An Overview of Montessori Math Curriculum
Recently I have had several requests to provide a brief overview of the Montessori Math curriculum. I have done my best to simplify the curriculum below, but there is just so much information to cover!
A Guide to Montessori Preschool Math: Materials and Curriculum Explained
First of all, there are the Montessori Sensorial Materials which indirectly prepare a child for work with the Montessori Math Materials. The Sensorial Materials allow the child to internalize and truly understand a wide range of concepts, each of which is done in a hands-on, concrete manner. The Sensorial Materials prepare the mind for a deep understanding of the principles of mathematics and at the same time prepare the child for work with the Montessori Math Materials.
A great example of this is the Red Rods, which are used for introducing the concept of comparative length. Through laying out the Red Rods one at a time, the child learns at the most basic concrete level how the quantities one to ten relate to one another. Upon mastery of the Red Rods, the child is now ready for the Number Rods.
Preschool Mathematics Materials
Once a child has a solid understanding of the basic quantities 1 to 10, you can now teach the numerals. The Sandpaper Numerals are traced by the child one at a time to associate the number names with the fixed quantities that they have experienced with the Number Rods. Once the child has learned the names of the numbers, it is time to merge the quantities and numerals together to give them absolute clarity in the accurate association of numeral and quantity.
Next, you can introduce materials such as the Spindle Box to allow the child to see what “nothing” or zero looks like. A child needs to understand that ‘0’ on its own means nothing, but when it is associated with a number (i.e. 2), it indicates a bigger number (i.e., 20). I find it effective to play different games with the children to reinforce the concept of ‘0’ and it is fun to see the children play the games on their own, when the teacher is not participating.
Next, the child is introduced to the Cards and Counters, where the child first lays the numerals 1 to 10 in the correct sequence and then below each numeral counts out the corresponding quantity. I find it absolutely brilliant that the entire Montessori Preschool/Kindergarten Math program reinforces the importance of 10 as the base for introducing the formal demonstrations of the Decimal System later on. On another note, I always have a few Cards and Counters activities available and I change the counters regularly to correspond with the current theme or season. Jordan especially loves the dinosaur counters and the river rocks which I spray-painted a golden color to look like pieces of gold … perfect for St. Patrick’s Day!
I often introduce children to the Bead Stair at this point as they now have the ability to count the quantity of each bead bar and to memorize the quantity that each colored bead bar represents.
Once you are confident that a student has a sound knowledge of numbers one to ten as well as their corresponding quantities, it is time to introduce him to the exciting world of the Decimal System, better known as the Golden Bead Material! The Golden Bead Material intrigues children of all ages and it is always enjoyable to introduce them to units, tens, hundreds, thousands through the concrete learning materials.
I love that the Golden Bead Material shows the decimal hierarchy in three-dimensional form:
units = single golden beads,
tens = a bar of 10 unit beads,
hundreds = 10 ten bars fastened together into a square,
thousands = a cube ten units long, ten units wide and ten units high.
The children learn to first recognize the quantities, then to form numbers with the bead material through 9,999 and to read them back. They also learn to read and write numerals up to 9,999, and to exchange equivalent quantities of units for tens, tens for hundreds, etc. I remember when I first introduced Jordan to the Golden Bead Material presentation tray. He immediately noticed that the unit bead is much lighter in weight than the thousand cube and even commented on how 1 is much less than 1000 … I knew we were off to a good start!
Through the Decimal System Material, the child is able to clearly understand that when a number reaches 10, it then proceeds to the next hierarchy. Exchanging is a difficult concept to understand but made so simple using the Golden Bead Material, coupled with a great deal of repetition. A child soon learns that if he has 10 ten bars, he must exchange those 10 ten bars for 1 hundred square, and if the child has 10 hundred squares he must exchange them for 1 thousand cube.
In the later part of the mathematics program, traditional number names are introduced again by forming quantities with the concrete material first and then associating each quantity with their written symbols through the ‘Seguin Boards’. Jordan needs a fair bit of encouragement to work with the Seguin Boards, as he feels he already ‘knows’ how to do it. He does know the names of the numerals, but needs help with associating the correct quantities with each numeral. We also have a teen frame in our class which has served as another great reinforcement tool for Jordan. He first places the numerals 11 to 19 in the correct sequence above the frame and hangs the corresponding bead bars below each numeral.
When a child gets to this point, he/she will continue to work extensively with the four operations (addition, multiplication, division and subtraction). However, the child will do so using the various boards, the Stamp Game (a manipulative system that represents the decimal system as color-keyed "stamps") and the Bead Frames (color-coded abacuses).
Related NAMC blogs:
- Montessori Curriculum Explained: Math Materials, Activities and Philosophy
- DevMontessori Math Materials and Curriculum for all Age Groups
- Montessori Philosophy: Moving from Concrete to Abstract
As much as possible, NAMC’s web blog reflects the Montessori curriculum as provided in its teacher training programs. We realize and respect that Montessori schools are unique and may vary their schedules and offerings in accordance with the needs of their individual communities. We hope that our readers will find our articles useful and inspiring as a contribution to the global Montessori community.