The Efficacy of link items in the construction of a numeracy achievement scale: from kindergarten to year 6

A large-scale numeracy research project was commissioned by the Australian Government, involving 4732 Australian students from 91 NSW primary schools. Rasch analysis was applied in the construction of a Numeracy Achievement Scale (NAS) in order to measure numeracy growth. Following trialling, a pool of 244 items was developed to assess number, space and measurement concepts. Link items were included in test forms within year levels and across adjacent year levels to enable linking of the forms and the construction of a scale spanning Kindergarten to Year 6 (5 to 13 years of age). However, results from the scaling were not consistent with expectations of increases in student abilities or item difficulties across year levels. Differential item functioning determined the problematic role of link items across year levels. After a different set of items was used for linking test forms, the results were consistent with expectations. A key finding was that items used to link forms must not exhibit differential item functioning across those levels.