How spontaneous repetition relates to mathematics

Auto Education is the human ability to self-construct knowledge in the brain without external extensions or guidance. Every individual child makes the neurological connections that form new knowledge. A child will only learn if he learns it themselves than being verbally inform. Therefore we can denote that Montessori material is crafted with learning by hands-on and this connection of the child with the material enabled auto education to emerge. Among the varied concept embedded in the material are quantities 1 -100, 1-10, 11-19, 1-1000. These materials involve skip counting or base ten operations. The child will construct concepts internally based upon personal experience with the material known as auto education. As the child constitutes his learning he will incorporate with his existing knowledge. According to Piaget’s theory, numerals fall into the category of logico- mathematical thought as physical knowledge itself is incapable to bring any understanding of quantity to the child. Therefore, numbers can only have value to a child when he creates a relationship between them which material like matching numerals and symbols and varied materials. Hence, the child will auto educate himself the fundamental of this association.

When Dr Montessori studied children’s spontaneous activity, as observed that children went through temporary periods in which they were intensely interested in very specific elements of the environment. As children begin each of development, new sensitivities appear and increase in intensity and focus for the first three-year phase; then. Over the next three years, they gradually fall away until the sensitivities of the next stage take over.

In the Montessori tradition these periods of heightened interest, called ‘Sensitive Periods, signal the opening of windows of developmental opportunity. During this deepened interest children tend to focus on particular objects and activities, while ignoring other aspects of the environment. Each special interest is so intense that it leads its possessor to perform a certain series of actions.

In the wake of a sensitive period, heightened interest leads a child to focus on an aspect of the environment, the spontaneous activity that followed was observed by Dr Montessori to involve a great deal of effort. Moreover, the child becomes completely absorbed in the activity for as long as they want, when they are finished, rather than being tired, they seem refreshed, calm and happy. Where other observers might describe children’s activity of this type as play, in the Montessori tradition it is called children’s work.

When a new sensitivity emerges, if children are to construct the corresponding ‘function’ in an optimal way, they need to find something in their environment to be the focus of their interest and activity. If the environment does not enable a child to explore a developmental opportunity signalled by a sensitive period, the opportunity may be lost and the child may find it much more difficult to achieve that same developmental step at a later time.

Montessori methods aim to prepare environments which match the interests of children during sensitive periods, and which, therefore, stimulate children’s activity at times when their potential to construct the corresponding achievement, easily and spontaneously, is at its peak. Hence, tailoring a learning environment to a developmental stage and observing closely a child’s freely chosen activity within that window period to be the best means for making judgements about how to meet an individual child’s developmental needs, sensitivities and interests.

The Absorbent mind is an effortless ability of the child to absorb information from the environment. It is a stage of non-selective process of which the brain takes in everything like a sponge from the environment. It is perpetually a mechanism of survival skills for the child to adapt to the environment that they were born. Young children learn and remember without knowing they are doing it ‘simply as a result of living, without any need for more effort than is required to eat or breathe!’ (The Absorbent Mind, Montessori).

Dr Montessori metaphor, the ‘absorbent mind’ epic the unique and powerful way young children learn and remember. Children ‘absorb’ impressions from the environment with their sensory ability and these impressions form the actual fabric of the mind and intellect into structure.

It is from birth to six what Montessori called all around formative period of the Absorbent Mind. It is the period where the child’s development that forms the foundation for later intellectual and psychological development. Montessori believed that it is important to take full advantage of this stage to fully enrich the formation of the child’s mind and body.

The absorbent mind enables children to adapt to the distinctive time and place into which they are born.

Montessori saw that the absorbent mind in two phases

Age 0-3 years (Unconscious absorbent mind) where the young child unconsciously acquires basic abilities without making any decision. The child will take into his being any experience that the environment presents. The child’s work during this period is to become independent from the adult for his basic human functions. He learns to speak, walk, gain control of his hands and master his bodily functions.  Once these basic skills are incorporated, the child will enter the next phase of development which Montessori called the conscious absorbent (Age 3-6 years). These phase will see the child’s mathematical mind requires themselves to be perfected, the child main vital in this stage is freedom to move, to choose and concentrate. We can relate this stage with as how a child learns the concept of numeral and symbols effortlessly absorbed by the manipulation of the mathematics materials. For example a child will feel and see the gold beads and link it to it’s quantify value. The child effortlessly absorbs the experience of quantity in the materials which establish the mathematical foundation of our base tens system of numeration. The decimal layout provides the experience of our base ten counting system that will prepare the child for later learning curve for in their mathematics.

The child effortlessly soaks in everything in his culture and environment. She saw that a tremendous need for the child to have respectful and intelligent help during this absorbent mind stage. The child will constantly unfolding and developing themselves. There is different stages of growth occurs during this development. In each stage, there is creative period of intense acquisition of skills or knowledge followed with a calmer period of consolidation, example as absorbing and making that knowledge one’s own.

