This system in which a child is constantly moving object; with his hands and actively exercising his senses, also takes into account a child’s special aptitude for mathematics. When they leave the material, the children very easily reach the point where they wish to write out the operation. They thus carry out an abstract mental operation and acquire a kind of natural and spontaneous inclination for mental calculations.
Are children able to learn in a mixed-age environment
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In Montessori, children of different ages learn together in the same classroom. This promotes collaboration, social skills, empathy, and the sharing of knowledge. Older children become mentors to younger ones, fostering a sense of community and mutual respect.
In Montessori, the bead chains are a math material for hands on learning. The purpose of the bead chains is to teach skip counting. However, the bead chains are also an indirect preparation for multiplication, understanding the squaring of numbers, and then understanding the cubing of numbers.
In the Montessori classroom, Mathematics is introduced through concrete materials to abstract materials.
Children at the first plane of development are Sensorial explorers. These concrete materials help children to understand the concepts of quantity and group operations through their senses.
As they have experiences in these concepts, abstract materials will be introduced. These abstract materials help children to understand the essential combination of numbers which allows children to solve mathematics quickly without the use of materials.
“We have to let children experience the beauty of arithmetic… it is always something to discover and to perceive by the hand before being understood by the mind.” – Philip D. O’Brien, from the introduction to Psychoarithmetic by Maria Montessori.
“Movement, or physical activity, is thus an essential factor in intellectual growth, which depends upon the impressions received from outside.
Through movement, we come in contact with external reality, and it is through these contacts, we eventually acquire even abstract ideas.” ~ Maria Montessori
 