Exploring a high achiever's and a low achiever's strategies and images in early number work

Abstract

Curriculum development within mathematics is often grounded in the belief that all individuals pass through the same sequence of learning, albeit at different paces. There seems to be a general assumption that there is universality in the learning process. For example the national curriculum in Cyprus offers a list of subjects that children need to cover every year, whilst in the U.K. a more detailed national curriculum specifies the sequences of levels through which children shall grow. However, in neither of the two is there any reference to the fact that children may be learning and doing things in completely different ways. This becomes even more fundamental in the case of children with learning difficulties. Our purpose in this paper is to look closer at what two children at the extremes of arithmetical achievement may be doing in their heads that may be facilitating or inhibiting their understanding in arithmetic.