Tell us about the community that you engage? eg. economic conditions, political structures, norms and values, demographic trends, history, and experience with engagement efforts.
I have been engaged with the Montessori community.
Today, lamentably, Montessori methods are available, more often than not, to those families that can afford private schooling; however, there are some public Montessori schools. It is also somewhat ironic that Maria Montessori began building her success caring for children of parents of the lowest strata of society, almost all were illiterate, and their children were undernourished both mentally and physically.
The following are major points of the Montessori method.
• It is based on observation of the true nature of the child.
• It reveals the small child as a lover of work, both of the intellect and of the mastery of the body (especially the hand).
• Each child works at his own pace, not competing with others or the clock.
• The child, more often than not, works from her own free choice. Many works are sequenced by difficulty. Once she accomplishes one work, a sense of accomplishment develops and propels her to try more difficult ones.
• There are opportunities for mutual work and help–joyfully given and received.
• It allows the child to grow independently with respect to his own needs. He grows within liberty, but not permissive license. Self discipline and respect for the rights of others originates from within, not imposed by artificial discipline or rewards and punishments prevalent under other methods.
• The child reaches the same or higher levels of scholastic attainment as under other systems.
• The child develops both intellectually, as well as, emotionally. He is trained in fundamental social qualities which form the basis of good citizenship.
• Its application is universal. The results can be successfully achieved in any country and with any racial, social, cultural, or economic group.
Montessori Math Rationale
The teaching of math is an essential part of the Montessori Classroom. Certainly, main goals are to have the child learn to count and then begin teaching the four basic operations: addition, subtraction, multiplication, and division. However, appreciating what is meant by the “mathematical mind” is key to understanding an even greater importance. We have given a name to this part of the mind which is built up with exactitude, and we call it “the mathematical mind.” "I (M.M.) take the term from Pascal, the French philosopher, physicist and mathematician, who said that man’s mind was mathematical by nature, and that knowledge and progress came from accurate observation. . . . And if we study the works of all who have left their marks on the world in the form of inventions useful to mankind, we see that the starting point was always something orderly and exact in their minds."
In a Montessori classroom developing a “mathematical mind” is not done separately from the other essential aspects of the curriculum. From the beginning, exactness and attention to detail in Life Skills activities cultivate aptitude for logic, mathematics, as well as, science, and composition. Cycles of activity are established: i.e., 1) preparation 2) execution, 3) cleanup, and 4) completeness and order of materials. Repetition in the life skills area allows for extended concentration. As within the whole of the Montessori environment, four learning objectives of the Sensorial equipment include order, concentration, coordination, and independence. Developing strong sensory discrimination lays the basis for higher mental faculties and for the ability to abstract, which the child needs for writing, reading, and math. The primary purpose of the Sensorial exercises is that the child train himself to observe; that he be led to make comparisons between objects, to form judgments, to reason and to decide. Children in a Montessori setting are immersed in Language. Teachers know the love that children have for words, and every opportunity is taken to expand their vocabularies, giving names to feelings, animals, plants, countries, etc. Math vocabulary that young children come to know include: number, numeral, set, unit, quantity, symbol, zero, even, odd, equal, exchange, borrow, column, row, spiral, place value, sum, remainder, product, quotient, equation, diagonal, whole, half, third, fourth, congruent, permutation, and commutative principle. Pre-reading works develop skills in organizing information by finding patterns, go-togethers, opposites, and sequences; all of which help develop the part of a child’s intelligence which is logical and mathematical.
Some adults will ask, “Why do math with such young children?” The answer is certainly not just to impress parents; but the answer lies in observing their hunger for it. The extreme exactness and concreteness of a child’s mind needs clear and precise help. Young children begin math needing to overcome difficulties. Take for example the quandaries the child can have with counting and quantity. The fact that a group is enlarged through the addition of a new unit and that this increasing whole must be considered constitutes the chief obstacle for children of three-and-a-half to four in learning how to count. Counting, that ritual of pointing to each object while reciting a counting word, does not contribute to a child’s understanding of quantity. If you ask a very young child to count four objects and then ask him to bring you four, the child will only bring the fourth object, not the entire quantity. When we count to four, four includes one, two, and three. This accumulative activity is unique to cardinal numbers; the child never experiences it in any other situation. For example, the letter “C” does not include “A” and “B” and when we say, dad, mom, and baby, “baby” does not include dad and mom. While working sequentially with the red rods, and then red and blue number rods, the exercise of the senses in recognizing longer and shorter pieces combines with that of counting. One-to-one correspondence and the association of the written symbol with quantity, both come through manipulating these materials and other various counting works, i.e. Spindle Boxes, and Cards and Counters. At this point, one might say that the foundations for counting and arithmetic are laid.
With the addition of Montessori math materials such as the alluring Golden Beads and the Binomial and Trinomial Cubes, combined with activities, young children become intrigued with “materialized” or concrete abstractions. The sense impressions received from these objects furnish material for the mind. As the child works for a long time, touching and moving about with such materials, “day after day, maybe month after month, working at his own pace, gradually there comes from the material the essence of the operation. It sinks quietly into his mind and becomes a part of him.”
Adults have a store of abstract ideas in our minds. “We possess within us, as part of our mental makeup, a capacity which in some mysterious way is able to draw off from things outside us certain abstract qualities or ideas which exist only in our minds. Thus, to take a simple example, from five similar objects placed in a group–five apples, five nuts, five pencils–the mind is able to abstract the idea five which can be applied universally to any such group of objects thus thought of. This no animal can do.” “This process of abstraction is by its very nature an individual one. No one can do it for another.” “Aristotle described the process of moving toward abstraction in terms of a gradual discarding of matter, until only the abstract idea is left.” Because “there is always going on a certain interdependence between the purely intellectual (abstract) and the purely material (concrete), Montessori compares it to an aeroplane which, in order to rise into the air by itself, needs first to run for awhile along the ground. But, when the right moment comes, the aeroplane will “take off” from the solid ground and rise into the more abstract medium of the air. But the mind will not remain perpetually on these high and abstract levels. As the aeroplane has to come down to solid earth, again and again.”
Teaching math in the Montessori classroom includes but, is much more than learning to count, to add, subtract, multiply, and divide by working through various corresponding manipulatives. An ability to classify and categorize develops within the child; an ability to perceive patterns and make sense of them, an ability to reason systematically, and an ability to reason abstractly, as well. “Abstraction is an inner illumination; and if the light does not come from within, it does not come at all. All we can do is to help children by giving them the best possible conditions which include presenting them with external concrete materials. In these materials the abstract idea or mathematical operation which we wish to teach is, as it were, latent.” An ability to follow long chains of reasoning is not far behind.
Bibliography for Math Rationale
Standing, E. M., Maria Montessori, Her Life and Work, (London: Hollis & Carter, 1957).
Montessori, Maria, The Discovery of the Child, (New York: Fides Publishers, Inc., 1967).
Montessori, Maria, Dr. Montessori's Own Handbook, (New York: Random House, 1914).
Cotter, Joan, “Enhancing Montessori Mathematics with Visualization,” March, 2007.
Montessori, Maria, The Absorbent Mind, (New York: Holt Rinehart and Winston, 1967); reprinted, (New York: Henry Holt and Co., 1995).