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How does number sense begin?

An intuitive sense of number begins at a very early age. Children as young as two years of age can confidently identify one, two or three objects before they can actually count with understanding (Gelman & Gellistel, 1978). Piaget called this ability to instantaneously recognise the number of objects in a small group 'subitising'. As mental powers develop, usually by about the age of four, groups of four can be recognised without counting. It is thought that the maximum number for subitising, even for most adults, is five. This skill appears to be based on the mind's ability to form stable mental images of patterns and associate them with a number. Therefore, it may be possible to recognise more than five objects if they are arranged in a particular way or practice and memorisation takes place. A simple example of this is six dots arranged in two rows of three, as on dice or playing cards. Because this image is familiar, six can be instantly recognised when presented this way.

Usually, when presented with more than five objects, other mental strategies must be . For example, we might see a group of six objects as two groups of three. Each group of three is instantly recognised, then very quickly (virtually unconsciously) combined to make six. In this strategy no actual counting of objects is involved, but rather a part-part-whole relationship and rapid mental addition is used. That is, there is an understanding that a number (in this case six) can be composed of smaller parts, together with the knowledge that 'three plus three makes six'. This type of mathematical thinking has already begun by the time children begin school and should be nurtured because it lays the foundation for understanding operations and in developing valuable mental calculation strategies.

Learning to count with understanding is a crucial number skill, but other skills, such as perceiving subgroups, need to develop alongside counting to provide a firm foundation for number sense. By simply presenting objects (such as stamps on a flashcard) in various arrangements, different mental strategies can be prompted. For example, showing six stamps in a cluster of four and a pair prompts the combination of 'four and two makes six'. If the four is not subitised, it may be seen as 'two and two and two makes six'. This arrangement is obviously a little more complex than two groups of three. So different arrangements will prompt different strategies, and these strategies will vary from person to person. If mental strategies such as these are to be encouraged (and just counting discouraged) then an element of speed is necessary. Seeing the objects for only a few seconds challenges the mind to find strategies other than counting.

This week we have been working on our subistising abilities by trying to remember what we saw, when a ten frame with dots on it was shown, and then saying how many dots there were.

If you would like to read more about developing children’s understanding of Maths, please visit:

(Article take from NRICH -Number Sense Series: Developing Early Number Sense Article by Jenni Way)


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