In daily exercises, homework and exams, students will have some wrong questions more or less. Let's call it the "wrong question" below. Different attitudes towards wrong questions will make a great difference in learning effect.

First, clearly explain the meaning and significance of wrong topic management.

Teachers need to choose effective ways to point out the significance and importance of wrong topic management to students, so that they have a positive attitude towards wrong topic management and are willing to do such things in their daily study.

First of all, teachers should clearly tell students that the management of wrong questions is essentially a self-monitoring process of students' learning, with the purpose of transforming all kinds of information implied in wrong questions into explicit or implicit knowledge, so as to facilitate the storage and application of knowledge, realize the sharing and exchange of knowledge, and transform and innovate knowledge to promote students' effective learning. Wrong topic management includes knowledge acquisition, storage, application, sharing and innovation.

Secondly, teachers should make students realize that the management of wrong questions seems to increase the learning task, but in fact it reduces the trouble for future study. Through the management of wrong questions, students can constantly find their own shortcomings, remedy them in time, eliminate learning obstacles and hidden dangers in time, cultivate good study habits and improve learning efficiency.

Finally, teachers should let students gradually assume the responsibility of mathematics learning and actively participate in the management of wrong questions.

Second, improve the management of students' wrong questions.

This mainly involves four links: collecting and archiving wrong questions, correcting wrong questions, sharing wrong questions and applying wrong questions.

Collection and filing of wrong questions: The wrong questions here not only refer to the wrong questions in all kinds of math exams at all levels, but also include the wrong questions in the usual math homework. It is best to extract all the wrong questions into a fixed book (hereinafter referred to as the set of wrong questions) for your future reference. Even the "wrong questions" that have been "missed" and have been completely mastered are best registered to form a unique learning track, which is conducive to the understanding, memory, storage and extraction of knowledge.

When collecting wrong questions, we must pay attention to classification. There are many kinds of classification methods, which can be classified according to the reasons of wrong questions, according to the knowledge chapters implied in wrong questions, and even according to the types of questions. The wrong questions sorted out in this way are systematic and will be more targeted in the final review.

Correction of wrong questions: after collecting wrong questions, the next step is to correct them, which is the purpose of wrong question management. Students should strive to analyze the wrong questions independently, and then find the correct answers and correct them. On the basis of independent thinking, if you still can't get the answer, then you need to take the initiative to ask others for help, whether it is a good classmate or a teacher. Let them help themselves analyze the reasons and make corrections under their own inspiration and guidance. To find the crux of the mistake, it is best to attach your own experience to the wrong question, and you can answer the following questions in turn:

What's wrong with this question?

Why is this question wrong? What's wrong with simplification? What's wrong with conceptual understanding? Error means understanding the meaning of the question? The fault lies in the logical relationship? What's wrong with generalizing? Mistake is carelessness? The fault lies in the quality of thinking? Analogy error? Wait a minute. )

What is the correct way to do this problem?

Is there any other solution to this problem? Which method is better?

The process of correcting mistakes is actually a process in which students re-learn, re-understand and re-improve. Make students' understanding of error-prone knowledge more comprehensive and firm, and improve students' autonomous learning ability at the same time. Generally speaking, any study needs reflection, and the correction of wrong questions is one of the concrete ways of reflection.

Sorting out the wrong questions is not for looking good, but for being practical and helpful to learning. So there is no fixed standard, the key is to conform to the students' own habits. However, students must take the time to read the results of their own efforts and review the wrong questions, sometimes they can get unexpected results and new experiences. In fact, the compiled wrong problem set is equivalent to the essence of a large number of exercises done before (which should be based on the careful arrangement of students), and it is the most suitable learning material for students, which is more useful and valuable than any reference book and problem set.

Wrong topic sharing: under the current high school learning system, students have a strong sense of competition, but their awareness of active communication and sharing is very weak. In fact, classmates are a huge learning resource pool. As long as every student is willing to open his heart, communicate sincerely, support each other, help each other and encourage each other, students can learn a lot from their classmates. As the saying goes, "You have an idea, I have an idea, and after communication, we will have two ideas at the same time", and the wrong problem sets among students can also communicate with each other. This is because each student makes mistakes for different reasons, so everyone's wrong problem set is also different. By communicating with each other, we can learn from other people's mistakes, broaden our horizons and get inspiration to warn ourselves not to make the same mistakes. Different people get different experiences from the same topic. Through communication, everyone can appreciate different aspects of knowledge, so as to master knowledge more firmly. In the atmosphere of communication, students have changed their learning methods and enhanced their enthusiasm for learning mathematics.

