The Computational and Mathematical Modeling Program (CAMMP) – Lessons Learned on Interdisciplinary Challenge-Based Learning

Practice Paper Recommended citation: Engelhardt, F., Wrede, S., Schönbrodt, S., Büsing, C., & Stamm, B. (2025). The Computational and Mathematical Modeling Program (CAMMP) – Lessons Learned on Interdisciplinary Challenge-Based Learning. 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.17631434. 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. The Computational and Mathematical Modeling Program (CAMMP) – Lessons Learned on Interdisciplinary Challenge-Based Learning F. Engelhardt a, 1 , S. Wrede b, S. Schönbrodt c, C. Büsing d, B. Stamm e a Teaching and Research Area Combinatorial Optimization, RWTH Aachen University, Germany, ORCID: 0009-0007-7705-4508 b Teaching and Research Area Combinatorial Optimization, RWTH Aachen University, Germany, ORCID: 0009-0000-8813-9952 c Department of Mathematics, Paris Lodron University of Salzburg, Austria, ORCID: 0000-0003-2383-6081 d Teaching and Research Area Combinatorial Optimization, RWTH Aachen University, Germany, ORCID: 0000-0002-3394-2788 e Chair of Numerical Mathematics for High Performance Computing, University of Stuttgart, Germany, ORCID: 0000-0003-3375-483X Conference Key Areas: Teaching mathematics and physics in engineering education, Engineering skills, professional skills, and transversal skills Keywords: Problem-based Learning, Project-based Learning, Mathematical Modeling, Case Study ABSTRACT Mathematical modelling is a key engineering competence. However, many textbook problems fall short of the complexity and ambiguity of the real-world. The Computational and Mathematical Modeling Program (CAMMP) is a cross-university project to foster skills in mathematical modelling, including model building, implementation and evaluation. During the CAMMP week Pro (CWP), Bachelor's and Master's students of different engineering disciplines and mathematics jointly work on real-world research problems from industry and academia. In this work, we present a case study of five iterations of the CWP. We outline the structure of the course and evaluate it based on qualitative analysis of student feedback and evaluation documents. We find that students sometimes struggle with the open nature of challenges, and that their study experience is strongly shaped by the supervision they experience. Furthermore, we derive practical recommendations 1 Corresponding Author F. Engelhardt [email protected] regarding collaboration, supervision and students' perception of their roles both as group members and as aspiring engineers and scientists. 1 INTRODUCTION To use mathematics in practice, mathematicians and engineers need to be able to model the real world mathematically, and to formulate and execute problem solving strategies that employ mathematical methods (Alpers, 2013). Challenge-based learning (CBL) describes a family of active learning approaches that focus on having students develop their skills by working on authentic, open challenges, generally as part of a multidisciplinary team; for a more detailed discussion see Gallagher & Savage (2020). Combining these two, the Computational and Mathematical Modeling Program (CAMMP) is a teaching and research initiative aimed at fostering mathematical modelling and problem solving competencies through real-world problems 2 , which “stimulates learning and helps developing important professional skills such as problem solving and interdisciplinary collaboration” (Hadgraft & Kolmos, 2020). Within the program, CAMMP week Pro (CWP) is a week-long block course for university students from computational engineering science, mathematics and simulation sciences. During the week, groups of students have to jointly solve a real-world research challenge. These challenges are provided either by the Jülich Research Centre (Forschungszentrum Jülich / FZJ), by researchers at RWTH Aachen University or by industry partners. In this practical work, we provide a case study of five CWP iterations, performed over the course of five years, including the Corona crisis. We qualitatively analyse student feedback surveys and internal evaluations using reflexive thematic analysis (Brown & Clarke, 2022). Based on this we provide insights for practice. We begin with outlining the context of the CWP in Section 2.1, followed by explaining the data analysed (Section 2.2) and the methods used for that (Section 2.3). In Section 3, we present and discuss the results of the data analysis. Finally, Section 4 offers a short conclusion. 2 CONTEXT AND PRACTICAL WORK 2.1 Context and Content of the Course The CWP is a multi-day elective block course. It is organised by the Aachen part of the CAMMP network. CAMMP predominantly organises mathematical modeling weeks for high school students (Schönbrodt et al., 2022). This builds on a long tradition of high school modeling projects at different German and Austrian universities (Vorhölter et al., 2019). Learning goals of the course include fostering students mathematical modelling competencies, and improving their competencies for research, specifically regarding teamwork and project/time management. Notably, for many participating institutes, acquiring student assistants and identifying promising students for research focused theses are the main reasons for participating in the CWP. The CWP was developed based on the high school CAMMP week, with a special emphasis on open research challenges. Overall, five iterations of CWP are considered in this study. Table 1 gives an overview of their locations, the challenges and the number of participants in each iteration. 2 CAMMP website: https://www.cammp.online/english/index.php, last access: 2025-03-26. Table 1. Challenges, locations and number of participants of the CWPs from 2020 to 2024. 