Background: A number of methods to investigate growth have been reported in the literature, including hierarchical linear modelling (HLM), latent growth modelling (LGM), and multidimensional scaling applied to longitudinal profile analysis (LPAMS). Aims: This study aimed at modelling the mathematics growth of students over a span of 6 years from Grade 3 to Grade 9. Sample: The sample comprised secondary longitudinal data collected in three waves from n = 866 Hong Kong students when they were in Grade 3, Grade 6, and Grade 9. Method: Mathematics achievement was measured thrice on a vertical scale linked with anchor items. Linear and nonlinear latent growth models were used to assess students' growth. Gender differences were also examined. Results: A nonlinear latent growth curve with a decelerated rate had a good fit to the data. Initial achievement and growth rate were negatively correlated. No gender difference was found. Conclusion: Mathematics growth from Grade 6 to Grade 9 was slower than that from Grade 3 to Grade 6. Students with lower initial achievement improved at a faster rate than those who started at a higher level. Gender did not affect growth rate.
[Copyright © 2014 The British Psychological Society.]

This study aimed to model mathematics growth of students from Primary 3 to Secondary 3 from two approaches, namely, growth in content domains, and in cognitive domains. The sample consisted of 866 Hong Kong students who were followed longitudinally from Primary 3 to Secondary 3. The data were originally collected by the Education Bureau of Hong Kong. Plausible values of achievements at Primary 3, Primary 6, and Secondary 3 in three cognitive domains (Knowing, Applying, and Reasoning) were obtained using between-item multidimensional Rasch partial credit modelling. A modified autoregressive cross-lagged design was used to predict later achievement in the cognitive domains by prior achievements in these domains. Analysis was repeated for growth in content domains (Number, Shape and Space, Measures, Data Handling, and Algebra). Analysis showed that students' later mathematics achievement was strongly predicted by their previous achievement in the Knowing and the Number domains.
[Copyright © 2014 Education Bureau, HKSARG.]