This blog post reports on recent work that has been supported by a TLC Research Collaboration Grant; the grant supported us in moving from interesting interdisciplinary conversations within the University to a practical exploration of a possible route for further development and we share here an overview of what has been undertaken and some reflections on what we see arising from the process.
There is sometimes a sense from literature of research projects arising from theoretical deliberations in a clean, almost inevitable sequence of steps. This short inquiry is an example of a project emerging from an unfolding conversation that flowed around an area of common interest, following possibilities as they emerged. The conversations drew on insights from colleagues in the School of Civil, Aerospace and Mechanical Engineering (CAME) and the Department of Engineering Mathematics as well as the School of Education. Making links between mathematical thinking and issues of global challenge (including, but not limited to, climate emergency) touched on intentions to prompt, in both learners and teachers, an awareness of putting the ‘documented curriculum’ for school mathematics to use in contexts that have a direct connection with questions of global and local interest and concern.
The particular aspect we explored here connected the development of outreach work by colleagues in the School of Engineering Mathematics with teachers in schools within our PGCE Partnership. New modelling prompts were developed collaboratively and then used with groups of Year 12 (16-17 years old) students. We looked to capture these teachers’ reflections on their own learning arising from the process of using such materials, in order to guide further efforts to enact in schools approaches to working with mathematics that support engagement with issues of precarity.
Doing
Funding through the TLC Research Collaboration Grant supported us bringing together teachers of mathematics in schools and academic colleagues in the University. We met with participating teachers, colleagues in the Department of Engineering Mathematics to work on and refine the tasks that would be taken in to schools. The resulting materials were used in two schools by the teachers involved, with members of the School of Education joining as observers. The final phase was a debrief discussion between the teachers and one of the observers, looking to capture reflections on the experiences and insights into further classroom work. The TLC grant supported release time for the teachers, as well as production of the physical materials and enabled us to meet together.
We explored three tasks in our first meeting – fuel sources for sustainable car journeys (If we powered all the cars on the M4 using biofuels grown on the verge of the road, how wide would the verge have to be?), algorithms for decision-making related to recycling household materials (How effective might a machine learning algorithm be at making decisions for recycling household waste?), and an exploration of publicly-available air quality data collected around Bristol. The significance of doing these tasks together as a group of educators was strongly apparent, provoking for us awarenesses of the tasks themselves and of our individual emotional responses. There was significance for each of us in having this space and time, which resulted in refined versions of each of the prompt tasks.
The next phase was to make the tasks available to students in schools. Each of the two teachers independently chose to work with the task based on fuel for car journeys, (15 students for 90 minutes, 12 students for 100 minutes). The school sessions were facilitated by the teachers, with members of the School of Education acting as observers to support the reflective conversation that followed with the two teachers shortly after the teaching sessions.
Reflecting
Several themes emerged from the participating teachers as we reflected together on experiences from schools. Beyond details of how the materials might be refined for further use, there was commonality in reflections on students experiencing a strong sense of difference between these sessions and their expectations of A-level mathematics lessons, both in terms of ways of working and the focus of the tasks. The teachers identified that they saw these sessions as opportunities to stimulate students’ collaborative working; indeed, both had planned their sessions to make use of groupings and structures that were different to usual, in terms of both who students worked with and how they were working. Whilst there was nothing in the tasks themselves that required such changes, the prompt of unfamiliar materials and an emphasis on mathematical modelling proved a sufficient perturbation for the teachers to bring to the foreground some of their underlying values and beliefs about engagement, communication, collaboration and the role of mathematics education at this level. Both teachers reflected on their own enjoyment of working with students in ways that drew on what the students brought to the contexts and noted that individuals in each group who did not generally contribute in class were offering ideas and participating spontaneously. Both teachers felt that the novelty of the ways of working were combining with the focus on issues of sustainability to create spaces where many students felt it was possible and appropriate to draw on information they had from engagement with environmental issues outside of school contexts. Alongside this, some students expressed a sense of disquiet that this was not ‘real maths’ or not sufficiently related to the A-level course to warrant lesson time. Whilst we are not seeking to offer here an evaluation of the materials or their use, we do observe that teachers and students experienced a strong sense of difference in the content and process of these lessons. The shared reflections on this short inquiry feed into our ongoing explorations of how the enacted curriculum in school mathematics might support and equip learners in these precarious times and how we might continue to be part of connecting education in schools, universities and contexts beyond our institutions.
The role of a TLC Research Collaboration Grant
Whilst the financial support of the Research Collaboration Grant has been valuable for this short inquiry, the structure and visibility of a specific award has generated and sustained momentum in this short inquiry. It has facilitated the involvement of teachers in schools, who have always more tasks to do than time to do them, and has supported visibility of their contributions within their schools in ways that are tangible and explicit; at the same time, the award of the grant has helped maintain the visibility of moving from valuable conversations with colleagues to practical action. In a previous TLC blog post, Caroline Ormesher has written about spaces in which “ways of knowing bump up against each other and the boundaries between them dissolve” and this description feels helpful in describing the work discussed here, allowing our engagement with pressing issues, interesting conversations and explorations of tangible responses to travel alongside one another and feed into further work. We thank the Research Centre for their support and would encourage others who are exploring conversations with colleagues in and out of the University to consider applying for Research Collaboration Grant.
Blog post written by Julian Brown