Imagining possibilities: innovating mathematics (teacher) education for sustainable futures

2.1. Teacher change and the role of criticality

One of our guiding principles as MTE-researchers (cited by Mason, Citation2002) is the Zen proverb, “I cannot change others; I can work at changing myself” (p. v). We take from this proverb that we can only work on changing our own practices as MTEs, that we cannot cause the PSTs that we work with to change theirs, neither should we expect them to. Thus, our focus as MTEs in supporting our PSTs, is to provide them with opportunities to realise for themselves, changes in their practices in relation to teaching mathematics for sustainable futures. As MTEs we see our role as supporting PSTs to take a critical stance in relation to their practices, and to promote a greater awareness of sustainability and its links to mathematics education. Like Skovsmose (Citation2011), we are convinced of the relevance of small-scale educational change as opposed to focussing on ways to instigate large, structural, or even global-scale changes which can feel unreachable. We imagine that multiple local-scale changes (local to the teacher educator, the teacher, or the students) can become significant on a more global scale through collaboration and dialogue. As with Stenhouse (Citation1975), who conceptualised and urged teacher-researchers to critically examine their own practices, we view criticality as essential to teacher change. According to Skovsmose (Citation2011), critique can mean an “exploration of possibilities which need not be related to socio-political changes overall”, rather, “one can consider possibilities in everyday situations, possibilities in the personal life of students, possibilities in the classroom” (p. 22). Criticality is therefore as much about “conceptualising alternatives to what is taking place” (Skovsmose, Citation2015, p. 114) as it is about considering the current situation.

2.2. Pedagogical imagination

Teacher change, even on a small-scale, can be challenging. As MTEs we find ourselves looking for mechanisms that support our PSTs in both imagining and realising changes in their practices. In any education system, the level of challenge is confounded by the constraints set by both the socioeconomic situation and the imposed curriculum structures and norms. Educational philosopher Maxine Greene argues that social imagination, that is, “the capacity to invent visions of what should be and what might be … in our schools” (Greene, Citation1995, p. 5), enables a divergence from taken-for-granted ways of being and doing as well as letting go of the familiar to contemplate more just and equitable futures. Similarly, Skovsmose introduced the notion of pedagogical imagination as an important aspect of critical mathematics education (Skovsmose, Citation2011; Citation2015; Citation2016; Skovsmose & Borba, Citation2004), explaining that being critical “means to recognise that what appears as given might be contingent” (Skovsmose, Citation2011, p. 23). Skovsmose suggests that contingencies are revealed not by description but through imagination. Engaging a pedagogical imagination involves a process of questioning what might be assumed as fact (including many classroom and curriculum norms):

3.1. Our model of action research

Many models of educational AR have been established (e.g. Altricher et al., Citation1993; Elliot, Citation1991; Kemmis & McTaggart, Citation1988; Whitehead & McNiff, Citation2006) since Lewin (Citation1946) first proposed a cyclical model consisting of four fundamental stages: planning, acting (implementing), observing, and reflecting. Common to all AR models is the cyclical, recursive nature of the process, whereby each cycle informs the next through an ongoing process of reflection such that the research and the actions of the practitioner-researcher are inextricable. We adopted a version of the AR model proposed by Kemmis and McTaggart (Citation1988, p. 11); the AR spiral as shown in Figure 1 is based on Lewin’s (Citation1946) original four stages.

Figure 1. The AR spiral (Kemmis & McTaggart, Citation1988, p. 11).

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Based on Figure 1, we developed the model depicted in Figure 2, which details the multiple phases and stages of our AR study. The phase one activities (acting and observing) were based in HK, phase two in the UK and phase three across both institutions; however, all phases involved collaboration (planning and reflecting) between various members of the wider WUN group and us as researchers. Thus, collaborative planning and reflecting were involved in every phase.

Figure 2. Our own AR process.

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The organisation of the subsequent sections within this article mirrors the process depicted in Figure 2, using the headings “planning and acting”, “observing” and “reflecting”. In order to represent more closely the process of AR (and our learning as MTEs) we present phases one and two before presenting phase three, to demonstrate how the design of phase three was shaped by our analysis of data from the earlier two phases. To recap, our primary research question (RQ1) with its focus on our own practices and curriculum innovations as MTEs is our overarching inquiry across all phases of our AR study. We specifically address RQ1 in the “reflecting” stages of each phase in order to learn about ourselves and to inform our future practices. RQ2 emerged whilst planning our initial phases (phase one and phase two) of AR. Specifically, we address RQ2 in the “observing” stage of phases one and two where we focus on the PSTs’ learning experiences in response to our curriculum innovations. RQ3 emerged in response to our observations and reflections during these two phases, and we address this research question in the “observing” stage of phase three.

