Mathematics is a basic subject with a long history, which has a great influence on human civilization. No matter people's livelihood, economy, military and other industries, it is inseparable from the knowledge of mathematics. In this process, people began to think about a method to make the learning and application of mathematics easier and easier to understand, and thus put forward "the method of proof" and "the method of discovery (invention and creation)". Obviously, the proof method of mathematics itself is linked with the rigorous and formal logical deduction method, or the method of mathematical proof is closely linked with the axiomatic method.

Many famous mathematicians in history hope to find a "universal method" to solve all mathematical problems and turn any problem into a mathematical problem, but it turns out that this method is not feasible.

But in this process, mathematicians have perfected the mathematical methods of solving problems from generation to generation, especially Paulia's "heuristic method". Before 1980s, the so-called mathematical methodology was actually Paulia's "heuristic method"-the mathematical method of problem solving, which had a great influence on mathematics education.

2. The emergence and development of mathematical thinking methods.

As mentioned above, after Paulia's heuristic method of "problem solving" became popular in education, mathematicians soon realized this. If we only pay attention to the study of methods, it is likely to become a new formal skill and method education!

Therefore, some scholars began to emphasize the importance of mathematical thinking, emphasizing that positive thinking in mathematics education far exceeds memorizing and mastering a specific method. Thus, as a form of mathematics education after mathematical methodology, mathematical thinking method has gradually formed a teaching system.

On the contrary, the concept of modern mathematics education holds that for the so-called problem solvers, the process of problem solving cannot and should not be a stylized logical process, but a creative process. Therefore, we should combine "problem solving" and "mathematical thinking (mainly creative thinking)" used in heuristic methods.

Especially in the field of western mathematics education, it is generally believed that the purpose of mathematics learning is not to master "mathematical knowledge and skills", but "general method to solve problems", that is, "mathematical thinking".

Moreover, regarding the education of mathematical thinking, mathematical researchers put forward the following three viewpoints:

1. The research of mathematical thinking method is closely related to the application of mathematical methodology, that is, mathematical thinking is the way of thinking to solve problems.

Secondly, the teaching of mathematical thinking methods not only emphasizes the methodological significance of mathematical methods, but also emphasizes the positive significance of mathematical thinking activities in these mathematical methods, that is, mathematical thinking ability.

Thirdly, the educational content of mathematical thinking method should be related to illogical thinking and creative thinking. In other words, mathematical thinking is not a stylized teaching.

It can be seen that mathematical thinking education is a way of thinking in the process of solving mathematical problems, a process, not a result. It is precisely when our parents educate their children that they often only pay attention to whether the final result is correct, and do not care whether the child's thinking process is correct.