Every human power is potentially present in the child, who has, by its very nature, the possibility to develop it, realise it and translate it into action through experience in the environment.

The psycho-arithmetic developed by Maria Montessori is based on the idea that children possess an innate predisposition, the mathematical mind, which enables them to understand mathematical concepts, formulate thoughts and abstractions if the activities of acquisition are supported by concrete experiences.

Montessori mathematical activities are developed through the use of manipulative materials. According to Montessori, children learn best through hands-on experience and the manipulation of concrete objects with which they have the opportunity to experiment with the relationships between quantities and numbers. They can create sequences, compare lengths and perform basic mathematical operations in a concrete and visual way.

The material is not for teaching purposes, that is , used by the teacher to illustrate abstract concepts, but is ‘developmental material’. In fact, it is presented in planes that follow the cognitive development processes of the child’s mind, helping the child to go through the various degrees of knowledge up to the abstraction of concepts.

The first plane presents the numerical symbols (1-10); the second plane presents the laws governing the symbols of quantities, i.e. the decimal system; finally, the third plane presents the concept of hierarchy according to the law of the positional value of digits.

The teacher presents the use of the materials and then lets the children work independently, choosing the activities that they are passionate about and progressing at their own pace. Classroom environments thus become real laboratories for developing and acquiring mathematical concepts represented in a manner increasingly close to abstraction. The children develop a passion for mathematics and acquire skills that will be useful throughout their lives.

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