Observation, as a purposeful and conscious perceptual activity, runs through the whole process of children's mathematical operation activities and is the premise of children's mathematical operation activities. Observation in operation contains two meanings: on the one hand, it is the life experience observed by children in early activities, the operation mode of others, the demonstration of teachers and so on. To provide rich perceptual experience for children's new operation activities, so as to ensure the smooth progress of operation activities. On the other hand, children's operation activities must be intervened by observation, including observation of operation materials and observation of peer operation process and results. The depth of this observation will also affect the operation of young children. For example, in the classification activities, the teacher provides a variety of bottle caps for children to classify in as many ways as possible. After accepting such a task, children should first observe the bottle caps, see what characteristics they have, think about "what standards to use for classification", and then operate while observing and complete the classification requirements. If children don't observe the materials carefully enough, they can't do multi-angle classification. At the same time, after completing their own operations, children will also observe the operations of children around them to see how other children's operations are different from their own, thus triggering their own new classification methods.
Observation provides rich perceptual experience for children's operation, which requires children's constant observation, and operational activities promote the development of children's observation ability.
2. Running memory
Memory is a process in which the human brain remembers, maintains and restores past experiences. According to the purpose of children's activities, memory can be divided into intentional memory and unintentional memory. The intentionality of memory is an important aspect of children's memory development and the most important qualitative leap in children's memory development.
(1) Mathematical operations need the intervention of memory. Mathematical operations are not random operations, and all mathematical operations have certain operation rules and requirements. In mathematical operation activities, teachers transform what children want to learn into specific operation rules, operation requirements and operation objectives, and children learn these contents by observing operation rules and realizing operation objectives in operation activities. Children's memory of operating rules and requirements is intentional or unintentional. When the teacher announces the operation rules, the children will actively and consciously concentrate on the operation activities, and consciously recall these rules during the whole operation activities, thus guiding their own operations.
Children also show obvious intentional memories in mathematical operation activities, which is actually the basis for switching from one operation mode of toy materials to another, or for migrating from one operation mode of learning content to another. Without this intentional memory, there will be no migration in the operation. This is because the operation rules, strategies or methods in many mathematical operation activities are the reproduction or migration of previous operation experience, and these similar operation rules and requirements constantly arouse children's intentional memory or recollection; At the same time, in order to better complete the operation task, children need to constantly recall or recall their past operating experience and operating strategies to help them better complete the operation task. For example, after learning the composition of numbers within 5, children already have the experience of dividing numbers within 5 into two parts and arranging them according to certain rules. When the teacher asks to insert six pieces on two boards, children will consciously or unconsciously recall the experience of decomposing numbers within 5, and insert the pieces on the boards in the order of increasing or decreasing.
(2) Children's memory strategies will affect the result of operation. In the observation, we found that the advantages and disadvantages of children's memory strategies will show different characteristics in operational activities. For example, in finishing activities, some children simply forget the operation rules in operation, but insert the chess pieces into the chassis at will; Some children mumble: "one red and one white" while reading books and inserting chess pieces; Some children are taciturn and sort correctly according to the rules. The first kind of children, they did not consciously remember the operation rules, so they could not complete the operation task; Although the children of the second and third types are in the state of intentional memory, their memory strategies are different, which reflects the difference of their memory level. The second kind of children's memory needs the help of explicit language, while the third kind of children's memory has reached the level of internalization. These two types of children may show differences in more complicated operational activities.
3. Imagination in operation
Imagination is the process of processing and transforming the existing image in the mind and creating a new image. Imagination is an important cognitive component in children's operational activities. There are abundant creative imagination and creative imagination in children's mathematical operation activities. For example, in the classification activity, the teacher asked the children to form a regular and beautiful railing with multiple combined toys (note: multiple combined toys are composed of chess pieces and bottom plates, and chess pieces with various colors can be inserted on the bottom plate or another chess piece, and several bottom plates can be spliced into a larger bottom plate). According to this requirement, children can recreate or create a new railing image in their minds and then guide the operation. Through observation, we find that the development of children's sorting ability is closely related to the mastery of the concept of "order", but also closely related to imagination. Children with weak imagination can only recreate their imagination according to the images in their minds (the colors that the teacher has demonstrated are arranged one by one), and discharge the railings with colors one by one (the colors change, and the rules remain unchanged), while children with strong ability can create their imagination according to the images in their minds, and arrange the railings in one, two or even three layers regularly, such as ABBA and AABBAABB(A and B represent different colors respectively).
In mathematical chess activities, children's creative imagination is particularly prominent. For example, according to the existing experience of gobang, flying chess and checkers, children can process a number of combined toys and create various new mathematical chess games, such as addition and subtraction, combination and decomposition, comparison of sizes, number guessing and chess fighting.
It can be seen that in mathematical operation activities, children's rich imagination can help children solve problems actively, thus showing great creativity.