Can mathematical thinking be trained? How can I improve my mathematical thinking?

Of course, mathematical thinking can also be trained, as long as you do more problems, master some problem types, and solve the corresponding ideas, you can have a very convenient way to do problems; If you want to improve your mathematical thinking, you can try to do more difficult problems, try to do some problems that can be comprehensively thought about and discussed, which will be of great help to your mathematical thinking practice.

Of course, because I was relatively bad at math before, but then I would think hard every day, and then ask more of my classmates, and my grades would improve by leaps and bounds, so you follow my method.

Mathematical thinking can be continuously cultivated through nurture, and if you want to improve your mathematical thinking, you should think more logically and thinking, and you can also try to do some exercises to improve your thinking.

After many students do a math problem, they often just check it and finish it. But Fang Fang is not like this, after she does a good math problem, she always looks at the problem and thinks about it, to see if she can find the problem from the problem again. Because she did this, she did better than others in math.

Let's give you an example.

Once, the teacher assigned such a math problem: a goldfish bowl with a length of 5 decimeters, a width of 4 decimeters, and a height of 3 decimeters, the depth of water in the tank is 2 decimeters, how many liters of water is in the tank?

Fang Fang quickly listed the equation:

5 4 2 = 40 (cubic decimeter) = 40 (liters).

After answering, she thought about it: why can't the condition of "3 decimeters high" be used? If all the known conditions in the question are used, what should the question be?

This question is very thought-provoking. First, because this question is not to find the volume of the cylinder, the condition of "cylinder height of 3 decimeters" is not used; Second, if this question is changed to find how many liters of water can be held in the tank at this time, then all the known conditions are used, and the equation is: 5 4 (3-2).

Look, isn't this kind of question and answer an extra opportunity for yourself to have a beneficial thinking training?

On another occasion, the teacher assigned such a question:

As shown in the image on the right, the volume of the stones in the glass jar is calculated. Before the stone sinks, the height of the water is 6 centimeters; After the stone sinks into the water, the water rises by 4 centimeters.

She lists the equation as follows: 20 30 4 = 2400 (cubic centimeters). After answering, she asked herself again:

If the equation is as follows, what do you find?

Students, can you?

Look for examples in life

For example, what is the theorem that the sum of the two sides of a triangle is greater than the third side? It is a direct corollary of the shortest line segment in the line between two points. Think of a puppy at the apex of a triangular pond, and if you throw a bone at the other vertices, the puppy will inevitably go one way to pick it up, not both.

Another example is the example of three people playing **: Xiao Ming has a question and wants to ask the old man for knowledge. If you tell it, Xiaopang will call ** twice, Xiaopang will tell Xiao Ming the mobile phone number of the old man of knowledge, and Xiao Ming will directly ask to call ** once.

Compared with the previous one, this example also abstracts the trilateral relationship of the triangle into the relationship between three people, which is the embodiment of abstraction ability.

Question-and-answer discussion

There must be a reason for a good solution! Children generally know how to use this good method, but they rarely think about why this method is good for tease, and even Shansui rarely thinks about when to use this method. This is also why children will always "listen to it, and give it up as soon as they do it"!

Parents can ask their children questions about a good way to do this, mainly in two ways:

1. What is the problem of using this method?

2. What are the benefits of using this method?

For example, children know that factoring is particularly useful, but few know what problems factorization is used in or why it is a good method.

In fact, the reason why factorization is easy to use is that it is essentially a decomposition of the number of polynomials, which is a typical descending method, and descending is the most central problem in algebra! As a result, factorization is frequently used in quadratic and above algebraic problems.

Learn to reflect

The process of reflection is the examination of one's own thought process. Through reflection, we can summarize the problems we have done and find out the commonalities and differences of the problems, so that we can apply them flexibly. To teach your child to reflect, here are two small strategies that can be used:

Teacher system: From the questions done in a week, let the children choose the most impressive topics to be the primary teacher and explain them to parents. In this process, the child should first review the whole process of solving the problem and find out the key points. Secondly, it is necessary to organize the language logically in order to speak smoothly.

Finally, this format also boosts the child's interest and confidence.

"Lazy" system: There are many workbooks that classify topics according to topics or question types, and if this classification is only hard brushing, it will form a "tendency" to solve problems in a routine. You can make an "agreement" with your child that if she tells the common points or even the core ideas and methods of these topics in the same type of topic, she can stop doing more such topics.

Parents who are good at this level of mathematics can even pick their own questions, making it more difficult for their children to identify the characteristics.

Learning taxonomy is to group some things in daily life according to some similarities, such as color, shape, use, etc. Parents should pay attention to guiding their children to find the basis for categorization, that is, the similarities of things. This allows children to pay attention to the details of things and enhance their observation skills.

