First of all, before learning new content, review the relevant knowledge.
The new curriculum strengthens the comprehensive connection, emphasizing the key points in the process of knowledge formation, the combination points of using mathematical thinking methods to generate problem-solving strategies, the connection points between mathematical knowledge, the divergence points of mathematical problem variants, and the recent development areas of students' thinking, and putting forward appropriate questions through columns such as "observation", "thinking" and "inquiry" to guide students' thinking and exploration activities. Make them go through the basic process of rational thinking such as observation, experiment, speculation, reasoning, communication and reflection, and draw new conclusions by themselves, which requires students to be familiar with the old knowledge in order to draw new conclusions by analogy. So before learning new knowledge, we should review the previous related contents. For example, when learning trigonometric functions, series and other chapters, we should look at the relevant knowledge of the previous functions; When learning "block diagram", you should look at the program block diagram in compulsory 3 "preliminary algorithm"; When learning reasoning and proof, you should look back at the inequalities in compulsory 5. In particular, the idea of function runs through the whole high school mathematics teaching, so we should always look back.
Second, we should always look back at the difficulties in the learning process.
In the process of learning the new curriculum, some knowledge is not understood by every student. If you really don't understand under the teacher's and classmates' explanation, you'd better put it aside, wait for a period of time (maybe a week or a month later), and then look back and you will be suddenly enlightened. This is called cold treatment. For example, finding the definition domain of abstract function in the compulsory course 1, many students can't understand it, and they don't know when it is the scope of the whole and when it is the scope of the independent variable X. It was very distressing to be trapped in that situation at that time. At this time, students should "not solve" and continue to learn the following knowledge. After a week, when they are guided to watch, most people will naturally understand. This method can prevent students from going into a dead end, having an aversion to mathematics and saving some unnecessary time.
Third, you should look back at every problem you have done.
If you want to learn mathematics well, the usual exercises are essential, but this does not mean that you should carry out sea tactics and pay attention to science when doing problems. A considerable number of students did not review and reflect on the problems they solved, did not learn from the mistakes in the test paper, did not take certain measures to prevent common mistakes in their problem solving, and did not try to solve and summarize the problems they solved with various solutions, which will inevitably make similar mistakes again. Students should pay attention to thinking and summing up when doing each problem, and then recall their own thinking after finishing it, from which they can sum up the general solutions to such problems, especially the special solutions to such problems. For wrong questions or questions that have not been worked out, we should understand the solution ideas of the answers, compare them with our own thinking methods, and see where the problems appear. Only in this way can the problems you have done be truly digested and absorbed and become your own things, otherwise it will be tantamount to practicing in vain. If you always don't want to look back, but only want to wear new shoes and take a new road, you are actually putting yourself into a sea of tactics. Many problems are not new, just slightly changed. There is a good saying: "Do the problem, do the problem, and do the problem until you die". If you don't turn your knowledge into your own, even if you take an original exam, it won't do. The mathematics of liberal arts students should focus on the foundation and implementation. Now that they have done it, don't let it go and don't let it go wrong again.
Fourth, always look back at your notebook.
High school students learn many subjects and have a lot to remember, so it is easy to forget what they have learned. This requires sorting out the knowledge in the textbook and adding it into notes by the teacher (this is called "from thick to thin"). You can take some notes during class, but the premise is that it will not affect the class effect. Some students are busy copying notes, ignoring the teacher's idea of solving problems. This is "picking up sesame seeds and losing watermelon", but some are not worth the candle. But just write down your notes, and then don't read them. It is best not to write it down. The best way is to memorize some keywords properly in class without affecting the class, and then sort them out independently after class, but you must look back in a few days, otherwise you will return what you have learned to books after a long time. Unfortunately, some students' notebooks, like overdue periodicals, have been abandoned for a long time and have not played their due role. In fact, one of the experiences of many college entrance examination champions is to make their notes into personal "study files", the most important review materials. Because good notes are the concentration, supplement and sublimation of textbook knowledge, and the display and refinement of thinking process. Rational use of notes can save time, highlight key points and improve efficiency.
Five, often look back at the wrong book.
The reason why students think they can't learn well is generally that they don't do well in the exam. In fact, failing the exam means that there are many wrong questions, which means that their studies are not solid enough at ordinary times. It doesn't matter if you don't learn well. Write this knowledge in your own mistake book, then ask your classmates and teachers, and then write the correct explanation or result on other pages. If we can pay attention to the matters needing attention in doing this kind of problems, the learning efficiency will be improved by 30%-60%. The reason why the answers or explanations are written on other pages is to think about the understanding and explanation of the knowledge points next time you look at the knowledge points or wrong questions, and then practice the exercises and answers of the questions. Of course, it is also necessary to regularly arrange supplementary notes in stages and establish a personalized learning material system. If we can establish a "set of wrong questions" through classification, we can sort out and analyze the mistakes in each exercise and exam; You can also organize your notes into categories such as "clever questions and clever solutions", "method comments" and "error-prone questions". As long as we persist in doing this and constantly expand our achievements, we can overcome the "blind spot" and get out of the "misunderstanding". In the tense comprehensive review stage, it will be easy and orderly, and you can spare more energy and time. Mistakes and failures are not terrible. As long as you can face them squarely, always look back and learn from them, everything will become the driving force for your success.
"always learn, review the old and learn new." As long as we can look back often, we can deepen our understanding of knowledge, connect scattered knowledge, weave knowledge networks, build a three-dimensional knowledge network structure system and consolidate knowledge; Check for leaks and fill gaps, so that knowledge is complete; Integrating and systematizing knowledge; Comprehensive application makes knowledge practical; Step by step, all-round preparation, perseverance, liberal arts students will certainly laugh at the end.