovery, inductive analogy, spatial imagination, abstract generalization, symbolic representation, operational solution, data processing, deductive proof and body.