Children can often count to ten from quite a young age. They learn through songs such as ’One, two three, four five, once I caught a fish alive,’ or count steps, sweets or jumps with their parents.
This practice of our number names doesn’t necessarily mean they can identify number quantities or can match numbers to items one by one. With practice, however they do. Many children then get stuck at this stage. They continue to count items one by one up to large quantities, sometimes up to one hundred. I have seen GCSE maths exam papers covered in tally marks. This is an obvious clue to the candidate’s weak facility in maths, he probably ran out of time in any exam using this method of calculation. This kind of student has failed to see the structure of our number system and doesn’t use the shortcut of counting in fives or tens. This makes maths laborious and often inaccurate.
Yet, amazingly very young children, babies even, can identify the difference in quantities between three and four items, and will be drawn to the larger quantity of sweets they like. They are not counting or using number words to decide the larger quantity. They can ‘see’ which the larger quantity is . It is considered that we have a template for number quantity that makes it possible for us to identify number quantities up to five without needing to count. We can also identify larger quantities providing the ratio is 4 to 5. By replicating this ratio we should be able to tell the larger quantity between 16 and 20, 200 and 250 etc without needing to count.
An example of this template in the brain was exemplified by Dustin Hoffman playing an Autistic Savant in the film ‘Rainman’. He could identify large quantities of matches so quickly that it was clear he was matching the number quantity to a template for that number in his brain, he did not have enough time to count. This exceptional ability is at the extreme end of this facility seen in the very young baby who identifies that a card with three big black spots deserves more scrutiny, and stares more intensely, than the card with two spots shown previously.
The easily identifiable field of five has been utilised throughout history – consider the music stave, originally in mediaeval times consisting of four lines, but now universally consisting of five lines
It would be much harder to identify a note were it to be placed on six lines of a stave. Instead we use the more easily identifiable leger lines, above and below the stave.
The Romans also used 5 in their chunk represented as V, and 6 was considered to be VI and 9 as one less than ten – IX. Isn’t it useful that we have two hands of five digits, ten digits altogether? Yet many children feel the need to count all fingers starting with one hand when asked to hold up seven fingers.
Many of our resources are colour coded red and white to aid recognition of quantities up to 100 – See how much easier it is to identify the quantity of ten in the following example: