Conference Agenda
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24 SES 05 A: Mathematics in Context: Modelling, Problem-Solving and Real-World Reasoning
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24. Mathematics Education Research
Paper The Effectiveness of the Hatsumon Method in Developing Students’ Thinking Skills Nazarbayev Intellectual Schools, Turkistan, Kazakhstan Presenting Author:The current education system is aimed at enabling students to deeply understand the knowledge provided, think critically, express their opinions openly and freely, and apply their knowledge in real life. Therefore, it is a modern requirement to use necessary and effective methods in the classroom that focus on developing students' thinking skills. This research was conducted within the framework of Lesson Study. The main goal of the study is to determine the effectiveness of the Hatsumon method in enhancing students' thinking abilities. The Hatsumon method is not just focused on receiving answers from students, but instead aims to develop students' thinking skills by asking quality questions, guiding students to clearly achieve the learning objectives of the lesson. The effectiveness of the Hatsumon method have been studied in three classes (9C, 9B, 9N). Additionally, a research group consisting of three teachers was formed based on the Lesson Study approach. The lesson was conducted in the "Trigonometric Formulas" section. The relevance of the research lies in the fact that trigonometry topics are considered difficult for students. In many cases, students simply memorize the formulas without understanding their meaning and significance. This leads to shallow mathematical knowledge and causes difficulties in mastering subsequent topics. Therefore, it is essential to use methods that encourage students to think deeply, analyze, and prove their solutions. Various levels of questions were posed to the students. These questions helped students deeply understand the topic and find the correct solutions to problems. During the research, nine students of different levels were selected for observation from each class. High-level students were able to immediately respond to the questions created based on the Hatsumon method and prove their solutions. Medium-level students, initially passive, became more engaged as the direction and content of the questions increased their interest, motivating them to express their opinions. Low-level students initially struggled, but with teacher support and well-posed questions, they gradually adapted to the questions posed to other students and began to take their first steps. The method proved to be effective for students at all levels. At the end of the lesson, teachers and students wrote reflections and shared their thoughts. Students mentioned that not only had they gained a deep understanding of the knowledge, but also paid attention to the origin and meaning of the formulas. Teachers emphasized the importance of guiding students' thoughts through questions. Based on the reflections and observation sheets conducted at the end of the lesson, the following conclusions were made:
In conclusion, this research demonstrated that the Hatsumon method develops students' deep thinking abilities, increases their interest in the subject, and improves their skills in justifying and expressing their thoughts. Through the observations and reflections gathered during the Lesson Study, an opportunity to improve teaching methodology in the classroom was created. It is recommended to continue using this approach in other topics of trigonometry and in other subjects, focusing on student development through teaching. Methodology, Methods, Research Instruments or Sources Used This study employs a mixed-methods research design to investigate the effectiveness of the Hatsumon method in developing students’ thinking abilities. The Hatsumon method, originating from Japanese lesson study, emphasizes the use of well-designed problem-posing questions to stimulate learners’ independent thinking, reasoning, and classroom dialogue. A mixed-methods approach is adopted to capture both measurable changes in students’ thinking abilities and in-depth insights into classroom processes. The study is conducted in a secondary school educational context, involving students exposed to lessons structured around the Hatsumon method over a defined instructional period. An intervention-based design is used, with an experimental group receiving instruction through Hatsumon-based questioning strategies and a comparison group experiencing conventional teacher-led instruction. Quantitative data are collected using pre- and post-assessment instruments designed to measure students’ thinking abilities, including analytical reasoning, problem-solving, and explanation skills. These assessments consist of open-ended and structured tasks aligned with curriculum objectives. In addition, rubric-based scoring frameworks are applied to evaluate the depth and quality of students’ responses, focusing on reasoning, justification, and conceptual understanding. Qualitative data are gathered through classroom observations, student work samples, and teacher reflective journals. Observation protocols are used to document the nature of teacher questioning, student engagement, and patterns of classroom discourse during Hatsumon-based lessons. Samples of students’ written and oral responses are analyzed to examine changes in reasoning strategies