1. Overall thinking.
Starting from the overall problem, highlight the analysis and transformation of the overall structure of the problem, discover the overall structural characteristics of the problem, and be good at considering some formulas or graphics as a whole from an integrated perspective, grasp the relationship between them, and carry out Purpose, conscious overall processing. Holistic thinking methods are widely used in algebraic simplification and evaluation. Solve equations (sets). Geometric proof. Factorization.
2. The combination of number and shape.
The famous mathematician Hua Luogeng once said: When the number is lack of shape, it is less intuitive, when the shape is small, it is difficult to understand; the combination of number and shape is good to isolate everything. In mathematics, number and shape are the two main research objects, and there is a very close relationship between them. Under certain conditions, numbers and shapes can transform and permeate each other. In junior high school mathematics textbooks, especially the idea of combining numbers and shapes runs through the entire textbook, such as learning quadratic functions, linear functions, inverse proportional functions, and so on. It can be said that the combination of algebra and geometry is a general method for solving mathematics problems in junior high schools and even high schools and universities. Looking at the finale of multiple choice questions in the senior high school entrance examination in recent years, quadratic function is usually chosen as the finale of choice. Therefore, we must deeply understand the key nature of solving mathematical problems.
3. Transform thoughts.
Converting ideas can usually obtain new ideas or conditions from a mathematically known condition. The thought of transformation inspires us to solve mathematical problems from multiple angles and multiple directions.
4. Thinking from special to general.
This idea is very important in junior high school mathematics. For example, when solving geometric proof problems, although we cannot directly get the idea of solving the problem, we can start from special places, special points, special line segments and other special places, think deeply, and finally realize the way to solve the problem數學老師.
5. Equation thinking.
The idea of combining figures and shapes and the idea of equations are two great ideas in mathematics. When solving mathematical problems, such as formulating equations, take junior high school mathematics application problems as an example. The idea of formulating equations is an important idea for solving such problems.
6. Analogical thinking.
Compare two (or two) different mathematical objects. If you find that they have the same or similarities in some aspects, then infer that they may also have the same or similarities in other aspects.
7. Analysis method and synthesis method.
Sometimes we often encounter many problems and cannot start. At this time, we should be able to use this method. Starting from the conclusion to be proved, or starting from the known conditions, extracting it, there may be unexpected results.
In short, you should pay attention to understanding, method, and thinking, these three key words in learning mathematics. In addition, you need to practice more and learn more. Also pay attention to studying mathematics, one type of multiple questions, one question with multiple solutions. Go the same way, find another way, no matter what angle you start from, as long as you are logically correct, you are right. And pay attention to summarizing a category of questions, summing up more mistakes, and reflecting frequently.