In the process of middle school students learning mathematics, such mistakes often occur, and the simpler the mistakes, the easier it is to make. Some mistakes are puzzling even to the students themselves, and they are often puzzling as teachers. In the end, it can only be summed up in four words: "too careless and not serious". In fact, the reasons why students make mistakes are influenced by non-intellectual factors such as study habits and interests. Non-intelligence factors are an internal driving force to guide and promote children's learning and growth, and play a role in promoting and orienting the development of children's intelligence and ability. It is also related to students' metacognitive ability, and the influence of individual metacognitive knowledge on students' learning focuses on students' sense of self-efficacy. Compared with students with low self-efficacy, students with high self-efficacy can show higher learning strategies and monitor their learning results better. It is also related to students' thinking ability. Students' thinking is easily influenced by "stereotypes". Often preconceived things have a positive side, that is, "positive migration", but also have a negative impact, that is, "negative migration."

Through research, we can improve students' cognitive level, attach importance to the role of "first perception" in students' thinking, weaken the influence of "stereotype", improve students' study habits, and thus achieve the goal of cultivating students' ability to correct mistakes in mathematics.

"Mistakes are the correct guide and the ladder to success." Teachers can study the causes of students' mistakes, make a fuss about them, make students turn "waste" into "treasure" and use the wrong resources to do things for teaching. Below, the author talks about some experiences based on his years of junior high school mathematics teaching practice.

First, the reasons for junior high school students' mistakes in solving problems

Students solve problems successfully and correctly, which shows that they have not been disturbed or overcome interference when analyzing problems, extracting and applying corresponding knowledge. If we can't eliminate the interference of the above links, there will be mistakes in solving the problem. As far as junior high school students' problem-solving errors are concerned, the interference that causes problem-solving errors comes from the following two aspects: one is the interference of primary school mathematics, and the other is the interference of knowledge before and after junior high school mathematics.

(A) the interference of primary school mathematics

In junior high school, some knowledge formed by students' learning primary school mathematics will hinder them from learning the basic knowledge of algebra and make them make mistakes in solving problems.

1. Error in examining questions is what people often say is carelessness. The main manifestations are: ignoring the meaning of solving the problem, or not carefully examining the problem, ignoring or omitting some special and implied conditions, or being influenced by thinking set, misinterpreting the meaning of the problem and making mistakes in solving the problem. In primary school mathematics, the result of solving a problem is often a definite number. Affected by this, students appear confused and wrong when answering the following questions. The original problem is this: there are a seats in the first row of the audience, and each row in the back has more 1 seats than the previous row. How many seats are there in the second row? What about the third row? Let m be the number of seats in the nth row, then what is M? When a=20 and n= 19, find the value of m. When students answer the above questions, they are influenced by the number determined by the results, and confuse the expression of m with the value of m, exposing the traces of the above interference in the thinking process. For example, some conclusions formed in primary school mathematics are also valid without learning negative numbers. In primary school, it is considered that the sum of students' logarithms is not less than any addend, that is, a+b≥a, but it is also possible that A+B < A after learning negative numbers. In other words, if you are used to discussing problems in a non-negative range, it is easy to ignore the situation that letters take negative numbers, leading to mistakes in solving problems. In addition, "+"and "-"have long been used as addition and subtraction symbols. Students are used to treating 3-5+4-6 as 3 minus 5 plus 4 minus 6, while junior high school students need to treat the above formula as the sum of 3 minus 5 plus 4 minus 6. The stronger the impression of habitual views, the more difficult it is to establish new ones.

2. Calculation class error. In addition to careless reasons, it is often unclear calculation or improper selection method, which is also the direct cause of inaccurate calculation or error. Students are used to solving application problems with arithmetic, which will interfere with students' learning algebraic methods and solving application problems with equations.

For example, find the meeting time of two trains (the distance between Station A and bilibili is 360km, the local train leaves from Station A at a speed of 48km/h, and the express train leaves from bilibili at a speed of 72km/h, and the two trains leave at the same time in opposite directions. How many hours did they meet? ), the listed "equation" is x=360/48+72. From this, we can see the traces of students' persistence in arithmetic solution. Junior high school needs to list the equation of 48x+72x=360, which shows students' mastery of the equal relationship between known numbers and unknown numbers.

