A mixture distribution of school performance growth throughout compulsory schooling

We investigated the growth in school performance of students throughout compulsory schooling, examining whether distinct types of growth trajectories can be identified, how many there are, and whether the probability of type membership can be predicted by variables at the level of the individual, the family of origin, and the school class. Data come from the Zurich Learning Progress Study, which comprises a random sample of about 2000 students who have entered school in the 2003/04 school year. School performance in mathematics and language was assessed three, six, and nine years after school entry by standardized tests reflecting the official curriculum. These tests were scaled using probabilistic test theory and linked across the three measurement occasions so that they could be compared on a common metric scale covering most parts of compulsory schooling. Using non-linear growth mixture modelling, we identified five distinct types of performance growth, namely the "average type" (20%), the "slow learning type" (26%), the "left-behind type" (9%), the "profiting type" (30%), and the "head start type" (15%). The various predictor variables had different relevance for each growth type, whereby psychometric intelligence, pre-schooling competencies in arithmetic, and independent learning and study habits played prominent roles.