What is the essence of mathematical knowledge? How do children acquire concepts? How to understand the mathematics education of preschool children? For these questions that people are quite concerned about, two different "voices" from the field of psychology bring us completely different answers. One is the "association theory" of behavioral psychology, which holds that mathematics is a set of facts and skills, and the purpose of preschool children's mathematics education is to help children acquire this skill. In the traditional practice of mathematics education, it is interpreted as an activity mode that aims at laying the foundation of primary school mathematics education, takes imitation, memory and practice as the process and strengthens children's mastery of mathematics knowledge and skills as the result. The other is the "constructivism" from cognitive psychology, which holds that the essence of mathematics is a set of relationships, and these relationships do not exist in the actual object, but a series of coordinated abstractions that act on the object (Piaget called "reflective abstraction"). In the view of constructivism, children's mathematics learning is the process of establishing the connection between their original cognitive structure and new learning knowledge. This connection appears in the form of assimilation or adaptation. Compared with "association theory", "construction theory" emphasizes and pays attention to the process of children's acquisition of digital concepts, not the results.

Attach importance to "learning by doing" []

When it comes to construction theory, Piaget can't be ignored. Regarding the acquisition of mathematical concepts, Piaget said: "It is a big misunderstanding to think that children only acquire the concept of numbers and other mathematical concepts from teaching. On the contrary, to a considerable extent, children develop these concepts independently and spontaneously. " Children don't learn arithmetic, but reinvent it. Piaget believes that children's thinking comes from action, and the origin of mathematical logic knowledge exists neither in the object itself nor in the subject, but in the complex interaction between them. Logical structure can only be achieved through self-adjusting internal balance, not the result of external reinforcement. Piaget suggested organizing and creating a suitable environment for children to do their best and develop fully when explaining how to let children learn mathematics. This environment not only includes all kinds of learning materials, tools, space and time, but also includes appropriate communication and cooperation between children.

Letting children do middle school is a great progress in mathematics education for preschool children. This progress is not only reflected in our goal of kindergarten mathematics education, that is, "getting some superficial mathematical concepts through children's own perception and operation", but also in the change of the form of kindergarten mathematics education from the traditional mathematics activities preset by teachers to the combination of children's self-selected mathematics activities. More importantly, teachers' understanding of the tasks of preschool children's mathematics education has changed from imparting mathematical knowledge and skills to how to create an environment for children's mathematics activities and provide operating materials to inspire children's mathematical thinking.

From "Operation Learning" to "Social Situation Learning"

Just as the significance of "operation" in children's mathematics learning is more and more deeply rooted in people's hearts, mathematics education activities show a kind of starting from children's perceptual experience, through bathing, discovery and other activities, and after the accumulation of experience, many research results and practical experience bring us some new questions, such as: Are the operating materials provided and prepared by teachers for children meaningful to children? Will the operating materials provided by the teacher limit the children's math study? Do children construct knowledge of mathematical logic in the same universal way? Can children link current learning with daily social life situations and turn them into solving practical problems in mathematics? These problems have been fully concerned by scholars who hold Piaget's constructivist position but constantly enrich and develop his theory. In their view, Piaget has realized that cognitive conflict is an important factor leading children to construct or reconstruct the concept of numbers, and also pointed out the role of social influence in children's development, but he did not clearly explain the social mechanism of cognitive development. In fact, children's mathematics learning does not just exist in an isolated way and state. If children are placed in social situations, the possibility of cognitive conflict will greatly increase. Mathematical problems from children's direct social life scenes are the background for children to reinvent arithmetic. The concept of numbers in children's minds comes neither from books nor from teachers' explanations, but from children's logical mathematics and physics about their own life reality.