Why are there no ideas when doing math problems?
First, basic knowledge. Every subject, every research project and every subject has a corresponding basic knowledge system. If you don't lay a good foundation, there is no doubt that the related learning in the future is based on floating clouds, which is not solid and cannot be developed. Many clues to solve problems are actually contained in the stem of the topic, but those who are not so simple often like to change the conditions of the topic or hide it a little. If students have a solid foundation, they naturally cannot associate correct theorems and concepts to translate, so they will not be able to take the next step. For how to learn to review mathematics concepts, please refer to how to effectively review mathematics in the college entrance examination. To put it simply, it is hoped that students will thoroughly understand the mathematical concepts and theorems in high school for three years, and it is best to push axioms and theorems by themselves, and then do examples in textbooks by themselves, so that knowledge points can be implanted into the whole high school mathematics system in an orderly manner and the relationship between knowledge points can be clarified.
In view of the problem that basic knowledge is unreliable, our course will review the corresponding basic knowledge quickly and deeply, help students to check and fill gaps, deepen their understanding of the essence of each knowledge point, and enable students to truly grasp the core of each concept, theorem and definition, as well as its relationship with other knowledge points.
Second, the problem of mathematical thinking. The classmate said, after reading your three tricks in mathematics, I still can't! Yes, you have seen how we work out this problem with three tricks of mathematics, but it is normal that we can't use it ourselves. Just like swimming and driving, no matter how many theories and videos you watch, you will never learn to swim and drive unless you jump into the water and operate the steering wheel yourself. If you just look at one thing and even know how to do it, it doesn't mean that you can really do it yourself. Only when you actually operate it and master it completely can you build a solid neural circuit.
Secondly, many students have become accustomed to the problem-solving thinking mode of "back-to-back problem-finding feeling" taught by school teachers in the past, and formed a thinking mode. When you make a problem, you will be used to finding the feeling of solving the problem from the question bank you have done, instead of rationally using the three tricks of mathematics to do the problem. This fixed thinking mode is like a roadblock, preventing you from going to a new field where you may find a solution, because our intuition is often misleading. When learning new things, we must abandon the wrong old ideas and methods. If you often use this way of thinking to solve problems, after solving many different problems, you will find that you have a deeper understanding of the reasons and methods behind the process. Compared with simply passively receiving information, you have a deeper understanding of the formation of conscious images constructed by the brain.
Third, fear of difficulties. Human nature likes to be relaxed and happy, and hates pain and frustration. But if you want to study hard and become smarter, you must be anti-human. The first step is to get out of your psychological comfort zone and overcome your fear of difficulties. To tell the truth, dajia in human history has not overcome many difficulties and obstacles to become dajia. There is no difficulty that is not worth doing. Life is not only champagne, flowers and winning the championship, but also full of uncertain valleys and torture. Students might as well take solving problems as a game to exercise their resilience and learn to enjoy the challenging transformation process.
A very famous law is called "deliberate training". Deliberate training is not simply repeating exercises mechanically, but deliberately choosing the most difficult part of the exercises. Finding out the things that we feel painful and difficult but can make us progress continuously, and then repeating these things repeatedly, can raise our ordinary brain to a natural level. Just as long-term weight-bearing training will make muscles more developed, you can deepen and expand this thinking mode in your mind by practicing a specific thinking mode.
Establish the concept of doing problems
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Basic knowledge points
Everyone knows that the foundation is very important. I still suggest that you consolidate and summarize the basic knowledge points according to the chapters and form your own framework system in your mind. Of course, this framework system can refer to my idea of explaining knowledge points in class, and I have already made it clear to you.
The consolidation review of basic knowledge points emphasizes the review of basic concepts and principles of knowledge points. Only when everyone is very familiar with the concept and can master the principle skillfully can we help you to judge the problem-solving boundary point corresponding to the conditions given in the topic very efficiently.
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Basic curriculum thought
The knowledge points in each chapter represent the core idea of this chapter. In the process of reviewing the basic ideas of the course, we should not only fully grasp, but also highlight the key points.
After everyone has mastered the curriculum ideas of each chapter, they should learn to cross-understand. What is cross-understanding? Cross-understanding means that you need to know how to connect these course ideas.
In the exam, the curriculum ideas are also clearly defined. It is necessary to focus on reviewing and understanding the key curriculum ideas, and combining these key curriculum ideas for summary and analysis will make you feel like a duck to water.
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Overview of ability differentiation
The annual examination not only examines everyone's mastery of knowledge points and basic ideas of the course, but also examines everyone's computing ability, logical reasoning ability and comprehensive application ability.
When we do the problem, we should reflect on this problem and examine what our abilities are. The ability to focus on multiple-choice questions, fill in the blanks and answer questions is different, as I said before.
When you finish the multiple-choice question and enter the answer to the fill-in-the-blank question, you should flash in your mind the mainstream investigation ability range of the fill-in-the-blank question. Similarly, when solving problems, we should further expand our ability.