Problem analysis: Before solving a mathematical problem, it is very important to know the requirements and conditions of the problem. Read the question and understand the meaning, analyze the main points of the question, and find out what the question asks and the unknown quantity to be solved.

Establishing mathematical model: The key to solving practical problems is to transform practical problems into mathematical forms and establish mathematical models. By defining variables, column equations or inequalities, mathematical relations are established and problems are abstracted.

Discovering laws: When solving problems such as series, figures and probability, observing data or phenomena and discovering laws are the key to solving problems. By discovering the relationship between series, the characteristics of figures or the law of probability, the method of solving problems is deduced.

Reverse thinking: sometimes thinking from the opposite direction of the problem, using reverse deduction or disproof, is helpful to solve the problem. Assuming that the expected result is false, the contradictory conclusion is deduced, thus proving that the expected result is true.

Divide and rule: for a complex problem, break it down into smaller parts, solve them one by one, and then synthesize the solution. By decomposing the problem, the complexity of the problem is reduced and the solution is easier to get.

Trial-and-error method: For some uncertain questions, try different methods or steps, and gradually approach the correct answer. Trial and error is also a way to get the right answer.

Apply theorems and formulas: When solving problems, apply corresponding theorems and formulas according to different branches of mathematics. For example, the formula of trigonometric function and Pythagorean theorem are used to solve geometric problems.

Geometric figure analysis: for geometric problems, analyze the characteristics and properties of figures, such as similarity, symmetry, area comparison and so on.

Reasoning and proof: In the problem of mathematical proof, we need to use strict logical reasoning and mathematical knowledge to draw a conclusion through reasonable deduction and proof.

Comparison of various solutions: For a problem, we can try various solutions, compare their efficiency and accuracy, and find the most suitable solution.