When parents come for admission to Montessori, they often proudly claim that 'My child can recite 1 to 10'. I cannot tell them that the child is just remembering these numbers by rote. I find it difficult to disappoint them by saying that with the child's prodigious memory, he can recite a lot by rote. When the child remembers the number by rote, he does not understand that the symbol '5' stands for quantity of 5 items, or 8 stands for quantity of any 8 items. 5 is a concept, not a concrete number. The number 5 can stand for 5 bananas, 5 chocolates, or 5 Rupees.
Montessori however manages to 'teach' this concept of 'number' by using these 6 steps:
Step 1: Help the child count the number 1 to 10 using 'number rod'
Before the introduction of numbers, the child is already introduced to 10 long rods, ranging from 10 cm to 100 cm. The child has learnt to align these long 'red' rods. See this picture below.
Long rods done by a child
Photo courtesy: Sapience Montessori
But now, instead of red color rods, number rods are marked as 'red' and 'blue' which the child uses to count a number. Smallest rod is 'rod of 1', second rod of blue and red is 'rod of 2', and so on. While counting the rod, the child often loses patience. Sometimes the child keeps on 'counting the number by his mouth', but his hand is 'stationary'. He often takes long time to count rods beyond '6'. If a child gets distracted while counting, he often forgets and counts it ahead without noticing that he has missed the count.
Long number rods 1 to 10
Step 2: Child traces the symbols 1 to 10.
These are sandpaper numbers. They help the child to remember the symbol of number. Observe the big numbers. Numbers 1 to 5 are kept on the mat, while the box of number is showing the card of '9'. Here the child's muscle memory is used to remember the 'symbol'.
Sandpaper numbers 1 to 10.
Step 3: Number symbol is 'associated with rod'.
In this step, the child associates the 'rod of 3' with symbol '3' and so on. This step is often the trickiest step. He either forgets the name of symbol beyond 6. Or he may forget the counting of number. To test the child's memory, he may be asked to pick a rod randomly, say rod of 5, then rod of 8 and so on. Some children at this stage find it so challenging, that they undergo performance-anxiety. They are reluctant to come to Montessori. In Montessori, lot of space is offered to the child to assimilate and resolve this.
Association of symbol of 1,2 etc with the rod of 1,2 etc
Step 4: Using small number rods for counting
If the child is doing long number rods well, he moves to counting of small number rods. These small number rods are smaller in size and can fit on a small mat. Child finds it more difficult to count small number rod. Sometimes we have also observed that the child goes back to long number rods and counts. This facilitates repetition of the counting.
Child counting small number rods and associating them with numbers
Photo courtesy: Sapience Montessori MHC
Step 5: Counting of spindles 0 to 9
Until the step 4, the child is counting contagious numbers. Now he starts counting discrete spindles. He may even ask a question 'What is zero'. This shift of discrete counting is more drastic for a child. He may start counting either from number 5 or from number 9. At this stage, his 'number association with symbol' is further strengthened. Therefore, at this stage, child's memory is tested. They often confuse 6 with 8, or 6 with 9, and so on. If the confusion persists, he has to be given the sandpaper number to trace once again. His patience and focus also gets tested.
Counting spindles with Spindle box 0 to 9
Step 6: Count the 'counters' and associate it with 'card'
This is the last stage of counting 1 to 10, where the child's capacity to associate symbol with quantity is tested. Using this foundation, he is later introduced to decimal system of units, tens, hundreds and thousands to count 4-digit numbers upto 1000.
Child counts 'counters' and associates it with number card
Step 1 to step 6 ensures that the child associates the symbol with the exact quantity, be it the quantity of bangle, or banana. A child takes about 2 to 3 months to go through these six steps. When I tell this to parents, they are often surprised. They cannot imagine that a child takes 2-3 months to 'understand' the concept of 1 to 10. If you observe these six steps, these six steps not only test child's memory; but it also tests his ability to keep focus and maintain patience. Even if the child tries to memorise in any of the step, his mistake gets spotted easily in the next step. He is almost 'forced' to 'understand' the number.
And because the Montessori method is child-centric, every child gets the concept of 'number' in Montessori. Some child get it early, some get it late. Some children may undergo performance-anxiety and will take more time to overcome this anxiety. During this period, the child could also be reluctant to come to Montessori. In Montessori, space and time for emotional-resolution is offered to every child. Emotional-resolution plays an important role in learning. In the traditional method of schooling, where children are taught in group, it is often easy to miss a child who 'does' not understand the concept of number. But in Montessori, this never happens. At the end of six steps therefore, every child gets the concept of number.