One of the most beautiful aspects of Montessori is that it brings abstract concepts to life so that children can truly understand what the concepts mean. Materialized abstractions in the Montessori classroom are found throughout the Sensorial area.
A concept is a cognitive unit of meaning that has been named by humans. It is an idea that is formed in the mind, which is usually abstract in quality. Abstract concepts are usually difficult to understand because they cannot be referenced to a specific concrete material or object.
Concrete materials convey abstract qualities.
Montessori however, provides the children with concrete materials that convey the abstracted qualities from what has been perceived and named by humans. From these concrete materials the children can understand the abstract concepts and the characteristics of them.
Using the Red Rods as an example, the abstract concept of length is introduced to the child.
From the moment the child first touches the red rods they are beginning the sensorial journey to understanding of the abstract concept of 'length'. They are shown how to carry the rods one by one (starting with the shortest rod) to their work mat. They feel in their hand how each rod becomes longer. The last few rods become so long that they have to carry them vertically with two hands, to avoid hitting others with them as they walk to their work mat!
When all of the rods have been placed randomly on their work mat, the teacher begins the process of placing the rods according to their length. The teacher visually locates the longest red rod and places it horizontally at the top of the work mat. She places her fingers tips from her left hand on the left edge of the rod. Using her right pointer and middle fingers, she slowly slides them along the rod from the far left to the right end of the rod: making sure her left fingers remain on the left of the rod.
start of the finger slide on each rod
end of the finger slide on each rod
Clearly she has to reach her arms quite far to stretch the length of the entire rod. The teacher has felt the concept of length. From the rods that remain randomly placed on the mat, the teacher once again selects the longest rod and butts it up against the rod she just slide her fingers along. She repeats the process of feeling the length by sliding her fingers across the rod. She continues this process for a few rods and then invites the child to continue to build the red rods and slide their fingers along each rod, until all of the rods have been placed in the correct order.
After the children have had a lot of practice with the red rods and they are able to build them correctly, the language of length is introduced. In order to establish the quality, the words long and short are given. If the child grasps the language and concept then the comparative of longer and shorter, and the superlative of longest and shortest are also introduced. This gives the child the language they require to verbally express their understanding of the abstract quality of length.
Materialized abstractions liberate the child
There are many other examples of materialized abstractions in the Montessori environment, specifically in the Sensorial area. The materialized abstractions liberate the child to become a free thinker. The child will not take things on blind faith if he is allowed to make his own discoveries through the use of the materials; the child will always seek out basic principles for himself.