but so to touch his imagination as to enthuse him to his innermost core.’

With the first mathematics materials the child is introduced to the numbers one through ten. The materials that follow will develop the concept of the decimal system, that is, a numerical system based on ten. Maria Montessori called the decimal system the “cell of our system.”

To understand the decimal system is not easy for a child. It took humans many years to realize that the value of a numeral is dependent on the position it occupies. It was much later that the concept of zero was developed, and even later that the decimal point came into existence.

Our decimal system (base 10) has nine numerals, one through nine. The presence of one or more zeroes allows us to create numbers beyond nine up to infinity. Thus, learning the numbers one through nine and their numerals, in addition to the concept of zero, is the only truly difficult part for the child. This he has already accomplished. Counting experiences (adding one more) up to 10 have preceded; now the child will learn to count beyond 10.

In the hierarchical orders-ones, tens, and hundreds of the simple class; ones, tens, and hundreds of thousands, and so on- there are nine units: one through nine. No matter in which hierarchy the numeral one appears, the absolute value of one is one. The relative value depends on its position. The limit between one hierarchical order lies in the ‘secret of ten’ and in the exact value of the numerals one through nine. It is necessary that the child fixes in his mind the concept of the hierarchical orders and their values. The materials that follow enable the child to avoid the confusion and difficulties he may otherwise encounter.