Especially in primary schools, math scores can't explain children's math thinking or math ability. Good grades can better show that children are highly cooperative and willing to put the teacher in. Poor grades in themselves will not have a devastating impact on children's learning. However, because of poor grades, under the current single evaluation system of education, parents are extremely anxious about their children's grades, and all kinds of negative labels attached to their children have a fatal impact on them, which will make them believe that they are not learning materials, which is untrue.

Z, a fifth-grade student, failed in math and came to me for counseling this winter vacation. He doesn't know much about what happened last semester in grade four. However, it's really not his fault, maybe it's just the way the teacher explained in class, which failed to make him understand well. In the textbook of Beijing Normal University, negative numbers appeared in the fourth grade (People's Education Edition textbook, negative numbers began in the seventh grade, that is, the first grade). If the teacher fails to explain in a way that the child can easily understand, it will only make the child look confused. Z students have no idea what a negative number is.

I asked my classmate Z, "Have you ever seen negative numbers anywhere in your daily life?" He shook his head.

I gave a hint: "Do you remember the floor number in the elevator?"

Z immediately remembered and said, "Yes-1."

I said, "Yes, what does this-1 mean?"

Classmate Z said, "It's a parking lot."

"Why is the parking lot-1?"

Classmate Z said, "Because it's down there."

I said, "Yes, because it's down there." Then I drew the floors, the ground 1-7 floors and the underground 2 floors. Let Z mark-1 where the floor is. He marked it correctly. I asked him if he had seen the elevator on the second floor, and he said he had seen it in Yicheng. Then I asked him to mark the location of the second floor, and he also marked it.

I asked, "Why do you think there are negative numbers?"

Classmate Z thought quietly for a while and said, "Because positive numbers are not enough."

I almost jumped up. I am surprised that Z's little brain is still very good, at least it is enough for learning mathematics.

After a pause, Z asked, "Teacher, what is the number of 0?"

I am even more excited: "Good question! What is 0? What do you think it is? "

Classmate Z thought for a moment and said, "It's not positive or negative." I agree.

I pointed to the floor on the whiteboard and said, "Here, the ground is positive and the ground is negative, so the meaning of positive and negative is opposite. Now you can understand, if earning 80 yuan is +80 yuan, then spending 20 yuan is positive or negative? "

Classmate Z said, "It's negative, -20." This is an exercise that he couldn't do before.

From the cognition of negative numbers to the final practice, these intermediate processes, if the child does not have the savvy to achieve fluency, and then the teacher does not help the child straighten out the intermediate process as I discussed above, the child who listens to irrigation is estimated to be able to recite the conclusion directly. Do the problem correctly; There is also a kind of child who, like classmate Z, can't move forward without understanding. In junior high school and senior high school, children who recite conclusions will eventually collapse in math learning; On the contrary, if a child like Z doesn't lose interest in learning because of his grades, he is likely to overtake with the development of his thinking ability and understanding ability.

Today, we are going to talk about fractions, starting from the meaning of fractions and also from the addition and subtraction of fractions. While smoothing the addition and subtraction with the same denominator, classmate Z asked himself a question: "Teacher, if the denominator is different, such as 5/8- 1/7, how to calculate such a problem?"

This is another exciting jump! A child who really enters the learning state, his brain is open, and he will be curious about the unknown himself! Classmate Z was so excited that I praised him. Then he began to solve the "difficult problem" he put forward.

……

Recording some clips of tutoring children in winter vacation, the deepest feeling is: no matter teachers or parents, don't judge children's ability arbitrarily by their achievements, and don't destroy their learning motivation because of our limited cognition. No matter whether Z's grades progress fast or slow, the most precious thing is that he saw many advantages of himself in my class and realized some valuable abilities he had. Good grades may not win a child all his life, but positive evaluation of himself and self-confidence from the inside out will definitely help him face the ups and downs in his life journey! Teaching and educating people is like this.