Children in the preoperative stage can only think through appearances, and the preoperative stage can be divided into two periods:
Pre-concept period (1), about 2 ~ 4 years old. At this time, symbolic associations began to appear, and it was found that some things could be represented by others. At the same time, there are internal forms of reproduction: imitation and symbolic games.
(2) intuitive thinking period (pre-logical thinking period), about 4 ~ 7 years old. Children will respond to superficial phenomena and say that irrelevant things are cause and effect. The outstanding feature of this stage is that self-centered thoughts and thinking are intuitive, universal and irreversible.
In real life, children in the early stage of operation have entered kindergartens and preschool classes, and they are exposed to all kinds of things and encounter all kinds of problems every day. These problems include not only the knowledge of number, quantity and shape, but also the concepts of space and time. Through comparison, analysis and synthesis, abstraction and generalization, judgment and reasoning, we can design a variety of sensory and perceptual materials to help children, so that their perceptual knowledge can gradually reach rational knowledge and develop into specific operational stages. In this process, children's logical thinking, observation, attention, memory and spatial imagination have all been developed.
In family education, dictation is one of the most common ways for parents to teach their children to count. But this kind of verbal calculation has the nature of "jingle", that is, it can be done orally, but it does not necessarily understand the practical significance of counting. In fact, children must master cardinal number, ordinal number, adjacent number, the composition of number and the conservation of number, which indicates that children have initially formed the concept of number.
Children's counting activities mainly include the following aspects:
(1) verbal ability, that is, the ability to say numbers in natural order.
(2)? One by one, according to the number of objects.
(3)? Grasp the meaning of the total, that is to say, the last counted number represents the total number of counted objects.
At the same time, the concept of logical thinking plays an important role in children's understanding of logarithm and develops with it.
The logical concepts that play a role in the formation of the concept of numbers are:
(1) Matching: The simplest and most direct method to compare object sets.
(2) One-to-one correspondence: the logical concept of determining the same amount through one-to-one correspondence.
This uncountable comparison is a prior concept. One-to-one correspondence is a basis for understanding logarithms.
(3) Comparison: Correlate objects.
(4) Sequence (serialization)
? When counting objects, children must consider them in a certain order to ensure that each object is counted only once.
(5) Class contains
? The relationship between "part" and "all" is the basis for understanding that number is a relationship.
(6) conservation of quantity
? That is, when judging the number of objects, we can realize that the number of objects remains unchanged regardless of the size and spatial arrangement of objects.
(1) one-to-one correspondence, comparing the number of objects.
Help children start with the comparison of two objects, observe the differences between them, and then gradually increase the number of comparisons. In the practice of distinguishing numbers, children should be guided to compare the numbers of two groups of objects in a one-to-one way.
At an appropriate time, increase the changes of some attributes of objects, so that children can understand that although the attributes are different, they have no effect on numbers, and deepen their understanding of the actual meaning of logarithm.
(2) practice oral calculation ability.
In the first step, some patrolling elves appear in the picture from time to time, and the children catch them by clicking "grab" (at this time, the elves stand still), accompanied by voice counting. This step helps children to establish the relationship between objects and numbers and deepen their ability to read and recite natural numbers by memory and sequence. For children with strong ability, you can add conditions to distinguish colors, such as "catching" only the red elf.
Step two, let the children count the number of elves on the screen again and click on the numbers on the sign. Guide children to grasp the meaning of the total, that is, the last number, that is, the total.
Step three, a small fork appears on the screen. Order the elf again with a fork. When the elves disappear, count the number of elves again. Experience the integral again. (Figure omitted)
The fourth step, for children with strong ability, you can add color conditions while practicing counting. For example, catch red and yellow elves and count them.
(3) the practical significance of perceptual cardinal number
Guide children to count the number of fruits one by one regardless of the color, size, shape and arrangement of objects, and understand the practical significance of the number.
(4) Conservation of perceptual number
The number of children's observation and experience is not changed by the change of external characteristics and arrangement, but the number of perceptions is conserved. For example, which ovens have six cookies.
(5) Combination and decomposition of numbers
The decomposition and combination of numbers is an intuitive training in the process of adding and subtracting thinking. Children can learn that a number can be divided into two parts, and the two parts are combined to form this number, and the relationship between the total number and the partial number can be mastered.
The decomposition and combination training of numbers emphasizes the thinking process. In the process of grouping, children may "take care of one thing and lose another", which can guide children to split and redistribute the "walnuts" that have been grouped.
(6) Comprehensive thinking practice of number and quantity
The following exercise requires that the spools be arranged from less to more. This is a comprehensive thinking exercise based on children mastering the sorting, counting and conservation of numbers at the same time.
To be continued, please see "Reflections on the combination of children's mathematical enlightenment and logical thinking in the pre-operation stage (II)"