What is the difference between the child developmental Montessori and Piaget ?
There really isn't that much difference, and for good reason. The experimental nursery school in Geneva, La Maison des Petits, where Piaget carried out his first studies of children in the 1920s, was a modified Montessori institution, and Piaget was the head of the Swiss Montessori Society for many years.
The two philosophies have a lot in common both Montessori and Piaget were constructionists who believed that children develop in a progression sequence or order. They also believed in hands-on, multi-modality activities, learning focused on creating mental models, not the pure rote memorization of facts, multiple measures of assessing learning to mastery, and incorporating students' prior knowledge into the curriculum.
What they disagreed on was timing. Piaget believed children had specific periods of "cognitive" or intellectual development, and did not reach their "concrete operational" stage until age seven. Montessori believed that while children had specific "sensitive periods" for development, they should be encouraged to develop all of their senses from a very early age since each child was different and there was no way to predict when and how learning would develop. Overall: Piaget claimed reading, writing and mathematics should be left until the period from 7 years onwards: Montessori: much earlier.