From modelling problems to socio-ecological awareness
The role of reflective discussions in mathematics education
Keywords:
mathematicsAbstract
The focus of this article is on how mathematical modelling problems can facilitate reflective discussions contributing to raising students’ awareness of socio-ecological issues. Drawing on theoretical concepts from critical mathematics education, particularly reflective discussions, environmental justice, controversy and uncertainty, two modelling problems, ”Artificial turf” and ”Wind farms”, are analysed. The analysis reveals multiple ways in which these problems can facilitate reflective discussions contributing to raising students’ awareness of socio-ecological issues. For instance, choosing a context that is authentic, complex, personalised, has multiple stakeholders, no obvious solutions, involves uncertainty, and is value based and controversial. Additionally, the problems offer opportunities for teachers to initiate conversations on topics such as energy consumption and impacts on the environment, environmental justice, and uncertainty, prompting students to take a stance and engage critically. This research suggests that teachers can engage students in modelling problems involving socio-ecological issues that aim to contribute to raising awareness, and future research can investigate how this could take place in the classroom.
References
Abtahi, Y., Gøtze, P., Steffensen, L., Hauge, K. H., & Barwell, R. (2017). Teaching climate change in mathematics classroom: An ethical responsibility. Philosophy of Mathematics Education Journal, 32, 1–18.
Andersen, I. (2024, 11. December). Strømprisen når nye høyder i Sørvest-Norge – over 13 kroner kilowattimen [Energy prices reach new highs in Southwest Norway – over 13 kroner per kilowatt hour]. Teknisk ukeblad.
Atweh, B., & Brady, K. (2009). Socially response-able mathematics education: Implications of an ethical approach. EURASIA Journal of Mathematics, Science & Technology Education, 5(3), 267–276.
https://doi.org/10.12973/ejmste/75278
Barbosa, J. C. (2006). Mathematical modelling in classroom: A socio-critical and discursive perspective. ZDM – Mathematics Education, 38(3), 293–301. https://doi.org/10.1007/BF02652812
Barbosa, J. C. (2009). Mathematical modelling, the socio-critical perspective and the reflexive discussions. In M. Blomhøj & S. P. Carreira (Eds.), Proceedings from Topic Study Group 21 at the 11th International Congress on Mathematical Education in Monterrey, Mexico (pp. 133–143). Roskilde Universitet
Barbosa, J. C. (2013). The students’ discussions in the modeling environment. In R. Lesh, P. Galbraith, C. Haines, & A. Hurford (Eds.), Modeling Students’ Mathematical Modeling Competencies. International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 365–372). Springer. https://doi.org/10.1007/978-94-007-6271-8_31
Barwell, R. (2018). Some thoughts on a mathematics education for environmental sustainability. In P. Ernest (Ed.), The Philosophy of Mathematics Education Today (pp. 145–160). Springer.
https://doi.org/10.1007/978-3-319-77760-3_9
Berget, I. K. L. (2022). Mathematical modelling in textbook tasks and national examination in Norwegian upper secondary school. Nordic Studies in Mathematics Education, 27(1), 51–70.
https://doi.org/10.7146/nomad.v27i1.149184
Bettini, A. (2022). Voices from a fractured landscape: Fracking, senses of place, and risks in Taranaki, Aotearoa New Zealand [Doctoral thesis]. University of Alberta. https://doi.org/10.7939/r3-jjha-7y67
Borromeo Ferri, R. (2025). Mathematical, modelling as a key practice for promoting learners’ competencies targeting the transformation of global, sustainability. In K. le Roux, A. Coles, A. Solares-Rojas, A. Bose, C. P. Vistro-Yu, P. Valero, N. Sinclair, M. Makramalla, R. Gutiérrez, V. Geiger, & M. Borba, (Eds.), Mathematics education and the socio-ecological (pp. 284–291). MATHTED and ICMI.
