We will present results from our ongoing study of how to develop pre-service teachers’ (PSTs) competences for teaching about sustainability in primary and secondary classrooms through mathematical modelling (MM). Our research is oriented by the need to address sustainability issues through learning and teaching in K-12 classrooms. Sustainability education is often informed by the Organization for Economic Cooperation and Development’s (OECD) Sustainable Development Goals (SDGs), which address a wide range of economic, environmental, and social needs. In this paper, we situate ourselves with respect to the SDGs in two ways. The first is by using the tools of mathematics, specifically MM, to identify, describe, and interpret critical, real-world issues, such as environmental degradation, in the teaching and learning of mathematics in K-12 classrooms. The second is by addressing SDG #4 (Quality Education), specifically, and the extent to which “education for sustainable development [is] mainstreamed…in teacher education” (United Nations, 2017, p. 6).

Sustainability, in particular environmental sustainability, is an increasingly important aspect of K-12 education and involves the social, economic, and environmental decisions we make today to “meet present needs without compromising the chances of future generations to meet their needs” (United Nations, 2023). MM is the cyclical process of representing and interpreting real-world phenomena with the tools of mathematics. It entails “familiarising oneself with [an] original problem situation, analysing it, and exploring possible solution paths,” (Niss & Blum, 2020, p. 24). We see MM as a powerful means of attending to sustainability issues in the classroom, but to do so, teachers need to develop specific modelling and sustainability-focused competences. In this paper presentation, we draw on data collected from PSTs at a large Canadian university (University of Alberta) as they engaged in what we denote as a modelling for sustainability (MfS) task. The research questions driving our analysis:

How do PSTs realize and interpret diverse meanings of value when engaging in an MfS task?

            The task PSTs engaged with is entitled the Tree Value task and was designed by the primary author (Markle, 2026). Both the task design and our analysis of participant data was guided by our MfS framework. As we will discuss in greater detail in our presentation, at the core of our framework are the competences required to engage in mathematical modelling, namely simplifying real-world phenomena, mathematizing those phenomena, working mathematically, interpreting the results, and validating the results in the real world (Jung & Brady, 2023; Maab, 2006). Wrapping around those foundational MM actions are competences for teaching MM. The model we integrate into our framework is adapted from Borromeo Ferri (2018) and specifies four dimensions of teaching competency (Theoretical, Task, Instruction, and Diagnostic), each of which contains three teaching competences (Borromeo Ferri and Blum, 2009; Borromeo Ferri, 2018). Finally, this is all nested within a framework of sustainability competences. To define these competences, we draw on GreenComp, the European Union’s framework for sustainable learning, which consists of twelve competences in service of 1) embodying sustainability values, 2) embracing complexity in sustainability, 3) envisioning sustainable futures, and 4) acting for sustainability (Bianchi et al., 2022). The results we share in this presentation are especially relevant to this first cluster of competencies, embodying sustainability values.

The overarching study uses a design-based research (DBR) methodology. Over the past two decades, DBR has emerged as a widely used methodology in education research, especially mathematics education research (Cobb, 2003; Stephan, 2021). Although DBR studies vary widely in focus (e.g., different mathematical topics) and contexts (e.g., classrooms, teacher education, etc.), they share the common aims to change practice through practical intervention in specific contexts and generate new, testable theories beyond those contexts. DBR shares affinities with other methodologies, such as action research, that seek to simultaneously research and resolve a previously identified problem (in this case, how to develop PSTs capacity for addressing sustainability issues through MM). However, DBR is distinguished by its iterative structure, the systematic revision to the intervention that structure entails, and the theoretical and methodological pluralism that allows researchers to address the distinct aims of studies that are both practice-based and research-oriented. Participants were all enrolled as pre-service teachers at the University of Alberta and voluntarily took part in a two-hour task-based session. Participants were first given the Tree Value task and asked to engage with it as learners. The aim of the task is to develop a mathematical model to determine the value of a tree, so engaging as learners entailed applying the MM actions described above. Next, participants were given some samples of grade 6 (age 10-12) student work on the same task and were asked to interpret the work from a teacher perspective. Finally, participants took part in a semi-structured task-based interview, in which they were explicitly asked about the role of value in the student work and their own modelling. All of the sessions were audio- and video- recorded and audio from the sessions and interviews were transcribed. We then conducted a qualitative content analysis of the transcripts using elements of our MfS framework, especially the GreenComp sustainability competences.

Our analysis provided insight into the complex role of value in mathematics when the latter is used to attend to sustainability issues in the K-12 classroom, especially those situations involving the natural world. One aspect of this complexity was the diversity in meanings of value in participants’ work and their interpretations of students’ work. This included human-, eco-, and pluricentric conceptualizations of value. We also found that engaging with rich student work (that is, work that foregrounded these diverse conceptualizations of value) meaningfully informed the participants’ reflections on their own modelling, which tended toward human-centric meanings of value (e.g., use value). Our exploratory study has implications for future research in the field. For one, we argue that incorporating diverse meanings of value is a potentially critical feature of sustainability-oriented mathematics tasks. As such, more research is needed into how PSTs engage with these kinds of tasks (which includes modifying, evaluating, designing, selecting, and sequencing such tasks). Additionally, more research is needed on how pre- and in-service teachers interpret diverse meanings of value in student work, and more generally, the extent to which they see value as relevant in the mathematics classroom. In this paper presentation, we use a single task focused on valuing the natural world to work towards a better understanding of key task affordances and constraints, and ultimately, toward a generalizable, theory-based result for the field of pre-service mathematics teacher education.

Bianchi, G., Pisiotis, U., & Cabrera, M. (2022). GreenComp: The European sustainability competence framework (JRC Science for Policy Report No. JRC128040). Publications Office of the European Union. Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer. Borromeo Ferri, R. & Blum, W. (2009). Mathematical modelling in teacher education – Experiences from a modelling seminar. In V. Durand-Guerrier, V., Soury-Lavergne, S., & Arzarello, F. (Eds.), European Society for Research in Mathematics Education – Proceedings of CERME 6 (pp. 2046–2055). Cobb, P. (2003). Investigating students’ reasoning about linear measurement as a paradigm case of design research. In N. Pateman (Ed.), Supporting students’ development of measuring conceptions: Analyzing students’ learning in social context (pp. 1–16). National Council of Teachers of Mathematics. Jung, H. & Brady, C. (2023). Modeling actions foregrounded in whole-class modeling discourse: A case study of a model-eliciting activity and a three-act task. Mathematical Thinking and Learning, 27(1), 1–24. Maaß, K. (2006). What are modelling competencies? ZDM – The International Journal on Mathematics Education, 38(2), 113–142. Markle, J. (2026). Three characteristics of mathematical modelling tasks for sustainable futures. Currently under review. Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modelling. Routledge. Stephan, M. (2021). Classroom design-based research: Designing for proportional reasoning in mathematics education. In Z. A. Philippakos, E. Howell, & A. Pellegrino (Eds.), Design-based research in education: Theory and applications (pp. 83–102). The Guilford Press. United Nations. (2017). Global indicator framework for the Sustainable Development Goals and targets of the 2030 agenda for sustainable development. https://unstats.un.org/sdgs/indicators/indicators-list/ United Nations. (2023). Fast facts – What is sustainable development? https://www.un.org/sustainabledevelopment/blog/2023/08/what-is-sustainable-development/