# Montessori Math Rationale

“The mathematic mind is a mind that is especially interested in mathematics. Rather than find them boring and absurd, they find them interesting and absorbing. It is a fact that most children in our Montessori schools manage to achieve great enthusiasm while working with mathematics. Is the preparation of their minds that allows them to reach this pleasure.” Maria Montessori, London Lectures, 1946, p 41

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Mathematics has always been a difficult subject for students. Many children have developed phobias and barriers towards mathematics, which prevail into adulthood, thus limiting their potential. This limitation implies problems of learning, resulting in the child a sense of inferiority. Mathematics for common education have been a process of memorizing away from the child’s natural development, apart from understanding, reasoning and interest. The problem then lies not in the major or minor child’s ability to understand or the age at which to learn mathematics. These are just prejudices of adults; rather the problem lies in the way in which we teach them. By contrast, in our schools, children show a real fascination for mathematics, which are presented from 4 years of age. Children learn in a few weeks what would take 2 or 3 years at a traditional school . Why is this difference so abysmal? What has education done to produce these reactions in children? The Human Tendencies, The Absorbent Mind and The Sensitive Periods governing child development from birth are fertile ground for planting and harvesting this new knowledge.

If we want to succeed and enthusiasm them in this area, we must continue their natural development. Numbers like the alphabet, not found in nature, have been an invention of man as a need to understand each other, to progress, for evolution and survival. Humans, as we know, were born with the innate ability to create a language to express the abstract aspects that we have formed of the things around us and their qualities and to share with others. Through civilization and evolution, the man felt the need to see things in a quantitative manner, then created another language we call “mathematics”. This language, this need, evolved until a registration system that took man to develop the numbers. Mathematics, like every creation of man, have evolved without really knowing how far you can
get with them: the scope of the computer, physics, chemistry, algebra, all are evidence of this. Every aspect of our culture is based in some way or another in Mathematics: language, music, dance, art, sculpture, architecture, biology, daily life. All these areas of measurements and calculations are accurate.

Even in nature, everything follows a precise pattern and a precise order: a flower, a shell, a butterfly, day and night, the seasons. All this makes mathematics essential for human life and they can not be limited only to a matter within the school curriculum; here lies the importance of teaching math in a pleasure, enjoyable and understandable way. Mathematics is an aid to the development of the child and should be seen as an aid to life and not as an obstacle in their lifes. Dr. Montessori said that man is provided with an innate power “The Mathematical Mind”. She takes this term of the French mathematic, physic and philosopher Blass Pascal (1623-1662), who was the first to say that the human mind naturally has the characteristic of being mathematical and if you think for a minute we see that all progress man has developed is because the human mind has a propensity for accuracy, order and precision. Maria Montessori observed scientifically and methodically this phenomenon in the development of children worldwide. The Montessori materials prepare the child indirectly to the formal study of mathematics.

This makes it the natural way and they learn with joy and follow a specific pattern that goes from the concrete to the abstract and are created specifically in order to build knowledge slowly and concretely, always using first the senses. These indirect preparations, or the lack of them, are one of the causes that awaken in children a love or hate for mathematics. They are essential in the construction process of the child and ensure the child’s success at work.

“The hand is the teacher of the mind.
We should never give to the brain more than we give to the hand. Merely impressions do not enter his mind, they form it.” Montessori Maria, “The Absorbent Mind” Holt & Company, New York, 1995.

One of the genius of Maria Montessori is to observe each of the difficulties that the child will be found throughout the learning process, and to isolate each of them beforehand preparing him for the big event (writing, reading and math). Students who learn math only by memorization often have no real understanding or ability to put their skills to use in everyday life. Learning comes much more easily when they work with concrete materials that show what is taking place in a given mathematical process. The concrete Montessori Math materials are perhaps the best-known and most imitated elements of Dr. Montessori’s work. These simply and beautiful materials hold a fascination for most children and adults alike. They proceed through several levels of abstraction, beginning with concepts and skills that are the most basic foundations of mathematics, presented in the most concrete representation, up through the advanced concepts of secondary mathematics, which are represented in increasing levels of abstraction.

All of the content for Mathematics is divided into sub-categories that reflect these increasing levels of abstraction. As I work with the Montessori math materials it still amazes me how much I didn’t understand about mathematics. For me, the Montessori math materials are truly unique. What makes them unique? First of all, the introductory materials are all hands-on rather than abstract; they are sequential (each one builds upon the one before) and also they contain many similar elements (colors for example) that enable the child to master new work quickly. As a student, I started doing math on paper with a pencil; in Montessori the abstract process of math is the final step of a long series of exercises. To me, and most traditional school students, numbers on the page are just that, symbols we are taught how to manipulate. To Montessori students, those symbols represent very concrete ideas that they have physically manipulated; they fully understand what they mean, how they work, and why, again by following the concrete/abstract rationale of Dr. Montessori. Kids are better able to understand abstract mathematical concepts because they have first handled the actual materials, and I believe this is why the mathematics area in a Montessori classroom is the best well known of all of them, and is the strongest area in most of the children attending a Montessori school.