Wrong questions are common problems in students' mathematics learning. In teaching, students' learning effects are different because of the different strategies and teaching methods used by teachers. In addition, different students' learning interests, abilities and thinking qualities will also make different mistakes. In teaching, experienced teachers can help students learn better through feedback analysis of common wrong questions. As Piaget said, "mistakes are very important for meaningful learning". If all the mistakes in students' learning are regarded as unreasonable, the development of students' own knowledge system will be in a bottleneck state, and mistakes will become "limiting factors" at this time. However, when we re-recognize the essence of mistakes with the ecological holistic view, the connection view and the dynamic balance view, and fully tap and utilize the reasonable components in mistakes, students' knowledge system can advance in waves in the process of approaching or expanding the bottleneck, and realize sustainable development. Therefore, the author studies how to effectively use students' wrong questions in mathematics learning, improve students' learning effect and promote teachers' teaching.

This article is some inspiration that the author got in the research process, hoping to get help and suggestions from colleagues.

First, the causes of common mistakes of students

(A) Teachers' incomprehension of students' wrong questions is the inducement.

1. The teacher is biased in studying students' wrong questions.

First, in class, teachers are afraid that students will not understand and make mistakes, so they talk too much about arithmetic, methods and quantitative relations. Without independent thinking, trial practice and hands-on practice, students can't construct their own knowledge, and teachers can't understand students' ideas and control teaching in time, so wrong questions will "emerge at the historic moment".

Second, when students make mistakes in new teaching, teachers are afraid to pass by if they can't complete the teaching progress; Turn a blind eye to a few mistakes that are not universal; For special mistakes, some teachers will tell students that "this is not right, find the reason yourself" and then continue the following teaching links. The student has no time to sort out his mistakes. Therefore, teachers can't grasp students' knowledge defects in time and give feedback in time. Teachers' excessive prevention and avoidance of mistakes and insufficient acceptance of mistakes subconsciously affect students. Students unconsciously form an attitude of not actively analyzing the causes of mistakes, not listening to and letting go of wrong questions, or waiting for teachers to explain the ideas and answers to solve problems, and passively correcting wrong questions, so that wrong questions can not be faced squarely and mistakes can not be solved.

2. Teachers' feedback evaluation is not targeted.

The main content of teachers' evaluation of students is the mastery of basic knowledge and skills. Usually, the right or wrong of solving problems is the only evaluation criterion. During the feedback, students were not exposed to the wrong thinking process, and no targeted corrective measures were taken. When encountering a wrong question, most teachers let the students correct it independently, and then the teacher will re-approve it. If it is still wrong, they will change it again, re-approve it, or the teacher will directly teach the calculation method of the whole question again ... Students are in a state of high tension, bewilderment and bewilderment during the whole feedback and correction process. After a few days, the same mistake will appear again or another new mistake will be derived ... It can be seen that the effect of correction is inefficient. From another point of view, this will increase students' learning burden, and even lead to the bad phenomenon of copying homework and avoiding mistakes, which will kill students' interest in mathematics learning in the long run. Therefore, teachers' lack of pertinence in the process evaluation of students' thinking process and thinking quality reduces the effectiveness and enthusiasm of students in correcting wrong questions, and also inadvertently "provides" soil for new wrong questions.

(2) Being influenced by psychological factors such as negative transfer and forgetting law is an important reason.

Psychologically, transfer, also called learning transfer, is a common phenomenon in the process of learning. It refers to the influence of acquired knowledge, skills, learning methods or learning attitudes on learning new knowledge, skills and solving new problems. Migration is the continuation and consolidation of learning, and it is also the condition for improving and deepening learning. Learning and migration are inseparable.

One kind of learning promotes another kind of learning is called positive transfer, and the other is called negative transfer. In the study of mathematics, students have the successful experience of learning new knowledge by using the law of migration, and have a strong desire to try to explore their own unknown fields by using the law of migration. For example, when I calculated 45÷5+40÷5 after studying the multiplication and distribution law of the fourth grade, I tried to rewrite the formula to (45+40)÷5, and found that this rewriting was effective, so I thought120 ÷ 4+120 ?

The research of educational psychology shows that knowledge learning is divided into five stages: perception, understanding, consolidation, application and transfer, and the correction of wrong questions belongs to the stage of knowledge consolidation. Ebbinghaus's "forgetting curve" tells us that the process of forgetting is fast first and then slow, and it will not be forgotten at a certain time. For example, fifth-grade students generally don't miss "∫2" when learning trapezoidal area formula, but they usually miss "∫2" when solving application problems with formula in the next exercise class, and students will basically not make this mistake again after correcting it. It can be seen that the law of forgetting is an important reason for students to do wrong questions.