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Forty live children, lifteen from each of two kindergarten year classes from different schools, and lifteen from a year one class from one of those schools, were interviewed to assess their knowledge of number word sequences and spatial patterns, and ability to recognise numerals and use counting to establish the numerosity of visible and screened collections. The schools were selected as typifying contrasting socio-economic levels. Five models, each of a different aspect of number development, and each containing up to five levels or stages, were used to generate for each child, aprofile of numerical development. This led. to consideration of the variations of children's number knowledge, within and between year levels and schools. Findings included a wide variation in the number knowledge of children beginning the kindergarten year, greater variation in the lower socio-economic school, and evidente that the kindergarten year mathematics curriculum is most suited to the least advanced.

During the last 30 years, British and United States factors have strongly influenced number topics in early childhood mathematics curricula: e.g. (a) Cuisenaire, which de-emphasised children's counting; (b) Piaget's theories, still a dominant influence on prenumber and early number; (c) the back-to-basics movement in the United States which continues to influence introductory topics on arithmetical operations; and (d) the re-emphasis on counting. As a result, dominant text series and, to some extent, new curricula are out of touch with current research, and there is an urgent need to review current practice. A recently developed model of young children's numerical development is advanced as a possible basis for such a review. Other relevant research is summarised, including two studies which concluded that, typically, children in the first year of school are under-challenged. The article concludes with recommendations for future Australian research and development in early childhood mathematics.

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