Abstract ability:

The ability to choose the attributes of different phenomena, focus on research, and seek general laws. For example: mathematical thinking ability [*] (mathematical analysis, law exploration, judgment and prediction);

Ability to exchange ideas and summarize.

Symbolic ability:

It is a way of thinking in natural science to expand and deepen natural language into compact and concise symbolic language. Including:

Ability to express quantitative relations and logical relations by symbols and forms;

The ability to use reasonable mathematical skills to transform problems and expand them to a wider range.

Axiomatic ability:

Mathematical demonstration ability. For example:

Reasoning, induction and deduction from premises, data, graphics and incomplete and inconsistent original data.

Ability to build models:

The actual phenomenon is analyzed, a certain mathematical model is established, and the quantitative and qualitative treatment is combined. Specifically, for example:

From a mathematical point of view,

Ability to ask questions and solve problems;

Modeling skills (digitalization of practical problems, graphics of practical problems, combination of several lines, etc.). ).

Able to use various tools and auxiliary equipment.

Optimization ability:

The ability to investigate all possibilities, seek the optimal solution from them, and continuously and creatively optimize existing results and algorithms. This ability is closest to the practical application of mathematics, and it also requires the highest comprehensive quality of mathematics. Note [*]: The so-called mathematical thinking includes thinking about mathematics itself and thinking from a mathematical perspective. Thinking about mathematics is high-level and meets the needs of a few students. But mathematics and rational thinking are what everyone needs. ........................................................................................................................................................................