Bratman, E., Auch, T., & Stinchfield, B. (2022). The fracking frontier in the United States: A case study of foreign investment, civil liberties and land ethics in the shale industry. Development and Change, 53(3), 469–494. https://doi.org/10.1111/dech.12707
Bulut, N., & Borromeo Ferri, R. (2025). Bridging mathematical modelling and education for sustainable development in pre-service primary teacher education. Education Sciences, 15(2), 248.
https://doi.org/10.3390/educsci15020248
Cevikbas, M., Kaiser, G., & Schukajlow, S. (2022). A systematic literature review of the current discussion on mathematical modelling competencies: State-of-the-art developments in conceptualizing, measuring, and fostering. Educational Studies in Mathematics, 109, 205–236. https://doi.org/10.1007/s10649-021-10104-6
de Almeida Luna, A. V., Souza, E. G., & de Souza Lima, L. B. (2015). Mathematical texts in a mathematical modelling learning environment in primary school. In G. A. Stillman, W. Blum, & M. Salett Biembengut (Eds.), Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences (pp. 535–543). Springer.
https://doi.org/10.1007/978-3-319-18272-8_45
Frankenstein, M. (1983). Critical mathematics education: An application of Paulo Freire’s epistemology. The Journal of Education, 165(4), 315–339. https://doi.org/10.1177/002205748316500403
Frejd, P. (2013). An analysis of mathematical modelling in Swedish textbooks in upper secondary school. Nordic Studies in Mathematics Education, 18(3), 59–95. https://doi.org/10.7146/nomad.v18i3.148516
Frejd, P., Ärlebäck, J. B., & Vos, P. (2024). Fostering student’s mathematical literacy through mathematical modelling tasks. In O. H. Bolstad, S. Goodchild, & M. Goos (Eds.), International perspectives on teaching and learning for mathematical literacy (pp. 178–203). Brill.
https://doi.org/10.1163/9789004710962_008
Fukuda, H. (2020). Research towards a Principle for the Statistics Curriculum in Japan from the Perspective of Context [Doctoral thesis]. Hiroshima University.
Galbraith, P. (2006). Real world problems: Developing principles of design. Identities, cultures and learning spaces, 1, 229–236.
Geiger, V., Galbraith, P., Niss, M., & Delzoppo, C. (2022). Developing a task design and implementation framework for fostering mathematical modelling competencies. Educational Studies in Mathematics, 109, 313–336 https://doi.org/10.1007/s10649-021-10039-y
Gutstein, E. (2006). Reading and writing the world with mathematics: Toward a pedagogy for social justice. Routledge.
Gran, B., & Bjøru, E. C. (2024). Konsekvenser av forbudet mot plastholdig fyllmateriale i kunstgressbaner. Rapport nr. 27-2024 fra Samfunnsøkonomisk analyse. SØA. https://www.fotball.no/globalassets/klubb-og-leder/anlegg/rapport-konsekvenser-av-forbud-mot-gummigranulat.pdf
Hauge, K. H., & Barwell, R. (2017). Post-normal science and mathematics education in uncertain times: Educating future citizens for extended peer communities. Futures, 91, 25–34.
https://doi.org/10.1016/j.futures.2016.11.013
Hess, D. E. (2009). Controversy in the classroom: The democratic power of discussion. Routledge. https://doi.org/10.4324/9780203878880
Huntley, J., & Wallis, L. A. (2024). Case study: The destruction of Australian Aboriginal heritage and its implications for Indigenous peoples globally. In J. A. G. Zarandona, E. Cunliffe, & M. Saldin (Eds.), The Routledge Handbook of Heritage Destruction (pp. 384–394). Routledge.
https://doi.org/10.4324/9781003131069-34
Hurlbert, M. A., & Datta, R. (2022). When the environment is destroyed, you’re destroyed: Achieving Indigenous led pipeline justice. Energy Research & Social Science, 91, Article 102711. https://doi.org/10.1016/j.erss.2022.102711
Idsø, J. (2021). Growth and economic performance of the Norwegian wind power industry and some aspects of the Nordic electricity market. Energies, 14(9), Article 2701. https://doi.org/10.3390/en14092701
Johnsen-Høines, M. (2020). Begynneropplæringen. Matematikkdidaktikk - barnetrinnet. Caspar Forlag.
Julie, C., & Mudaly, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. L. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 503–510). Springer. https://doi.org/10.1007/978-0-387-29822-1_58
le Roux, K., Coles, A., Solares-Rojas, A., Bose, A., Vistro-Yu, C. P., Valero, P., Sinclair, N., Makramalla, M., Gutiérrez, R., Geiger, V., & Borba, M. (2025). . MATHTED and ICMI.
