The main purpose of letting children learn mathematics in early childhood is to help them have a preliminary concept of mathematics. The most important thing about the concept of number is to understand the practical meaning of number and master the internal relationship between number and number. Some parents think that the more children, the better, and even take addition and subtraction as the only content to train children's mathematical ability. This kind of understanding and practice is very one-sided. In mathematics learning, we must first learn the number within the total number 10, and correspond mathematics with the number of objects.
Give children 10 pictures, each picture is painted with objects in the range of 1 to 10, and ask children to compare the number of objects with the numbers in the order of 1 to 10.
Let the children read from 1 to 10 in turn. Parents randomly point to a card, cover the number and ask the child what it is. If the child can't answer, let him count the objects (small pictures) and familiarize him with the relationship between number and quantity.
Parents can write numbers on drawing paper for their children to see, and then let them see them in different colors to increase their interest in writing.
The focus is on training thinking.
Addition and subtraction can train children's thinking. However, many parents simply let their children do addition and subtraction, satisfied with the right or wrong answer, but rarely use addition and subtraction to train their children's thinking. This kind of education is one-sided, and the correct way is:
Let children know how to exchange relationships by addition and subtraction.
The exchange relationship is to let children master the exchange of addend and addend, and the number remains the same. Many children know that 2+3 = 5 and 3+2 = 5. Does this mean that he has mastered the exchange relationship? No, because when children calculate the above two formulas, they only regard them as isolated arithmetic problems and don't look at them together. He doesn't analyze the relationship between 2+3 = 5 and 3+2 = 5. Parents just want to help their children establish this relationship. Children can be trained by image method. "Mom gives you 2 pieces of candy, and Dad gives you 3 pieces of candy. How many pieces of candy do you have? (2+3 = 5); Dad gives you three sweets and mom gives you two sweets. How many sweets do you have? (3+2 = 5). "Then let the children think about the relationship between these two formulas. Make children master the exchange law of addition and subtraction, so as to train thinking flexibility.
Learn the reciprocal operation of addition and subtraction and master the reciprocal relationship of addition and subtraction.
Further develop the flexibility and generality of children's thinking, so as to cultivate children's initial logical thinking ability. Give the child three red pens and four green pens. Ask the child how many pens there are. 3+4=7; If you are given four green pens and three red pens, and one is * * *, how many pens are there? 4+3=7; If you take three red pens from seven pens, how many are left? 7-3=4; If you take four green pens from seven pens, how many are left? 7-4=3。 Then let the children compare these four formulas and find out the reciprocal and exchange relationship between them.
Train children's thinking flexibility with a variety of questions
When adding and subtracting children, they can be expressed in different ways. Don't simply use fixed sentence patterns such as "one * * *" and "the rest", so that children can find more than one number. There are two apples in red, light blue is more than red 1 apple, and light blue has several apples. You can also find a known number. There are two apples in Dazheng. There are as many apples in Zheng Xiao as in Dazheng. How many apples do they have?
Gradually establish abstract thinking
The development of children's logical thinking is the premise for children to learn mathematics, but its characteristics make it difficult for children to construct abstract mathematical knowledge. Therefore, with the help of concrete things and images, we must gradually build an abstract logical thinking system in our minds, and we must constantly strive to get rid of the influence of concrete things, so that those knowledge related to concrete things can be internalized in our minds and become mathematical knowledge with certain generalization significance. In this way, the psychological characteristics of children's mathematics learning are transitional. The specific performance is as follows.
From concrete to abstract
Mathematical knowledge is an abstract knowledge, and its acquisition needs to get rid of other irrelevant characteristics of specific things. Children's understanding of mathematical knowledge needs the help of concrete things, which are obtained from the abstraction of concrete things, so it will inevitably be influenced by concrete things. For example, children in small classes can often tell that there are fathers, mothers, grandfathers, grandmothers and themselves at home, but it is not easy to tell abstractly how many people there are at home. When children in large classes learn the composition of numbers, they are also influenced by the concept of equal division in their daily experience. For example, a child thinks that "3" cannot be divided into two parts, "because it is not easy to divide unless one is taken off." This shows that children can't get rid of the specific characteristics of things, thus abstracting the quantitative characteristics. This kind of interference caused by the specific characteristics of things will gradually decrease with their understanding of the abstraction of mathematical knowledge.
From individual to general
The formation of children's mathematical concepts has a process of gradually getting rid of concrete images and reaching abstract levels. At the same time, the understanding of mathematical concepts also has a process from understanding individual specific things to understanding their universal significance. For example, when children don't fully understand the general meaning of logarithm, in the activity of taking things by numbers, children often think that they can only take one card with the same number of objects and correspond it to a math card (or thought card). Only when he really understands the general meaning of numbers will he think about how many cards he can hold, as long as the numbers correspond. For another example, children aged 5-6 just start to learn the composition of numbers, and when they understand the relationship between division and combination, they often stay on the specific things (or things) it represents. Only under the guidance of adults, with the in-depth study of the composition of numbers, can we gradually realize the similarity between some specific things, that is, the numbers they represent are the same, so they can be expressed by the same switching formula. In fact, children also go through the same generalization process for learning other mathematical knowledge.
From external action to internal action
Some people say that children's learning mathematics is a process from "the action of numbers" to "the concept of numbers". This sentence vividly illustrates the process of children's acquisition of mathematical knowledge: from external actions, it is gradually internalized into the mind.