Our initial local activities took place in our respective MTE courses: Action Research in Mathematics Classrooms in HK with 20 fourth-year undergraduate mathematics PSTs and a one-year postgraduate Certificate in Education (Mathematics) course in the UK with 30 PSTs. As part of our MTE curricula, we facilitated a series of learning activities for the PSTs to design, use and critically reflect on mathematics curricula tasks addressing the urgent climate crisis and sustainable mathematics education (Renert, Citation2011). Inherent in the context of teacher education are the potential power imbalances that can arise when researching PSTs’ responses to tasks that are “set” by teacher educator-researchers as part of the PSTs teacher education programme. We were keen to minimise these issues and built in a number of checks and balances over the course of our study. For example, we emphasised to the PSTs that we were interested in the quality of reflections rather than the content of their responses. The PSTs voluntarily participated in the phase three activities as optional learning enrichment, which took place immediately after the end of the teacher education programme in the UK and the end of the course taken by HK PSTs; therefore, they were informed and provided consent that their participation was not linked to any assessed modules or units in any way. Most significantly, we are not using the findings to make general claims about PSTs. Instead we are looking to critically reflect on and improve our own practices as MTEs in relation to the responses from our PSTs.

3.2. Data collection and analysis

As in AR methodology, our data collection is cyclical and comes from multiple sources. In addition to our field notes from all stages and phases of the study, we collected the PSTs’ written reflections upon engaging in the initial phases, and video recordings of the meeting between UK and HK PSTs, along with their joint speculative fiction writing as a form of artefact as generated in phase three of the study. In terms of data analysis, we began by reviewing all data sources. We followed principles of qualitative analysis to generate plausible responses to the RQs based on evidence indicative of changes in the discourse of the PSTs; what they perceive in relation to their teaching as contingent and fixed; their identified constraints and possible alternatives in teaching for sustainable futures. For example, we noted instances where the PSTs claimed that they were surprised, became aware, acquired new perspectives, or when they expressed strong emotions or sentiments about teaching for sustainable futures, and why. We continued to sort through, identify and refine relationships from the data collected in the observing stages of each phase. Finally, we synthesised these observations in the reflecting stage which helped us learn about our own practices, for instance, what we might then do to encourage further possibilities.

As Wright (Citation2021) states, the trustworthiness of qualitative research such as the current AR can be established through seeking credibility, confirmability, transferability and dependability. First, we undertook prolonged engagement with PST participants and triangulated our data collected over a ten-month period, as well as examined transcripts of the participants’ original written responses to delve into any tacit knowledge, such as one’s culture and values, in the analyses to ensure the credibility of the results. We addressed confirmability by keeping an audit trail for the research process, such as making records and taking field notes for analyses. Finally, in addressing transferability and dependability, we provided thick descriptions of the context and design of the study, and we held discussions during data analysis to ensure the research process was logical, traceable, and clearly documented.

4.1. Planning and acting

Our study began in HK, where Oi-Lam had designed and implemented a set of blended-learning activities as complementary to her course objectives to familiarise her students with the nature of action research in reflective and critical perspectives, drawing on the work of Mason (Citation2002) as a form of reflective practice in action research. The PSTs first viewed a five-minute video on the documentary The Inconvenient Sequel: Truth to Power (Skoll et al., Citation2017) and then engaged in a related face-to-face discussion. Next, the PSTs perused two web resources—the “Climate Change 2014 Synthesis Report” prepared by the Intergovernmental Panel on Climate Change (Citation2014) and the “Climate Change in Hong Kong” website (Hong Kong Observatory, Citation2019) – to inquire about global and local climate statistics and projections, respectively. The PSTs were prompted to reflect on the video and reading on a personal level and as educators; this included a task in which they were to design a lesson or project that they would like to implement in their future practice while addressing issues of sustainability in a mathematics education context. To facilitate further reflections and peer learning, Oi-Lam prepared a class blog on which the PSTs could post their responses and engage in asynchronous discussion with their peers. The blogging activities generated 20 reflective posts and 60 additional comments, which we used as sources of data.

