Co-Creating Authentic Learning Experiences in Mathematics: Integrating Sustainability into Engineering Calculus

Practice Paper Recommended citation: Haller, L. J., Boussé, M., & Phillips, G. (2025). Co-Creating Authentic Learning Experiences in Mathematics: Integrating Sustainability into Engineering Calculus. In Kangaslampi, R., Langie, G., Järvinen, H.-M., & Nagy, B. (Eds.), SEFI 53rd Annual Conference. European Society for Engineering Education (SEFI), Tampere, Finland. DOI: 10.5281/zenodo.17631267. This Conference Paper is brought to you for open access by the 53rd Annual Conference of the European Society for Engineering Education (SEFI) at Tampere University in Tampere, Finland. This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License. CO-CREATING AUTHENTIC LEARNING EXPERIENCES IN MATHEMATICS: INTEGRATING SUSTAINABILITY INTO ENGINEERING CALCULUS L.J. Haller a, M. Boussé b,1, G. Phillips c a FSE, Maastricht University, Maastricht, the Netherlands b Department of Advanced Computing Sciences, FSE, Maastricht University, Maastricht, the Netherlands, ORCID: 0000-0003-2090-0682 c Faculty of Science and Engineering, Maastricht University, Maastricht, the Netherlands, ORCID: 0000-0003-4443-0822 Conference Key Areas: 3) Teaching mathematics and physics in engineering education; 7) Sustainability and society in engineering Keywords: Mathematics, Sustainability, Co-creation, Authentic Learning, Curriculum Design ABSTRACT Calculus often presents challenges to engineering students due to its abstract nature and lack of perceived real-world relevance. This study explores how integrating sustainability themes into a first-year calculus course can increase student engagement and foster authentic learning experiences. Within the context of an engineering program focused on circularity and global responsibility, sustainability topics were embedded into lectures, assignments, and preparatory tasks. The redesign was structured using the ADDIE instructional design model and anchored to the Sustainable Development Goals framework. Central to this process was a cocreation approach, actively involving students and faculty throughout the project. Through iterative feedback cycles, including surveys (N=40) and preand postcourse focus groups, we assessed the impact on student learning and engagement. Results indicate that students perceived the sustainability integration as meaningful and relevant, particularly in helping them recognize the applicability of calculus to societal challenges. While many students did not report an increased understanding of mathematical concepts, they valued the broadened perspective on how calculus can contribute to solving sustainability issues. This practice paper provides a replicable blueprint for integrating sustainability into core STEM curricula through cocreation and structured instructional design, offering insights for educators aiming to connect foundational mathematics to real-world applications. 1 Corresponding author M. Boussé [email protected] 1 INTRODUCTION Calculus, an essential introductory mathematics course in engineering curricula, can often be experienced as abstract, boring, and challenging by beginning students. In order to tackle this issue, we have redesigned the first-year calculus course in the BSc Circular Engineering (CE) program by making the topics more engaging and tangible and aligning more closely with the program vision as a program that educates globally responsible engineers by weaving a macro-, mesoand micro understanding of sustainability into a general engineering curriculum (Mulder et al., 2012). By introducing sustainability topics into a core mathematics course, we aim to bridge the gap between abstract mathematics and its practical applications. This interdisciplinary approach simultaneously provides students with a comprehensive approach to real-life problems, while conveying the importance of sustainability in various fields (Steiner & Posch, 2006; Koss, 2018). The focus on sustainability in the BSc CE program aligns with the broader goals of Maastricht University (UM), which strives to educate all students as responsible global citizens and critical thinkers who can make a meaningful contribution to society and act—locally and globally—as agents of positive change. To give concrete shape to our efforts to educate change agents for sustainability, we have established four objectives: 1) Infuse sustainability principles into all the programs of the authors’ university; 2) Facilitate staff in acquiring the necessary knowledge and skills; 3) Stimulate sustainability initiatives involving staff and students on campus; and 4) Improve the environmental and social sustainability of our education. As a core mathematics course in the CE program, calculus builds the mathematical foundation for other key courses such as linear algebra, multivariable calculus, and various engineering courses where calculus is heavily applied. It is crucial that students grasp the concepts and understand their importance and relevance in their future studies and work (Quadrado et al., 2013). Connecting the lecture material and assignments to sustainability examples makes those topics more concrete through mathematical modeling, and at the same time calculus becomes more tangible. The Sustainable Development Goals (SDGs) developed by the United Nations (UN) in 2015, create a framework for addressing the complex topic of sustainability. They manage to summarise and connect various global themes in the form of goals, which all UN member states aim to achieve as part of the 2030 Agenda for Sustainable Development. We use the SDGs as a guiding structure to create a clear path for the students to follow, by linking each change made in the course to a specific goal. This creates a connection between sustainability themes with core calculus concepts, such as derivatives, integrals, and differential equations (Kioupi & Voulvoulis, 2019). 