Mathematical problems can be divided into two categories, one is the application of mathematical laws, and the other is the discovery of mathematical laws. The problem of applying mathematical laws refers to the problem that students need to solve by applying the mathematical laws they have learned before. The problem of discovering mathematical laws refers to a problem that has nothing to do with the mathematical laws that students have learned before. Students are required to find out the laws from known things before they can solve them. Most of the math problems that students do belong to the first category.

The discovery of mathematical law problems can enhance students' innovative consciousness and improve their innovative ability. Therefore, in recent years, people began to pay more attention to this kind of mathematical problems. Especially in the last two years, the senior high school entrance examination in most cities in China has such questions. The idea of discovering mathematical laws and solving problems can not only improve students' test scores, but also help to cultivate innovative talents.

First,? Be good at grasping the main contradiction.

Some topics look big and complicated, but in fact there are not many key contents. Make a detailed analysis of the topic, get rid of the rough, get rid of the false and keep the true, and extract the main and key contents, so that the difficulty of the topic will be greatly reduced and the problem will be solved.

Second,? Grasp the variables in the topic

Finding the topic of mathematical laws will involve one or several variables. The so-called finding the law, in most cases, refers to the changing law of variables. Therefore, grasping the variables is equivalent to grasping the key to solving the problem.

Third,? Good at comparison.

Only by comparison can we tell. Through comparison, we can find the similarities and differences of things, and it is easier to find the changing law of things.

To find a regular topic, we usually give a series of quantities in a certain order, which requires us to find a universal law according to these known quantities. The laws revealed often contain the serial numbers of things. Therefore, it is easier to find the mystery by comparing variables with serial numbers.

Fourth, be good at finding the cycle of things.

Some topics contain the circular law of things. If we find the circular law of things, other problems will be solved.

Fifth, we should grasp the hidden invariants in the topic.

Some topics have changed in form, but the essence has not changed. As long as we always pay attention to finding its invariants in the process of observing morphological changes, we can reveal the essential laws of things.

Sixth, try to calculate

Looking for rules, of course, looking for mathematical rules. Mathematical laws are mostly analytical expressions of functions. Analytic expressions of functions often include mathematical operations. Therefore, to find the law, to a great extent, is to find a mathematical expression that can reflect the known quantity. Therefore, starting with calculation and trying to do some calculations is also a good way to solve the problem of finding the law.