Have you ever thought about how children represent numbers in their head when they learn to count?

The dominant theory is that numbers are stored along a mental number line, with small numbers associated with the left-hand-side of space and large numbers associated with the right (for languages where one reads from left to right). Just like a tape measure.

When children are young and they learn numbers, the tape measure in their head is not yet very accurate and their idea of how numbers relate to each other might be incorrect. For example, whilst the distance (2) between number 1 and number 3 is the same as between numbers 7 and 9, when asked to place numbers on a blank number line, young children might place 1 and 3 more far away than 7 and 9 (Figure 1).

Figure 1. Line A shows the representation of a compressed number line, typical of young children.

Line B shows the representation of a developed number line.

The more children learn how numbers relate to each other, the more their number line will develop. It has been shown that children who have a firm mental number line are better at manipulating numbers (add and subtract numbers but also multiplicate and divide) and, as a result, they have better mathematical abilities.

For further reading see:

Siegler, R.S. & Booth, J.L. (2004), Development of Numerical Estimation in Young Children. Child Development, 75: 428-444.

http://www.cs.cmu.edu/afs/cs/Web/People/jlbooth/sieglerbooth-cd04.pdf

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