However, this college student is very bookish and thinks that this teaching method will only hurt children's mathematical thinking. Therefore, every time he meets a new question type, he will stick to the principle of "breaking the jar and breaking the fall" until the child understands it. As a result, the college student teacher was complained by his parents that "the progress was too slow" and was eventually laid off.
Parents' anxiety is understandable. After all, if you only look at the results of short-term exams or competitions, it must be that children with more learning questions have better grades. However, these parents, who are complacent because of their good grades, did not expect that these scoring learning methods are destroying their children's mathematical thinking, which is tantamount to drinking poison to quench their thirst.
The most typical example is the problem of "Venus height" in this year's college entrance examination mathematics paper. This is entitled the fourth multiple-choice question. Judging from the distribution of test papers, it was originally a "sub-topic". However, it has caused countless candidates to vomit afterwards, just because such materials and questions have never been seen, and they have never recited its "problem solving steps."
If learning the steps of solving problems is like building steel bars in a tall building, then mathematical thinking is the foundation of a tall building. The higher the building is built, the more it needs a solid foundation. But have parents ever thought that the math exercises you asked your child to do when he was "laying the foundation" in elementary school may be destroying his math thinking?
1, brush questions, recite questions, and turn children's brains into "assembly line workers." I remember helping my eldest son analyze the math test paper in the third grade. I was surprised to find that some children did it right, but they couldn't say why. Only by careful understanding can we understand that teachers teach many "skills" to solve problems in order to make children get better test scores, but ignore the thinking of solving problems.
For example, "on a 5-meter street, plant a tree every other meter, and plant both ends." How many trees can a * * * plant? " For such a problem, the teacher will tell the child that if you plant two plants, you will add one, and if you plant a tree, you will not add it. Children don't know the reason, just follow the teacher's formula and use these formulas when they encounter problems. Because I don't understand it at all, of course, I often recite "plus one, MINUS one" and the topic is wrong.
In this mode, the thinking function of the brain becomes an "assembly line worker". Whenever a "question type" floats by, the "part" of the problem-solving method is extracted and installed. This is the working state of the brain when the child brushes the questions every day. Except for a small part of the brain that needs to be used for "assembling parts", other areas are in a "inhibition state".
The longer this state is maintained, the less active the suppressed area of the brain is, and the child will not think, but present what we often call a "learning stupid" state.
Countermeasure: It is better to let the children say it ten times.
Every week or two, I let my child be a little math teacher. I will help my children prepare some typical math problems (especially those that children often make mistakes when checking their homework), and ask them to be teachers and give lectures to me as a student.
Studies have shown that children can only learn 60% knowledge through listening, reading and practicing, and they must master more than 90% knowledge if they want to speak out. In the process of explaining, children have a deeper understanding of the topic.
Not only that, children should make a topic clear, not only have a deep understanding of the topic, but also organize the language order. This is the best way to train children's logical thinking ability, and logical thinking is also an important part of mathematical thinking.
Tips:
Let the children prepare a small blackboard and try to simulate the state of the classroom during class. Parents must take off the mask of authority, sit on a small bench and become primary school students. Of course, it would be more convenient to have a younger brother and sister of the same age at home. The lower the posture of the "student", the stronger and more relaxed the child's self-confidence. Only in this way can he show a practical level of thinking.
2, the pursuit of difficult problems, Olympiad, may make children completely "insulated" from mathematics. A friend saw that all the children around him had gone to learn Olympic Mathematics, and took his second-grade children to an Olympic Mathematics class. As a result, after listening to the class for the first time, the child cried because he didn't understand it at all. As a result, the teacher of the Olympic math class said that it was normal not to understand, so parents should take notes and go back and tell their children several times. ...
After more than a month's persistence, this friend adopted my suggestion to stop the child from "suffering". This more than a month's study of Olympic mathematics has not helped children improve their math scores.
The ancients said that "teaching students in accordance with their aptitude", every child will be enlightened sooner or later, there is really no need to aim too high. Blindly increasing the difficulty will not only undermine children's self-confidence, but also make parents miserable.
Xiong Bin, head coach of China Olympic Mathematics Team, once asserted that only 5% of children are suitable for learning Olympic Mathematics. Forcing unsuitable children to learn Olympic Mathematics can not only improve their mathematical thinking, but also encourage their weariness of learning and make them completely isolated from mathematics. When children hear the word math, they hate it. What about mathematical thinking?
Countermeasures: It is better to lay a solid foundation than to pursue difficult problems.
My friend found an experienced math teacher to help the children make up lessons. After chatting with the child for a while, the teacher asked her a few questions and said meaningfully: It is rare to see a child not "destroyed" by the Olympic Games. Under the guidance of this teacher, the children's mathematics has made remarkable progress, and their grades have rapidly increased from the middle and lower reaches of the class to the top ten.
Teacher Gao didn't let the children brush the questions, nor did he make it difficult for them to learn. She just makes sure that everything in the class is understood clearly. What are the concepts, connotations and practical problems of multiplication and division?
The teacher took a lot of "Go", averaged the score over and over again, counted it several times or put a square on the chessboard. Children understand the practical problems solved by calculation while doing it. Strange to say, many problems are solved by children who understand multiplication and division itself.
The definition of mathematical thinking in Baidu is: the way of thinking to solve practical problems with mathematics.
The cultivation of mathematical thinking should start with practical problems that can be seen and touched. When a child understands chess pieces by playing with his hands, his brain begins to abstract these concrete objects into concepts such as points, lines and numbers, which is the formation of mathematical thinking.
Tips:
In the study of mathematics, letting children do more work can activate the left and right hemispheres at the same time, make children's thinking more flexible and agile, and deepen their memory. When choosing "teaching AIDS", use whatever you have at hand. My child is a "car fan", so I always use his car for demonstrations.
I remember a high school exam, when the whole class was brushing questions, and the top three students in mathematics were reading math textbooks carefully. Only by brushing questions, cultivating mathematical thinking and laying a solid foundation can children learn mathematics once and for all in the future.