During the WUN project collaborations, Tracy was inspired by Oi-Lam’s work with her PSTs and consequently designed a virtual session for her PSTs in the UK. Based on enactivist principles (Brown et al., Citation2018; Brown et al., Citation2019) that emphasise one’s experiences as the basis of their learning, Tracy’s goal was to unpack her PSTs’ own experiences (experiences with learning mathematics, observing in mathematics classrooms, and teaching mathematics) to support their learning as practitioners (Brown et al., Citation2021). Her three-part virtual session, Teaching mathematics in a time of crisis: What does mathematics have to offer? began with the PSTs reading and responding to Renert’s (Citation2011) article via an online discussion forum. They then worked on a mathematics task based on an “inquiry-based learning situation on sustainability” [see Savard (Citation2017) for the task and a description of an inquiry-based learning situation]. Finally, the participants designed and tested their own innovations by teaching one another using tasks and resources they had designed and provided one another with feedback. The tasks and resources were designed to address one or more global challenge, including but not limited to the climate crisis.

In the next section, we report of our observations in relation to phases one and two of the AR study, with a focus on RQ2, by drawing on the concepts introduced in Section 2 and described in relation to data analysis in Section 3.2. Note that the names used for the prospective teachers throughout this paper are pseudonyms.

4.2. Observing

To begin, we observed that most HK PSTs realised that the climate crisis is more urgent than they had previously imagined. While they identified themselves as contingent for making local-scale changes to mitigate the problem, they suggested that the overall situation is more or less fixed. Some PSTs expressed a sense of powerlessness and scepticism toward large-scale changes that might take place for a more sustainable (mathematics education) future. While perceiving their actions as insignificant, they did position themselves as agents for change by taking responsibilities to take some kinds of actions personally, as illustrated in Dan’s post.

For the UK PSTs, we observe that they mostly endorsed Renert’s (Citation2011) views regarding sustainable mathematics education. Besides, some PSTs revealed how they imagined the ideas might directly influence their practices, as illustrated by James’ comment:

In the next section we reflect on our observations from the previous section to focus on our primary research question, RQ1.

4.3. Reflecting

Firstly, we were intrigued by the diverse range of emotions and feelings expressed by our PSTs, which included powerlessness, concern, frustration, scepticism, responsibility, hopefulness, etc., in response to the learning activities. We think that these emotions and feelings suggest the PSTs’ high engagement with the learning resources, which ranged from local/global climate data to more conceptual ones, such as Renert’s article. It seems that our resources succeeded in helping the PSTs in recognising the need for taking alternative actions on a personal level to make local-scale changes for a more sustainable future, although many of them were not clear how to go about it. This demonstrates how mathematics teacher education curricula can support PSTs toward teacher change, namely by providing opportunities for PSTs to feel connected to the cause personally and thus empowered to make a difference. Especially, we suggest that the visual and moving images viewed by the HK PSTs was a powerful media for personal reflection, noting that several PSTs had mentioned how seeing the melting glacier had made a lasting impression for them, and they felt responsible to do something about it. In addition, we realise that some UK PSTs wanted to hear more about how conceptual ideas, such as Renert’s sustainable mathematics education, can be applied in practice. Some PSTs were less convinced about the prospect of and their ability to change their practice in relation to sustainable futures, especially considering the constraints of current mathematics curricula and imagined normative structured within the schools and the education system more broadly. In other words, though they see themselves as contingent to change, they either did not see what changes might look like, or how their local-level changes might lead to large-scale changes in the long term.

From this experience, we have learned that, first, for mathematics teachers to develop new practices, we must go beyond the formulation of ideas. Ideas can be powerful, particularly when formed in dialogue with others, but more so when teachers can realise the ideas in their practice. Second, it was difficult for PSTs, who had various experiences and expectations about mathematics teaching and learning, to visualise something different – both in terms of how they might teach and what their impact on learning might be. For these reasons, we designed a speculative fiction task (see Section 5.1) to be implemented in the next phase of our AR, which we hypothesised might support PSTs in not only perceiving their pedagogy as contingent, but also imagining and realising new possibilities toward teaching for sustainable futures. We were thus interested in using speculative fiction as a curriculum innovation within mathematics teacher education and in better understanding the impact of using such tools in our teaching as MTEs, and we elaborate in the next section.

