Montessori Arithmetic - A Brief Overview

At our little yellow school, it is amazing to witness the variety of Arithmetic activities being worked with in the span of a day.  From the tiny beads of the Multiplication Bead Board and Golden Beads to the ever changing Cards and Counters to the Bead Cabinet where number chains hang like beautiful necklaces, the materials attract the children with their shapes, colours and sizes.  When working with these activities, the children feel that they are doing very important and big work!  They just can't get enough of these materials.  I understand how the children feel as the Arithmetic materials are among my favourite.

In the Montessori classroom, it is not unusual for the children to sit and observe when someone is receiving a lesson.  Last year something amazing happened when I was presenting the Fraction material to the graduates (those children who would be leaving us for grade one).  I called the graduates to the mat and began the presentation.  During the presentation, the classroom became quieter as children left their work and came to observe.  By the end of the lesson, the entire class was gathered around the mat watching and listening.  It was definitely an amazing experience that illustrated the power and the beauty of these materials.

The Montessori Arithmetic curriculum is divided into five sections - Numbers 1 to 10, The Decimal System, Teens and Tens, Memorization (Arithmetic Facts) and the Passage to Abstraction. The beauty of the Montessori Arithmetic materials is that they build sequentially on previous learning, are self-correcting, isolate the concept being learned and introduce the concrete before the abstract.  A very brief description and photographs of a few exercises from each section follows.

Numbers 1 to 10  - This section forms the foundation for all math work.  Here the children learn the quantities 1 - 10 and the concept of zero.  The children then learn the symbols and the sequencing of those numbers.

The Spindle Boxes - Matching Quantity and Symbol to 9

Cards and Counters - Matching Quantity and Symbol to 10
The counters are changed frequently.

The Decimal System - This section introduces the children to the names of the decimal categories (units, tens, hundreds, thousands) and their relative proportions.  The children will form large numbers with this material and experience the operations of addition, subtraction, multiplication and division.  Teens and Tens work parallels the Decimal System.

Introduction to the Decimal System Materials - Beads and Number Cards are introduced separately.

Exploring 'Hundred'

The Golden Beads - Formation of Complex Numbers

The Golden Beads - Addition

Teens and Tens - This work parallels the Decimal System and focuses on counting beyond 10.  The child is introduced to numbers 11 - 19 through the Teen Boards and numbers 11 - - 99 through the Ten Boards.  The child will also be introduced to linear and skip counting.

Teen Boards - Matching Symbol and Quantity

The Hundred Board - Linear Counting to 100

Linear Counting Beyond 100

The Bead Cabinet - Skip Counting the Squares and Cubes of Numbers 1 to 10

The Bead Chains - A Section of the Cube of 5 Chain

Memorization - The purpose of these exercises is to help the child memorize math facts in all four operations (addition, subtraction, multiplication and division).

Subtraction Finger Chart

The Multiplication Bead Board

Passage to Abstraction - The child uses the knowledge gained from the Golden Bead Material and the memorization of facts and is lead to the point where s/he can do operations abstractly.

The children are introduced to other mathematical concepts such as Fractions, graphing, money and measurement.

Montessori Fraction Circles - The Denominator

Fractions - Making a Fraction Booklet

Graphing - How many syllables are in your name?

Graphing - How many people are in my family?

Baking - Using a Measuring Cup

This brief snapshot of the Montessori Arithmetic curriculum illustrates just how attractive and inspiring the Montessori Arithmetic materials are.  The children are able to move through the curriculum exploring, understanding and mastering the concepts at their own pace. In the Montessori classroom, math is exciting and fun!

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

- Maria Montessori