Maria Montessori referred to the part of the mind that deals with order and abstraction and is precisely and logically constructed as “the mathematical mind”.
"This system in which a child is constantly moving objects 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."
(The Discovery of the Child, Maria Montessori)
The Mathematics program provides the framework for a strong understanding of concepts. Manipulative materials are used to enhance the child's grasp of mathematics and to illustrate practical applications. Dr. Montessori observed human tendencies to abstract, investigate, calculate, measure, imagine and create.
If the child is allowed to develop these tendencies through manipulating concrete materials, allowing for repetition and concentration, there is an easy transition to abstraction and a love for mathematics.
Of all the Montessori materials, the math materials are the most impressive in design. They are designed to give the child his own manipulative experience with numbers as we move step by step from the concrete to the abstract. A child who doesn't love math is a child who has been to led to abstraction before he has a concrete understanding of the concepts.
In doing addition, subtraction, multiplication and division, the children actually carry, borrow and change the golden beads to reach their answer.