and cognitive engagement over time. Teacher reflective journals provide insights into instructional decision-making and perceived shifts in student thinking. To capture learners’ perspectives, student questionnaires or focus group interviews are administered, exploring students’ experiences of Hatsumon-based lessons and their perceptions of how questioning strategies influence their thinking processes. Quantitative data are analyzed using descriptive and inferential statistical methods to compare pre- and post-intervention outcomes. Qualitative data are analyzed thematically to identify recurring patterns related to cognitive engagement, reasoning development, and classroom interaction. Ethical considerations include informed consent, confidentiality, and voluntary participation. Conclusions, Expected Outcomes or Findings The study is expected to demonstrate that the Hatsumon method effectively enhances students’ thinking abilities by fostering deeper cognitive engagement, reasoning, and problem-solving skills. By emphasizing carefully designed, open-ended questions, the method encourages learners to actively construct knowledge rather than passively receive information. One anticipated outcome is that students exposed to Hatsumon-based instruction will show measurable improvements in analytical reasoning, conceptual understanding, and the ability to justify their ideas compared to students receiving conventional teacher-led instruction. Pre- and post-assessments are expected to reveal gains in the quality, depth, and creativity of students’ responses. In addition, the study expects to show that the Hatsumon method promotes metacognitive awareness, as students reflect on their own thinking while responding to challenging questions. Classroom observations and student work samples are anticipated to reveal increased engagement in discussion, higher frequency of reasoning aloud, and more collaborative problem-solving among peers. Teacher reflective journals are expected to highlight the instructional value of Hatsumon questioning, including insights into lesson planning, scaffolding strategies, and the adaptation of questions to diverse student needs. Student feedback is anticipated to indicate that the method increases their confidence in reasoning and expressing ideas, fostering a more participatory classroom environment. Overall, the study is expected to provide evidence that Hatsumon is a practical and scalable approach for cultivating higher-order thinking skills in secondary education. The findings will contribute to research on lesson study, classroom questioning strategies, and cognitive development, offering practical implications for teachers aiming to implement thinking-focused instruction. Additionally, the research may identify potential challenges, such as the need for teacher training in effective question design and strategies to support all learners in responding thoughtfully. References Cajkler, W., Wood, P., Norton, J., & Pedder, D. (2014). Lesson study as a vehicle for collaborative teacher learning in a secondary school.Professional development in education,40(4), 511-529. Al-Ahdal, A. A. M. H., & Aljabr, F. S. (2023). The Role of Interlanguage Practices in Feedback Mechanisms: A Case Study with Saudi EFL Learners.World Journal of English Language,13(8), 638-638. Coenders, F., & Verhoef, N. (2019). Lesson Study: professional development (PD) for beginning and experienced teachers. Professional Development in Education, 45 (2), 217–230. https://books.google.kz/books?hl=en&lr=&id=PInAAwAAQBAJ&oi=fnd&pg=PA38&dq=structural+approach+grammar&ots=sYRhk7z2nJ&sig=IxzwRHR3rsk3GcPPXIK1UTbg9UY&redir_esc=y#v=onepage&q=structural%20approach%20grammar&f=false https://www.educationaldesigner.org/ed/volume3/issue11/article44/ 24. Mathematics Education Research
Paper Systematic Literature Review of Studies on Fermi Problems in Mathematics Education 1: Eskisehir Osmangazi University, Turkey (Türkiye); 2: Bogazici University, Turkey (Türkiye) Presenting Author:Fermi problems, initially introduced by Nobel Prize–winning physicist Enrico Fermi, are defined as "open, non-standard problems requiring the students to make assumptions about the problem situation and estimate relevant quantities before engaging in, often, simple calculations." (Ärlebäck, 2009, p.131). Fermi problems differ from traditional mathematical problems in that they seem ambiguous and require limited information, as illustrated by the question, "How many technologically advanced civilizations exist in our galaxy?" (Efthimiou & Llewellyn, 2007, p. 255). These complex problems can be solved using estimation without exact calculation (Chandler, 1990), enabling quick approximate answers (Carlson, 1997). According to Ärlebäck (2009), Fermi problems are characterized by their accessibility to learners across different educational levels, their grounding in meaningful real-world contexts, and their open-ended nature, which involves neither predetermined solution strategies nor given numerical data; instead, they require students to identify relevant information, make reasonable estimates, and engage in discussion by drawing on prior knowledge and experience. These rich and meaningful features lead to its frequent usage in both physics and mathematics education. In this sense, solving Fermi problems can require examining models and principles in physics (Robinson, 2008) and doing mathematics (Meyer & Greefrath, 2025) without reaching the exact