[jojoo]

I said: " The immense impact and usefulness of Piagets stages of cognitive development are orginally his and not to be found in Montessoris Teachings"

Montessori via your source on mathematics: "Mathematics: Formation of the concepts of quantity and operations (addition, subtraction, multiplication, and division) from the uses of concrete learning materials. (birth to 6)" Quite general.

Piaget has a few sub-skills concerning Quantities:

  * conservation (xxx has the same amount of x'es as x x x)
  * classification (x is a letter and lowercase)
  * seriation (x X y Y could be orderes XY; xy, but also Xx, Yy)
  * transitivity and others

This insights are very useful if you want to make - for an example - a pre-numeric mathematical game concerning quantities.

Montessori does not provide such deep insights into pre-numeric mathematics.

[mkempe]

Rubbish.

You pretend to "infer", from a one-sentence description of how the Montessori method uses concrete materials to teach the basic arithmetic operations, that somehow other mathematical principles are absent from the Montessori pedagogy.

Of course these principles are demonstrated and taught in Montessori schools, also with concrete learning materials.

You may not know much about Montessori, or you may have an axe to grind, or ...? Either way, you should stop making demonstrably false statements about her pedagogy (and about Piaget).