It is a valid wonder the question, Why does the Montessori Method present the learning concepts to the children concretely before they have the expectation for the child to work abstractly. There is always the question: When is it the right time for children to work mathematics abstractly (paper only) as presented in traditional schools and concerns if the children are not going to be able to perform in a traditional setting.
First I would like to present the idea of concrete to abstract as defined by the Association Montessori Internacionale:
The main idea to hold true to the Montessori Method is Dr. Montessori’s greatest belief that she expressed in everything she wrote and in every lecture she gave: “what the hand does, the mind remembers.” (M.M.) It is a hard rule she insisted upon, and it is feverishly given to the guides in training. We must trust the material to isolate a concept and through its manipulation the student will gain the full depth of the idea displayed in front of him or her. When is the child ready to move to pen and paper (work abstractly)? We understand this happens when the child demonstrates he or she has internalized the patterns, sequence, or logic of what is being presented and no longer needs the Montessori material to manipulate the concept to gain an accurate result.
In mathematics the material represents the abstract concepts of fundamental operations and assists in the development of the child’s “mathematical mind”. By manipulating the material the child has a logical, clear and visual way of grasping the concept. They can see and feel that 10 is more than 1 and that 1,000 is a quantity much larger than 1. Not just by the notion of memorizing a number or seeing it on paper but by the exercise of actually counting beads to internalize how much more counting is necessary to get to 1,000. This is extremely important when the child moves into dynamic operations (carrying the 1 to the next category). They get to visual and physically carry over to the next category. They see math and the manipulation of quantity and can then begin the process of analysis and working story problems, which brings them to the abstract of mathematic work. The most important gift the concrete material gives the child is to bring order and sequence to the understanding of mathematical computations, theorems, and problem solving.
Language work provides a fantastic break down of each function of words and with symbols and colors children are able to compartmentalize language and truly get a since of all the Parts of Speech and their use in a sentence. Sentence analysis work is what outside of Montessori is called diagraming sentences. This material is also a gift to the child in breaking down syntax and sentence structure and physically moving words in a sentence to truly understand its position in a sentence and purpose.
The beauty of Cosmic Education lies in all the charts and timelines that lays out an amazing amount of concepts that are presented in a concrete way that can be manipulated, organized, replicated and recompiled in a way that is meaningful to the child in the intent to internalize the concepts and expand beyond what they know. Only until the information is internalized can the child truly express him or herself abstractly.
In our classrooms the children enjoy the freedom to work with Montessori concrete material, books, educational objects (globe, maps), specimens, nomenclature (information cards), art supplies and lots and lots of paper to express their acquisition of new knowledge.
A key to our work in the classroom is to follow Dr. Montessori’s Golden Rule: