The transition from informal to formal mathematical knowledge: Mediation by numeral knowledge.

The purpose of the present study was to determine if numeral knowledge—the ability to identify Arabic numerals and connect Arabic numerals to their respective quantities—mediates the relation between informal and formal mathematical knowledge. A total of 206 3- to 5-year-old preschool children were assessed on 6 informal mathematics tasks and 2 numeral knowledge tasks. A year later, these children were assessed on 2 measures of formal mathematical knowledge, namely, the Woodcock-Johnson III Calculation Subtest and a formal number combinations task. Mediation analyses revealed that the relation between informal and formal mathematical knowledge is fully mediated by numeral knowledge, but only when both the skill of numeral identification and an understanding of numeral to quantity relations are considered.