In short, in the junior and senior high schools, the reason why students make mistakes in solving problems can often be traced back to the influence of primary school mathematics knowledge on their new knowledge. Sorting out the differences between new knowledge (such as numbers represented by letters), range (positive numbers, 0, negative numbers) and methods (algebraic sum, algebraic methods) and old knowledge (specific numbers, non-negative numbers, addition and subtraction operations, arithmetic methods) is helpful to overcome interference and reduce errors in the initial stage.

(B) the interference of knowledge before and after junior high school mathematics

With the development of junior high school knowledge, junior high school mathematics knowledge itself will interfere with each other.

For example, when learning the subtraction of rational numbers, the teacher repeatedly stressed that subtracting a number is equal to adding its opposite number, so the symbol "-"in front of 7 in 3-7 is a negative sign, which left a deep impression on the students. After learning algebraic sum, we should emphasize that 3-7 is the sum of positive 3 and negative 7, and "-"has become a negative sign again. Students can't help wondering whether "-"is a negative sign or a negative sign. If this confusion can't be eliminated well, students will make mistakes in operation.

For another example, understanding the solution set of inequality and applying the basic property 3 of inequality are the difficulties in inequality teaching. Students often make mistakes here, because both sides of the equation can be multiplied or divided by any number, and the solution of the equation is a number. Facts have also proved that comparing the related contents of inequality with the corresponding contents of equality and equation is helpful for students to understand the similarities and differences between them and learn the contents of inequality well.

The performance of students in solving single and comprehensive problems can also explain this problem. Students need to extract and use less knowledge when answering single questions, so they are less disturbed by knowledge and less likely to make mistakes. However, when encountering comprehensive questions, the choice and application of knowledge are greatly disturbed and prone to mistakes.

In short, the interference of this kind of knowledge will often make students confused when learning new knowledge, and make mistakes in choosing or using wrong knowledge when solving problems.

Second, the training of junior high school students' error correction skills countermeasures

1. Educate students to have good active study habits. Educating students to have good active study habits is a feasible way to reduce students' homework mistakes and educate students to correct math mistakes. Teachers should fully realize that mastering basic knowledge (knowledge is the summary of human production and life experience) is the key for students to learn mathematics well. Suppose a student makes even a little mistake in these basic knowledge (knowledge is the summary of human production and life experience), we should guide him 100% to make it clear. In addition, efforts should be made to minimize mistakes when reviewing questions. Teachers start with educating students to examine questions carefully, list all the questions or conditions they know in the form of lectures, and then select useful conditions, and then see what conditions are missing or hidden. When the necessary conditions are ready, you can choose the appropriate methods to answer them.

2. Master arithmetic and improve the correct rate. Many calculation problems make students easy to make mistakes. In mathematics classroom teaching, the accuracy of operation is the basic requirement of operation skills, and the operation (actual behavior) is required to be carried out slowly and systematically according to the operation requirements of calculation and topic. The concepts, formulas and rules applied in the whole operation process should be accurate, and finally the accuracy of the operation results can be guaranteed. As long as there is a problem in a certain link in the whole operation process, the whole operation will go wrong.

3. Carefully organize teaching to reduce the difficulty of learning mathematics for students with learning difficulties. Teachers should carefully explore teaching materials (consisting of information, symbols and media, which are used to impart knowledge, skills and ideas to students) and choose reasonable teaching methods according to the main contents of teaching. In view of the fact that students with learning difficulties often make mistakes, teachers should highlight key points, disperse difficulties and reduce the difficulty of learning mathematics for students with learning difficulties. This requires teachers to have a strong ability to master teaching materials (consisting of three basic elements of information, symbols and media for imparting knowledge, skills and ideas to students) and to integrate teaching materials (consisting of three basic elements of information, symbols and media for imparting knowledge, skills and ideas to students). For example, in the teaching of "three-line octagon", it is difficult for students to find out congruent angles, inner angles and inner angles of the same side because of the complicated graphics. It can be concluded that the letter "F" is in the same angle, the letter "N" is in the same inner angle, and the letter "L" is in the inner angle.

As a math teacher, in a sense, correcting a mistake is more important than imparting a new knowledge (knowledge is the summary of human production and life experience). Moreover, we should also pay attention to the principle of friendship and harmony. No matter how to correct mistakes, students should not feel that the teacher is very picky, which will lead to disgust and unhappiness. In short, in order to improve the effectiveness of mathematics teaching, in order to let every student get different degrees of development, let us pay attention to students' mistakes and make our mathematics teaching wonderful!