Students' learning is a process from ignorance to understanding and never having a meeting. In this process, students of all ages will make mistakes of one kind or another. These are normal and inevitable phenomena. In classroom teaching, teachers should be good at finding out the causes of students' mistakes, screening and using them correctly, so that these "mistakes" become "bright spots" in the classroom and become effective resources for students to acquire new knowledge.

key word

Error causes, error screening, and error utilization

The mistakes made by students in learning are valuable learning resources with special educational functions, which are generated from the learning activities themselves. In class, teachers expect to hear students' "accurate" answers; In homework, teachers expect to see students' "flawless" answers. However, it often backfires. In the process of cognitive development, students will make mistakes at any time, especially in the classroom. Whether students' error resources can be effectively used in classroom teaching depends on teachers. Teachers use ingenious methods to make students reflect on their mistakes and correct them correctly, thus making the classroom more efficient.

First, the causes of students' errors in mathematics classroom

(A) students' understanding of concepts and methods is not clear. Concept is the basic form of students' thinking and an important basis for students to do problems. And students' learning tends to develop towards the trend of "memorizing concepts and formulas". They don't understand the true meaning of concepts and formulas. For example, in the second volume of the fifth grade, "Looking for the Law", the number of different sums is found in the example = total number-box number+1. Students can use this formula to solve a series of similar problems, but if the topic is changed slightly, students will have the problem of rigid application of the formula.

(B) students' knowledge structure is not perfect. Learning is not a simple knowledge transfer, but a process in which students construct knowledge and experience. Students' incomplete knowledge construction often leads to mistakes in learning. For example, in the second volume of the second grade, "A Preliminary Understanding of Diagonal Angle", some students mistakenly think that "the longer the side of the angle, the bigger the angle". Therefore, in teaching, teachers should let students construct "the size of the angle has nothing to do with the length of the side, but with the size of the side fork" in the process of hands-on operation.

(3) Students lack practical life experience. Mathematics comes from and serves life, and the lack of practical life experience often leads to various mistakes of students. For example, in understanding centimeters and meters, a cucumber is 25 (), and many students fill in the word "meter", which is caused by students' inexperience.

Second, teachers' effective screening of classroom error resources.

Psychologist Gayer believes: "Whoever doesn't consider trial and error and who doesn't allow students to make mistakes will miss the most productive learning moment." Indeed, some students' wrong resources have great development and utilization value. But not every mistake students make in class is an effective teaching resource. When some key and universal mistakes are caught by teachers in time and refined into new learning materials for the whole class, and students are guided in time and properly, unexpected results will often be achieved. Therefore, teachers should use keen insight to screen students' mistakes.

For example, in the class of "Compare the size of numbers within 100", after comparing 46 and 32, I asked the students what a good comparison method is.

Health 1: Because 46 is behind 32, I think 46 >: 32;

Teacher: Your idea is really good. You will compare the figures with the "hundred watches" you learned yesterday!

Health 2:46 forties, 32 thirties, of course, forties;

Teacher: That's true. What a great idea you have!

Health 3: I directly look at the tenth number, 46 is the tenth 4, and 32 is the tenth 3, so 46 >; 32;

Health 4: I think it's a number, 6>2, so 46 >; 32;

A student's unintentional words gave me a brainwave. Why not let them test their ideas for themselves? So, I said, "Which of these two children's methods makes sense? Let's try again: please compare sizes 54 and 38. " This time, they began to discuss: if you look at ten, it is 54 & gt48, and if you look at it, it is 48 >; 54. What is this? Next, I asked the children to release the sticks by themselves or dial the counter, so that they could visually compare the sizes of the two numbers in actual operation. After a few minutes, they all felt it. When I asked the student to answer again, he gave me an unexpected answer: I should look at the top ten figures, because 54 has five tens, 38 has only three tens, and it must be five tens. But there are still some students who haven't changed their views. In this case, I didn't repeat this knowledge point in class, but gave individual counseling to several students after class.

A casual remark and a small action of students in class may become effective teaching resources. Teachers should be highly sensitive to these resources, capture and screen them in time, and make them "bright spots" in the classroom.

Second, teachers make effective use of the wrong resources in the classroom.

(A) the rational use of mistakes to enhance students' learning motivation.

Cognitive psychology believes that mistakes are the inevitable product of learning. It is normal for students to make all kinds of mistakes in their studies. When students give wrong answers in their speeches, if the teacher immediately gives a simple "wrong" evaluation, they will correct the students' answers one by one, or personally, and present the correct answers with both hands. In the long run, students are very worried about making mistakes, and even some students have a sense of fear. Many students are afraid of being discriminated against by their classmates, so they dare not speak in class and lose many learning opportunities.

The new curriculum standard also points out that students are the main body of mathematics learning, and teachers are the organizers and guides of mathematics learning. Teachers can't ignore the mistakes made by students in the process of accepting new knowledge in pursuit of "perfect" answers. Then, in order to fully mobilize students' enthusiasm for learning mathematics and make them fall in love with mathematics classes, the first task is to respect students and respect their thinking development process.