2 CONTEXT AND PRACTICAL WORK Our redesign adopted a co-creation approach structured by the ADDIE model, a widely used instructional design framework (Kurt, 2017). Involving learners as equal stakeholders ensured that the redesigned materials were relevant and engaging (Könings et al., 2020). The systematic phases of ADDIE (Analysis, Design, Development, Implementation, and Evaluation (and Dissemination)), provided a structured process for integrating sustainability into calculus while preserving mathematical rigor (see Fig. 1). Fig. 1, ADDIE approach timeline where student assistant involvement is highlighted in red. The analysis phase examined the prior course evaluations (N=26, 58% of cohort) and feedback from learners and instructors to identify areas for improvement in the calculus course. A pre-focus group organized, led, and evaluated by a student assistant, was conducted with learners who had previously taken the course to explore their perspectives on integrating sustainability topics. This session highlighted the importance of ensuring that sustainability would complement, rather than overshadow, the mathematical core of the course. Additionally, consultations with the program director, other instructors in the program, and experts in sustainability education provided valuable insights on aligning the course with the program’s vision on circular engineering. These steps helped identify relevant SDGs and real-world examples that could be integrated into the course material. During the design phase, ideas from the analysis were translated into plans for revising the course. The co-creation process was central to this phase, as faculty collaborated closely with a student assistant to ensure that the sustainability examples and assignments were meaningful and engaging for students. Other instructors and past winners of the UM Sustainability Grant were contacted to gather input on effective strategies for embedding sustainability into core STEM courses. The input informed the design of new lecture materials, pre-tasks, and a team assignment, all tailored to ensure that sustainability topics would enhance students’ understanding of calculus concepts without diminishing the mathematical rigor. In the development phase, the new materials and assignments were created based on the design plan and in collaboration with the student assistant. Lecture examples were revised to incorporate sustainability themes, ensuring alignment with the identified SDGs and their relevance with engineering solutions (Rosen, 2012). For instance, examples involving differential equations were adapted to model realworld sustainability challenges, such as optimizing solar panel efficiency (SDG 7) and analyzing pollutant diffusion in water bodies (SDG 6). To maintain a balance between sustainability and mathematical rigor, the examples retained their focus on core calculus concepts while providing meaningful context within the theme of the program. Additionally, pre-tasks were developed to introduce sustainability-related problems and prepare students for deeper engagement during on-site activities. The team assignment, redesigned to combine integrals and differential equations, was structured to emphasize authenticity and foster collaboration. Throughout this phase, feedback from teaching corps were incorporated to refine the materials. The implementation phase involved running the revised version of the calculus course during the first academic period. The updated lecture materials, pre- tasks, and team assignment were integrated into the course structure, with students being introduced to sustainability topics from the outset. The pre-tasks and lecture examples emphasized active participation, allowing students to engage with realworld sustainability problems while applying calculus concepts. The team assignment aimed to encourage collaboration and creativity, requiring students to explore sustainability challenges relevant to their personal contexts. During this phase there is no involvement by the student assistant, as the teachers are responsible for delivering the course and implementing the new material. The evaluation phase focused on gathering and analyzing student feedback to assess the impact of the redesigned course. A mixed-methods approach was employed, combining quantitative data from preand post-course surveys with qualitative insights from a post-focus group. The surveys, completed by 40 students, included a mix of scaled and open-ended questions to evaluate the effectiveness of the sustainability integration in improving student engagement, awareness, and understanding of calculus and sustainability concepts. The post-focus group brought together first-year students and retakers, providing a comparison of their experiences with the previous and updated versions of the course. Retakers offered unique perspectives on how the new sustainability-focused examples enhanced the course. Additionally, standard course evaluations (N=22, 50% of cohort) provided further insights into areas of success and potential improvement. These data were used to inform reflections on the project’s outcomes and guide future iterations. To ensure broader impact, we created a video and organized a CPD workshop to share project outcomes and inspire colleagues. These dissemination efforts, detailed in Section 4, promote the integration of sustainability into STEM curricula and offer a replicable model for other courses and programs. As seen in Figure 1, the student assistant was actively involved in all the previously mentioned steps of the evaluation and dissemination phase. 