The development of mathematical strategies in the early years

Current research has shown that children develop a repertoire of mathematical strategies by progressing though five 'counting stages'. These are: perceptual - students are limited to counting those items they can perceive; figurative - students count from one when solving addition problems with screened collections; initial number sequence - students can now count on to solve addition and missing add-end problems with screened collections; implicitly nested number sequence - students are able to focus on the collection of unit items as one thing, as well as the abstract unit items; explicitly nested number sequence - students are simultaneously aware of two number sequences and can disembed smaller composite units from the composite unit that contains them, and then compare them. The importance for classroom teachers to be able to identify each child's strategy and thus his or her counting stage is emphasised in this paper as a starting point for mathematics/numeracy teaching in the early years. The results of clinical interviews used for assessing each child's counting stage are discussed. The paper highlights the strategies that have been used to assist children overcome common difficulties. These strategies can be incorporated into teaching by classroom teachers to enhance their mathematics programs so all students succeed with mathematical tasks. [Author abstract, ed]