Application of wrong questions: collecting wrong questions together and correcting them does not completely show that students have filled the loophole in this knowledge point. In the best case, for each wrong question, students themselves must look up the information, find out the same or related questions and practice answering them. If there is no difficulty, it means that students may have mastered this knowledge point. At this point, students can try to do something more difficult-adapt the wrong questions and change the conditions and conclusions in the questions. Is it still true? Whether to weaken the conditions or strengthen the conclusion, the proposition still holds? Or try to make up a similar topic, ok? ..... After this baptism of thinking, students will have a deeper understanding of knowledge and a more thorough grasp of methods. No matter how the conditions change, they can basically cope.

Under normal circumstances, students may not have enough time to do such things at school, but students help each other, find a type of topic or put forward an idea, and the whole class basically finds all the topics and adapts many similar topics.

Third, the wrong topic management grading guidance, grading strengthening

The survey data shows that there are grade differences, achievement level differences and gender differences in the management of wrong questions. Teachers have to pay attention to these differences and teach students in accordance with their aptitude when teaching students the management of wrong questions.

In view of the differences in different grades, teachers should pay special attention to the whole process of wrong topic management in senior one, and attach importance to supervision, guidance and demonstration. Because students have just entered the new era, their learning methods are relatively simple, and their learning ability needs to be strengthened. Careful guidance from teachers is indispensable. Excellent students' good experience in wrong question management and standardized wrong question set have good demonstration value. Senior one students are relatively simple, cooperative communication is easy to organize, and it is possible to share wrong questions. Once good habits are formed, students will not go with the flow because they can't find the direction. Senior one students have relatively abundant study time and have time to sort out their mistakes in detail. Teachers should seize this good opportunity, cultivate their good error management habits and accumulate valuable materials for future review. In the second year of senior high school, students' learning pressure increases and their sense of autonomy is stronger. Teachers should emphasize the effective integration of all aspects of wrong topic management, such as timely revision and communication every day and centralized arrangement at the end of the period. By the third year of senior high school, students have learned the basic content, but they have to face the great pressure of college entrance examination. At this stage, they have a lot of papers and questions to finish every day, so they don't have enough time to do the wrong set of questions. Therefore, the wrong questions sorted out by senior one and senior two students are of great use, and students can review basic knowledge and methods. For the wrong questions in senior three, students only need to correct the mistakes, reflect on themselves and save the test papers.

In the training of boys and girls, teachers should make use of boys' strong hands-on ability and strive to strengthen their understanding of right and wrong issues. Good execution and correct understanding will make boys do better. In view of the fact that girls have a good understanding of right and wrong questions, but their strategies and implementation are poor, teachers should focus on cultivating their correct methods, and strengthen communication with them and supervision over them, which will eventually have good results.

It is normal and reasonable for students to have differences. For students of different levels, teachers need to carry out hierarchical management. In the management of wrong questions, different requirements are put forward for students of different levels, so that they can get different degrees of development.

Fourth, supervise the management process of middle school students' wrong questions

After the students' wrong problem set is established, teachers can't let it go. Every once in a while, we should review their wrong problem sets, affirm their work and encourage them to persevere; At the same time, for those who fail to analyze the causes of wrong questions, teachers need to supplement them to help students find the crux of the problem.

Teachers can also try to establish a class communication mechanism, build a platform for students to exchange wrong questions, and promote the sharing of wrong questions resources in the whole class. For example, give students a self-study class or a math class every week, so that students who do well can report their typical mistakes in the whole class (teachers can review them), and teachers will listen to the students' reports as students at this time. In this process, the roles of teachers and students have been exchanged, and both teachers and students have made progress. The teacher will keep the contents of each report. After a period of time, the class will have a wrong question bank, and the teacher will print them into newspapers and send them to the students for the whole class to share. Not only did they learn knowledge, but they also changed students' learning methods and improved everyone's interest in learning mathematics.

In addition, in daily teaching activities, teachers should also pay attention to recording the typical wrong questions made by students, concentrate on making a test paper after a period of time, and then let students do it again. On the one hand, it can test the effect of students' wrong question management, on the other hand, it can give students positive feedback, so that students who do well can stick to it, and students who do badly should reflect on why they make mistakes repeatedly.

Usually, when teachers assign homework, they can also adapt some typical wrong questions for students to do again, instead of constantly giving students different new questions and getting them into the sea of questions. Or quietly adapt a typical wrong question in the exam and take it again.

The management of wrong questions is helpful to students' mathematics study. However, wrong topic management is not the purpose of learning, but a means to help students learn effectively and improve teachers' teaching quality. Doing a set of wrong questions is not a task, nor does it have to be exquisite and comprehensive. It is just a carrier for training thinking. The most important thing is that neither students nor teachers can easily let go of the wrong questions, thoroughly understand the problems reflected by the wrong questions and apply what they have learned. In the process of reflective learning, we should improve our knowledge structure, improve our ability to solve problems, and achieve the ultimate goal of effective learning and teaching.