Making calculus sustainable!?
A calculus course is not the obvious place to encounter sustainability. For Circular Engineering student Leoni Haller, that absence felt like a missed opportunity. While her programme focused on circularity and environmental challenges, mathematics often seemed disconnected from those themes.
That changed when she had the chance to help rethink the course using sustainability-related examples. The formulas stayed the same, but the context shifted.
"Quantifying concepts using calculus can make sustainability more understandable, while connecting sustainability to real-world issues makes calculus more relatable,” Leoni explains.
Read her story below.
Facing an uncertain future
I would describe myself as a generally positive person. However, when I think about the future of humanity on this planet, things look slightly different. The fragile state of our Earth crosses my mind when I go for a walk and see forests slowly diminishing, or when I live through yet another once-in-a-century weather event. When someone asks me where I see myself 10 years from now, I picture a world exhausted beyond repair. And it scares me.
For me, the best way to fight this hopelessness is to be part of the solution to climate change. This is why I decided to study Circular Engineering at Maastricht University, an engineering degree with a focus on the circular economy. In the first year, the programme focused on sustainability and circularity, where we learned about waste management, production emissions, and resource consumption, as well as possible solutions to tackle these issues. However, in order to create the scientific basis of our studies, there were many periods dominated by Science, Technology, Engineering, and Mathematics (STEM) courses, where environmental issues were barely mentioned.
Where is sustainability in mathematics?
This was especially true for our mathematics courses, where any discussion of the environmental crisis was almost non-existent. It bothered me, but I couldn’t really explain what else I had expected. Is it possible for sustainability to connect with mathematics, or with any other STEM class, for that matter? Spoiler alert: it’s not as difficult as it may seem.
As my first year came to an end, our calculus lecturer, Martijn Boussé, posted a message on the university portal. Having received a UM Sustainability Grant, he proposed reworking the lectures with sustainability-related examples and explicitly invited student input, describing it as an opportunity to “make a lasting mark” on Circular Engineering education.
This was exactly what I had been waiting for! Even though I couldn’t yet visualise how sustainability and mathematics could connect, I applied for the student assistant job, and once we started the project, it became clear. Throughout the summer break and my entire second year, Martijn and I worked on bringing the concept to life. We worked together as equals and learned from each other’s perspectives. As the project unfolded, the value of our work became increasingly clear, especially when we started to redesign the course material and actively engage with it.
A eureka moment
Our eureka moment came when we saw how we could use two complex topics, sustainability and calculus, to explain each other: quantifying concepts using calculus can make sustainability more understandable, while connecting sustainability to real-world issues makes calculus more relatable.
We kept the original flow of the course more or less the same but changed the perspective, using the 17 UN Sustainable Development Goals (SDGs) as a framework. In the revised course, every time mathematics is linked to sustainability, whether in the lecture slides or in a task, we mentioned the respective SDG icon. This gives students a consistent structure and context, showing how what they learned relates to sustainability issues, from the optimal use of fertilisers to the efficiency of solar panels.
Change does not only happen through large-scale solutions, but also through small, deliberate choices in our everyday lives.
Leoni HallerCalculus in real-world context
To give a concrete example, during the calculus course, the students learn how to compute the surface area of three-dimensional shapes. Instead of seeing a simple cone shape, they are presented with an image and dimensions of a wind turbine tower, a cone-shaped structure. The task itself, as well as most of the calculations, remain the same. However, it is now embedded in a real-world example. By calculating the surface area, students can estimate the amount of corrosion protection needed or determine the strength of the tower. By linking this exercise to SDG 7, “Affordable and Clean Energy”, the students not only understand the necessity of learning a computation skill but also see how it can be applied in a sustainability context.
I speak from experience when I say that the incentive to study is higher when I understand the purpose behind what I’m learning and can see the bigger picture. As we worked on redesigning this task, I was surprised by how easily we could make a connection between mathematics and sustainability and by the effect it had. By adding a scenario and explaining the relevance, the task became something meaningful and relevant to me and my fellow students, without taking the focus away from mathematics.
Another topic the students cover in the revised calculus course is volume computation. A task on one of the lecture slides asks the students to find the largest volume of a box with certain constraints, such as the height or width. Once again, we didn’t change the exercise, but now there’s a new scenario around it. The task is framed around a makeup company that aims to reduce its packaging material. To achieve this, the students are asked to maximise the volume of a box while working within the constraint of using the smallest possible amount of material. Again, it turned out to be amazingly simple to connect seemingly abstract exercises to real-world applications, while simultaneously addressing sustainability topics.
In the classroom: turning a calculus problem into a clean energy case
Click the image icon to view the slides
Small changes, big perspective shifts
The small changes we made encouraged me to think more deeply about the discussion surrounding sustainability. Often, this discussion is dominated by ideological debates and global policies, which can make me feel helpless. However, working on this project helped me understand that the pursuit of a more sustainable future is deeply personal and can look different for everyone, depending on their capacities and situations. Even something small, that may seem too technical, abstract or insignificant at first, can have an impact. It showed me that sustainability has a place in every field, even in a calculus course. It also made me think that this project may have inspired others to include sustainability in their own field, even if the connection might not seem obvious at first.
This feeling was amplified when working on the dissemination of the project, encouraging other educators to adopt a similar approach in their teaching. We created a two-minute video summarising our work and wrote a practice paper on the project, which was accepted at an international engineering education conference (SEFI). It was a personal highlight to present it in Tampere, Finland, in September 2025. Talking about this project to a room filled with educators interested in advancing engineering education was an incredible feeling. Being there, presenting Martijn’s and my work, showed the impact co-creation can have, and witnessing the audience’s interest in combining sustainability and calculus showed the relevance and potential of integrating real-world challenges into mathematics education.
Meaningful education
When I think about meaningful education, the way this project was done comes to mind. We changed the course by asking ourselves what it is we want the students to learn. We want it to have a lasting influence and help them connect knowledge across fields. It can be more work to create a curriculum that works towards meaningful education, but it is worth the effort.
As mentioned before, the co-creation approach was valuable. I brought in the student’s perspective, while Martijn used his experience working at the university, especially his understanding of what happens behind the scenes in educational design. I am thankful to Martijn for his open-mindedness and willingness to collaborate with a student, as well as his encouragement to pursue opportunities I had not even considered.
Even though I’m still afraid of what the future will hold, being part of this project gave me hope. It showed me that change does not only happen through large-scale solutions, but also through small, deliberate choices in our everyday lives. It shifted my view on meaningful education, changed my understanding of the amount of time and effort it takes to design a course, and made me think about the different ways in which we can reach our sustainability goals. Next time I will go for a walk through the forest, or I think about our planet, our home, I will think of all the projects like these, and the people who actively work towards a better future.
By Circular Engineering student Leoni Haller, Faculty of Science and Engineering, Maastricht University