Is there any easy way to quickly expand the thinking of middle school mathematics, especially mathem

In short, it's just what is lacking and what is missing.

Why do you know what is missing, when you want to use a certain theorem, or a formula, you find that the conditions are insufficient, then this is the entry point for solving the problem, around to find this condition, then you are looking for other conditions, use all the conditions, you have the idea of solving the problem, often train like this, your mathematical thinking is very sharp, and the problem should really be very clear, not thinking.

Learn to summarize, summarize is to solve the formula theorem what elements are composed, to know clearly, and to learn to use a simple model to prove these theorems, verify each other Your formula is not easy to remember.

Personally, I think that you don't need to spend your fists and legs on solving problems, you don't have to pursue how many ways there are in a question, what you have to master is to use only one method of a principle, and the exam mainly examines how well you have mastered your knowledge, not looking for those geniuses. How well you have the knowledge is what I discussed above.

Mathematical thinking should be a rational thing, your perspective of thinking.

This book of mathematics, physics and chemistry for middle school students is really good, it can diverge thinking, and it has a certain depth and thorough analysis, which is worth recommending.

If the spatial imagination ability is not very good, you still have to do more questions... This is a must!!

1. Cultivate flexibility in thinking.

Flexibility of thinking refers to the timeliness of being able to adapt to changes in things, and not being too influenced by fixed mindsets. If we lack flexibility in thinking, our thinking will be more inclined to a specific way and method, and it is easy to get into the situation of drilling into the horns of the bull, one-sided pursuit of problem-solving patterns and procedures, and in the long run, resulting in inertia in thinking.

good at breaking away from old patterns and general constraints and finding the right direction; The ability to use knowledge freely, the use of dialectical thinking to balance the relationship between things, the specific analysis of specific problems, and the ability to adapt and adjust ideas, etc., are the direct manifestations of the development of thinking flexibility.

2. Cultivate the rigor of mathematical thinking.

The rigor of thinking refers to the rigorous and well-founded consideration of problems. In order to improve the rigor of students' thinking, it is necessary to set strict requirements and strengthen training.

To implement it in children's learning and life, it is required to start from the basic concept when learning new knowledge, so that it can be steady and steady under the premise of clear thinking, and gradually go deeper, develop the habit of thinking carefully in this relatively slow process, and grasp enough reasons as the basis for argumentation and reasoning; When practicing the test questions, he is good at paying attention to the hidden conditions in the question stem, answering the questions in detail, and writing out the solution ideas without hesitation.

3. Cultivate the profundity of mathematical thinking.

Thinking profundity refers to the degree of abstraction and logic of thinking activities, as well as the depth and difficulty of thinking activities. I believe that most students have had such a situation, sometimes the teacher comments on the test papers, and it is easy to understand the process of solving the wrong questions, and suddenly realize that they have made such a low-level mistake, but once they leave the book and the teacher, they will not be able to understand the method and essence of the problem solving, and realize independent problem solving. This requires students to see the essence of mathematics through phenomena, grasp the most basic mathematical concepts, and gain insight into the connections between mathematical objects, which is the main manifestation of profound thinking.

Transformation is both a method and a way of thinking. Transforming thinking refers to changing the direction of the problem from a different perspective when encountering obstacles in the process of solving difficulties, and looking for the best way to make the problem easier and clearer.

Logic is the basis of all thinking. Logical thinking is the whole process of thinking, in which we observe, compare, analyze, synthesize, abstract, induct, distinguish and logically reason things by means of definition, discrimination, and logical reasoning in the process of understanding. Logical thinking is widely used in dealing with logical judgment problems.

Reverse thinking, also known as heterogeneous thinking, is a method of thinking that reflects on things or ideas that are taken for granted as if they have been concluded. Have the courage to "think the opposite", let the thinking develop from the opposite perspective, explore at a deep level from the opposite side of the problem, shape a new development concept, and create a new brand image.

The thinking of matching the state of Xiangqin is to create an immediate correlation between the arrangement and combination (including the quantity difference, the quantity multiple, and the quantity rate). The more common ones are general matching (such as the correspondence between two or several quantities and the difference between the multiples) and the volume rate matching.

Independent innovation thinking refers to the whole process of thinking to solve difficulties with novel and original methods, according to which the boundaries of basic thinking can be improved, and independent thinking can be carried out in unconventional and even unconventional methods and angles, and ingenious solutions can be proposed. It can be divided into four types: difference, exploratory, ascensive and negative.

System software thinking is also called overall thinking, and system software thinking refers to having an understanding of the knowledge involved in the actual question type when doing the problem, that is, to obtain the question type, first analyze and distinguish which knowledge points belong to, and then recall what kind of problem is divided into and the corresponding processing methods.

Comparative thinking refers to the thinking method of comparing strangers' and unknown problems with familiar problems or other things according to some similar characteristics in things, discovering the relevance of common sense, finding its essence, and then solving difficulties.

The key to brand image thinking refers to the thinking method that is generated when everyone chooses things and phenomena in the process of understanding the world, and refers to the thinking method of using visual images to solve difficulties. Imagination is an advanced way of thinking about brand image, which is also a fundamental method.

By doing more similar questions to help children form problem-solving thinking and ideas for the same type of problems, in the time and space when children have spare time and space to learn, you can enroll your child in some math interest classes or Olympiad math competition questions, which can well cultivate children's comprehensive mathematical thinking ability.

I think you can memorize more mathematical formulas, observe life more, always practice more math problems, and ask others more how this problem is made, so that you can improve your mathematical thinking.

You should do more questions to keep an eye on the state, and you should ask the teacher more questions that you can't do, and you should also develop a particularly good habit of learning mathematics, and you must know how to grasp the mathematical knowledge you often learn, and if you can't, you should ask the teacher more.

Mathematical thinking is a form of thinking, which is mainly used to think about related problems and solve them; If you want to improve your mathematical thinking, you should observe and discover more in your daily life, be good at using your brain, and make a series of associations, so as to effectively cultivate your logical thinking ability.

Mathematical thinking is the way you think when you solve mathematical problems, and to improve mathematical thinking, you need to do more problems and summarize more.

Mathematical thinking plays a very important role in learning mathematics, and mathematical thinking is when you see a problem, you can immediately think of starting from the **? What should I do as a first step? This should be done more to accumulate experience.