**Contributors: Sandra Beckford-Henry, Ben Breen, Alison Ford, Gwen Ineson, Ines Makonga, Cristina Mio, Lisa Pollard, Suchi Srinivas**

The reading group is for those wishing to engage with research literature on TMSJ and discuss its relevance to practice. The second reading group meeting took place via Zoom on 27^{th} April 2022 and was attended by 26 members of the Teaching Maths for Social Justice Network. We chose to discuss Ole Skovsmose’s 2021 paper: A philosophy of critical mathematics education. We began by breaking into smaller groups to discuss the following questions:

- What is the author’s position on ‘social justice’ in relation to mathematics?
- What are the implications of the paper for approaches to teaching mathematics?
- To what extent do the ideas from the paper echo with your own practice and experiences?

We were joined for the second half of the meeting (from Sao Paulo, Brazil) by the author, Ole Skovsmose (a leading figure in the world of critical mathematics education).

Each group generated one question to put to Ole which prompted a thought-provoking and inspiring plenary discussion around the issues addressed in his paper.

Ole finished by recommending some other open-access papers for TMSJN members to read:

– Skovsmose (2020): Mathematics and ethics

– Skovsmose (2021): Mathematics and crises

Here are some reflections on the paper and the meeting from those who attended …

**Ben Breen (Dartford Grammar School):**

*Primarily, I felt reassured by the article. The author argues that Mathematics Education for Social Justice is not about teaching what social justice is, but about getting students to consider what social justice might mean. This feels quite liberating, when I consider the activities I could use for this in my classroom, and also helps to avoid the pitfall of coming across as a preachy know-it-all when covering topics with a class.*

*Skovsmose mounts a powerful critique of the idea that Mathematics itself – or indeed Mathematics Education – can ever be value-free and neutral. I now have a perfect response to those who want to avoid discussing social justice and ethics in Mathematics: even if the knowledge being generated seems entirely abstracted from society, there is no guarantee it will remain that way. Additionally, the article provides a useful reference for the ways in which mathematics interacts with power: technological imagination; hypothetical reasoning; justification and legitimation; realisation; and the dissolution of responsibility. This is something I have struggled to articulate in the past, and I am sure the ideas will make their way into a department meeting or sixth-form Theory of Knowledge lesson in the future.*

*Skovsmose’s discussion of monologic versus dialogic epistemologies was something I found more difficult to grapple with. I think there is certainly a place for the teacher as an expert imparting knowledge to (hopefully willing!) pupils, but when I look at the ways this knowledge is actually constructed and internalised, they all involve a dialogue. That dialogue can take a variety of forms: student-student; teacher-student; or student-resource.*

**Alison Ford (Bideford College):**

*Whilst thinking back over the reading group, it struck me that we had been engaging in constructing our understanding of critical mathematics education through dialogue. This neatly parallels the pedagogy that Ole argues for and was a great example of how it can be possible. We had more than one form of dialogue, between peers, and then between ‘teacher’ and ‘students’. We then came away to reflect individually, which to me is a further form of dialogue with the text and with the ideas of the evening. The discussions themselves reinforced for me how important it is to engage critically with the maths that we are teaching and to facilitate ways for our students to do the same. I am becoming more aware of the power of my subject both as a tool to address issues of social justice but also as a key component of inequality itself. This raises the value of teaching beyond the sharing of knowledge and passing of exams, and gives us a roadmap of sorts to follow as we continue to discuss, consider and develop together.*

**Lisa Pollard (Palladian Academy Trust):**

*Skovsmose’s article was persuasively written, creating emotional responses in our discussion. A couple of members in our small group discussion shared how they had not only received resistance from colleagues to engage in openly social justice focused lessons, but that there were elements of resistance from the students themselves. “Is this maths?” “Is this in the exam?” “What does this have to do with mathematics?” These members were feeling disheartened, particularly those at the start of their career, especially when others including the leadership in their department or school, were much more didactic, engaging in monologic teaching and using knowledge sharing as their main teaching stance. *

*As a group, we discussed overt and covert curricula, and how the colonisation of the curriculum did not happen overnight by children being forced to learn in detail about the mainly white, European men given as model mathematicians, but rather the relentless drip feeding that subconsciously accumulates bias and inequity over time. We discussed that, whilst a learning objective, for example, may be ‘to draw regular polygons that are reflectively and rotationally symmetric’, one could use visuals and information about, for example, ‘mandalas’, including what they are, where they can be found and occasions during which they are used. This lesson and its reflections could then be shared with colleagues who may wish to observe, reflect and collaborate in further planning and delivery.*