Dr Montessori believes Spontaneous repetition is an inner desire to repeat and master by a child. Every child has an inner desire to repeat everything new to them and wanted to master it. It happen without an adult making the suggestion to repeat the material.

An average child or normal child willingness to repeat comes naturally while non- normal child needs teacher to remind them which is a sign of a child with learning disability.

Spontaneous repetition took place when a child spontaneously repeats an activity until it is mastered. The repetition enables the child to differentiate between the slightest differences and variations in the world around him.

In mathematics material, the children are guide to repeat such as in counting activities, matching numerals and symbols. The pattern of repetition in mathematics such as counting the beads from one to ten, or matching the by saying “This is ten”(pointing at the beads) and simultaneously at the symbol 10 enable the child to repeat the association of the both the counting and symbols.

The Development of the Will is the human characteristic which guides decision making. It is an ability to choose something without conscious intent develop gradually over the first phase of life and is reinforced through practice which is close to development of internal order of the child. When a child concludes a decision, the child is making a Will. The exercise of the Will is when a child balancing impulse and inhibition. Given an example, if a child had an impulse to run but inhibit himself to walk. We can relate the development of the Will in mathematics material by when a child laid out the material in a very precise manner. The child will handle the materials with focus and respect. The organization of materials placing by left to right, top to bottom and the materials are kept within the compound of the rug.

In comparison when a child working with the material, we can denote that a child will develop the Will to be patient as in working with taking turn to pick up the beads from the ‘bank’ when working in a group with ‘Addition with the bead Frame’.

The Exercise of the Will is the observed behaviour (when we see how a child is working). Development of the Will is in mind but exercise of the will can be seen by how they work by what their procedure. For example, we can recognize how the child carries out their numerals. “Are they placing the card accordingly?” or we can observe how the child place the rug for the preparation of the work.

Normalization is a term Dr. Montessori used to distinguish one of the processes that she saw in her work with children in Rome. This is a process occurs when development is proceeding normally. She used the word ‘normalization’ so that people would think that these qualities belonged to all children instead for some special few. Normalization is the result of the balance between impulse and inhibition. It can observe when a child is relaxed, harmonious and focus when using the Montessori math material. The ability to retain organization of the maths materials is critical in solving problems.

Normalization appears through repetition of three step cycle.

I) The child will gather necessary material for the preparation of the activity. The movement and the thought involved in the preparation serves to call the attention of the mind to begin in focusing on the activity.

II) The activity which is so captivated by the child that he reaches a deep level of concentration. This step is which all educators recognize as important for education.

III) Rest, generalized as feeling of satisfaction and well-being. It is thought that at this point some inner formation or integration of the person takes place.

There are four characteristics that indicate the process of normalization occurs:

Love of work, Concentration, Self-discipline and Sociability

“All four characteristics must be present for us to say that a normalized type common to the whole of mankind is appearing- no matter how brief the appearance of the characteristics. The process is usually invisible to us because the normalization is hidden by characteristics not proper to the child.”                                              (The Absorbent Mind, p202)


Observation is a major role of the teacher.

Preparer of the Environment is a major role of the teacher. From the time a child learns to walk, Montessori educators claim, the child is saying to any adult who cares to listen, ‘Help me to do it by myself!’ (Montessori 1949:p136)

All Montessori educators keep this in mind as they prepare the learning environments and learning materials. First, through observations that we realize the early years will be many spontaneous expressions of normality even when the environment is unfavourable or the obstacles very greatly. The child must continuously struggle alone because no one recognizes and assists his bid for life. The child may become immersed in his own deviations.

Secondly, lay aside pride and anger- The child needs helps more than physical care. They need the adult who knows humility rather than pride; patience instead of anger. Most adults is easily impatient with children as they tend to neglect to understand their needs to grow, and comes down to their level of maturity. Teacher need to implant confidence to the child. They need to know himself, educate themselves in their work and give appropriate assistant should there a need arise. Adult need to facilitate the child to become aware of his mistakes and to correct them for himself so that he understands that it is all right to be wrong and learn from the mistakes instead of being reprimanded for the fault.

Teacher can contribute appropriate by interrupt the deviated cycle whenever it appears because it’s deterring development. Another contribution is by offering interesting activities to consume the psychic energy in a productive way. It is the return to the normal work cycle that is healing instead of kindness and strictness. The appearance of normalization is explosive. It must be protected and it happens in a moment. In that moment, the processes of deviations are gone. That is the first observation task of the teacher. Teacher need to learn to see, protect, and guide those moments and refrained from interrupting them while the concentration lasts. A teacher should prepare the classroom before the children arrived. The teaching is checking the materials to ensure they are in perfect order. Anything damaged or lost is replaced. Teacher should check that all consumables have been replenished. The teacher makes sure everything is clean and bright, and in exactly the right place, before the children arrives.

Note:Teacher Resources on Montessori Philosophy and Rationale Paper


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