Computational modelling for educational research
Project Description
We would like to offer an interdisciplinary PhD project at the Department of Mathematics and the Centre for Higher Education Research and Scholarship. Ultimately, the research conducted by the student will address complex topics in education while leveraging mathematical methodologies to offer insights with real-world implications for policy and practice. We will thus focus on understanding what drives inequities in STEM and related careers, including gender equity. We will address the topic using mixed approaches with a strong quantitative outlook. This will include mathematical modelling to explore fundamental aspects of learning or decision-making through agent-based models. The agent-based models will be complemented and informed by simpler mathematical models and by using Bayesian statistics and machine-learning methods applied to real-world data. This will include existing large national datasets, such as the Administrative Data Research UK (ADR UK, https://www.adruk.org/data-access/data-catalogue/) catalogue and flagship datasets (https://www.adruk.org/data-access/flagship-datasets/). Beyond a literature search, an exploration of existing data will thus be an essential starting point for tailoring the modelling approach.
Existing background work
Mathematical models of learning and cognition are widespread in computational psychology and educational research. Thus, agent-based models have been applied to simulate and understand the underlying behavioural dynamics for a wide range of phenomena in social science (e.g., https://www.biorxiv.org/content/10.1101/2024.06.16.599026v1, https://onlinelibrary.wiley.com/doi/full/10.1002/andp.202100277), including gender equity (https://royalsocietypublishing.org/doi/10.1098/rsos.221346), and recently agent-based models using large language models have emerged as a new and fruitful avenue (e.g., https://arxiv.org/abs/2304.03442). Agent-based models are thus the ideal tool to explore how the decisions of individuals lead to emergent properties on a societal level. The behaviour of larger populations, on the other hand, can be modelled, e.g., using diffusion decision models or other game-theoretical concepts.
In general, quantitative methods, including advanced statistical analyses, play a fundamental role in educational research. Integrating quantitative approaches with qualitative methods thus offers a robust methodology in the field and a more comprehensive understanding of educational phenomena.
Dr Andreas Joergensen has a strong background in developing and applying mechanistic models, such as agent-based models, across a wide range of fields, including astrophysics, biology, and environmental conservation. Moreover, he has combined these models with Bayesian inference and machine-learning frameworks to successfully use them to shed light on real-world data. His interdisciplinary expertise will support the application of these techniques to educational research. Additionally, Professor Camille Kandiko Howson brings extensive expertise in educational research, including the development and analysis of national student surveys and measures of educational quality and learning gain; large-scale research into educational inequalities in Physics and wider Physics Education Research; and research on applied methods for learning analytics. Together, they have previously explored synergies between mathematics and education, particularly through a project proposal on gender equity at Imperial, which will flow into the PhD project.
Main objectives of the project
This project aims to apply quantitative and computational methods to address complex challenges in education research, with a specific focus on inequities in STEM fields. The goal is to derive actionable insights that can influence educational policies and practices. While large-scale patterns of engagement and inequality in education are often tracked through national datasets, many researchers lack the computational expertise to analyse this data or to model the underlying dynamics. This project, therefore, seeks to bridge that gap by developing computational methodologies that connect and analyse mathematical models, addressing previously unexplored aspects of existing data.
The agent-based models in this project will be tailored to inform policies and practices, leveraging an understanding of the current data landscape. This includes identifying suitable proxies for inequity, such as degree progression, career outcomes, and academic performance in higher education. Additionally, useful summary statistics and underlying mechanisms will be incorporated to ensure the model’s relevance to real-world scenarios.
The agent-based models will be built on Bayesian principles, allowing them to capture how individuals interact with social information and navigate complex environments. By exploring the impact of different model parameters, we aim to uncover the mechanisms driving emergent social phenomena. Furthermore, surrogate models, such as emulators or simplifying approximations, will be introduced to enable comparisons with real-world data using Bayesian inference.
Details of Software/Data Deliverables
The student will be responsible for developing the code necessary for the project. This will include mathematical models to simulate educational processes, but it will also entail the code needed for incorporating and dealing with real-world data. All code developed during the project should adhere to best practices in open science and be made publicly available upon publication to ensure transparency and facilitate future research. This will allow the broader scientific community to benefit from the tools and methodologies created during the PhD project.