*Teachers talked about the tightness of the mathematics curriculum and whether there may be something cross-curricular to pull out overtly the maths for social justice. One example of this related to time and large numbers (Year 6 upwards in the national curriculum) and the example of estimating how long it would take to count to 6 million. Why 6 million? It is not only the approximate number of Jewish people killed by the Nazis during the holocaust but also the approximate number of deaths worldwide due to Coronavirus. The power of discussion of what is the same and what is different about the contexts, through the construct of one number, can be extremely powerful.*

*During the question-and-answer session with Ole Skovsmose, our small group posed this question: “Have you any thoughts as to how mathematics being taught in other subjects, with non-maths specialists, can use this very powerful dialogue for social justice (e.g., History/Geography)?” Ole discussed uses in economics and humanities subjects, and we reflected on the collaboration between colleagues with subject expertise in each subject, coming together to use the content wisely but in a way that could open discourse and dialogue, thus empowering students to view the world and its injustices through exposure to elements of inequity and ethics. I have always known mathematics to be powerful and divisive but Ole’s paper, and the following discussions, reminded me that, whilst it is neither harmless nor innocent, maths can be used in a negative or even destructive manner. As Ole affirmed: ***“You cannot do without mathematics, but you can do wrongly with mathematics!”**

**Sandra Beckford-Henry (Conisborough College):**

*I really enjoyed the evening. It was refreshing to hear different viewpoints and share in such important discussions.*

*I recall during the discussions Ole mentioned the topic of social justice (SJ) as being a very important topic but with no set answers. I came away thinking all I can do as a mathematics teacher is to open up the dialogues around the subject of SJ through the pedagogies used to deliver a maths education and allow students to explore their own ideas and conceptions based on parameters within their own ‘life-worlds’. Facilitating where necessary – without exerting my own ideas or beliefs – in helping students formulate questions and articulate uncertainties regarding SJ. One could possibly employ hypothetical reasoning to facilitate. Students could hopefully see the relationship between mathematics and power. *

*It was very encouraging to read the section on ‘Teachers’ Life-Worlds’; Just knowing that someone has acknowledged the daily demands on teachers, and writes/publishes it, contrasts with the notion in schools, which is, ‘It comes with the territory, so we just have to get on with it’.*

**Cristina Mio (University of Glasgow):**

*After the reading group meeting, and maybe because of my role as a teacher educator, I found myself reflecting on what the author calls the teachers’ life-worlds. He writes that “Teachers are not only educators but also salary workers”. I think we sometimes forget this, and we hold teachers to impossible standards. The demands and expectations that we have of teachers should be reconciled with the constraints they operate with, such as, among others, a finite amount of time and emotional energy. I felt that some of the questions we posed to the author in the second part of our meeting highlighted how much we, as teachers, feel the responsibility we have towards our students. We (or maybe only me) were hoping for some answers that would tell us how to do things ‘right’. But the author stated a few times that social justice is a matter of concern, not a matter of solutions. So, maybe we, as teachers with our life-worlds and their constraints, should accept that there is no ‘closure’, no ‘recipe’ for engaging in social justice issues. Maybe all we can do is to remain committed to questioning what happens around us and the actions we take, so that, paraphrasing the last line of the article, we are permanently searching for what to do.*

**Suchi Srinivas (India):**

*Skovsmose’s idea of criticality in mathematics education is two pronged: being critical with respect to mathematics; and being critical by means of mathematics. A crucial construct in this discussion is the notion of ‘social justice’. Skovsmose argues that ethical conceptions like social justice are not to be discovered, but to be socially constructed, and a truly critical mathematics education would be one that engages students and teachers in this process of developing and refining this construct.*

*Skovsmose’s own notion of social justice is inspired by Rawls’ theory of social justice. But while Rawls’ idea, based on the notion of ‘fairness’ and equal distribution, is more of a thought experiment, Skovsmose takes a more pragmatic approach and dwells on how the process of constructing conceptions of social justice in real life contexts, in particular, the classroom. A part of this process, according to Skovsmose, is “addressing and reworking conceptions of social justice”. A discussion-point regarding this came up during our breakout group discussion. What if the process of ‘construction’ throws up notions of social justice that are radically different from those that are essentially based (like that of Rawls) on the idea of fairness? After all, with the strong neoliberal discourses that are prevalent in the present-day scenario, isn’t it likely that many students develop notions that are much more aligned, for instance, with Robert Nozick’s conception of social ‘justice’ – where unequal distributions of wealth and power are justified simply if they are considered a ‘legitimate’ entitlement? Skovsmose’s response to this question was that the responsibility of the teacher and the students is to engage in dialogue and deliberations on the idea of social justice, without trying to force any specific outcomes. This seems reasonable, although I do have lingering doubts about the efficacy of this approach in posing a real challenge to neoliberal discourses, and would like to know more about any successful experiments that have managed to achieve this even to a limited degree.*

