Montessori Mathematics Activities
Naturally, children are attracted to numbers. Young children are always trying to make sense of their environment and the world that is around them.
Children are born with the ability to be able to see similarities and differences, as well as sequences and patterns. Children learn how to recognize and adapt to the changes that occur in their environment and they are then able to feel comfortable in a new space.
Maria Montessori recognized that children are born with a special mind, one that likes to order. It is this that enables humans to be able to calculate and make judgments.
As we are born with this particular mindset, Montessori believed that we need to provide mathematical opportunities from an early age, as they are appropriate for the kind of mind that we have.
Maria Montessori knew children aged under six learn through their senses and need hands-on activities as traditional mathematics education does not tend to be taught using a hands-on approach.
We will now, therefore, take a more detailed look at how Montessori mathematics is taught and the materials used to teach mathematical concepts and activities.
The First Steps
To begin with, the curriculum focuses on concepts that are concrete. Afterwards, abstract concepts are introduced.
The same applies to the Montessori mathematics curriculum. When we refer to the word concrete we are talking about something that can be held in the hand. An object that can be held may symbolize something else e.g. a number.
As children develop, they stop using these objects and are ready to work things out on paper or in their own heads. It is at this point that we call things abstract.
Early Montessori Mathematics and Activities
It’s quite surprising what preschoolers are actually able to do when it comes to early mathematics.
Materials such as number rods (blue and red rods which can be arranged to make a stair pattern) allow children the opportunity to experience mathematics before they can even count.
Alternatively, sandpaper numbers help children to form their numbers before they are actually able to write them.
Once a child is ready to learn simple operations there are many Montessori materials available to help them.
An example of this is the Montessori golden beads. With these beads, one bead represents the number 1. 10 beads in a line represent the number 10 and 100 beads, which are fixed to a square represent the number 100.
When it comes to the number 1000, there is a cube, which is visually 1000 times bigger than the one bead.
The golden beads enable children to understand number visually and they can be used to teach children addition, subtraction, multiplication and division, using numbers up to 1000.
Children soon begin to understand that 10 of the 1-beads is the equivalent of 1 of the 10-beads and this is due to the fact that they can physically hold the numbers in their hands.
The Next Stage
Between kindergarten and lower elementary children begin to use other Montessori materials for their mathematical development.
An example of a material would be the Stamp Game. This consists of a wooden box, which contains separate sections.
Inside each section, there are some green tiles labeled ‘1,’ blue tiles labeled ’10,’ red tiles labeled ’100’ and other green tiles labeled ‘1000.’ (Hierarchical colors) Now rather than having a large cube, which represents 1000 as they had before, the children are able to use tiles that are differentiated by color and a label rather than by size.
Once again this game teaches addition, subtraction, multiplication and division using numbers in the thousands.
The materials used in Montessori mathematics activities are not set to a specific age group. They can be used for different purposes when children are of different ages.
For example, the golden beads can be first used to teach children how to count. They can then later be used to help children to memorize multiplication facts and for skip counting.
The next step that they can be used for is to make sure that all concepts are understood and concrete such as cubing or squaring.
Once children are confident with the operations taught through the stamp game, they are ready to move on and use a Montessori material known as the bead frame.
This can teach multiplication, addition and subtraction. The frame looks similar to an abacus and it has 10 beads on each rod and uses the hierarchical colors.
Once a child is comfortable with the bead frame, they are usually ready to add and subtract large numbers using only a pen and paper.
As Children Progress Further
The next step would be to use a material known as the checkerboard, which is used to solve problems related to multiplication.
To start with, the numbers that the children use are small but they soon begin to use larger numbers.
When it comes to long division in Montessori mathematics, children can use a material known as the racks and tubes.
When children get to grips with both the checkerboard and the racks and tubes they will confidently be able to multiply and divide large numbers and no longer need to use any of these materials.
Other Mathematical Aspects
As we all know mathematics is more than just operations and therefore Montessori mathematics also teaches fractions and geometry from a young age.
With regards to geometry, children from an early are able to identify complex shapes such as rectangular prisms, square based prisms and ellipsoids and not just spheres and cubes.
As they continue to progress, children begin to learn about other aspects such as angles and polygons.
With fractions, children begin with a lesson using an object such as an apple and look at how to divide it fairly (the link between division and fractions is recognized early on.)
The next step would be to look at fraction insets and eventually children are able to both multiply and divide fractions.