The optimal achievement model and underachievement in Hong Kong: an application of the Rasch model

Termed the optimal achievement model, a new method for the estimation of underachievement relies on measuring student potential (P) and achievement (A) using Rasch models and calculating an achievement index, IA, for each individual. This study extends a previous report (Phillipson & Tse, 2007) that estimated the proportion of Hong Kong students in Primary 5 to now include a sample of students from Primary 3 (n = 1406), Secondary 1 (n = 756) and Secondary 3 (n = 578), across six districts of Hong Kong. The students were administered a standardized test of mathematical achievement and the Ravens Progressive Matrices Test. Using the optimal achievement model, estimates of underachievement at six percentile bands showed that the proportion of students who were underachieving ranged from 10 % at the 50-59th percentile band up to 30 % at the >95th percentile band for Primary 3, Primary 5 and Secondary 1 students, and 50 % of Secondary 3 students. The estimation of IA at the level of the individual allows the researcher the possibility to directly study the interaction of the environment on student potential.