Children must have a multitude of sensorial experiences with size, dimension, and form before they are introduced to any mathematical concepts of quantities and their symbols. Before formal lessons in math, children need to be able to compare, classify, pattern, map, and be familiar with the idea of sets. Many exercises are thus designed to lead the child to discover similarities and differences – to sort and arrange objects in one-to-one correspondence, and to manipulate sets of objects. The child needs to experience many opportunities to rote count after which he or she is ready to begin working with materials to associate quantity with mathematical symbols.
Once the child is familiar with the association of quantity and symbols 0 – 10, an overview of the base 10 decimal system with numerals 0 – 9999 is begun. The children then work with the squares and cubes of sets of numbers 1 to 10.
The Montessori approach to math is special for many reasons. All the operations learned in math come from concrete manipulations of our materials such as rods, beads, spindles, cubes, cards and counters to mention a few. The children do not merely learn to count; they are also able to visualize the whole structure of our decimal system and to perform the operations of addition, multiplication, subtraction and division using a variety of concrete materials to manipulate.