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materialised concepts

Aristotle said, “There is nothing in the mind which is not first in the senses”.

Montessori provides a complete curriculum area devoted to enhancing the child’s ability to process and refine information gained via the 5 senses.

The “concept” of number is first introduced, for example, in a “material” known as the “number rods”.

These banded rods are a natural progression from the “red rods” in the sensorial curriculum, but are “banded” to indicate the value. Each band is 10cm so that the “10 rod” is a metre long. By moving and working with the rods, the children absorb concepts.

An example of these is when the “9 rod” and the “1 rod” are placed alongside the “10 rod”. The equal length makes visibly plain to the child that they are of equal lengths or values.

Addition and subtraction concepts flow easily because of the concrete learning which has taken place.

Numeracy, geometry and even algebra is offered to the 3-5 year old child in this concrete “play” format.


You may have noticed that all the mathematics materials are very tactile, concrete items.    The children are able to work with these items in very practical ways, hence understanding some mathematical processes which ordinarily we would have thought as being appropriate for much older than this age.

Montessori created apparatus that were “materialised concepts” – that is, abstract concepts made into concrete objects.     Adults encountering these materials have commented that their experiences of mathematics at school would have been much more positive had the learning been provided in this way.  Some have learnt for the first time what it means to “carry the one” from one “place” to another.

Other materials are available for this age group, and beyond, that cover the whole range of mathematical learning.



Matching the size of the “red rods” in the sensorial curriculum, the number rods are a natural progression.   The banding of red and blue shows the number as a total value on the one rod.   When proficient,  tablets with the numerals are added.  Children can start to compare and add by  moving the rods around.


Working in the same way as the sandpaper letters, the shape and name of the numeral is introduced to children whilst they still like touching and feeling.