For example, in the teaching of the second volume of "Two Numbers Plus Integer Decimal, One Number (No Carry)" in Senior One, I mainly let the students perceive the calculation method in the activities of swinging the stick and dialing the counter, and on this basis, abstract the algorithm of "adding the same number". In fact, many students can already calculate this kind of carry-free addition. In their words, one digit adds one digit, and ten digits adds ten digits. So when practicing, most students can calculate correctly. Some students with poor foundation have encountered difficulties, such as the second set of exercises of "Want to Do" 1: 50+34 and 5+34, which put whole numbers and one digit in front, which has brought them a lot of trouble in their calculation. In order to give students with poor foundation more learning opportunities, I invited a so-called "poor student" to answer. Without thinking, she said, "50+34=84, 5+34=84". Laughter broke out in the classroom. The student blushed at once and bowed his head quietly. Faced with this situation, teachers can't simply say "you are wrong" to students. Excavating the positive factors in students' mistakes can not only protect their self-esteem and enthusiasm, but also help them think boldly. So, I smiled and said, "Hey? The addends of these two addition formulas are not exactly the same. Why are their sums the same? " The student thought for a moment and said, "I made a mistake!" " "

Teacher: Then what do you think is wrong?

Health: 5+34. Add 4 to this 5, and the total is 39.

Teacher: Why should 5 be added to 4 instead of 3?

Health: 5 is in one position, and 4 is also in one position.

Teacher: Oh, it turns out that this five means five ones. Together with four, it is nine ones, and then with three tens, it is thirty-nine. Your analysis is really reasonable! what do you think?

At this time, other children gave her a thumbs up. In fact, it is a common phenomenon that some students with learning difficulties make mistakes in class. Using these wrong resources skillfully in the teaching process can kill two birds with one stone, which can not only enhance their confidence in learning mathematics, but also deepen their impression of other students.

(2) Carefully presuppose mistakes and improve students' critical thinking.

There is an old saying: "Everything is done in advance. If you don't do it in advance, it will be abolished. " According to the teaching content, students' possible mistakes are preset, the teaching content is adjusted appropriately, and some useful contents that are not arranged in the teaching materials are added to enhance the planning and pertinence of teaching.

Listen to Book Two of Grade Two, Three plus Three (No Carry). The focus of this course is to let students experience the exploration process, understand the arithmetic of three-digit plus three-digit (no carry) and master the algorithm, but the difficulty is to develop good calculation habits in the process of understanding arithmetic and mastering the algorithm. The examples in the textbook are arranged as 143+ 126. Students are unlikely to make mistakes when calculating this problem vertically, because both addends are three digits. Then the calculation of three digits plus two digits is not so ideal. The teacher fully presupposed this, so the teacher immediately arranged a judgment question after highlighting "digital alignment":

2 6 3

+ 3 2

5 8 3

Some students think this question is right, others think it is wrong, and there is an argument in class. So the teacher invited a student who thought it was wrong to get up and talk about the reason. The student said: 2 of 236 is 200, 3 of 32 is 3 10, and 3 can't be aligned with 2. After listening to his answer, all the other students gave thumbs up! With the foreshadowing of this question, students' correct rate has been obviously improved when they complete exercises similar to three-digit plus two-digit exercises.

The teacher's preset judgment questions are "wrong questions" that students are easy to confuse. In a limited time, let students find out the true meaning of "number alignment" through identification, analysis, debate and discussion, and let the students who make mistakes find the reasons for their mistakes, correct their own wrong judgments and turn "wrong points" into "bright spots".

(3) reflect on mistakes in time to improve teachers' reflective ability and students' cognitive ability.

Professor Friedenthal, a world-famous mathematician and mathematics educator, pointed out that "reflection is the core and motive force of mathematical thinking activities". "Without reflection, students' understanding level cannot be sublimated from one level to a higher level. "Timely reflection can not only promote students to master knowledge better, but also promote the rapid growth of our young teachers.

In the teaching of "more, less, more, less" in grade one, students' understanding of these concepts is in place and the exercises are completed satisfactorily. It shows that they have a good grasp of the size of intuitive numbers and the numerical order within 100. But an exercise in the exercise book is badly done: there are 40 eggs in the same two baskets. How many apples may there be in a basket? The answers given are 5, 25, 45. Most students choose 45, which fully shows that students lack practical life experience.

The New Curriculum Standard points out that the organization of mathematics content should handle the relationship between process and result, between intuition and abstraction, and between life, situation and knowledge systematization. After class, I reflected in time: students' real life experience and abstract thinking play a very important role in learning mathematics. So, the next day, I brought a bowl of eggs and a bowl of apples into the classroom. The students immediately noticed that the number of apples was less than that of eggs, but not much less. Ask a question: Why? They scrambled to answer, because the apple is big! Yes, why not make our math class full of life? This will also be a great inspiration for my future teaching. In teaching, we should constantly reflect on our own teaching, and take this opportunity to constantly enrich our teaching wisdom and guide students to acquire new knowledge in a more suitable and effective way.

In a word, we will always encounter "wrong" ambush in the mathematics classroom teaching of the new curriculum. Teachers treat students' mistakes from the perspective of resources, presuppose and screen them carefully, make full use of students' mistakes in learning, guide them according to the situation, turn them into important learning resources, and let students make continuous progress in the process of "correcting mistakes", "thinking mistakes" and "correcting mistakes".