Maria Montessori observed that humans have a mathematical mind, that works to understand, measure, quantify, sort, and categorize the world around us. The Montessori Math curriculum follows the evolution of mathematics in humans, starting with one to one ratios and simple counting and tallying and progressing to complex operations and representations. All the materials support later mathematic precision and the math materials are tangible representations of complex operations, allowing a deep understanding of the relationships of numbers, rather than a rote memorization of facts.

At the toddler level, simple counting exercises such as counting the plates when setting the table, counting the children as they line up, and through counting songs and rhymes, introduce the concept of quantity and the names of numbers.

At the primary level, children’s mathematical sense is built on the strong foundation of the sensorial materials where many fundamental concepts. For example, the child has experienced length, volume, gradation, sequencing, and grouping, via the senses. These activities make the abstract concepts of mathematics concrete for hands-on learning. Each activity isolates a particular concept and integrates with other activities to form a strong foundation for further exploration.

Beginning primary math activities include the concept of 1 to 10 (sequences, quantity, numeral names, combinations of ten, basic arithmetic). Additionally the materials include concepts such as teens, tens, introduction to the decimal system, and the operations of addition, multiplication, subtraction, and division.

Children explore fractional equivalences and the fractional names with manipulative materials. They use a wide variety of two and three-dimensional geometry materials and learn the basics of geometric nomenclature. They see and explore binomial and trinomial patterns in certain materials. These experiences help the child gain a visual and tactile impression for later work such as squaring, square root, cubing, and cube root during the elementary years. The emphasis is always on examining patterns and sequences and the connections between arithmetic and geometry in order to help children develop their mathematical minds from an early age.

At the primary level, the focus in on the procedure and concept of the operations, not on accuracy. That is, until the child is determined to find the correct answer.

The elementary level mathematic curriculum revolves around the “Great Lesson” of humankind’s invention of numeration and measurement systems. This story and timeline is a key that opens the door of the imagination to the world of mathematics and geometry. At the Lower Elementary level, students often investigate the number systems of civilizations as diverse as that of the Egyptians, the Romans, and the Mayans. The guide presents ancient measurements such as the cubit and the span and they are used by the children. Upper Elementary students research mathematics, geometry, and invention in the Hellenic world and elsewhere.

Sometime around the age of 5-7, children are making what Montessori called a “passage to abstraction” where they can hold abstract symbols in their mind and connect them with their meaning. Therefore, the children can progress from manipulating very tangible materials to working with increasingly more symbol-based materials, and finally to symbols written on paper. Montessori education is unique in its ability to meet the child where they are in that process and allow the child to move away from tangible materials to solve mathematical problems when they are ready.

Specific skills, concepts, and lessons during the elementary years include the decimal system and mastery of the four operations of arithmetic, study of multiples and factors, geometry, fractions, decimals, percent, money, time, statistics, graphs, pre-algebra, and beginning algebra.