Li, H. C., & Tsai, T. L. (2022). Education for sustainable development in mathematics education: what could it look like? International Journal of Mathematical Education in Science and Technology, 53(9), 2532–2542.
https://doi.org/10.1080/0020739X.2021.1941361
Miljødirektoratet. (10 november 2023). Plastholdig fyllmateriale på kunstgressbaner. https://www.miljodirektoratet.no/ansvarsomrader/avfall/avfallstyper/gummigranulat-fra-kunstgressbaner/
Ministry of Education and Research. (2017). Verdier og prinsipper for grunnopplæringen - overordnet del av læreplanverket [Values and principles for primary and lower secondary education].
https://www.udir.no/lk20/overordnet-del
Ministry of Education and Research. (2019). Læreplan i matematikk 1.–10. trinn [Curriculum for Mathematics year 1–10].
https://www.udir.no/lk20/MAT01-05
Moggridge, B. J., & Thompson, R. M. (2021). Cultural value of water and western water management: An Australian Indigenous perspective. Australasian Journal of Water Resources, 25(1), 4–14.
https://doi.org/10.1080/13241583.2021.1897926
Maaß, K. (2010). Classification scheme for modelling tasks. Journal für Mathematik-Didaktik, 31(2), 285–311.
https://doi.org/10.1007/s13138-010-0010-2
Maass, K., Zehetmeier, S., Weihberger, A., & Flößer, K. (2023). Analysing mathematical modelling tasks in light of citizenship education using the COVID-19 pandemic as a case study. ZDM – Mathematics Education, 55(1), 133–145. https://doi.org/10.1007/s11858-022-01440-9
Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modelling. Routledge.
Ojala, M. (2023). Hope and climate-change engagement from a psychological perspective. Current Opinion in Psychology, 49, Article 101514.
https://doi.org/10.1016/j.copsyc.2022.101514
OSPAR. (2024). Background Document on reducing microplastic contamination from performance infill in artificial grass pitches. OSPAR Commission
Paredes, S., Cáceres, M. J., Diego-Mantecón, J.-M., Blanco, T. F., & Chamoso, J. M. (2020). Creating realistic mathematics tasks involving authenticity, cognitive domains, and openness characteristics: A study with pre-service teachers. Sustainability, 12(22), Article 9656.
https://doi.org/10.3390/su12229656
Rosa, M., & Orey, D. C. (2015). Social-critical dimension of mathematical modelling. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical Modelling in Education Research and Practice (pp. 385–395). Springer. https://doi.org/10.1007/978-3-319-18272-8_32
Simic-Muller, K., Fernandes, A., & Felton-Koestler, M. D. (2015). ”I just wouldn’t want to get as deep into it”: Preservice teachers’ beliefs about the role of controversial topics in mathematics education. Journal of Urban Mathematics Education, 8(2), 53–86. https://doi.org/10.21423/jume-v8i2a259
Skovsmose , O. (1994). Towards a philosophy of critical mathematics education. Springer.
Skovsmose, O. (2023). Critical mathematics education. Springer.
https://doi.org/10.1007/978-3-031-26242-5
Solares-Rojas , A., Arellano-Aguilar, O., García González, M. M., López-Vargas, M. d. R., Coles, A., & Méndez Serrano, A. (2022). Mathematics education and social-environmental crises: An interdisciplinary proposal for didactic innovation with rural communities in Mexico. Research in Mathematics Education, 24(2), 202–223. https://doi.org/10.1080/14794802.2022.2062781
Steffensen, L. (2023a). Modellering: matematikk for skole og samfunn. [Modelling: mathematics for school and society]. Caspar forlag.
Steffensen, L. (2023b). Sustainability and mathematical modelling in 5th grade. Prometeica 27(10/2023), 241–251. https://doi.org/10.34024/prometeica.2023.27.15290
Steffensen, L., & Kacerja, S. (2021). Carbon footprints calculators and climate change. In F. K. S. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.), Mathematical Modelling Education in East and West (pp. 513–523). Springer. https://doi.org/10.1007/978-3-030-66996-6_43
Stillman, G. A., Brown, J. P., Faragher, R., Geiger, V., & Galbraith, P. (2013). The role of textbooks in developing a socio-critical perspective on mathematical modelling in secondary classrooms. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 361–371). Springer.
