The Montessori materials are scientifically designed to awaken concentrated attention to a general idea or principle, helping the child acquire a concrete idea of a concept or idea laying the groundwork for an abstract idea of the principle or idea. Though a series of uses of the material the child moves from a concrete manifestation of the idea or principle to an abstract idea that with some materials results in the written expression of the principle. For example, the concrete mathematical materials teaching the concept of addition are sequenced so the child understands addition through the manipulation of objects to gradually expressing the idea in written form and then solves an addition example using the written numerals alone. The material does not in the first place teach factual knowledge but rather is makes it possible for the learner to reorganize their knowledge according to the isolated principle in the material. (Boehnlein, Montessori, Mario Jr.)

“They will be able to learn for themselves something which we could not transmit by using words alone. We give an abstraction. They learn to understand this abstract concept by using the material. We call this mechanism materialized abstractions [which] can be given in the form of objects, because this is the natural way for children of this age to learn.” (Montessori, Maria, The 1946 London Lectures, p. 70)