We can often observe that when children finish some math exercises, they are often accompanied by explicit actions. For example, for young children, when counting, they often need to count by hand. With the increase of age, the movements are gradually internalized, and the number of objects within 10 can be directly counted by visual inspection. In large classes, children have a certain ability to internalize movements. For example, children can look at pictures and understand the quantitative relationship expressed in pictures, and an internalized action appears in their minds: increase or decrease. Can add and subtract in 10 according to the abstract action representation of static pictures in your mind. Of course, the formation of children's action representation is based on children's existing experience of addition and subtraction at the action level, which is a generalization and internalization of these experiences and does not appear in their minds out of thin air.
From assimilation to adaptation
Assimilation and adaptation are two forms of infant adaptation. Assimilation is to bring the external environment into one's existing cognitive structure, and adaptation is to change the existing cognitive structure to adapt to the environment. In the interaction between children and the environment, assimilation and conformity coexist, but the ratio of the two will be different. Sometimes assimilation is dominant, sometimes adaptation is dominant, and the two are in a dynamic balance.
In math learning and solving math problems, children also show the characteristics of assimilation and adaptation. For example, when children count and compare numbers, they often judge by intuition or according to the space occupied by objects. This method is sometimes effective, but sometimes there are mistakes. The reason for the mistake is that inappropriate cognitive strategies are adopted to assimilate external problem situations. Although children know that one-to-one correspondence and counting are also methods to compare numbers, they will not consciously use these two methods. Children will not seek new solutions until they feel that the existing cognitive strategies cannot adapt to the problem situation (for example, comparing the number of objects in two rows with the same number but different spatial arrangements). At this time, adaptation began to dominate, and cognitive strategies were changed by one-to-one correspondence or counting points to adapt to the external environment, thus reaching a new balance with the environment.
It can be seen that the interaction between children and the environment, from assimilation to adaptation, and finally to a new balance, is also the process of children's cognitive structure development. However, this process takes place through children's self-regulation, not the result of education.
From the unconscious to the conscious
The so-called "consciousness" refers to the consciousness of one's own cognitive process. Children often lack self-awareness of their own thinking process. The main reason is that their actions have not been completely internalized, and their judgment on things still stays at the level of concrete actions, but fails to rise to the level of abstract thinking. The degree of consciousness of his thinking is related to the degree of internalization of his actions.
For example, when children around 3 years old classify objects, they often disagree with what they say. Many children can judge the same characteristics (such as the same shape) according to their senses and classify them, but they are not consistent in language expression (such as the characteristics of color). Obviously, their language expression is arbitrary and unclear in the process of thinking. Only with their age and cognitive development, and with the gradual internalization of actions, can language gradually play a role. Of course, adults should let children express their operation process in words in activities, and at the same time raise their awareness of their own behavior, which will help children internalize their own behavior.
From egocentrism to socialization
The self-consciousness of children's thinking is synchronous with their socialization. The more children realize their own thinking, the more they can understand others' thinking. When children only pay attention to their own behavior and cannot internalize it, it is impossible to cooperate effectively with their peers, and there is no real communication at the same time. For example, some 3-year-old children classify graphics cards according to their color characteristics. When they see that other children have different classification methods (such as classification by shape characteristics), they will say to others, "You are wrong." Adults asked them what to divide, but they couldn't answer. It can be seen that children are not aware of the basis of their own classification, and cannot consider problems from the standpoint of others and make corresponding judgments.
Therefore, the socialization of children's mathematics learning not only has the significance of social development, but also marks the development of their thinking. When children can gradually think about their own behavior in their minds and have more and more consciousness, they can gradually overcome the self-centeredness of thinking and try to understand their peers' ideas, thus producing real communication and cooperation, and at the same time being inspired by communication and mutual learning.
Contact with daily life
Teaching children mathematics must be connected with daily life. Some parents ask their children to recite formulas, such as "1 plus 1 equal to 2" and "2 plus 2 equals 4" ... This practice goes against children's physiological characteristics and easily leads to children's weariness of learning. Teaching children mathematics is inseparable from concrete objects. Parents should grasp the links in daily life and implement mathematics education. Doing so can not only increase interest, but also be easily accepted by children. For example, when eating, you can ask your child, "How many people are there in the family? How many bowls do you need? How many pairs of chopsticks? " If someone finishes eating, take away a bowl and a pair of chopsticks, and then ask the child to say, "How many bowls are there on the table now? How many pairs of chopsticks? " Shopping allows children to calculate how many things they have bought.
Parents can also make up application questions with their children, so that children can get rid of physical objects and calculate them with appearances. Parents can make up different types of questions, some seek "sum", some seek "difference", some seek "addition" and some seek "addition". For example, "there is a plate with red beans and mung beans, and there are three red beans and two mung beans in it." How many beans are there on the plate? " You can also ask, "There are five red beans and mung beans in a plate, including two mung beans. How many red beans are there? " You can also ask, "There are five red beans and mung beans in a plate, including three red beans. How many mung beans are there? " This application problem can also be compiled into subtraction for children to calculate. "There are five beans in a plate. If you take out three beans, how many are left on the plate? " Combining with specific examples, letting children operate by hands can improve their understanding of addition and subtraction procedures and promote the development of their mental arithmetic ability. In order to stimulate children's interest, children can also be asked to give questions and parents can calculate.