https://doi.org/10.1007/978-94-007-6540-5_30
Supreme Court of Norway. (11 october, 2021). Licences for wind power development on Fosen ruled invalid as the construction violates Sámi reindeer herders’ right to enjoy their own culture. https://www.domstol.no/en/supremecourt/rulings/2021/supreme-court-civil-cases/hr-2021-1975-s/
Syam, S., Wijaya, A., & Retnawati, H. (2019). Comparison of modelling tasks in Indonesian and Singaporean mathematics textbooks. Journal of Physics: Conference Series, 1320, Article 012057.
https://doi.org/10.1088/1742-6596/1320/1/012057
Tesfamicael, S. A., & Enge, O. (2024). Revitalizing sustainability in mathematics education: The case of the new Norwegian curriculum. Education Sciences, 14(2), Article 174. https://doi.org/10.3390/educsci14020174
UNEP. (2 march, 2022) Historic day in the campaign to beat plastic pollution: Nations commit to develop a legally binding agreement. https://www.unep.org/news-and-stories/press-release/historic-day-campaign-beat-plastic-pollution-nations-commit-develop
Valero, P. (2009). What has power got to do with mathematics education. In P. Ernest, B. Greer, & B. Sriraman (Eds.), Critical issues in mathematics education (pp. 237–254). Information Age Publishing.
Vásquez, C., Alsina, Á., Seckel, M. J., & García-Alonso, I. (2023). Integrating sustainability in mathematics education and statistics education: A systematic review. Eurasia Journal of Mathematics, Science and Technology Education, 19(11), em2357. https://doi.org/10.29333/ejmste/13809
Vásquez, C., Seckel, M. J., & Alsina, Á. (2020). Belief system of future teachers on Education for Sustainable Development in math classes. Uniciencia, 34(2), 1–15. http://dx.doi.org/10.15359/ru.34-2.1
Villarreal, M. E., Esteley, C. B., & Smith, S. (2015). Pre-service mathematics teachers’ experiences in modelling projects from a socio-critical modelling perspective. In G. Stillman, W. Blum, & M. Salett Biembengut (Eds.), Mathematical Modelling in Education Research and Practice (pp. 567–578). Springer. https://doi.org/10.1007/978-3-319-18272-8_48
Walker, T. R., & Fequet, L. (2023). Current trends of unsustainable plastic production and micro(nano)plastic pollution. TrAC Trends in Analytical Chemistry, 160, Article 116984. https://doi.org/10.1016/j.trac.2023.116984
Watson, A., & Ohtani, M. (2015). Themes and issues in mathematics education concerning task design: Editorial introduction. In A. Watson & M. Ohtani (Eds.), Task design in mathematics education: An ICMI study 22 (pp. 3–15). Springer. https://doi.org/10.1007/978-3-319-09629-2_1
Wess, R., Klock, H., Siller, H.-S., & Greefrath, G. (2021). Mathematical modelling. In R. Wess, H. Klock, H.-S. Siller, & G. Greefrath (Eds.), Measuring Professional Competence for the Teaching of Mathematical Modelling: A Test Instrument (pp. 3–20). Springer. https://doi.org/10.1007/978-3-030-78071-5_1
Wiegand, S., & Borromeo Ferri, R. (2023). Promoting pre-service teachers’ professionalism in steam education and education for sustainable development through mathematical modelling activities. ZDM – Mathematics Education, 55(7), 1269–1282.
https://doi.org/10.1007/s11858-023-01500-8
Wolfsberg, A. (2015). ’Literature’ on mathematical modelling from a teacher perspective: A textbook’s portrayal. In K. Krainer & N. Vondrová (Eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (CERME9, 4–8 February 2015) (pp. 951–957). Charles University in Prague, Faculty of Education and ERME.
World Commission on Environment and Development. (1987). Report of the world commission on environment and development: Our common future. United Nations.
Wright, P. (2021). Transforming mathematics classroom practice through participatory action research. Journal of Mathematics Teacher Education, 24(2), 155–177. https://doi.org/10.1007/s10857-019-09452-1
Zapata-Cardona, L., & Martínez-Castro, C. A. (2021). Statistical modeling in teacher education. Mathematical Thinking and Learning, 25(1), 64–78. https://doi.org/10.1080/10986065.2021.1922859
Zwaneveld, B., Perrenet, J., van Overveld, K., & Borghuis, T. (2017). Mathematical modelling in Dutch textbooks: Is it genuine mathematical modelling? In G. A. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education (pp. 503–514). Springer.
Downloads
Published
How to Cite
Issue
Section
License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.