Childrens understanding of number in the primary school years : a unifying view from early counting knowledge of place value

Previous research has tended to focus on the development of separate number\ud components (e.g. counting, addition, written numbers) and so, cannot comment on\ud how development in one component affect development in others. The purpose of this\ud thesis was to provide preliminary evidence towards a unifying view about the\ud development of children's number competence, from early counting skills, at age four,\ud to knowledge of place value, at age seven. To accomplish that aim 152 children from\ud three different cohorts (Reception, Year 1 and Year 2) were given thirteen maths tasks,\ud three times along one school year, assessing their understanding of four separate\ud number components: counting and knowledge of the number-word sequence;\ud generation of verbal number-words and the understanding of the structure of the\ud numeration system; understanding of the arithmetical operations; and the ability to read\ud and write numbers and understanding of the principles underlying place value. Beyond\ud the assessment of these various number components, special emphasis was given to\ud the separate role of each component and the developmental inter-relations amongst\ud components in the child's development of progressively more complex ideas about\ud number.\ud Based on the children's performance on these tasks and the exploration of their\ud relationships along time, it was possible to outline a preliminary proposal about\ud children's number development. The evidence suggests that each number component\ud plays a significant role at key times. For example, no children could develop the\ud counting-on strategy or succeed in the arithmetical operation tasks without prior\ud knowledge of continuation of counting. The data also showed that no development is\ud possible without the inter-related development of several components, at other times.\ud For example, no child could understand the structure of the decade numeration system\ud without previous combined understanding of continuation of counting, addition and\ud multiplication. Between 93% and 97% of the children fitted the model proposed in the\ud various assessments.\ud Although limited by the constraints of a correlational design, these findings\ud suggest that the present inter-relational approach is relevant and worth further\ud investigation through the introduction of intervention studies and the rigorous\ud examination of causality