## Why number sense?

There is an international consensus that poorly developed number sense underlies later mathematical failures. Moreover, without appropriate intervention, which research shows can be effective, children who start school with limited number sense are likely to remain low achievers throughout their schooling.

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## Definitional confusion

The expression *number sense* is ubiquitous in the literature but problematic in its having been used in different ways according to the research domain in which it is located. Our purpose is to clarify a particular form of number sense in ways that teachers, researchers and policy makers may find useful. Our aim is to characterise those essential number competences that require instruction and which year one children need to acquire if they are to become successful learners of mathematics.

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## Three forms of number sense

Our reading of the literature has identified three related but fundamentally different characterisations of number sense. These, for convenience, we label *preverbal number sense*, *foundational number sense* and *relational number sense*. Here we summarise the first and the last of these before presenting our systematic review of the second.

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