According to the psychological structure of children's number concept, the education of number concept can be divided into nine stages. The first stage: classify and sort objects, so that children can master the mathematical skills of classification and sorting, and provide an empirical basis for establishing the concepts of class, order and set.
The second stage:-Compare the relationship between the two groups, so that children can learn to compare the number of elements in the two groups in a one-to-one way, and initially form concepts such as "more", "less" and "as much".
The third stage: the conservation of quantity, so that children can learn to realize the conservation of quantity without being disturbed by the external characteristics such as the spatial form and size of objects. The fourth stage: sort by number, let children classify object sets by equivalence (equal numbers) with the concept of class, and abstract the practical meaning of numbers; Using the concept of order, the object set is sorted by arithmetic progression (the difference is 1) to experience the order of numbers.
The fifth stage: use digital symbols to represent numbers, help children know numbers, understand the meaning of numbers, and learn to use numbers to represent the number of objects.
The sixth stage: natural series within 10, let children compare the size of numbers, arrange natural series within 10 by using the concept of order, and understand the difference relationship and order relationship between numbers (decimal before, big after).
The seventh stage: classify the object set twice to help children further construct the concept of class and understand the relationship between class and subclass.
The eighth stage: the composition of natural sequence within 10, learning the decomposition and combination of natural numbers within 10, and mastering the inclusion relationship between a number and its partial numbers, the complementary relationship and exchange relationship between partial numbers and partial numbers.
The ninth stage: the addition and subtraction of integers within 10 helps children understand the meaning of addition and subtraction, master the skills of addition and subtraction of integers within 10, and develop their reversible thinking ability by using the reciprocal relationship of addition and subtraction and the exchange relationship of addition.
When designing the education system of the concept of quantity within 10, Dr. Montessori first used specific teaching AIDS and the operation methods of pairing, sorting and classification to let children establish the concept of number, so as to master the concepts of quantity, number and several names and their relationships, and then understand the meaning of "0" and be familiar with the correct arrangement of numbers and even and odd numbers.
These nine stages will effectively help children understand the meaning of large numbers.