answer. The real-life context of its (Peter-Coop, 2009) can enable the construction of a bridge between different subjects, as it has an interdisciplinary nature (Sriraman & Lesh, 2006). Although Fermi problems were initially employed primarily in science contexts, following Ärlebäck's (2009) study on their potential for introducing mathematical modeling, they have been increasingly used in mathematics education research, specifically focusing on students' mathematical modeling and estimation skills. The scope of the recent studies comprises examining students' Fermi problem-solving process, larger number estimation and modeling skills (Albarracín & Gorgorió, 2019), mathematical model development process (Albarracín, 2021; Brunet-Biarnes & Albarracín, 2024), and measurement estimation skills (Er & Sezer, 2025; Segura et al., 2025). Within this scope, Fermi Problems enhanced students' mathematical skills across grade levels from primary school to high school. However, Fermi problems, which support students’ various mathematical competencies, need to be more widely recognized and used at the global and international levels. Thanks to their flexible structure, Fermi problems can be used in various mathematical contexts and foster a range of skills in students. In this respect, determining the research trends in existing studies on Fermi problems in mathematics education and identifying existing research gaps can provide an important roadmap for future studies. In the literature we reviewed, we encountered only one review study, conducted by Ärlebäck and Albarracín (2019), that examined the use of Fermi problems. However, this review primarily focused on the development of twenty-first-century skills and examined STEM disciplines broadly. Consequently, there remains a clear need for an in-depth examination of the use of Fermi problems, specifically within the field of mathematics education, with particular attention to publication trends over time, research methodologies, participant characteristics by countries and educational levels, and how Fermi problems are addressed in different mathematical contexts. In this regard, the purpose of this study is to systematically examine the studies that focus on the use of Fermi problems in mathematics education published in Web of Science (WoS), Educational Resources Information Center (ERIC), and Scopus databases with the following research questions: 1) What are the research trends in studies on the use of Fermi problems in mathematics education in terms of publication years, research methodologies, participant characteristics by countries, and educational levels? 2) How have Fermi problems been addressed and utilized in mathematics education research? Methodology, Methods, Research Instruments or Sources Used In this study, the PRISMA (Preferred Reporting Items for Systematic Review and Meta-Analysis) framework (Moher et al., 2009) was used to systematically review studies through the following steps: identification, screening, eligibility, and inclusion. WoS, Scopus, and ERIC databases were selected for their inclusion of high-quality education journals. In December 2025, each database was searched using the following strings: “Fermi problems AND mathematics”; “Fermi problems AND modelling OR modeling”; “Fermi problems AND estimation”. As a result of this search, 110 studies were obtained. After duplicates were removed, 76 records remained for screening. To systematically identify and select studies on Fermi problems in mathematics education, inclusion and exclusion criteria were established. Thus, 52 studies conducted outside the field of mathematics education, published in languages other than English, systematic reviews, book chapters, theses and dissertations, non-peer-reviewed publications, and conceptual, theoretical, or descriptive studies without empirical data were excluded. Accordingly, 24 English-language, peer-reviewed journal articles and conference papers on Fermi problems in mathematics education remained. During the eligibility assessment, three additional studies were excluded as they did not report empirical data. Thus, 21 studies that met all inclusion criteria were included for the data analysis. To ensure transparency and consistency, data were extracted using a structured coding sheet developed by the authors. Information was recorded on this sheet, including bibliographic details (author(s), title, publication year, document type), research aims, methodological characteristics (research design, participants, data collection, data analysis), key findings, and how Fermi problems were addressed in each study. Descriptive and qualitative content analysis methods were used to analyze data. Descriptive analyses were employed to determine the studies’ research design, publication years, participant characteristics by country, and education level. Then, a qualitative content analysis was used to identify the mathematical contexts of studies and how Fermi problems were addressed. During this process, each researcher independently reviewed and categorized the studies. They then met to compare their analyses, resolving any discrepancies through discussion until a consensus was reached. This categorization provided a systematic comparison of each study, illustrating how Fermi problems are conceptualized and utilized within mathematics education research. Conclusions, Expected Outcomes or Findings Descriptive analysis showed that studies predominantly