The Montessori math materials are perhaps some of the most inviting and beautiful works in a Montessori classroom. We all gravitate to the math shelves when we come into the classroom. The children want to touch and learn how to use the materials. “Show me this!”, “How does this work?”, they ask. Adults usually sigh and wistfully say, “I wish I had learned math this way”.
Mathematics is considered as a language, that’s why we have this material in Primary, as language is one of the sensitive periods, very active between 3 and 6 years. Also, Mathematics and language are the foundations of our human condition.
The child between 3 and 6 years old is in a sensorial development process, they are in a sensitive period called sensory refinement. The material is presented in this sensory way, so that the child can ‘understand’, not in the abstract (the abstract is the goal, the result), but in accordance with the specific conditions of her age and for its development needs.
In theory, we will present the mathematical material around 4 years old (4-6 years). This material prepares for mental arithmetic:
– Understand the concept of unity (one, two, three, six, ten… of any objects) and number.
– The decimal system key: how it works / the mechanism of operations.
– Memorize simple operations (“2 + 7=”), all the simple combinations. The ability to conceptualize, retain operations without needing a support.
– Abstraction development. Construction of the intelligence.
– Adaptation to the environment: counting and reading are the basis, culture.
– Self-confidence , self-esteem.
If we believe Maria Montessori, the children can absorb mathematical concepts naturally: Dr. Montessori discovered that a child who could count and recognize the symbols 1-9 could count in quantities of hundreds and thousands. The “Golden Bead” material was developed to give children the concrete exploration of the decimal system.
Dr. Montessori noticed that children need activities to work on and also need time to practice with the material provided. The adults need to reduce the speech (practice and experience before language), provide the strict minimum that it’s needed.
She also noticed that children liked to work alone without being interrupted and that they love the tasks that adults believe to be difficult. Per her observations, she concluded the child repeats and often repeats the same exercise when she is working with interest. She found that more the children could manipulate, more they could have access to the abstraction.
So, she made available to children materials containing abstract concepts. But, everything begins with ORDER, SEQUENCE AND STEPS. Before working in maths the children experience already the concepts of order, sequence, calculations, and exactness with the Practical Life and the Sensorial activities:
Order and exactness
Example: the way we set up and organize the shelves and trays and how work is laid out on the rug in the environment.
Each activity is broken down into logical and sequential steps.
With the Sensorial material we work with the senses, we classify the perceptions (dividing things into groups according to their qualities) This property leads naturally the mind to the abstraction. As Dr. Montessori said: “The senses, which are the explorers of the environment, are paving the way for the knowledge.”
We distinct, isolate the different impressions through a material that the children can manipulate. We offer the child the opportunity to make simple experiments and analyze a complex reality into simple elements that isolate qualities; these are basic mathematical skills.
The sensorial material is our exploration key and a way to develop the mathematical mind. It is the base of the mathematical material.
That is why our mathematical material is a sensorial material as well: much more elaborate and complex.
The entry into abstraction happens in three process: Accumulation (indirect preparation), maturation time, then explosion.
– Indirect preparation. Our method is basically indirect, it is the experience that prepares children for a future, physical and mental ability. It is the transmission of unconscious knowledge.
– Inner knowledge. The maturation time, as a result of having being practicing.
– Awareness. In general, this awareness is in a flash. This is the phenomenon of the explosion of language, writing (we cannot transmit this, it emerges and belongs to the child; the adult doesn’t know when this awareness appears, it is difficult to assess because it is a real work happening inside). It is an individual process.
The effortless way the mind of the child can come to an abstraction of mathematical concepts is one of the joys of the Montessori approach. The small child’s mathematical mind, properly nourished by experience, becomes clear, exact and ordered. Unlike many, the Montessori child comes to “love” math and enjoys the progression into more abstract and difficult work.