Maria Montessori believed that children were born with a ‘mathematical mind’. She defined this as a natural tendency for exactness, orientation and order. This usually manifested in older children as the capacity for logical, systematic thinking.
In her writing in The Absorbent Mind, Montessori compares this genetic gift to the warp on a loom. Experiences and learning are woven in as the child develops.
Current research confirms young children’s early capacity to recognise that two objects are different from one object as early as the first year of life.
The activities of everyday living and sensorial materials in the Montessori classroom explore these mathematical qualities. They provide a strong foundation for later systematic learning of arithmetic, geometry and algebra.
However, even before we introduce young children to these areas of learning, we can observe their natural instinct to organise.
They usually demonstrate this capacity by schematic behaviours. They repeatedly use trajectory, enveloping or enclosure to express their natural tendency for repetition and organisation in a particular way.
Elinor Goldschmied based the heuristic bag activities on toddlers’ natural tendency to compare, match and grade objects.
Fitting paper tubes into each other, or posting shapes through appropriate openings not only enhances their eye-hand coordination. It also boosts children’s capacity to note similarities and differences.
During the second year of life these experiences are often accompanied by adults’ comments that encourage what is happening: “Try it again”, “Take your time”, “Yes, you have done it!”.
We also explain: “Yes, the cube fits into the square”, “Twist the piece until it fits”, “You have too many, take some out”, or perhaps ‘”Which comes next?”, “Which one is different?” or “Are they the same size?”.
This is a perfect example of how mathematical language accompanies children’s experiences from early on, alongside the encouragement toddlers receive from their parents and carers.
As children settle in a Montessori nursery, we introduce them to cylinder blocks. These give them opportunities to experience one-to-one correspondence as they learn to find the right sockets.
This is first by trial and error and later by visual discrimination. The experience of the cylinder fitting snugly into only one of the holes highlights that they belong together.
Children will have similar experiences highlighting one-to-one correspondence later. On their third birthday they may find that the three candles on the cake match with the numeral three written in icing or on a birthday card.
In a Montessori setting, we encourage young children to hold the knobs of the cylinders with their thumb and first two fingers as they try to fit the cylinders into the sockets.
This focus on handling the cylinders enhances their pincer grip and supports their ability to hold a pencil. As adults we carefully, deliberately and precisely model the movements.
By paying attention to details and the handling of resources you can maximise levels of concentration through careful manipulation.
As children continue to use the cylinders, introduce language such as ‘big’ and ‘small’, ‘wide’ and ‘narrow’, ‘tall’ and ‘short’. Through first-hand experiences like this we can scaffold children’s understanding of the cylinders and build the foundation for later learning.
Alongside Piaget, Montessori understood intuitively the importance of real experiences as an essential foundation for the development of conceptual frameworks.
Her golden bead materials demonstrate perfectly her deep understanding of how children learn to understand quantities and mathematical language while manipulating objects.
The golden beads are an excellent example of her thinking. We introduce them to children who have a secure understanding of numbers to 10.
Using the units, tens, hundreds and thousands as represented by the beads in their bars of tens, squares of hundreds and cubes of thousands, children have an opportunity to experience and compare one unit (one bead) with the feel and weight of the one thousand cube with its 1,000 individual beads.
At a later date they’ll also have the opportunity to actually count the 1,000 beads – organised in 100 ten-bead bars.
This activity clearly demonstrates to young children conservation and reversibility of number. This enhances their mathematical mind by weaving experiences of the organisation of the decimal system into the warp of the mathematical mind and scaffolding their developing abstract thinking.
Barbara Isaacs is the academic director of Montessori Centre International.
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