Brian Williamson

During the COVID-19 pandemic universities around the globe were forced to transition from face-to-face teaching to remote, online learning. This was always intended to be a short-term solution until physical doors re-opened and face-to-face teaching recommenced. However, the challenges of the sudden transition to online teaching also resulted in innovative and creative teaching and learning tools and practices which came with unexpected benefits and opportunities. The recognition of this has resulted in transformations within post-COVID teaching and learning strategies.



The purpose of the case studies in this book is to identify innovative transitions across all faculties and schools of a Higher Education institution in the UK – the University of Bolton – and how these are driving the development of new forms of blended and hybrid teaching and learning approaches.

A meta-analysis is the analysis of the results of several independent studies and offers an opportunity to combine the outcomes of comparable studies. We define a Living Meta-Analysis as a qualitative meta-analysis with inclusion criteria set to Living-Educational-Theory research, and suggest two scenarios:
1. where the researcher proposes to build their own living-educational-theory (let) informed by their meta-analysis of the living-educational-theories of others, and:
2. where the researcher does not propose to build a living-educational-theory (let) but the influence of Living Educational Theory (LET) research is still prominent in the study through the life affirming energy of the other.
We propose an initial classification of the LET research literature, identify, and explore potential research questions, and methods of implementation of cases (1) and (2). We discuss the limitations, choosing a methodology for your research proposal and the contribution that could be made by Living Meta-Analysis to spreading the global influence of Living Educational Theory research.

I define my ‘living mathematics’ as my living-educational-theory of teaching and researching mathematics. I define ‘Living Mathematics’ as the overarching values-based approach to the teaching and research of mathematics as a parallel to the distinction made between ‘living-educational-theory’ and ‘Living Educational Theory research’. In this article I ask the question ‘how do I improve my practice of teaching and researching here?’ by exploring how I:
As a teacher can support mathematical thinking and the understanding of textbook concepts using a value based approach and, As a researcher can enhance my mathematical thinking and modify, or create, mathematical models by calling upon my lived experiences, capturing and representing them in a symbolic form.
I define teaching and research pathways in Living Mathematics as sequences of useful and focused key actions. Four exemplar case studies of my living mathematics are discussed; two from the teaching pathway and two from the research pathway.

The literature suggests that students tend to prefer in-person lectures to video lectures. This paper identifies potential causes of this phenomenon and triggers of student engagement in a flipped-classroom environment.
Eight short in-house mathematics videos were prepared and made available to foundation engineering students on the university’s virtual learning environment, prior to each topic being discussed in class. The in-house videos were viewed more than accompanying external on-line video lectures for all topics covered. Students preferred in-house videos with a voice describing a drawing as it is being drawn, not one drawn earlier, and an equation as it is being written, not one written earlier. In-house videos that were produced using high numbers of pre-prepared pages tended to be viewed less. These findings suggest a gradient of student engagement from the external on-line video lecture to the interactive group learning experience. Three evidence-based stages of student engagement are proposed: (1) external video, (2) in-house video with high numbers of pre-prepared pages and (3) in-house video with low numbers of pre-prepared pages. Further validation of these stages of student engagement, and an exploration of lecturer preparedness and social presence during the production of short in-house mathematics videos, is recommended.

The literature suggests that students tend to prefer in-person lectures to video lectures. This paper identifies potential causes of this phenomenon and triggers of student engagement in a flipped-classroom environment.
Eight short in-house mathematics videos were prepared and made available to foundation engineering students on the university’s virtual learning environment, prior to each topic being discussed in class. The in-house videos were viewed more than accompanying external on-line video lectures for all topics covered. Students preferred in-house videos with a voice describing a drawing as it is being drawn, not one drawn earlier, and an equation as it is being written, not one written earlier. In-house videos that were produced using high numbers of pre-prepared pages tended to be viewed less. These findings suggest a gradient of student engagement from the external on-line video lecture to the interactive group learning experience. Three evidence-based stages of student engagement are proposed: (1) external video, (2) in-house video with high numbers of pre-prepared pages and (3) in-house video with low numbers of pre-prepared pages. Further validation of these stages of student engagement, and an exploration of lecturer preparedness and social presence during the production of short in-house mathematics videos, is recommended.

The literature suggests that students tend to prefer in-person lectures to video lectures. This paper identifies potential causes of this phenomenon and triggers of student engagement in a flipped-classroom environment.
Eight short in-house mathematics videos were prepared and made available to foundation engineering students on the university’s virtual learning environment, prior to each topic being discussed in class. The in-house videos were viewed more than accompanying external on-line video lectures for all topics covered. Students preferred in-house videos with a voice describing a drawing as it is being drawn, not one drawn earlier, and an equation as it is being written, not one written earlier. In-house videos that were produced using high numbers of pre-prepared pages tended to be viewed less. These findings suggest a gradient of student engagement from the external on-line video lecture to the interactive group learning experience. Three evidence-based stages of student engagement are proposed: (1) external video, (2) in-house video with high numbers of pre-prepared pages and (3) in-house video with low numbers of pre-prepared pages. Further validation of these stages of student engagement, and an exploration of lecturer preparedness and social presence during the production of short in-house mathematics videos, is recommended.

This paper describes my development of a useful, descriptive model that one-to-one practitioners could use to analyse transcripts of their sessions, design new strategies and even test them out. Further, this work has the potential to offer a framework that students, patients, clients and colleagues could use to communicate the types of interactions they prefer.
The narrative in my educational life around the domain of heuristic generates a living-educational-theory as a values-based explanation for my educational influences as a tutor. The living contradictions I encounter, and praxes I make up to help me imagine solutions, are portrayed visually and verbally; and this leads to my proposal of a five-cycle living visual taxonomy of learning interactions.
I consider the application of my living-educational-theory to other domains, for example, confidence; and to power dynamics, autism support, student engagement, expert behaviour, external influences, understanding negative feedback, and remoteness in heuristics.
Interestingly, one future possibility is to use my taxonomy to develop a ‘positivist/scientific flavoured’ quantitative instrument to support learning analytics and educational data-mining; to optimise learning, and the environment in which it takes place.