How to cultivate children's mathematical thinking and habits?

How to Cultivate Children's Mathematical Thinking and Habits

Mathematical ability has two aspects, one is the ability to calculate and the other is the ability to think.

Computing ability is a low-level ability. Emphasis on memory, proficiency (complex operation requires some skills),

Thinking ability is an advanced ability, which emphasizes thinking and reasoning with the help of abstract digital symbols and concepts.

Computing ability is also more important for primary school students. This topic will be discussed later. Today, let's talk about the cultivation of thinking ability.

The basic skill of mathematical thinking is counting. The sound, shape and meaning of each number should be clearly stated.

It is not enough to count from 1 to 9, but also know the specific number corresponding to each number.

After this, you can enter the study of addition.

For adults, we see the equation "3+5=8", combined with our life experience,

It is easy to concretize this abstract equation into: three XX plus five XX is eight XX.

Further concretization will lead to:

Three bananas plus five bananas equals eight bananas.

Three horses plus five horses equals eight horses.

Three monkeys plus five monkeys equals eight monkeys.

If the number is replaced, for example: 5+6= 1 1. You can produce countless concrete expressions.

The meaning of mathematical symbols is a high generalization of infinite concrete things. Although seemingly abstract, the source is concrete.

And mathematical thinking is to express all kinds of concrete things and their relationships with abstract digital symbols.

It is not difficult to exercise children's thinking. The mathematical application problems that children usually do are essentially a kind of mathematical thinking training.

Parents can consciously write application questions according to the above principles to train their children's mathematical thinking, such as:

Three monkeys plus two monkeys, how many monkeys are there?

There are three monkeys in the cage and two others. * * * How much? (Although the word "plus" is not mentioned, it hints at this idea. )

I have two pens, and Aunt Zhang gave me three more. How many do I have now?

Spiders have eight legs, and centipedes have 100 legs. How many legs does a * * * have?

I walked for ten minutes in the morning and twenty minutes in the evening. How long have I been gone?

If the child can't answer, let the child count with some physical objects. In this process, the most important thing is for children to list mathematical expressions such as 3+2. If a child can list expressions like 3+2 instead of 3-2, it means that he will think with mathematical thinking. As for whether 3+2 is equal to 5 or 8, this is the problem to be solved by the operation. The process of calculating formulas, similar to drawing drawings by engineers, is a kind of advanced thinking activity, while the answer to calculating 3+2 is a kind of low-level thinking, similar to a kind of manual labor. This is the difference between mathematical thinking and operation. We must make clear this difference, and don't neglect the cultivation of thinking ability because of too much emphasis on computing ability.

If this step is successfully completed, the children can ask their own questions in turn. For example, give the child an equation: 2+3=5, and ask the child to make up a topic similar to the above. This process is from concrete to abstract, and then from abstract to concrete. No matter how changeable people's thinking is, it is inseparable from this basic process.

When children compile topics, they exercise not only mathematical thinking, but also language ability, logic and divergence of language. The more topics a child can make up, the more "inventory" he has in his mind. If your child can't make up several questions, you don't have to worry. Maybe you didn't give your child enough "input". You still have to fill a lot of questions for your children and try to improve their language ability.

Say addition first and then subtraction.

Subtraction training is more abundant than addition training. Taking the equation "5-3=2" as an example, the following thinking training questions can be designed:

I have five apples, I ate three, how many are left?

He has three pens and I have five pens. How many pens does he have less than me?

I have three pens and he has five pens. How many more pens does he have than me?

There are five seats in the car, and three people have already taken them. How many people can we take?

My home is five miles from the station. I have walked three miles. How many miles do I have to walk?

After you have given the question, let the child work it out by himself. It is easy to see whether the child can understand the true meaning of this mathematical expression. Pay attention to these red words. Behind these words is a mathematical thinking. You should summarize more and summarize more. The more comprehensive you summarize, the deeper and more comprehensive your child will understand these expressions.

It is a study habit that I have developed for many years to test myself by giving questions.

Not only science can be studied in this way, but so can liberal arts. Only by knowing ourselves and ourselves can we be invincible.

In the cultivation of all kinds of thinking ability, the cultivation of creativity is the most difficult, because there is no way to imitate in advance, so you have to come out by yourself. And this problem-solving thinking ability is relatively easy to cultivate. Because you can understand and simulate the questioner's thinking by studying his thinking mode. It's like playing cards. You know his cards. How can he beat you?

Although I only gave a simple example, you should know that any complex topic is changed from the simplest one, and there is nothing new under the sun.

If you feel that your ability to solve problems is not good. Then, you can find children's textbooks, problem sets and simple Olympic math problems, and collect ready-made problems in them. Come along. Then draw inferences and improvise according to the actual life of the child. For example, make up the corresponding topic in the supermarket, make up the corresponding topic in the zoo and make up the corresponding topic at home. If you can be flexible and give your children questions at will, it will actually become an interesting intellectual game. If learning becomes a game, will children still complain?

It doesn't matter if the child's thinking ability is insufficient and he doesn't think it's fun enough. You can bring some physical objects, such as toys, chess pieces, poker, small dolls and various teaching AIDS, and talk from door to door. Foreign teachers teach children math just like playing house. Look at the picture below These teaching AIDS are very common in foreign countries, not only for fun, but also combined with the cultivation of mathematical thinking.

How to cultivate children's mathematical thinking ability? How to cultivate children's mathematical thinking ability? How to cultivate children's mathematical thinking ability?

Many children are good at math in the lower grades, but not in the middle and upper grades. The reason is probably that calculation is more important than thinking, results are more important than process. Because junior students despise thinking training, when senior students have more application problems, the weakness of insufficient thinking is exposed. Therefore, thinking training should be carried out from an early age.

In addition, as can be seen from the above explanation. Chinese ability and mathematical thinking ability complement each other. The stronger the child's language understanding ability, the better the understanding of the topic will be. Similarly, if you can insist on training your children in mathematical thinking, their Chinese understanding ability will also be improved. In fact, every subject has something in common, and there is no absolute barrier.