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.