3 RESULTS AND DISCUSSION 3.1 Pre-focus group The pre-focus group with the previous year’s calculus students highlighted enthusiasm for integrating sustainability topics in the calculus course, provided that the integration does not overshadow the course’s mathematical focus and rigor. One student mentioned “Don’t sweep calculus under the rug; don’t lose the focus on the fundamentals and the mathematics.” which all focus group participants agreed on. Throughout the session, students continuously emphasized the need for proper balance between sustainability topics and core calculus learning objectives. Students also suggested relevant themes, such as renewable energy, optimal land usage, and climate modeling, relevant to them within the context of the program, which informed the selection of examples and assignments in the design phase. On the question, “How can we include sustainability in calculus?” a student responded with an insightful reply that informed the design of the team assignment: “Everybody comes from a different background, facing different issues. Perhaps students can think about relating the team assignment to their own communities so that it becomes more personal and meaningful. This is also nice for the other students as they learn about other perspectives.” Another student mentioned that the “SDGs could be a framework for students to think about a possible topic of the team assignment,” which is something we have directly implemented. 3.2 Changes to the course material Throughout the redesign, the core course structure was maintained while integrating sustainability as a complementary element, as highlighted in the pre-focus group. The revised lecture materials followed two approaches: active and passive. The former used interactive in-lecture exercises, focusing on engagement and collaboration, while the latter relied on worked-out examples to illustrate problemsolving steps directly. In the module on differentiation, the more active approach was showcased via two sustainability-focused in-lecture student exercises. The first exercise modeled the relationship between fertilizer usage and crop yield. Students determined the optimal fertilizer amount to maximize yield, calculated the marginal yield at a specified output, and identified when the yield would drop to zero. This example reinforces derivative concepts and underscores environmental considerations, addressing SDG 2 ("Zero Hunger") and SDG 15 ("Life on Land"). In the second exercise, a scenario was used where students examined solar panel efficiency and its dependence on roof temperature, by calculating key parameters like the maximum temperature and its rate of change, linking the exercise to SDG 7 ("Affordable and Clean Energy"). We added seven exercises using a more passive teaching approach to the lecture materials, embedding sustainability contexts within worked-out examples to highlight the real-world relevance of calculus without compromising its mathematical integrity. The first two are related to differentiation concepts: - In the first exercise, students maximized the volume of an open box. While the task remained unchanged from previous years, a new scenario was added: a cosmetic company aims to optimize packaging by maximizing volume while minimizing material use. This links to SDG 12 (“Responsible Consumption and Production”) and shows how small contextual changes can integrate sustainability without altering core tasks. - The second example follows the same concept. Students calculate the largest area of a rectangle inscribed in a semicircle. The scenario involves a farmer optimizing space in a hoop greenhouse by exploring vertical farming, aligning the task with SDG 2 by promoting more efficient farming methods. The next three examples are related to integration concepts: - The third example focuses on the CO2 absorption of plants by calculating a tree’s total leaf area. Larger leaf areas can increase water evaporation and CO2 uptake (Cordak et al., 2025). Using hemispherical photography the leaf area index can be calculated from a scan image, or manually by summing individual leaf areas. Students then estimate the total number of leaves and compute the average leaf area (see Fig. 2, a), linking the task to SDG 15. - Wind turbines, relevant to SDG 7 and 9 (“Industry, Innovation and Infrastructure”), were used to reinforce volume and surface area concepts. Students calculated the nacelle’s volume, focusing on space efficiency, material use, aerodynamics, and regulatory compliance. - Students also computed the wind turbine tower’s surface area to estimate the required corrosion protection coating and assess its structural integrity. The last two examples focus on ordinary differential equations (ODEs): - The first example focuses on SDG 11 (“Sustainable Cities and Communities”), as it focuses on insulation in the Netherlands and shows how this complex phenomenon can be modeled. - The final example models a water retention pond, with stormwater runoff and phosphor as input and filtered water as output. Students calculate phosphorus levels 20 minutes after heavy rainfall, linking the task to SDG 15. 3.3 Changes to the team assignment The team assignment covers integration and differential equations, which used to be two separate assignments. In the redesign, the topics were merged, reducing overall workload, increasing authenticity and autonomy, and lowering transactional distance. To enhance authenticity, students apply calculus to real-world sustainability or circularity challenges relevant to their program. To strengthen personal relevance, each team connects their topic to the hometown, city, or country of one team member. This personal connection increases ownership and motivation, as students often select issues they care about or are familiar with. The open-ended nature of the assignment encouraged a wide variety of creative projects, such as “Optimizing water distribution in Lima”, “Insulation design improvement for Bari”, “Flood modeling of Rotterdam’s water square” (see Fig. 2, b), “Soil management for rice cultivation”, and “Optimizing cycling safety using mathematics”. a) b) Fig. 2, Changes to course material: Excerpt of a) lecture material and b) team assignment By grounding projects in familiar contexts and connecting them to real-world sustainability issues, students could link abstract calculus concepts to tangible problems. This not only enhanced engagement but also deepened their understanding of both mathematics and its applications in sustainability. The assignment was deliberately designed as an open-ended task, granting students significant freedom to define and structure their project. This low-structure approach encourages students to take ownership of their learning process by