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The Manipulatives, Order & Numeracy Program, The Love For Numbers

The Manipulatives, Order & Numeracy Program, The Love For Numbers The Manipulatives, Order & Numeracy Program, The Love For Numbers

Often in this world children learn math by rote, without any real understanding or ability to put their skills to use in everyday life. Learning comes much more easily when they work with concrete educational materials that graphically show what is taking place in a given mathematical process.

In Montessori, we use hands-on learning materials that make abstract concepts clear and concrete. Children can literally see and explore what is going on. Our approach to teaching Mathematics is based on the research of Drs. Maria Montessori and Jean Piaget. It offers a clear and logical strategy for helping children both understand and develop a sound foundation in numeracy and geometry.

As an example, consider the very basis of Mathematics: the decimal system: units, tens, hundreds, and thousands. Since quantities larger than twenty rarely have any meaning to a young child, Dr. Montessori reasoned that we should present this abstract concept graphically. Children cannot normally conceive of the size of a hundred, thousand or million; much less the idea that a thousand is equal to ten hundreds or one hundred tens.

Montessori overcame this obstacle by developing a concrete representation of the decimal system.

Units are represented by single one centimetre beads; a unit of ten is made up of a bar of ten beads strung together; hundreds are squares made up of ten ten-bars; and thousands are cubes made up of ten hundred-squares. Together, they form a visually and intellectually impressive tool for learning.

Great numbers can be formed by very young children. ‘Please bring me three thousands, five hundreds, six tens and one unit.’ 
From this foundation, all of the operations in Mathematics, such as the addition of quantities into the thousands, become clear and concrete, allowing the child to internalise a clear image of how the process works.

We follow the same principle in introducing plane and solid geometry to very young children, using geometric insets and three dimensional models which they learn to identify and define. Five-year-olds at the Montessori Stepping Stones® Centres can commonly name geometric forms that most adults would not recognise. The study of volume, area and precise measurement in everyday applications around the school is introduced in the early years and continually reinforced and expanded.

From this foundation, all of the operations in Mathematics, such as the addition of quantities, become clear and concrete, allowing the child to internalise a clear image of how the process works.