Reflections from the first reading group meeting

Contributors: Graeme Austin, Yasmine Fahmy, Alison Ford, Elizabeth Lake, Lilian Nyaranga, Fin McLaughlin, Lisa Pollard, Helen J Williams

The reading group is for those wishing to engage with research literature on TMSJ and discuss its relevance to practice. The first reading group meeting took place via Zoom on 17^th November 2021 and was attended by 28 members of the Teaching Maths for Social Justice Network. We chose to discuss the 2017 paper: The socio-politics of teacher explanation in mathematics education. We began by breaking into smaller groups to discuss the following questions:

• What are the key messages in the paper about teacher explanation and power relations between mathematics teachers and students?
• Is it possible for teacher explanation to play a more empowering role in the mathematics classroom?
• To what extent do the ideas from the paper echo with your own practice and experiences?

Here are some reflections on the paper and discussions from members of the network …

Alison Ford (Bideford College):

Although I do think carefully about my explanations, this is not a part of my pedagogy that I have previously thought about in regard to teaching for social justice and so I really appreciated the prompting to do so. It made me aware of how important this aspect is to the students, how the teacher’s attitude and pedagogical values can impact on their explanation design and practice, and how the wider classroom culture is itself a factor of inclusion in understanding. I have been much more aware of my own explanations this week and have started to question their impact and their level of inclusivity. I have noticed differences in my explanations between classes, particularly in how much more attention I give them in lower attainment classes over higher attainment ones and how the pace of explanations also varies. This has led me to want to examine how this may impact on disadvantaged students in higher attainment classes and how this might relate to Jo Boaler’s work on setting and pace.

Graeme Austin (Luton Sixth Form College)

Between reading David Kollosche’s article and attending the meeting, I found myself asking for silence in my sixth form classroom and noticed the guilt I experienced by doing so in light of what I had read.

The article was challenging in that it appeared to present the teacher’s voice as embodying Foucault’s disciplinary power, even though teacher explanations should be brimming with explanatory power instead. During the meeting, David noted that no matter how much a teacher might wish to minimise the impact of their surveillance of the class and attempt to democratise their classroom, while they mark student work and provide other judgements about performance, then their classroom authority is unavoidable.

In my discussion group, we shared ideas of different ways of facilitating increasing student understanding without relying on explanation. We considered flipped classrooms and discovery learning. Both these proposals have inspired me to carve out time to construct KS5 discovery worksheets. And I might attempt to operate some flipped lessons too.

Yasmine Fahmy (Royal Academy of Engineering)

Finally having the opportunity and time to work with like-minded professionals was incredibly inspiring for me.  I learnt so much from them and really appreciated their sharing of knowledge, skills and experience.

Attending the TMSJN was a great opportunity to engage in conversation with other maths educators around a number of topics that we all felt passionate about. Having the literature as a foundation for discussion was a great way to guide conversation, allowing us to pull out many key topics around existing and accepted classroom dynamics and how we might be able to disrupt these, how we can include more young learners in exploratory learning, and sharing of great ideas that others already have in place. I left the session feeling motivated, inspired and unified in attitudes to others at the session.

Helen J Williams (Early Years)

“Deeper insights could lead the way to a teaching practice which incorporates teacher explanation without constructing the student as a passive subject to mathematics.” (Kollosche 2017: 8)

I was struck by the above sentence in David’s paper, and by the question asked in the ensuing discussion, which I think was: “How can we use teacher explanation to disrupt the power relations in a maths classroom/maths teaching?”

There is no doubt in my mind, having worked in maths education for over 30 years, that mathematics is used as a tool to maintain power structures. As someone who has worked mainly with children who are under 7 years of age (and their teachers), explanation plays a different role in our maths work to that described in David’s paper. I don’t begin with an explanation, I want children to bring something to our maths session, and to do this I start with some exploration of an idea to ascertain what they already know, and we build from there. My explanations and interactions include ponderings, questions and noticings as we work on the maths. I cannot think of one maths session which has not included a teacher explanation of some sort, and to polarise ‘explanation’ (or more commonly, currently, ‘direct instruction’) and ‘exploration’ as two diverse approaches to teaching maths is unhelpful. I have learned that how I begin a session, along with the tone I use when I respond to – often surprising – noticings and questions that occur, not only fundamentally affects how children respond, but how they feel about maths over time. I was struck in the session this evening that perhaps making sure that students come to a lesson having already ‘done’ something themselves (such as through ‘flipped-teaching’, pre-teaching and assigning competence) might work in a similar way to disrupt the power structures in a classroom and send a message to older students that mathematics is as much about what they do and think as it is about what someone else does and thinks.