5.1. Planning and acting: speculative fiction as method

Certain catalysts exist that can prompt changes in teaching practices, such as new assessment systems, curriculum reforms or, as we now know, a monumental event, such as a global pandemic; however, though these situations can prompt change, it is still the teachers who enact those changes (or not). In our conversations as researchers, we each expressed a desire to design a task at this phase of our study that encouraged global dialogue between the PSTs from HK and the UK that also enabled them to develop their pedagogical imaginations (Skovsmose, Citation2011, Citation2015, Citation2016; Skovsmose & Borba, Citation2004). As previously mentioned, to strengthen our AR study, and the design of our teacher education curricula, we are drawn to generative methods that look towards the future, supporting “what if?” questions as opposed to purely “what is?” For these reasons, we looked beyond traditional research methods towards arts-based approaches.

Greene (Citation1995) advocated integrating the arts to invite learners to use their imaginations and to perceive things differently as a way of transforming realities. She promoted many types of dialogue to reshape the imagination in a way that “refuses mere compliance”, such as … 

Whilst climate modelling has been the prevailing way in which we predict climate futures, Urry (Citation2016) notes that the causes and consequences of climate change must entail “multi-disciplinary research and theory” (p. 156), which “concerns social and not just physical or technological futures” (p. 157). As several studies suggest, formal scientific approaches to altering the attitudes and behaviours of children and young people toward climate change has been largely ineffectual (e.g. Brownlee, Powell, & Jeffery, Citation2013; Dijkstra & Goedhart, Citation2012; Rousell, Cutter-Mackenzie, & Foster, Citation2017). This issue applies not only to young people, but to us all, including teachers committed to changing their teaching practices in relation to issues of climate justice. If the task of reimagining education requires the capacity to speculate on potential futures, our PSTs must be “given space to practice and cultivate their imaginative skills” (Howlett, Citation2018, p. 115). With the effects of climate change being commonly perceived as both distant and abstract as well as “overwhelming and difficult to grasp” (Raven & Stripple, Citation2021, p. 223), it has been argued that combining quantitative modelling with imaginative engagements and qualitative tools of the social sciences and humanities could bring climate change closer whilst making it more concrete by exploring climate-changed futures (Levy & Spicer, Citation2013; Urry, Citation2016). Utopian and dystopian fiction are two well-known genres of speculative fiction, both sharing the method of depicting an alternative society. Dystopia constitutes a warning of what may happen if we go on as we are, whereas utopia projects a desired future. Levitas (Citation2017) writes about “utopia as method”, as one form of speculation that “encourages us to think differently, systemically, and concretely about possible futures […] it allows us, in imagining an entirely different society, to break from the present at least in imagination” (p. 7). It is the “breaking from the present” that we feel is of particular relevance in our work with PSTs. Speculative fiction could therefore encourage PSTs to break, even momentarily, from the perceived constraints associated with daily norms and structures (including habitual ways of thinking) to think more freely about what might be possible in their mathematics classrooms (i.e. engage their pedagogical imaginations). Utopia addresses issues of present concern by projecting a different future in which they are resolved. According to Levitas, the “process of speculation about a potential better future – what we might call the Imaginary Reconstitution of Society – is a method rather than a blueprint” (p. 8, emphasis added).

We found no examples of speculative fiction as a method within mathematics education research, but examples do exist in teacher education more broadly. For instance, Tomin (Citation2021) reports on a project using speculative storytelling to support PSTs in imagining the future of education to “dismantle singular notions of what education might look like and the role that education might play in a changing society” (p. 241). We have been inspired by the ideas of speculative fiction and utopia as method in our work with PSTs, as a way of developing pedagogical imagination required to bring about change, the specific details of our own use is presented in the following section. We see speculative fiction as a curriculum innovation as well as a novel research method, the product of which forms the basis of analysis in phase three of our AR study.

Based on our reflections from phases one and two, we adapted a task from https://workthatreconnects.org (Brandt, Citation2017), where we invited pairs of PSTs (UK–HK) to engage in writing a speculative fictional story or dialogue prompted by the idea of having met a mathematics teacher from the future at a “point outside of time” (Brandt, Citation2017) to communicate their image of the future of mathematics education and their own classrooms. The speculative fiction task was based on two assumptions, which were shared with the PSTs:

5.2. Observing and reflecting

As the designed speculative fiction featured a dialogue between present and future teachers, we were particularly interested in two aspects, namely the temporal and dialogic nature of the PSTs written responses. By paying close attention to the PSTs’ word choice and form in these two aspects, we found emerging themes as to how the speculative fiction task might support the PSTs’ pedagogical imaginings and innovations (Sections 5.2.1 and 5.2.2). We then focussed on the content of their writing to explore how the possibility of change was conceived by the PSTs (Section 5.2.3).