GTMS Life > Blog January 5, 2023

Primary ADM: Mathematics in Montessori

In this blog we will discuss the mathematics curriculum in the Montessori classroom and how it appears through the first, second, and third year children. “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 […]

In this blog we will discuss the mathematics curriculum in the Montessori classroom and how it appears through the first, second, and third year children.

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 can thus carryout an abstract mental operation and acquire a kind of natural and spontaneous inclination for mental calculations.

Maria Montessori
The Discovery of the Child, p. 27

Whether we are aware of it or not, we use math in everyday life. We interact with mathematics in a multitude of ways, such as, asking for more or less, taking inventory of things or people around us, measuring quantities, sharing, etc. While watching children learn mathematical concepts, it is truly impressive to see how capable and eager to learn they are.

Throughout childhood, children will enter different sensitive periods that are able to be nurtured in a Montessori environment. Beginning around the age of four, children enter a sensitive period for order; this comes with a greater awareness of patterns around them, counting, and classification. A child’s sense of order is what pushes them into exploring their mathematical mind. This term was coined by Dr. Montessori to describe the development of a more precise way of thinking which includes abstraction, calculation, estimation, and reason. Their sense of order will push them to discover patterns they see, quantities of objects, and space around them. These sensitive periods are nurtured by the different distinct curriculum areas in the classroom. The math curriculum has its own area, with the materials ordered on the shelf from simplest to most complex from left to right and top to bottom. The materials will start from concrete representations of mathematical concepts to most abstract. Everything in the class is ordered and classified. Other curriculum areas in the classroom also inadvertently introduce math to children as they interact. Many of the Sensorial Materials introduce children to dimension, geometry, and the decimal system. Materials like the Red Rods, Pink Tower, Cylinder Blocks,  Constructive Triangles, and Brown Stair all introduce different mathematical concepts like length, width, and depth all while working with a base of 10. 

Mathematics is a tactile experience in the Montessori classroom. The materials are designed in such a way that allows children to experience abstract concepts like quantity and numerals in a concrete way. The materials are made of attractive materials like wood and glass which carry weight. Interacting with physical materials that grow larger and noticeably heavier as the quantity grows helps engrain in the children the concept that 100 is more than 10, and 10 is more than 1. Materials like the Number Rods, Golden Bead Material, Cards and Counters, and Spindle Boxes all are useful in teaching this concept.

Quantity and Numerals

A large part of early Montessori math is learning how to associate quantities with numerals! Children are able to learn this concept through the Bead Stair, Spindle Boxes, and Cards and Counters. With the Bead Stair children learn to match bead chains with 1 bead up to 9 beads with their associated numerals. Spindle Boxes allow children to count and group small wooden rods and put them into the boxes with their associated numbers. The Spindle Boxes also introduce the concept of zero. With Cards and Counters children can take different objects and match quantities with the number written on the card. All of these materials allow the children to manipulate the object and have a visceral experience for what larger and smaller quantities feel like. Through these materials the children become confident with counting, recognizing, and matching quantities and numerals 1-10.

Decimal System Introduction

After a lot of practice with associating quantities with numerals, the child can be introduced to the decimal system through the Golden Bead material. There is still a principle focus on the tactile nature of the material. The children are introduced to the concept that one single bead is 1 unit, a bar of 10 unit beads represents one 10 bar, ten 10 bars fastened together represents one 100 square, and a cube that is 10 units long, 10 units wide, and 10 units high represents one 1000 cube. The children learn to name and recognize these materials, then form numbers with the bead materials from 1-9,999. They learn to sequence numbers through number cards that are used alongside the Golden Beads. Children find large numbers fascinating and exciting which holds their interest as they form these numbers with the material. They learn to exchange quantities for one another, such as exchanging ten unit beads for one 10 bar, or ten 100 squares for one 1000 cube. The golden bead material familiarizes children with the hierarchy of numbers and the concept of teens, tens, hundreds, and thousands. 

The Four Operations

Children are introduced to the four operations (addition, subtraction, multiplication, and division) through group lessons with the golden bead materials. This allows the continuation of a sensorial experience by having the child physically combine and remove Golden Beads as equations are being performed. Once they become more comfortable with each of these concepts, they can move from the Golden Bead material to the next stage of abstraction. In their next stage of learning they begin working with the stamp game. In the Stamp Game, each stamp is the same size and weight. They are color coded and have number categories of 1, 1o, 100, and 1,000 printed on them. The Stamp Game helps the child make an incremental step away from relying on the concrete material and allows them to move further towards internalizing the concepts of the four operations. 

Memorization

There are several activities children perform after being presented with the decimal system that help them with memorization of math facts for all four operations. Once they memorize certain key combinations, the child quickly realizes they can solve any equation, regardless of digits, because they are only ever really working with numbers 1-9. Materials in the classroom, such as the Snake Game, Four Operations Strip Boards, and Four Operation Finger Charts help meet the child where they are developmentally. After having worked through long equations with large numbers, these materials help them solve equations more quickly while internalizing these math facts. 

“Children display a universal love of mathematics, which is par excellence the science of precision, order and intelligence.”

Maria Montessori in E.M. Standing’s Maria Montessori: Her Life and Work, p.344.

Throughout their time in a Montessori classroom, children are consistently encouraged to explore different concepts and strengthen their abilities. Through an ordered environment, necessary materials, and a lot of repetition children are able to nurture their mathematical minds in a fulfilling way. We hope they carry their interest and love for learning throughout their whole lives!

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