Mathematics in Montessori 0
What is Mathematics?
“The laws of Nature are written in the language of mathematics.. the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word”. Galileo Galilei
Maria Montessori understood that mathematics is a language we use for interpreting and understanding the the world around us. She realised that mathematical concepts need to be first absorbed through the senses before children can abstract mathematical information.
For this reason the Montessori mathematics curriculum moves from concrete experiences to increasingly abstract representations. Before children are asked to learn symbolic representations of numbers and memorise number facts and rules, they should first be immersed in a myriad of sensorial experiences with numbers. In the Montessori classroom, the sensorial curriculum prepares children for later abstract work with numbers.
When using the sensorial materials children experience various dimensions and shapes and relationships between these. The materials isolate one concept and are self correcting and encourage independence and problem solving. Each sensorial piece of equipment is designed using the base ten system. Children need to know numbers to ten to work with the decimal system.
As children work with the materials they unconsciously absorb the relationships between numbers one to ten. When a child works with the red rods for example, the tenth rod is ten times longer than the first. When they work with the pink tower, the smallest cube is 1cm3 while the largest is 10cm3.
The exactness of the materials allows children to make their own mathematical discoveries. When using both the green and yellow sets of knobless cylinders children can create the rainbow number facts to ten.
As children progress through the mathematics curriculum they are gradually introduced to the symbolic representations of number. Children work with operations with numbers and also use the materials to help memorise mathematical facts.
What are the Key Montessori Materials? 0
The Montessori curriculum is a scientific based curriculum. Each resource and material has been made during Maria Montessori’s time studying the children in her Casas. In the 3 – 6 prepared environment the classroom and the materials are divided in five sections. The five sections are practical life, sensorial, language, mathematics and culture. The practical life area contains activities on trays and baskets that teach the child life skills, for example sweeping, pouring, chopping and how to hold a book. The sensorial section works on refining the senses. The senses are visual, auditory, tactile, olfactory, gustatory, baric, thermic and stereognostic. The language section begins with teaching stencilling and pincer grips, next teaches all the letters in a phonetic and tactile way before moving on to the pink, blue and green language series and finishing with grammar. The mathematics section begins with teaching works all the way up to multiplication, division and even long division. The culture section covers everything from botany, zoology, biology, geography, astronomy and history.
In all of the above sections there are very famous and memorable materials used to teach the concepts.
One of the most famous material is the pink tower. If you google Montessori, pick any link or website and the words ‘pink tower’ will appear very quickly. The pink tower is in the visual discrimination area of the Sensorial section. It works on the concept of height discrimination. There are ten cubes each differentiating in size of 1cm cubed. The biggest cube is 10cm cubed and the smallest cube is 1cm cubed. The children make a tower, using the biggest block on the bottom and working up to the smallest cube on the top of the tower. This is always a favourite in the classroom and gets used every single day! http://www.iammontessori.com.au/search?q=pink+tower
Another key Montessori Material is the Movable Alphabet. This is used in almost all of the exercises in the Language section. It is a box with 26 sections in it and 4 or 5 of each letter in the boxes. It is usually wooden but can sometimes contain plastic letters. Letters are used to spell out words. We use it all the time and it means that every child can be ‘writing’ words even if they struggle with pincer grip and pencil work. http://www.iammontessori.com.au/search?q=movable+alphabet
The culture section contains puzzles of the world, the continents, and the countries. These begin with the sandpaper globe and coloured globe. We then do the world puzzle, move onto the different continents and then move onto the countries. For example, we do the world puzzle, move onto the Puzzle of Asia and then move onto Map of China. When teaching geography, we begin with the biggest and move onto the smallest. We teach the solar system, then the earth, then the continents, then the countries and then the towns in that country etc. http://www.iammontessori.com.au/collections/cultural/products/puzzle-map-of-ocean
The mathematics section is famous for the golden bead materials. The beads are used throughout the section. They start with one bead which represents a unit, a ten bead bar which is ten beads, a hundred square which is one hundred and a thousand cube with is one thousand. They children are introduced to the beads and explained what they mean and the different hierarchy and placement of numbers before they are shown the written symbol for each bead. Beads can be used for addition, subtraction, multiplication, division and for learning numbers, for example 64 has six ten bead bars and 4 units. http://www.iammontessori.com.au/products/45-golden-beads-bars-of-10-w-box
In the infant and toddler prepared environment the most popular materials are the imbucare boxes. These are posting boxes with different 3D shapes to be placed in the boxes. http://www.iammontessori.com.au/products/imbucare-box-w-large-cylinder
All Montessori products are available on www.iammontessori.com.au in the ‘shop’ section.
Why Montessori Maths just makes sense! 0
I would like to share with you a story that I remember from when I was teaching a year one class in a Brisbane primary school. I walked in to relieve a teacher who had some planning time.
The lesson I was to complete teaching was a lesson on weight. Students were apparently learning the concepts of “heavy” and “light”.
I walked over to a little boy who had been unengaged and asked him if I could help him. He looked at me with a very serious expression and said, “No you can’t. He asked me to circle the heaviest one but they are both the same”. As he said this he pointed to two drawings on a page. One was a drawing of an elephant and the other a drawing of a mouse. The boy continued, “They are the same on the page, it’s the same page and its the same pencil. That is not heavier”.
As soon as this six year old had spoken I realised a few things; firstly, how clever he was, secondly, how correct he was and thirdly, what a stupid and abstract activity this was to give children who were meant to be learning a sensorial concept like weight!
Mathematics should begin as a concrete and physical experience. It is only when we have experienced with out senses concepts like heavy, light, full, empty, long, large, small, big etc, that we are able to remember the essence of these experiences and then solve abstract problems.
Asking a six year old to decide if an elephant is heavier than a mouse based upon a drawing on a piece of paper is assuming a lot of information about this child. To get this seemingly simple question right, the child would have to; have already hefted heavy and light objects and remember the “feeling” and meaning of each of those words, know what an elephant is, know the true size of an elephant, know what a mouse is and how large it would be in real life and know how to “circle” a picture. Without knowing it, the teacher had bombarded the children with a poor abstract example, that actually presented many other challenges that the adult had not even thought of.
The Montessori Mathematics curriculum is unique because it still acknowledges the fact that true understanding comes from initial concrete experiences. Children get to feel the number nine when they hold nine spindles in their hands. They get to feel how much longer and bigger the number ten feels as they carry the longest red rod across the room. Children get to experience tall when they build the pink tower. They get to feel and see the number 1000 when they carry a cube with one thousand beads or lay 1000 beads out in a long snake on the floor. The Montessori Maths curriculum is carefully designed to help children develop a true understanding of number and quantity, not just the ability to count by rote or recognise number symbols.
Maria Montessori recognised that children learn through their senses. It is only when we give children the ability to have these sensorial number experiences that they will really internalise the mathematics they are learning. The greater their foundational understanding of mathematics is, the greater they will be able to abstract from this later and understand harder mathematical concepts.