Maria Montessori was a scientist interested in psychology and the unfolding of the adult through childhood.  Pedagogy, and mathematics came second.  This is an important point; her primary interest was in the process of learning, not in any one specific area. How did the physical environment as well as the human environment affect education?

When she was given the opportunity to work with children, she soon discovered that their greatest need was for activity.  She first gave the young children materials, sensorial materials, and the language associated with those objects, the red rods, the pink tower, etc…  Ever the scientist, the observer, she noted that they retained very little of the concept, and “met her with blank stares”. (honestly, I’ve had my share of those reactions over the years as well).  So instead, she simply showed the children the activity itself, the sorting, the discrimination of size or shape or color.  And? The children understood!  And Dr. Montessori understood as well.  Create manipulative materials that isolate a concept. Give the child exact instructions on how to use it, and later, but only later, will the child be responsive to language, the word lessons. Pondering upon the phenomenon, Dr. Montessori realized that 3 important things had occurred, always starting with activity: “formation of the subconscious knowledge”, “point of consciousness”, and “indirect preparation”.

The formation of the subconscious knowledge is the accumulation of impressions not consciously registered, but stored in the subconscious- An illustration of this is a person who, having for many years walked through a woods on the way to work, certainly had stored the impression of innumerable leaves. Yet he might have paid no attention to the difference between a lobed and a smooth/even Ieaf, A casual remark from a botanist would bring the difference immediately into focus. Why? because the knowledge was already there subconsciously. But if the Iong experience with leaf-impressions had not been there, would the botanist’s remark have aroused such immediate understanding? Yet something is needed to build a subconscious knowledge into the light of  consciousness’ It may be a spontaneous sudden realization, or a word after years of sub- conscious experience: a point in a Iong line that stretches into miles!

“So”, she reasoned, “this point oI consciousness can come either spontaneously or it may be provoked purposefully or otherwise”‘The indirect preparation was the unconscious or purposeful incorporation in an attractive experience of items which will prepare an ability necessary for a future task.

“Sensitive periods” were her next discovery  During these, at a determinate age, certain activities had an irresistible attraction but left indifferent younger or older children. Though the attraction lasted for a limited period, while it lasted, it made young children very eager to Iearn. This eagerness garnered Dt. Montessori a lot of criticism and misunderstanding on the part of pedagogues and psychologists who accused her of forcing children oI a tender age to do things which older children found difficult and distasteful. The greatest misunderstanding was, and arguably still, is in the field of the acquisition oI mathematical knowledge.

A few of things to keep in mind. Dr. Montessori was not interested in teaching children any particular subject. So she did not specially try to “teach mathematics”. Her interest was in the child itself and the task she imposed on herself was to try to discover the process of the natural development of the child in its various aspects. She prepared an environment which contained objects the use of which caused the children to arrive at an abstraction. The children were of mixed ages, 3 years at least, and the different groups {three to six, six to nine, etc.) were in communicating rooms so that the children could circulate from one to the other. There was no time-table as {ar as subject-teaching was concerned so that children could remain practicing the same subject for an indefinite length of time. This gave them the possibility of storing a subconscious knowledge which culminated into a conscious realization at a certain

Montessori discovered that abstraction was the result of individual experience and the time involved in reaching it vaded with the individuals. Also, the interest in the exercise was determined not by the efforts of the teacher, but by the sensitive period of the child. And finally, the materials she gave the children contained either an indirect preparation for something to come in the future, or the possibility of bringing into the light oF consciousness certain items which the child already possessed in the subconscious.

The basis of mathematics for children is counting.  Associating symbol to quantity. It was logical to conclude that the next step would be to continue with I l, 12, 13 and this D/. Montessori did for many years until one day when by chance children of this age were present at a lesson given to seven year olds with materials which presented in concrete form the working of the decimal system. The seven year olds were luke-warm, but surprisingly the younger ones showed great enthusiasm. In a day or two, they had gained possession of the materials and brought it to their room. This was another example oI the sensitive periods: what Ieft the older children more or less indifferent aroused intense interest in the younger ones.