Assessing Development in Numeracy of Students from Different Socio-Economic Areas: A Rasch Analysis of Three Fundamental Tasks

Development in the ability of 11-year-olds to solve numerical problems of addition, multiplication, and proportion was analysed by means of three Rasch models of change. The students, who had participated in a New Zealand numeracy project in 2002, comprised two groups that differed in socio-economic status: 1,274 students came from low socio-economic areas, and 564 students came from high socio-economic areas. The Rasch analysis showed that students from low socio-economic areas found all three tasks difficult, although they made some progress during the course of the year. Their development was consistent with a model in which each student underwent their own specific development. The development of students from high socio-economic areas was best described as stemming from two latent classes, one of which made substantial and uniform progress and the other of which made no progress. The cumulative nature of the tasks meant that failure on addition propagated to failure on multiplication and proportional reasoning.