DR. MONTESSORI DEMONSTRATED that if children have access to mathematical equipment in their early years, they can easily and joyfully assimilate many facts and skills of arithmetic. On the other hand, these same facts and skills may require long hours of drudgery and drill if they are introduced to them later in the abstract form.
DR. MONTESSORI DESIGNED concrete materials to represent all types of quantities, after she observed that children who become interested in counting like to touch or move the items as they enumerate them. By combining this equipment, separating it, sharing it, counting it, and comparing it, they can demonstrate to themselves the basic operations of mathematics.
CHILDREN IN A MONTESSORI class never sit down to memorize addition and subtraction facts; they never simply memorize multiplication tables. Rather, they learn these facts by manipulating concrete materials to perform these operations. Materials such as Number Rods, The Golden Beads and Fractions lead naturally to abstraction, rather than memorization.
WHEN THE CHILDREN WANT TO DO arithmetic, they are given a sheet of paper containing simple problems. They work the problems with appropriate materials and record their results. Similar operations can be performed with a variety of materials. This variety maintains children’s interest while giving them many opportunities for the necessary repetition. As they commit the addition facts and the multiplication tables to memory, they gain a real understanding of what each operation means. In a Montessori classroom there are many materials that can be used for numerization, adding, subtracting, multiplying, and dividing.