Preview is a process of self-learning the content of a new lesson before class, which has a great influence on learning. Preview can remove the knowledge obstacles in classroom learning, improve the level of listening and speaking, and strengthen the pertinence of taking class notes, thus improving the quality of classroom learning; Preview can promote the improvement of self-study ability and change the passive situation of learning.
2. Strive to improve the efficiency of classroom learning.
"Highly involved, excellent and efficient" is a high standard requirement for classroom learning. The main battlefield of mathematics learning is in the classroom. In order to have a good class, we must prepare lessons first. In addition to the preview, make sure not to be late and arrive at the church a few minutes in advance; Put textbooks, notebooks, classroom exercise books, pen stationery, etc. Put it on the table and wait for the teacher to come to class. Relax before class and remember the important concepts, theorems and formulas in the last class for one or two minutes. As soon as the bell rings, you should be energetic, highly concentrated and concentrate on the class.
3. Pay attention to after-class review and improve the quality of homework.
Practice is an integral part of mathematics learning and a necessary condition for students to learn mathematics well. "Learning from time to time is a pleasure!" The purpose of the exercise is to further understand and master the basic knowledge of mathematics, train, cultivate and develop their basic skills and abilities, find and make up for the omissions and deficiencies in learning in time, and cultivate good study habits and quality. The purpose of learning is to apply. Homework after class is an important part of applying the knowledge and methods learned in class. Don't finish your homework just to finish it. Before doing your homework, you should review and consolidate what you have learned in class, deepen your understanding, deeply understand the ideas and steps of solving important examples, and find out the reasons; Understand and strengthen the memory of important theorems and formulas, and systematically sort out and summarize scattered knowledge. Do a good job of reviewing and sorting out, and then start to finish your homework independently. Learning mathematics is inseparable from solving problems, and it is difficult to understand whether a certain number of problems can be completed to form a skill change. But the more problems you solve, the better. The key to solving the problem lies in quality rather than quantity. The topic is not greed, but wonderful, so we should think carefully and finish it independently. If there are mistakes in your homework, you should find out the reasons and correct them in time. There is a book to record and correct mistakes and read it from time to time. Mistakes are often the forerunner of correctness. People always deepen their understanding of the correct law and make continuous progress by constantly correcting mistakes. We should pay attention to multiple solutions to one problem, optimize the ideas and methods of solving problems, and seek shortcuts in comparison; We should pay attention to the unity of multiple problems, find the law and explore the law of solving problems; We should always sum up the thinking methods of solving problems and find the connection between them. We should pay attention to the typicality and diversity of topics, study the types and structure of topics, get rid of the rough and the fine, get rid of the false and keep the true, and from here to there, from the surface to the inside, in order to master the essential relationship between topics and their solutions, that is, the law. After the homework is completed, you should carefully check yourself; After the homework is corrected and sent back by the teacher, we should conscientiously sum up the revision: whether the wrong one can be corrected will become right, and whether the right one can become mature and skilled. After learning a unit and a chapter, we should sort out and summarize the exercises we have done, reflect on associations and re-examine them from a higher angle. If we can sum up typical problems, examples and categories from the summary, we can use typical examples as guidance, and then draw inferences from others to achieve mastery and ingenious application of knowledge and methods.
4. Review in time and systematically.
"Always learn, review old things and learn new things." It is difficult to master all the knowledge learned in one day in class, and it needs to be further mastered through after-class review. Reviewing after class is very important in time. Through hard memory, careful reading (teaching materials), sorting out notes, reading reference books, etc. We can digest and understand what we have learned in class and absorb it into our own knowledge structure. Not only that, but also actively carry out systematic review. Through unit review, the scattered knowledge is linked and communicated to form a whole. Through stage review (weekly review, monthly review and pre-test review) and systematic review (chapter review and special review), we can deepen our understanding of knowledge, weave knowledge network and build a three-dimensional knowledge network structure system. Systematic review can bring many benefits: recalling attention and consolidating knowledge; Check for leaks and fill gaps, so that knowledge is complete; Integrate knowledge, systematize and comprehensively apply it, and make it practical.
5, from thin to thick "and" from thick to thin "
From thin to thick is a process of learning and acceptance, and from thick to thin is a process of digestion and practice. For example, we read a book, a thick one, and add our own annotations. The more we read, the thicker we know, and the more we know. But this process is mainly a process of acceptance and memory. "Learning" doesn't stop there, and "slowness" doesn't stop there. To really learn to understand, we must also go through the process of "from coarse to fine", that is, chew, digest and integrate what we have learned and ask key questions. We often have this experience: when you read a book or a selection of materials, if you thoroughly study their content and spirit, thoroughly understand and master the main points and keys, you will feel that the book and the selection of materials have become thinner. It seems that you get less than before, but in essence it is digested and turned into refined things. Not only in quantity, but also in quality. Only through the process of digestion and refining can the foundation be consolidated. Then, practicing on this basis is not ordinary acrobatics. Re-learning will not be crammed into your mind one by one, but will become adding some new contents and methods on the basis of richness. After the process of "from thin to thick" and "from thick to thin", we can understand what we have learned, eat it thoroughly, and then understand it after digestion, even if we really lay a good foundation. With this foundation, learning can be greatly accelerated in the future. This process also embodies the law of gradual progress in learning and scientific research.