N is for Number line
The number line, often displayed above the Board or down the side, is an essential but often underutilised tool in school classrooms. While it is typically visible to children, it is not always used as effectively as it could be.
Research suggests that most children have an innate sense of a number line, however researchers don’t agree whether this early mental number line is linear (equally spaced) or logarithmic (the numbers get closer together as they get larger) or a mix of both (Siegler, R. S., & Booth, J. L. (2004)).
A number line is generally the 1st step after the concrete phase for counting on, where children have been using physical objects such as beads or an abacus to help count on numbers, working potentially with 5s and 10s to help children with spatial representation of number (Bobis, J., & Bobis, E. (2005)). Moving on from this type of representation to a number line can be challenging and requires some careful thought possibly working alongside the concrete tools to aid in their understanding.
Eventually children benefit from using an Empty Number line where students can fill it in themselves developing their own strategies for a question. This allows children to model their number operations and allow both methods and errors to be visible (Bramald, R. (2000)). As a model, it supports the development of more formal and efficient strategies; whilst allowing children the freedom to come up with their own and not have them prescribed by the teacher. This may strike fear in to the hearts of some teachers however letting students experiment and play with number allows them to develop their problem solving skills, and also gives them confidence to approach new problems on their own. (Bobis, J. (2007))
There is strong evidence to suggest that training children to use a number line competently supports their development of arithmetic, proportion and, with use of empty number lines, problem solving. Number lines can be brought in when playing games, Siegler, R. S., & Ramani, G. B. (2009) found that low income pre-schoolers had better numerical understanding after they had played linear number board games.
The NCETM has some great resources for introducing and using a number line and plenty more can be found online. A number line is not a new concept but it is one that could be used more effectively right across the range of ages, alongside concrete tools for those that require additional support.