Lilian Nyaranga (Elimu Shop):

I had a great time being part of the group meeting discussions yesterday. I had fun sharing and learning from math educators with diverse experiences. As a math educator from Kenya, my biggest takeaway was that our students have similar challenges and experiences in math classrooms, even though infrastructure and resources vary geographically. And that the role the teacher plays, and the teaching methodology used, is pivotal in ensuring equity in the mathematics classroom. I can’t wait to be part of the next meeting. Thanks.

Lisa Pollard (Boolean Maths Hub):

The paper from David Kollosche raised questions and thought for further exploration. In our small group discussion, we spent time attending to the potential levels of confidence and skills of the participants’ teachers involved in the study. Relating the teaching within this paper to practice we have seen, one might ask if the use of explanation as referred to in this article is about control and confidence, rather than power. Where a teacher has the subject knowledge, both content and pedagogical, there is a higher quality of teaching and thus greater confidence in empowering the students in leading their learning. One student in the paper, Ingo, spoke of how, (if he were a teacher) he would adapt the level of explanation for the individual students. This could be inferred as scaffolding the support (differentiating) to ensure all students achieve, which the student did not feel happened in the maths class.  What was evident was the clear understanding that the students from across the study had of their own standing within their maths class. They have a perceived picture (whether accurate or not) of all the groups and individuals in their maths class, either with regards to behaviour or the speed of understanding any explanations given. However, whilst the seating plans have been implemented by the teachers, the subsequent support and challenge appears, from the views of the young people, not to have been. It was interesting to hear from David that the teachers were not engaged at all in the paper; it was written purely from the view of the students in interviews. It would be interesting to hear the teachers’ reflections on the quality of their own practice and what impact, if any, the paper had on their own practice with regards to explanation or otherwise.

Fin McLaughlin (Cabot Learning Federation):

Great to have time to discuss ideas with colleagues that all share a passion for maths education. The space created for dialogue based on a piece of research enabled everyone to share their own perspectives and for us to learn from each other. The research emphasises a gap between the maths education research community and day to day classroom practices and this also surfaced in the perspectives of our small group. The persistent belief that ‘what teachers do is explain’ is perhaps unsurprising; it is one of the important tools we employ to aid learning. However, if the responsibility of the teacher ends with the giving of the explanation (as perceived by students interviewed in Prof Kollosche’s study) then it seems unlikely that learning will take place. If an explanation is offered as a conjecture and as one opportunity (amongst others) for co-construction of knowledge, then explanation may be seen as ‘useful’ but not ‘central to’ teaching and learning. The discussion provoked some questions:

• Do teachers need to be more explicit with learners about how they are being (or expected to be) active in the learning process by identifying the opportunities they are given to engage with, interrogate and reason about an explanation?
• Does ITE (or the ECT framework) need to more pro-actively tackle the engrained beliefs / understandings of the role of explanation in teaching?
• Is the education system (e.g. DfE, OFSTED) discouraging a belief that learners need to be active participants in developing their understanding and entrenching the belief that ‘to teach (well) is to explain (well)’?

Elizabeth Lake (University of East Anglia):

The discussions that we had were quite challenging as they brought into question my beliefs about what actually happens in schools. In my role of training mathematics teachers, I am continually discussing and encouraging the early career teachers to use techniques which we might consider appropriate if we are using a social justice agenda. This would include, for example, continual articulation by students of mathematical thinking, group work and teaching to misconceptions. The discussions we had in a small group made me wonder about how significant the barriers are between what teachers want to do (including what they have learned about in university), compared to what is realistically possible once they are in the classroom and are exposed to the constraints of school cultures and ethos, which are in themselves likely barriers to pursuing practices that support social justice in the mathematics classroom.