1. Empathy: Sometimes, when solving a problem, we will rely too much on our own inherent knowledge and ignore the problem itself. Empathy, trying to look at the problem from the perspective of the questioner, and understanding their intentions and thoughts may bring you new perspectives and solutions. This method is particularly effective in solving some ingenious and difficult problems.

2. Combination of numbers and shapes: Mathematics is abstract, but it can also be perceived. By transforming abstract mathematical problems into graphics or intuitive models, we can understand the essence of the problems more clearly. This method is especially suitable for solving problems such as geometry, algebra and probability statistics.

3. Reverse thinking: Some problems are complicated to solve, but reverse thinking can find a breakthrough. Reverse thinking can help us explore problems from different angles and directions, so as to gain a more comprehensive and in-depth understanding. This method is particularly effective in solving mathematical proof problems and logical reasoning problems.

4. Special value method: For some unknown problems, special value method is a very practical skill. By substituting some special values, we can see the law and trend of the problem more intuitively and find the general solution. This method is especially fast and effective in solving multiple-choice questions and fill-in-the-blank questions.

Step-by-step solution: For some big problems, we often feel that there is no way to start. At this time, a big problem can be broken down into several small problems and solved one by one. Through step-by-step solution, we can decompose complex problems into simple parts, which is easier to understand and solve. This method is especially often used to solve large-scale calculation problems and synthesis problems.

Methods to improve mathematical thinking ability;

1. Cultivate interest in mathematics: Being interested in mathematics is the basis of improving mathematical thinking ability. You can try to solve some interesting math problems, or read some interesting books and articles about math to stimulate your interest in math.

2. Cultivate the habit of mathematical thinking: in daily life, try to solve problems with mathematical thinking. For example, calculate discounts when shopping, or calculate travel distance and time when traveling. This can help you form the habit of mathematical thinking.

3. Do more exercises: Practice is the key to improve mathematical thinking ability. By doing more exercises, you can be familiar with all kinds of questions and master problem-solving skills.

4. Learning mathematical methods: Mastering some mathematical methods, such as induction, deduction and analogy, can help you better understand mathematical concepts and solve problems.

5. Take part in the math contest: Taking part in the math contest can exercise your math thinking ability. By solving some challenging math problems, you can improve your math thinking ability.

6. Accept diversified problem-solving ideas: When solving problems, don't be limited to one method or idea. Try to accept diversified problem-solving ideas and think about problems from different angles, which can broaden your way of thinking.

7. Pay attention to the study of basic knowledge: the cultivation of mathematical thinking ability is inseparable from the mastery of basic knowledge. So we should pay attention to the study of basic knowledge and understand the basic concepts, principles and formulas of mathematics.