First, the development characteristics of the concept of children's number
Three-year-old Honghong can clearly count from 1 to 10, but once the teacher asked him to count the dolls on the toy (to buy toys) cabinet, he counted them by hand and told the teacher: toys (to buy toys).
Four-year-old Pingping already knows Arabic numerals and knows that the number of objects can be represented by numbers. For example, the number "1" can represent 1 apple, 1 ball, 1 doll, etc. And the number "2" can represent two ... Once, he saw four apples painted on the paper and stamped "4" on it.
The performance of the above two children reflects some characteristics of the formation and development of the concept of the number of children. Although Honghong can count objects with his mouth and hands, he has no concept of total, so he can't say the number of dolls correctly. Pingping's understanding of the meaning of numbers is under construction. He knew that four apples could be represented by four numbers, but he didn't fully understand the meaning of each number representing the number of objects, so he stamped 1 number "4" on each apple. Only by understanding these characteristics can teachers better educate their children.
The construction of children's number concept is a long and complicated process, and it is also a process of continuous development. The whole process can be divided into several stages, and there are differences and connections between them. The formation and development of children's number concept includes the development of counting ability, the understanding of logarithmic order, the conservation of number and the mastery of logarithmic composition.
(A) the development of children's counting ability
Counting is an activity with purpose, means and results. If people want to know the number of elements in a set, they must count them. The process of counting is to establish a one-to-one correspondence between the elements of the set to be counted and the natural sequence. In the process of counting, no matter what order, as long as there is no omission or repetition, the result is always the same. In other words, the result of counting has nothing to do with the order of counting. German and others believe that children must follow five basic principles when counting:
(1) One-to-one correspondence principle, that is, when counting children, one number can only correspond to one object.
(2) Ordering principle, that is, there is an invariable order between numbers (1, 2,3 ...).
(3) Cardinality principle, that is, the value counted to the last number represents the number of elements contained in this set.
(4) the principle of order independence, that is, the number of a set has nothing to do with where to start counting.
(5) The abstract principle, namely the counting principle, can be applied to anything.
Children's counting ability marks his understanding of the practical significance of logarithm and the initial formation of the concept of children's number.
The development order of children's counting ability is: oral calculation, counting by things, telling the total number, and taking things by numbers.
Children aged 3-4 can generally count from 1 to 10, but most of them recite these numbers like nursery rhymes, which have the nature of a jingle, and there is no one-to-one relationship between each number and an object, so children still don't understand the actual meaning of numbers. At this stage, children's oral arithmetic shows the following characteristics:
(1) The average child will only start with "1" and count down in turn. If they are disturbed, they don't count.
(2) Children generally don't count from any middle number, let alone count backwards.
(3) In oral calculation, there is often a phenomenon of missing or repeating numbers.
After the age of 5, many children can count from any one in the middle and then count down, which shows that they have gradually established a stronger connection between numbers. However, children generally can't carry it correctly. Every time they count from 9 to 10, they often make mistakes, often counting from the beginning.
Therefore, oral arithmetic is only mechanical memory, and children's counting is actually a kind of "singing".
2. According to the number of things, children are required to link numbers with the number of objective things on the basis of the number of mouths, and establish a one-to-one correspondence between numbers and things, so that they can count them in unison. Counting by objects is more complicated than calculating by mouth, which requires a variety of analyzers to participate in activities. When children count things and say numbers correctly, they need hands, eyes, mouth and brain to work together. Before the age of 5, due to the hypoplasia of cerebral cortex, inflexible hand-eye coordination and unskilled verbal calculation, there will be various hand-mouth inconsistencies. For example, the mouth of (1) can be counted from 1 to 10, but the hands cannot be located one by one according to the physical objects, but are scattered; (2) Although we can put them one by one according to the order of objects, the number of mouths is random, such as 1, 2, 3, 8, 9, 10, etc. Among them, there are often only the first few and the last few.
The numbers are said in order; (3) Although the mouth and hands can cooperate rhythmically, it is not one-to-one cooperation, that is, not counting one object, but counting two objects, or vice versa.
3. Telling the total number refers to the total number of objects that children can tell after counting. The development of the total number is slower, which requires children to understand the counted objects as a whole, that is, to understand that the last object counted is the total number of objects in this group, that is, to establish a connection between numbers and the number of objects. Being able to tell the total number is the key to the development of counting ability, which shows that children can use numbers and understand their practical significance. Some 3-4-year-old children can count objects correctly, but they often can't tell the total number of counted objects, but just say a number at will.
4, according to the number of objects, that is, take out the same number of objects according to a certain number. This is the practical application of the logarithmic concept. Picking things by number first requires children to remember the number of items they need, and then take out the corresponding items according to the number. Children aged 3-4 can only take out three or four physical objects according to the quantity. Generally speaking, it is not as good as counting the number of objects to say the total number and take things by number.
Children's early counting ability is unstable, and many factors will affect children's counting activities. Research shows that the factors that affect children's counting activities are as follows:
Under the same spatial distribution of objects, the size of counting objects will have an impact on children's counting activities. For example, if a child counts toys (buying toys) and animals with a volume of about 10 cubic centimeter (animal toys (buying toys) are lined up), his range of counting pairs is slightly larger than that of Go players who are also lined up. Therefore, the size of the object that provides points for children should be appropriate.
The spatial distribution of counting objects also has an influence on counting activities. For example, Weiqi players line up in a row, the distance between them is about half a centimeter, and the other one is closely arranged together, so that children score better in the former case and worse in the latter case. If the arrangement of Go players is very irregular, the score of points will be even worse.
The way children count activities will also affect their performance in counting activities. For example, arrange a row of Go chess pieces on the desktop, let the children move the Go chess pieces one by one and count them at the same time; Another method is to let the children count one by one with their fingers; The third method is to let the children take the chess pieces out of the container one by one and put them on the table, counting them. As a result, the counting performance of the first method is better than the other two methods. Because compared with the first way, the second way is more likely to make children confused when counting, while the third way has many and complicated hand movements, so the children are busy taking out the pieces from the container and forget the task of counting.
Presenting and maintaining the same counting objects at the same time is beneficial to children's counting activities, but it is difficult to present and replace counting objects in turn. For example, counting with visual objects is better than listening to the bell. If the child rings the bell and counts at the same time, the result will be lower. At this time, the child focused on ringing the bell and forgot the task of counting.
Therefore, when teaching children to count, we should consider and use the above factors to promote the development of children's counting ability.