Disordering mathematics: reflections from the third reading group meeting

Contributors: Sandra Beckford-Henry, Jane Goodland, Hilary Povey, Helen Thouless

The reading group is for those wishing to engage with research literature on TMSJ and discuss its relevance to practice. The third online reading group meeting took place 15^th November 2022. We chose to discuss Hilary Povey and Gill Adams’ 2021 paper: Disordering mathematics, citizenship and sociopolitical research in mathematics education amongst the “rubble of words”. We began by breaking into smaller groups to discuss the following questions:
~ What do the authors mean by ‘radical citizenship’? How can this be seen as ‘disordering’?
~ What are the implications for bringing citizenship into the mathematics classroom?
~ How might the ideas in the paper relate to your own classroom practice?

Here are some reflections on the paper and the meeting from those who attended (including one of the co-authors) …

Jane Goodland (Newmarket Academy)

I really enjoyed reading the paper and thinking about what it means to teach in a radical or transformative way. I enjoyed the vignettes that broke up the text. For me, it made the paper feel more like a story than a report, it felt like it was moving somewhere. Reading the paper made me realise how we often talk about radical or transformative maths education. But we often talk about it in a more abstract way, and I often feel like I align with papers like this as I’m reading them, but then come away wondering what I should be doing in my classroom. Reading this paper and reflecting in this way made me realise how embedded the status quo is in my own practice and mind. I feel like what I’m trying to do in the classroom is so far away from what a paper like this is advocating, but at the moment I just can’t see what the classroom would look like. I think there is a real problem in education, even amongst more progressive educators, of being stuck in a system that we can’t get out of. I would like to unpick some of the terms that are used in this paper and think deeply about what they actually mean in practice.

Sandra Beckford-Henry (Conisborough College, SE London)

I really enjoyed the discussion, especially hearing both Gill and Hilary saying that the feedback from the group was very insightful. Furthermore, Hilary mentioned that for the next few days she would be in deep thought about the discussions that were had and the paper itself.
One thing that really resonated with me were the inserts. I thought they were very powerful and aptly placed. Somehow their disordered placement helped order my thoughts while reading, plus aided the text very well, especially for a novice academic reader as myself. The idea that ‘mathematical models’ are used in the configuration of immigration policies for citizenship, somehow validates the policies simply because mathematics is involved, without much concern for the assumptions and parameters embedded within the policies. The same policies are then, on the one hand, used to include (golden passport holders) and, on the other hand, preclude others.
I was able to identify with the section that talked about being colonized by software and AI. I feel that we are now at a point with technology where we are being controlled by it rather that it just being a tool to assist. Also, the idea that one way to fight against institutionalization was with disordering mathematics. Realistically one could use the disordering of mathematics to challenge the ‘norms’.

Helen Thouless (St Marys University, Twickenham)

As well as the three prompts, our group discussed the role of technology in colonisation and the role of the vignettes in disordering the structure of this article. I was particularly interested in the different ways that we had read the vignettes. When I read the article, I, as an academic well-versed in reading academic papers, skimmed over the vignettes because I was focusing on the argument in the rest of the article. However, the other members of my group had engaged more deeply in the vignettes and found them helpful for understanding what they were reading. These members of the group referred back to the vignettes when illustrating their understanding of what radical citizenship meant. One of the members of my group stated that the vignettes reminded her of Brecht, in that they intentionally broke the flow and thus exposed the artifice of the writing. This discussion made me think about how the way we write academic papers is not natural and value free, but the result of cultural norms that we have learned and internalised.

Hilary Povey (One of the co-authors of the paper)

I really enjoyed the session and found the format lent itself to really in-depth discussion. I look forward to joining future sessions as a participant. I found many of the responses and contributions thought-provoking. One in particular sent me immediately looking for further connections. This related to our attempt to interrupt the flow of the article.
I had known about Brecht’s commitment to interruption in his plays, for example, in an actor speaking directly to the audience ‘outside’ the play. I know very little about this, but I understand it to be a way of halting emotional engagement to allow a space for critical reflection and, importantly, doubt. According to Ilit Ferber (2005), Walter Benjamin argued that the gaps created by interruption “are the openings through which truth can reveal itself, provided that they allow the reader to pause for further contemplation and doubt what he or she is encountering” (p. 37).  She adds that he claimed that “too flawless an argument does not allow for any such gaps and is constructed as such in order to avoid any risk of doubt which could undermine it” (p37).  This has strong resonance with what Gill and I were trying to achieve, that is, to create doubt about and disordering of our argument.
Ferber, Ilit (2005). Interruptions in Brecht and Benjamin. In Assaph: Studies in the theatre, 19-20, 35-52.

Hilary and Gill recommended another of their papers from 2018 that you may be interested in: Possibilities for mathematics education? Aphoristic fragments from the past