In a Montessori classroom, math is presented in a fun and interesting way by using hands-on materials that help children develop the mental connection from concrete knowledge to abstract thinking. Mathematics instruction is a crowning and identifying Montessori teaching methodology that requires the integration of the previously learned activities of the Practical Life and Sensorial curricula as well as teacher attentiveness to the Sensitive Periods.

Although activities such as red rods, the pink tower, the brown stair, geometric solids, binomial cube and trinomial cube are considered Sensorial exercises which begin to be introduced around the age of three, they are the concrete basis for and act as “hard-wired” connections to the central nervous system in order to lay the groundwork for mathematical understandings such as sequencing, recognizing gradations, quantifying, matching and differentiating. Also, in prior Practical Life activities the young child, beginning at the age of two-and-a-half, develops  a sense of order, concentration, coordination and independence which are important precedents in the training of a mathematical mind to perform abstract operations.

Remember also that in math, as is true in other Montessori curricula, children have free choice to satisfy the sensitive period stimulated by their own inner needs. Through this free choice as well as repetition, children are able to acquire mathematical knowledge step by step depending on their own maturational pace; not on the needs of the teacher, parent or a preordained curriculum. When children build their knowledge by themselves there is no pressure to hurry and no fear of failure.

The Math activities in a Montessori classroom begin with materials that teach numeration from one to ten. These materials include Number Rods, Sandpaper Numbers, Printed Numerals, Spindle Box, Cards and Counters, Colored Bead Bars and the Memory Game. Through these materials children build the basic concept of one to ten in their memory and learn the natural order of numbers. They also learn to recognize quantity.

After mastering the basic concept of one to ten, children need to understand place value. The Decimal System introduces Montessori children to place value up to thousandths long before it is introduced in traditional schools. Through working with the Golden Beads, the Formation of Complex Numbers, Teen Boards, and Ten Boards, children develop mathematical concepts beyond the quantity of ten.

When children recognize the written numerical symbols and know their meaning, they perform exercises to remember more complex numbers which is made possible through the use of the following materials: Sequence Board, Addition Strip Board, Subtraction, Multiplication Bead Board and Division Bead Board.  In addition, the Bank Game helps pre-school children learn the concepts of addition, subtraction, multiplication and division.

Dr. Montessori's math materials are ingeniously interesting and thoughtfully designed and they allow children to perform math steps sequentially and individually in order to build knowledge. The teacher's responsibility is to prepare the environment with these logical materials, introduce the child to their appropriate use, and observe the child carefully. Keen teacher observation is meant to remove obstacles and guide learners to the next step according to their own needs and desires.