To understand large groups and small groups, children should be taught some names of relevant groups, such as furniture, animal food, etc. Make your child understand that every group has a certain component. At the same time, children should also understand that large groups contain many small groups, and small groups are combined to form large groups.

Such as animals - birds - sparrows. The concept of solving the order is an important way to train children's logical thinking. These orders can be from largest to smallest, hardest to softest, sweet to light, etc., or the other way around.

You can give him some pocket money, tell him not to use it, keep it first, and spend it all at once when the time comes to buy what he needs, and buy what he likes the most to the greatest extent, so that he can exercise his mathematical thinking very well, and he will know how to distribute this wealth and how to maximize his own interests.

I think it is a long-term and tedious task to train children's mathematical thinking. Because mathematics is used in all aspects of our lives, I look at time, counting objects, etc., all need mathematics. Therefore, to train children's mathematical thinking, I think we should cultivate children in some aspects of life.

For example, let the child know the clock, let the child know that the needle goes to **40 minutes, and feel how long it is 10 minutes. As parents, we must also spend more time with our children, treat it as a game, and don't let our children learn boring in mathematics.

Let children get in touch with some math books, including math storybooks, do some thinking exercises, and appropriately increase the difficulty of doing problems, which can exercise children's thinking skills.

First of all, to cultivate his interest, you can let him do more interesting math problems, these math problems can not be homework problems, to make them interested in mathematics, secondly, you can guide, for a math problem embodies what ideas, to explain to them clearly, not just the answer.

Children's mathematical thinking skills can be trained in the game, and they can usually give or play some cards. When my daughter was very young, others taught her children to know fruits and vegetables and animals, and I taught her to distinguish different colors and shapes, which will undoubtedly exercise her logical thinking skills.

I think the core thinking of mathematics is logic.

No matter what you do, you have to have a cause and effect, what is the reason, I want to do it, and what result I will achieve by doing this. Or think about it the other way around, what is the reason for such a result? This is a very simple logical thinking.

But what I want to say is that this does not improve a person's math score, if you want to improve your math score, you have to do more practice problems, and finally form a conditioned reflex, not mathematical thinking.

I think the main thing to cultivate children is to do more types of problems, and in the process of doing problems, summarize and summarize and find out the rules, which is the key to cultivating mathematical thinking!

At the latest, from the kindergarten class, I should buy some books on children's logical thinking problems and insist on doing them, step by step from simple to complex, and exercise my thinking ability. The more you use your head, the more alive it becomes.

Mathematical thinking training methods are:

1. Multiple solutions to one problem, exercise children's variant thinking.

Symmetry is a very important type of variant thinking. Symmetrical thinking can often solve a lot of problems. To take a real-life example, a Japanese monosodium glutamate manufacturer held an in-house seminar for a period of time when profits were not rising.

At the meeting, many methods were proposed, such as reducing costs, but none of them were adopted because the effect was not obvious.

Later, when conducting consumer research, a housewife said that MSG is bottled, and there are many small eyes on it, which can increase the size of the eyes.

This suggestion was implemented, and it worked very well. In fact, employees consider problems from the source of production, while housewives consider problems from the consumer side, which is the symmetry of thinking.

2. Solve multiple problems in one and exercise inductive thinking.

There are actually only a few mathematical methods used in each grade. It is often possible to use the method of solving multiple problems in one way to guide students to figure out a certain mathematical method, for example, this lesson will only talk about equation ideas, and the next class will talk about another topic.

3. Give lectures to students from the perspective of development.

In other words, it is necessary to use the perspective of development to give students a lecture, or this old question: 1 2 + 1 4 + 1 8+...+1/256。Students can be encouraged to use the method of general scoring to do it, and in the process of doing it, it can be extended to the knowledge points learned in high school, such as equal difference and equal ratio number series.

Children will learn easily later on.

4. Explain to each other and collide with the spark of thinking.

One student said, "My math grades are based on lectures. Because I am patient and good-tempered, many of my classmates will ask me questions, and in the process of explaining, I gradually found that my knowledge has been consolidated and my thinking ability has improved. ”

In addition, it is also very important to argue with classmates who are at a similar level or slightly higher than your own level about what you have mastered or what you have not mastered, and it will often achieve twice the result with half the effort, and even the knowledge learned through arguments is deeply understood and unforgettable.

5. Innovative methods.

Innovative thinking refers to the thinking process of solving problems in a novel and original way, through which the boundaries of conventional thinking can be broken through, and the problem can be thought about in an unconventional or even unconventional way and perspective, and a unique solution can be proposed. It can be divided into four types: differentiation, exploratory, optimized and negative.

6. Systematic approach.

Systems thinking is also called holistic thinking, and systematic thinking refers to having a systematic understanding of the knowledge points involved in specific topics when solving problems, that is, to analyze and judge what knowledge points belong to the topic first, and then recall what types of problems are divided into and the corresponding solutions.