used a qualitative approach (71%), followed by mixed-method (24%) and quantitative studies (5%). Annual publication trends indicate that research on Fermi problems increased following Ärlebäck's (2009) study, which used Fermi problems to introduce modeling, with a notable rise in recent years, including five studies in 2021 (24%) and four in both 2023 and 2025 (19% each). The participants' characteristics of the studies showed that the vast majority (71%) were from Spain. Turkiye (14%) and Sweden (10%) follow Spain. In most studies, participants were pre-service teachers (33%), high school (33%), and middle school (24%). students. Considering the real-life context of Fermi problems (Peter-Coop, 2009) and their positive effect on students' estimation and modelling skills (Albarracín & Gorgorió, 2019), it is recommended to conduct further studies with primary school students. Content analysis demonstrated that Fermi problems were used in studies in two ways: either as the study's research objective, focusing on the Fermi problems themselves (e.g., solution processes, strategies, and errors), or as a tool to develop or examine a skill. While Fermi problems were used as a research objective in 10 studies (48%), 11 studies (52%) used Fermi problems as a tool. Studies that used Fermi problems as a research objective focused on problem-solving (PS) skill, specifically on PS processes (20%), PS strategies (30%), PS misconceptions and mistakes (30%), and PS flexibility and performance (20%). Studies that used Fermi problems as a tool examined a skill (73%) or supported a skill (27%). Predominantly, students' mathematical modeling skill was examined or supported using Fermi Problems as a tool. Future research could leverage the open-ended nature of Fermi problems (Ärlebäck, 2009) to foster a broader range of mathematical skills, with a stronger emphasis on their instructional potential rather than solely on examining skills. References Ärlebäck, J. B. (2009). On the use of realistic Fermi problems for introducing mathematical modelling in school. The Mathematics Enthusiast, 6(3), 331-364. https://doi.org/10.54870/1551-3440.1157 Ärlebäck, J. B., & Albarracín, L. (2019). The use and potential of Fermi problems in the STEM disciplines to support the development of twenty-first century competencies. ZDM, 51(6), 979-990. https://doi.org/10.1007/s11858-019-01075-3 Albarracín, L., & Gorgorió, N. (2019). Using large number estimation problems in primary education classrooms to introduce mathematical modelling. International Journal of Innovation in Science and Mathematics Education, 27(2). https://doi.org/10.30722/IJISME.27.02.004 Albarracín, L. (2021). Large number estimation as a vehicle to promote mathematical modeling. Early Childhood Education Journal, 49(4), 681-691. https://doi.org/10.1007/s10643-020-01104-x Brunet-Biarnes, M., & Albarracín, L. (2024). Exploring the negotiation processes when developing a mathematical model to solve a Fermi problem in groups. Mathematics Education Research Journal, 36(1),177-198. https://doi.org/10.1007/s13394-022-00435-9 Carlson, J. E. (1997). Fermi problems on gasoline consumption. The Physics Teacher, 35(5), 308-309. https://doi.org/10.1119/1.2344696 Chandler, D. (1990). How to split hairs on Fermi questions. The Physics Teacher, 28(3), 170. https://doi.org/10.1119/1.2342979 Efthimiou, C.J., & Llewellyn, R.A. (2006). Cinema, Fermi problems and general education. Physics Education, 42(3), 253 - 261. https://doi.org/10.1088/0031-9120/42/3/003 Er, Z., & Sezer, S. R. (2025). Effectiveness of Fermi problem approach in enhancing seventh-grade students’ measurement estimation skills. Sage Open, 15(3). https://doi.org/10.1177/21582440251366051 Meyer, M., & Greefrath, G. (2025). Students’ use of benchmarks in the process of solving Fermi problems. In Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME 14). Moher, D., Liberati, A., Tetzlaff, J., Altman, D. G., & PRISMA Group. (2009). Preferred reporting items for systematic reviews and meta-analyses: The PRISMA statement. PLoS Medicine, 6(7), e1000097. https://doi.org/10.1371/journal.pmed.1000097 Peter-Koop, A. (2009). Teaching and understanding mathematical modelling through Fermi problems. In B. Clarke, B. Grevholm, & R. Millman (Eds.), Tasks in primary mathematics teacher education (pp. 131–146). Springer. https://doi.org/10.1007/978-0-387-09669-8_10 Robinson, A. W. (2008). Don’t just stand there—teach Fermi problems! Physics Education, 43(1), 83–87. https://doi.org/10.1088/0031-9120/43/01/009 Segura, C., Gallart, C., & Ferrando, I. (2025). Influence of pre-service primary school teachers’ prior knowledge of measurement and measurement estimation in solving modelling problems. Journal of Mathematics Teacher Education, 1-26. https://doi.org/10.1007/s10857-025-09685-3 Sriraman, B., & Lesh, R. A. (2006). Modeling conceptions revisited. ZDM, 38(3), 247-254. https://doi.org/10.1007/BF02652808 24. Mathematics Education Research
Paper Pre-service Teachers' Interpretations of Value in a Modelling for Sustainability (MfS) Task 1: University of Alberta, Canada; 2: Cape Breton University, Canada Presenting Author: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. Methodology, Methods, Research Instruments or Sources Used 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. Conclusions, Expected Outcomes or Findings 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. References 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/ | ||