Mathematical modelling and statistical analysis of school-based student performance data.

Abstract

In order to improve the education system so that students are not only reaching the minimum standards of literacy and numeracy but are also given the opportunity to excel, accurate measures of school performance are vital. These measures need to focus on student progress so that schools and teachers can focus on improving all students - particularly those most in need. A current trend in primary and secondary education in Australia is national testing, with the introduction of the National Assessment Program - Literacy and Numeracy (NAPLAN). This, along with similar tests like the Basic Skills Tests, measures student performance and progress over sequential years. The issue now is how to interpret these results for individuals, schools and educational authorities. The education system can be modelled with a hierarchical model due to the nesting of variables at the education system, school, classroom and student levels. Intertwined with the hierarchical nature of the model is also the longitudinal aspect of the data as students sit biennial NAPLAN assessments. We mainly investigate hierarchical modelling techniques, such as linear multilevel mixed effects and a Bayesian approach, to fit a statistical model which incorporates student and school predictor variables. In addition to hierarchical modelling methods, we also consider longitudinal techniques. The objective of this thesis is to investigate and determine what conclusions about student progress and school performance can be reliably drawn from regular standardised system-wide assessment, such as NAPLAN. Various models are investigated and the end result is a model which comprehensively and accurately models the results of students, from which we can predict students' scores and assess the effect of schools in that way.