Children’s mathematical competencies in school impact on their long-term outcomes at work and in general life. Moreover, those who start school behind their peers are likely to stay behind. Successful school-readiness in mathematics starts during preschool years. Many children are already at-risk of long-term difficulties with mathematics by four years of age.

This paper presents the results of a four-year longitudinal study – including two years of preschool (age 4 years), kindergarten, and first grade – designed to identify the early quantitative competencies that predict readiness to learn mathematics at school entry.

The key school-entry competencies include number system knowledge, that is, a network of associations among number words and numerals, understanding their relative magnitudes, and operating on these magnitudes.

This means that children’s school-readiness can be directly observed by children’s count list (i.e., the ability to count, 'one, two, three…'), how well they use counting to enumerate (i.e., determine how many) collections of objects, and especially their conceptual understanding of the magnitudes represented by number words and numerals.

The findings of this research point to the need for early interventions that target parent-child number-related activities, preschool experiences, and child-centred factors (e.g., to promote better attentive behaviour in classroom settings).