Starting from children's daily life, Dr. Montessori inspected mathematics education from three aspects, pointed out the necessity of early mathematics education, and summarized all stages of mathematics education, namely:

Arithmetic-the science of numbers

Algebra-abstraction of numbers

Geometric abstraction

Considering the importance of order, environment and accuracy, Dr. Montessori emphasized: "It is necessary to prepare in advance, that is, sensory education must be carried out before mathematics education."

(A) based on sensory education

First of all, by summarizing the various attributes of things, explaining and demonstrating to children, we can fully mobilize children's various sensory organs, let children concentrate on their own sensory organs, achieve full attention, and let children firmly grasp those abstract elements and relationships.

Then, based on the three operating modes of sensory teaching AIDS (see below), help children analyze and synthesize, cultivate their logical thinking ability, and make them master the essence of things.

(B) the concretization of abstract things

In order to help children better understand teaching AIDS, and at the same time let teachers know how much children absorb and understand teaching AIDS, "three-stage teaching method" can be adopted in the teaching process of name practice, which runs through every link of teaching. This can not only achieve the purpose of heuristic teaching, but also expand children's vocabulary.

When children operate, they need to show them different objects and compare them. For example: big-small, big-bigger-largest, rough-smooth, light-heavy, uppercase-lowercase, small-smaller-smallest, heavy-light, hard-soft, etc.

(C) a complete curriculum system

Dr. Montessori used appropriate teaching AIDS in Mathematics Education, focusing on the decimal method, and then entered the four operations of using memory, closely combining "quantity", "number" and "numeral". In the implementation of teaching, we should start with the concept of "quantity" and give systematic guidance repeatedly and carefully according to the teaching system. In the teaching process, adults should choose appropriate teaching AIDS according to the different characteristics of children and make a learning plan for teaching AIDS purposefully.

(D) The characteristics of Montessori mathematics teaching AIDS

1. Take sensory education as the basis of mathematics education.

2. Start with real quantitative understanding. For example: counting rod, spindle box, etc.

3. Pay attention to the relationship between quantity, number and numeral. For example, count sticks, numbers and chips.

4. Use Arabic numerals and unify fonts. For example, the same Arabic numeral font is used for sandpaper numeral boards, numerals and chips, headstock, etc.

5. Pay attention to the concept of "0" and decimal calculation. For example: headstock and decimal.

6. Generally, the operation standard of synthetic decomposition is "10" instead of "5". For example, several strokes.

7. In order to indicate the orientation or calculate the quantity, the principle of "color classification" should be applied to the quantity and quantity of teaching AIDS. For example, the unit, tenth and hundredth digits of stamp games are green, blue and red respectively; Color beading is also the number corresponding to color, usually red beading 1, green beading 2, etc.

8. In the "error correction" project in mathematics education, the function of prompting is realized in the form of calculation or error control panel. For example: 100 board, addition table, etc.

9. The design and teaching of Montessori mathematics teaching AIDS follow certain logical principles, so when operating teaching AIDS, we should first master the basic concepts of numbers, and then proceed in the direction of "combination" and "decomposition".