- Title
- Multivariate approaches to modelling educational data
- Creator
- Alzahrani, Ali Rashash
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2022
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- The broad objective of this thesis is to contribute to educational research though the uptake of multivariate statistics, with a focus on mathematical education. This is particularly important in the current climate given the abundance of educational research that is becoming increasingly available combined with the current shortage of employees with suitable data analytical skills. This will be achieved by examining both the cross sectional and longitudinal relationship between several student and teacher related factors, including interest and performance in mathematics at secondary school, methods of teaching mathematics as well as the uptake of science, technology, engineering and mathematics (STEM) study at tertiary level. High school students enrolled in Australian schools participating in the Programme for International Student Assessment study are followed up across time in a secondary study, the Longitudinal Surveys of Australian Youth (LSAY). Information on students participating in both studies enabled the longitudinal aspect of this relationship to be assessed. Multilevel linear modelling further enabled school level data to be adjusted for in the examination of the effectiveness of different teaching methods on mathematics exam performance. This multilevel approach to modelling was the first to ever be applied to Qatar mathematics outcomes, and was particularly important given that mathematics performance of students in Qatar is considerably lower than global average standards. Students performed better when cognitive-based approaches to teaching were used. These findings can be used to potentially supplement existing practices in the teaching of mathematics. It is proposed that teaching strategies in Qatar could potentially be reviewed with a view to better cater to the needs of students who are anxious about studying mathematics, in an attempt to improve the performance of students nationally. Interestingly, it was observed that males were significantly more anxious compared with females in Qatar, while in Australia, females were significantly more anxious compared with males. Cluster analyses techniques were also investigated in the educational research framework, which contrasts with other statistical methods as it analyses correlations between students instead of between variables. The assessment of data at student level is conducted by forming groups of students that are homogenous within and heterogeneous between groups, by the simultaneous assessment of several variables. The cluster analysis methodology helped to ascertain student attributes that discriminate between different groups of students with varying levels of performance in mathematics. Grouping students has the potential benefit of enabling educators and policy makers to create student profiles based on demographic information collected at student level upon entry of the child into the schooling system. This can be used to better allocate learning resources to relevant groups of students based on their associated needs. This thesis further demonstrates the methodology of hierarchical and k-means clustering in the educational context, and illustrates the benefits of these approaches compared this with model-based clustering, to examine factors influencing mathematics performance of high school students in Qatar. This highlighted both benefits and limitations of model-based clustering techniques and poses guidelines on how the inherent inadequacies of other clustering approaches can be better explored using model-based methods. Moreover, this thesis demonstrated how the mclust package can concurrently analyse and compare different models, in order to select the preferred clustering model according to the Bayesian Information Criterion, and to estimate parameters of the associated model using maximum likelihood estimation. Structural Equation Models were constructed to estimate the effect of mathematics performance and perception on the study of mathematics in later secondary school. The results indicate that mathematics study uptake among students in Year 12 varied depending on performance and interest in mathematics, instrumental motivation in mathematics and gender. These findings can inform educators and policy makers how to potentially address the issue of declining student participation rates in the study of mathematics education and contribute to a gap in the existing literature regarding the factors that may predict the participation of students in mathematics which is of primary importance in the current world that has a recognised international shortage of employees with suitable data analytical skills to be able to analyse the abundance of data that is becoming available at exponential rates in today’s society. The importance of adjusting for baseline measures of student experiences with mathematics in the classroom is further demonstrated with the longitudinal assessment. This model is extended using Bayesian theory to enable more informative representations of the relationship between mathematics anxiety with uptake of mathematics at secondary level and/or beyond. This builds on Bayesian methodology in structural equation modelling. The resulting model additionally provides a more informative representation of the relationship between attitudes towards mathematics and STEM career uptake, and provides further support for the strong association between mathematics exam performance in secondary school and the study of STEM courses at tertiary level. This strengthens results from the classical structural equation model conducted on these data that fails to incorporate information about study uncertainty and provides further support for the relationship observed in the classical framework that mathematics anxiety impacts on the study of mathematics in later years.
- Subject
- educational research; multivariate statistics; mathematical education; modelling educational data
- Identifier
- http://hdl.handle.net/1959.13/1513232
- Identifier
- uon:56700
- Rights
- Copyright 2022 Ali Rashash Alzahrani
- Language
- eng
- Full Text
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