Constructivist learning view points out that learning is not a passive acceptance of knowledge given by teachers, but an active construction based on their existing knowledge and experience. There must be a process of deepening and developing students' understanding, including some mistakes and repetitions. Therefore, we should adopt a more understanding attitude towards the mistakes made by students in the learning process, instead of simply denying them, we should try to find out the reasonable components and positive factors. Students' mistakes can not be corrected by positive demonstration and repeated practice, but must be a process of "self-denial", which is based on self-reflection, especially the internal "conflict of ideas". In teaching practice, we can often see quite a few students make the same mistakes over and over again, which greatly reduces their learning efficiency. In order to use the wrong questions as resources to serve teaching, we encourage and help students to set up a set of wrong questions.

1. First of all, the "wrong problem set" is a systematic summary of its own mistakes, which is helpful to check and fill the gaps.

As a front-line teacher, you should have had such an experience: after every practice or exam, teachers and students have many regrets. Many topics have been discussed, done and even tested, and some have even been done many times, but they are still wrong in the end. I often see students complaining about the wrong questions on the test paper: "Alas, how can such a simple question be wrong?"

The reason is not only because the learning foundation is not solid, some knowledge points and skills are not well mastered, but also because students don't know enough about the value of right and wrong questions. For the wrong questions in the usual exercises, they are often simply corrected, without in-depth analysis of the reasons and no record of wrong questions. If there is no teacher's supervision, some students will even be lazy and finish correcting by asking questions and copying. This provides a greater possibility for the error to happen again.

2. Secondly, the "wrong problem set" can enhance students' sense of self-efficacy and contribute to autonomous learning.

In teaching, we often find that students often correct their mistakes. After a long time, they became indifferent. There is no way to check when they change their exercise books. There are countless students in my heart and countless teachers in my heart. Later, there was no basis for reviewing remedial measures, so the net was cast in an all-round way, which led to weak pertinence and greatly reduced efficiency. If a set of wrong questions in mathematics is established, each student's wrong questions in various situations are concentrated on the set of wrong questions according to their true colors, which is equivalent to establishing a ledger, and both teachers and students have accurate review basis. Only in this way can students reduce the burden and increase efficiency, and truly achieve "light burden and high quality"

3. "Wrong problem set" is helpful for teachers and students to improve teaching quality.

Engels had such a theory: "No matter where you study, the speed of your study can't keep up with the consequences of your mistakes." The establishment of "Mathematics Wrong Question Set" is to gather all the wrong questions at ordinary times, find out the cause of each mistake, make a systematic and comprehensive analysis and diagnosis, and then improve the correct rate of the whole class in a large area and reduce the mistakes to the lowest point.

In the practice of mathematics teaching for many years, we find that the mistakes made by each student when learning the same teaching content are strikingly similar. However, every teacher only corrects these mistakes in time, lacking in collection, analysis and utilization, which leads to the continuation of these mistakes year after year, and teachers and students have done a lot of useless work. With the "wrong math problem set", both teachers and students have a lesson from the past, and they can take fewer detours on the road of learning.

Based on the above ideas, our math group put forward the research topic of effectively using the "set of math wrong questions", devoted to the collection, classification and cause analysis of students' wrong questions, and explored the corresponding implementation strategies to be applied in peacetime teaching, so that students' learning process can achieve "light negative and high quality".

Second, the use of mathematical wrong problem sets.

After a year of hard work, our method is:

1. Read often to avoid making mistakes again.

A good set of "wrong questions" is a dictionary of your own knowledge loopholes, and "wrong questions" are not finished by writing down the wrong questions. Students should often take out a set of "wrong questions" in their spare time or prepare for the next exam, browse and look for "gold" in the wrong questions. You can set the 2 minutes at the beginning of class every day as the "thinking" time. During this time, students can read or do the wrong questions in front, especially the wrong questions of the previous day, to test whether they really understand. Or read the right of self-reflection made in front of you, and sound the alarm for yourself again. In the spare time after class or when preparing for the next exam, take out the wrong book to review, so that the mistakes you have made can be "negated" again in your mind to avoid making mistakes again.

2. Exchange reading to prevent mistakes.

As the saying goes, learn from mistakes. Because of the different students' foundation, the "wrong problem set" established by students is also different. By exchanging reading and communication with each other, students can learn from other people's mistakes and get inspiration from them, thus warning themselves not to make the same mistakes and improving the accuracy of exercises.

3. The wrong questions were scored and "eliminated" one by one.

The requirement is to sort out the mistakes on the same day, summarize them once a week, once a month and once a semester.

The specific method of weekly summary is to browse the wrong questions recorded every day first. At present, put an "X" and a "?"on the topic of "fully understanding and ensuring that you won't make mistakes in the future" Put a △ in the question "I don't know why I didn't understand" on the topic "I don't fully understand, and I may make mistakes in the future".

The specific way to finish it in one month is to sum up "?" Weekly summary. Try to solve the problem thoroughly. If you can't do it yourself, you must ask the teacher to "eliminate". You are welcome to copy the △ title again. If there is no new discovery, it will be upgraded to ∞ title and downgraded to?. At the end of next month, try to "destroy" it and downgrade it to "X".

Third, the extension of mathematical wrong problem set.

Teachers record the topics with high error rate in the whole class according to the unit content, and print the collected wrong questions into a math exercise paper, so that students can consolidate their exercises and revise them again, so as to shorten the time left by the wrong questions in their minds as much as possible. By the end of the semester, teachers will accumulate the usual wrong papers into a book, and conduct systematic and targeted review at the end of the semester to avoid inefficient review without purpose and focus. At the same time, the accumulated "wrong math problem set" can also provide reference for students in the next class.