*Another key idea propounded in Skovsmose’s paper was about the importance of dialogue in this process of developing a conception of social justice. While, on the face of it, this seems difficult to argue with, I believe there is some scope for debate. For instance, do all cultures accord the same value to dialogue? If not, might we not (perhaps inadvertently), be reaffirming Eurocentric epistemic approaches? There seems to be a need for more research and a deeper discussion on this issue. *

*One idea in Skovsmose’s writing that I consider extremely powerful is that of students’ “foregrounds”. While in this session this idea could not be discussed, I would welcome opportunities to discuss and understand it further.*

**Gwen Ineson (Brunel University London):**

*Many of the eight elements of mathematics education that Ole Skovsmose discusses in his paper (social justice, maths in action, students’ foregrounds, teachers’ life-worlds, sustainability, citizenship, dialogue and critique) resonated with my work in initial teacher (primary) education. One of the biggest battles I find myself having in discussions with my student teachers is about the extent to which they are able to digress from the dominant discourse around direct instruction, to free up space for dialogue. It seems that without dialogue, it is not possible to even begin considering the other seven ideas discussed in the paper, yet many beginning teachers are deterred from deviating from the prescribed lessons already planned in advance, or from the published scheme that the school follows. It is difficult to build in sufficient opportunities for student teachers on a teacher education programme to discuss and critique their ideas about mathematics education and, if schools aren’t open to this dialogue, how will beginning teachers learn to question their own developing practice?*

*Ole’s commentary on students’ foregrounds also caused me to reflect on the extent to which we consider pupils as “full human beings located in a complexity of life-worlds” (p.8). Despite the evidence of the benefits of mixed-attainment teaching, many schools persist with setting pupils by ability, so much so that often beginning teachers never have the opportunity to teach or observe mixed attainment teaching. Therefore, discussion about their teaching typically involves explanations about their “lowers” and the limits placed on their learning through rather closed and dull activities. Ole’s discussion about this includes the lack of motivation that these pupils may feel and suggests that “hopelessness is a devastating obstruction to learning” (p. 9).*

*Having considered these, and other excellent points in the paper, the discussion about Teachers’ Life-worlds offered a welcome acknowledgement that the critique presented was as a result of the limitations placed on teachers (i.e. through policy, curriculum and exam frameworks, etc). Ole suggests that teachers able to incorporate the elements of critical mathematics education discussed in their teaching are “super-teachers” (p.11), but also emphasises that it isn’t realistic or appropriate to expect this of teachers.*

*It was great to discuss our reflections with colleagues as part of the reading group, including the implications for our own practice, and to hear Ole himself talking about some of these ideas – a truly wonderful opportunity!*

**Ines Makonga (Hampstead School):**

*According to Ole, social Justice in terms of mathematical education is not about teaching what social justice is, but rather integrating it in our teaching to show students how it should look like in real life. After reading the article, because of the term critical mathematics education, I wanted to understand my place as a teacher: a powerful person transferring knowledge who tells students what to do? or a person who creates a safe place for discussion and who is open to criticism?*

*The author stated the importance of dialogue in critical mathematical education. In that respect, the teacher has many roles: to facilitate dialogue between students; to allow students to engage in investigations. The role of the teacher is still different from that of the students; the teacher is still powerful but helps students’ understanding. However, with regards to social justice, the teacher and students can both challenge each other.*

*The author stated that the purpose of critical mathematics education is about dealing with concerns rather than finding solutions. The challenge with implementing critical mathematical education can be found in what the author called ‘pathological learning’. Currently, students learn to get ready for national exams, and addressing social justice in the classroom can impact students’ exam preparation and create/maintain inequality in opportunity between different socio-economical groups.*

**Reflection**: I have enjoyed the meeting, but I have found that critical mathematical education for social justice is full of contradictions. Mathematics is beautiful and very powerful: it impacts all aspects of life and has the power to build and destroy lives. It has implications for all aspects of life and, as mathematics teachers, we are in positions of power. However, teachers need to know and understand ways to utilise this power to shape students’ lives. In order to do so, teachers need to understand mathematics and its implications for different aspects of life. However, I believe in the need to change the curriculum and the assessment/exam system to allow for students, as well as teachers, to implement critical mathematical education for social justice in the classroom.