Longitudinal Statistical Modelling of a Personalised Learning System for Mathematics students

Educators around the world face a wide range of challenges on a daily basis, such as keeping students motivated, providing individual feedback, and customizing their teaching to students' needs. Recent developments in educational technology have made it possible to create a personalized learning experience for every student based on their current abilities. While collecting and storing large amounts of student data has become less of a problem, there is still a long way to go in terms of creating adequate methodologies that can be used to process it. This project aims to address the issue that the current statistical methodologies for modelling learning trajectories of students struggle to account for the complex dependency structure in the data. For example, for each question, there is a temporal dependence with other questions. Furthermore, the data has a hierarchical structure with multiple levels: students within classrooms within schools. There is also the added complication that the questions presented are not random but are deterministic based on the current ability of the student. The research interests centre around identifying factors that predict correct answers to questions and to try to model the different learning trajectories within the longitudinal data. Much of the modelling will be based on a variant of multilevel models known as a discrete-time survival model but methodological interests also involve looking at approaches to speed up execution of such models with large datasets, looking at extending these models to control for the unusual lack of independence caused by the question generation mechanism, and considering alternative modelling approaches for the data. The expectation is that developing techniques for analysing longitudinal data in this way will provide powerful new insights into some key areas, namely: measuring student attainment and progress based on usage data; a multivariate approach to characterizing student's maths abilities; and understanding how different schemes of learning at the school level affect individual students learning trajectories. To ensure that the developed methodologies are practically useful in educational research the project will be partnered by Sparx. Sparx Maths is a personalised blended learning platform that is used by schools for bothhomework and classwork. Each week pupils receive a set of homework questions that are personalised to their ability, and their difficulty level will adapt with the student as they progress along their learning trajectory.

The COMPASS Centre for Doctoral Training will have the following impact.

Doctoral Students Impact.

I1. Recruit and train over 55 students and provide them with a broad and comprehensive education in contemporary Computational Statistics & Data Science, leading to the award of a PhD. The training environment will be built around a set of multilevel cohorts: a variety of group sizes, within and across year cohort activities, within and across disciplinary boundaries with internal and external partners, where statistics and computation are the common focus, but remaining sensitive to disciplinary needs. Our novel doctoral training environment will powerfully impact on students, opening their eyes to not only a range of modern technical benefits and opportunities, but on the power of team-working with people from a range of backgrounds to solve the most important problems of the day. They will learn to apply their skills to achieve impact by collaborative working with internal and external partners, such as via our Rapid Response Teams, Policy Workshops & Statistical Clinics.

I2. As well as advanced training in computational statistics and data science, our students will be impacted by exposure to, and training in, important cognate topics such as ethics, responsible innovation, equality, diversity and inclusion, policy, effective communication and dissemination, enterprise, impact and consultancy skills. It is vital for our students to understand that their training will enable them to have a powerful impact on the wider world, so, e.g., AI algorithms they develop should not be discriminatory, and statistical methodologies should be reproducible, and statistical results accurately and comprehensibly communicated to the general public and policymakers.

I3. The students will gain experience via collaborations with academic partners within the University in cognate disciplines, and a wide range of external industrial & government partners. The students will be impacted by the structured training programmes of the UK Academy of Postgraduate Training in Statistics, the Bristol Doctoral College, the Jean Golding Institute, the Alan Turing Institute and the Heilbronn Institute for Mathematical Sciences, which will be integrated into our programme.

I4. Having received an excellent training, the students will then impact powerfully on the world in their future fruitful careers, spreading excellence.

Impact on our Partners & ourselves.

I5. Direct impacts will be achieved by students engaging with, and working on projects with, our academic partners, with discipline-specific problems arising in engineering, education, medicine, economics, earth sciences, life sciences and geographical sciences, and our external partners Adarga, the Atomic Weapons Establishment, CheckRisk, EDF, GCHQ, GSK, the Office for National Statistics, Sciex, Shell UK, Trainline and the UK Space Agency. The students will demonstrate a wide range of innovation with these partners, will attract engagement from new partners, and often provide attractive future employment matches for students and partners alike.

Wider Societal Impact

I6. COMPASS will greatly benefit the UK by providing over 55 highly trained PhD graduates in an area that is known to be suffering from extreme, well-known, shortages in the people pipeline nationally. COMPASS CDT graduates will be equipped for jobs in sectors of high economic value and national priority, including data science, analytics, pharmaceuticals, security, energy, communications, government, and indeed all research labs that deal with data. Through their training, they will enable these organisations to make well-informed and statistically principled decisions that will allow them to maximise their international competitiveness and contribution to societal well-being. COMPASS will also impact positively on the wider student community, both now and sustainably into the future.