formulating their own problem statements, selecting relevant sustainability contexts, and determining appropriate applications of calculus. Complementing this openness is a high level of dialogue: students are expected to collaborate extensively within their teams and engage regularly with instructors for guidance and feedback. To further facilitate idea generation and peer learning, the assignment included a brainstorming session, co-hosted by the CE student association ‘Möbius’ and faculty members. This session fosters a collaborative learning environment where students and staff share insights and explore diverse project ideas together. By combining low structure with high dialogue, the task reduces transactional distance and fosters a learning environment that supports autonomy, competence, and relatedness—core elements of self-determination theory. The task flexibility promotes student agency, while the requirement to collaborate and connect projects to personal or community-relevant topics enhances motivation and engagement. 3.4 Changes to the pre-tutorial tasks The change made to the pre-tutorial task encourages students to connect an optimization exercise to circular engineering. Similar to updates made to the lecture material, the core of this task was kept the same, with minor additions applied. Keeping the results from the pre-focus group in mind, the changes were kept at a minimum, in order to not overwhelm the course material with sustainability topics. 3.5 Survey results The survey results show a general positive response to the integration of sustainability topics into the calculus course. The relevance and integration of the topics are seen as very successful with 27 students rating the former and 19 students the latter as “Strong” or “Significant”. None of the students found the topics completely irrelevant or the integration failed. The comments showed that even though most students felt like the examples themselves did not teach them new calculus concepts, they found the sustainability topics as a successful add-on, increasing their understanding of mathematics. One student expanded on the question “To what extent have the sustainability examples helped deepen your understanding of calculus?” with the following answer: “They didn't necessarily deepen my understanding but broadened my understanding of where calculus is applicable.”, showing that the goal of bridging sustainability and calculus concepts was successful. On the question “To what extent did looking at sustainability topics through the lens of calculus enrich your view on sustainability?”, one student responded “It brought me hope that engineers can make a difference to improve today’s society. I wouldn’t have had the opportunity to view sustainability from this perspective from outside of the course.”, which once again, emphasizes the program vision and highlights the importance of approaching the education of students on sustainability topics from different angles. Adding the sustainability topics was an example of contextual learning, a method that is proven to increase student motivation and understanding (Afni & Hartono, 2020). The conducted survey is a way to see how the students perceive this change. However, as the BSc Circular Engineering is a relatively new program, multiple adjustments were made each year, making it challenging to measure and compare the impacts these changes have. In the future we aim to evaluate these effects in greater detail. Fig. 5, Survey results for questions: 1) “To what extent were the sustainability examples relevant to the calculus topics covered?”, 2) “To what extent were the sustainability topics well integrated into the calculus course (i.e. without detracting from the focus on calculus)?”, 3) “To what extent have the examples on sustainability in the calculus course increased your awareness of sustainability?”, 4) “To what extent have the sustainability examples helped deepen your understanding of calculus?”, 5) “To what extent did looking at sustainability topics through the lens of calculus enrich your view on sustainability?”, 6) “To what extent did working actively with the Sustainable Development Goals during the team assignment additionally increase your understanding of sustainability?” 3.6 Post-focus group The post-focus group (N = 5) held with students, including retakers, revolved around three elements: 1) the integration of calculus and sustainability, 2) the real-world relevance of the integrated topics, and 3) the structure of the team assignment. The participants expressed appreciation for the integration of sustainability topics into the calculus course, feeling that calculus concepts became more tangible to them. As one participant mentioned: “Seeing how math connects to sustainability made the abstract concepts much more concrete.” Participants agreed that the examples enhanced the learning experience, while educating about sustainability topics. When asked how the integration of these examples into the course was perceived, the participants found it went well, placing value on the connection to real-life examples: “The sustainability examples made me appreciate calculus, showing its immediate real-world applications.” This transforms mathematical concepts from something abstract into concrete exercises, increasing students’ understanding of its relevance and practical applications. Building the connection between mathematics and sustainability through real-life applications, additionally emphasizes the CE program vision and prepares the students for their future. As one participant mentioned during the focus group: “Going into the future we’ll be faced with mathematical and sustainability problems, and it is really useful to bridge the gap between the two - to recognize the math in everyday scenarios.” The participants found the team assignment to be a useful exercise to implement the knowledge gained from the calculus course. Even though the students agreed that the low structure of the assignment was challenging, they saw it as useful. One participant mentioned: “Coming up with your own ideas and