2020 Online 2021 Aachen 2022 Voeren 2023 Voeren 2024 Simmerath 33 students, 13 staff 20 students, 9 staff 40 students, 12 staff 34 students, 11 staff 23 students, 7 staff Anomalous Diffusion in Membranes Process Design for Polymer Recycling A Particular Matter of Coordination: Understanding Solid Two-Phase Percolating Modeling the Transportation of Hospital Beds Discovering Stochastic Petri Nets Diagnosing the Porous Structure of Fuel Cell Electrodes It's all connected! Percolation theory applied to fuel cell catalyst layers. Reconstructing the Topology of Spiking Neural Networks Based on the Firing Activity Accelerated Conformance Checking 3D Structure Generation in Computer-Aided Molecular Design Supply Chain Management for Polymer Recycling Correction methods for temperature retrieval in the upper atmosphere Identifying Gravity Wave Events from Atmospheric 3D-Temperature Data Robust Capacity Expansion Planning for Energy Systems Timely Diagnosis: Predict Diagnosis Time to Uncover Disparities in Health Access for Breast Cancer Machine learning in Materials Science Feature extraction in evolved/optimized spiking neural networks Communication Infrastructure for Planetary Exploration Bayesian Optimization for Chromatography Models Parameter Estimation Model predictive control for district heating networks Working at the Centers of Disease Control and Prevention Reactor Modelling and Simulation for Microgel Production Quantum Annealing Particle Matching in DEM Simulations Identifying Gravity Wave Events Data processing chain for Heterodyne spectrometer And the memories bring back, memories bring back you: shape - memory polymers Quantum Annealing Shape Memory Alloys Frequency Response Diagnostics of Fuel Cell Participants were predominantly from computational engineering science (n=36), mathematics (n=50) or simulation sciences (n=55) in their Masters (n=107) or at the end of their Bachelors' degrees (n=40). As all students' subject fields are closely related, this constitutes a domain project, following the framework by Kolmos et al. (2024). Critically, this implies a narrow interdisciplinarity, where students share some knowledge paradigms, which simplifies collaboration. Challenges: Industry partners of the partaking institutes, researchers from industry, RWTH and FZJ are asked to provide research problems from their current work. For example, a RWTH chemical engineering institute challenged students to improve a genetic algorithm they use to optimise molecular structures, and a local company planning renewable heat systems set up students to plan a heat supply network for part of Aachen. In line with Johnson et al. (2009), cases represent open research questions that are motivated by societal, as well as economic questions. The case holders researchers also advise students during the CWP. Before the week: Students register several weeks in advance. They are then given a choice of challenges to vote their preferences on. Teams of 4-6 students are created based on preferences and based on the concept of mixing different courses of study to ensure multidisciplinary teams. Students are told their group composition and challenge a few days in advance to have time to install software. During the week: The CWP itself generally spans Monday-Friday and takes place in a youth hostel. In 2020, CWP was instead done remotely over the course of two weeks. Normally, participants are welcomed on Monday morning with general information on the program and mathematical modelling. They then do some team exercises, since for many students this will be their first group project. An exemplary exercise consists of pairs of students picking and discussing random sequences of prompts on teamwork and communication to raise awareness of potential issues, since collaborative learning is a key element of CBL (Doulougeri, 2024). Then, students work on their challenges. That includes initial sessions with the advisors, where the problems are explained in detail. The first/third evenings are designated for social events. The third evening is also used as a networking and feedback opportunity with invited external guests, like case providers and further researchers. Students may continue working after dinner, although this is not expected. On Friday, students have their final presentations, and a social event in the evening. Assessment: All assessment is designed to be formative, as this serves to foster student learning and motivation (Sanchez-Lopez et al., 2023), which is the key goal of the CAMMP project. During the week, each advisor continuously interacts with their group. On the second day, all advisors have a joint meeting to evaluate progress, which is repeated on Thursday. On Wednesday a quick feedback round is done with the students to identify potential challenges and to check in on progress. Thursday afternoon students have to give a mock group presentation to prepare for their final presentation on Friday. The mock presentation is accompanied by a feedback session with the students case advisor together with other case advisors or some of the organising professors. A focus is put on presentation skills, the use of appropriate visualizations and clear communication. The final group presentations are between 20-30 minutes and should outline the given challenge, its relevance and what methods were used to address it. This is followed by a discussion session, generally initiated by a positively framed feedback round by the advisor, to support self-efficacy. Each group also has to hand in a report of 8-10 pages describing their work as well as the git repository with code and results by the end of the week. Students are given written feedback on their reports, with a focus on general scientific writing advice. Depending on their course of study, students may receive 35 ECTS for the course. Students that get more ECTS have to hand in an individual report as well. In line with the formative focus of the course, grading is done on a pass/fail basis only. Here, a central part of the course design is continuous feedback. This constitutes an important part of effective CBL (Dikilitaş et al., 2025), specifically as students get to provide feedback to advisors and organisers during CWP, as well. 2.2 Data Used for Case Study Students were asked to fill out anonymous feedback surveys during and after the course. In total, students filled out 62 surveys. The surveys consist of open questions on students' expectations, their experiences, their level of prior knowledge and whether they would have liked any additional information concerning CWP. Students were also asked to give recommendations for further iterations and to provide feedback on their group's challenge, the group work and individual learning gains. Finally, they could provide open comments. As noted before, the advisors generally hold two joint meetings during the week, where feedback is collected. There is also a joint feedback session after CWP. Its meeting notes were also consulted. 2.3 Data Analysis We categorised student evaluations into multiple overarching themes. We discuss them in sequence, adding references to internal documents when needed. Some sources were in German, those were translated to English. Since most participants are not native English speakers, to improve readability we corrected spelling and grammar mistakes when citing students. All data analysis was done by two independent researchers. This was done following the recommendations for thematic analysis outlined in Maguire & Delahunt (2017), based on the process for thematic analysis outlined in Brown and Clarke (2006). First, student survey results were skimmed over multiple times. Then, they were inductively coded and initial themes were generated from the data. Afterwards, those were reviewed together and iteratively defined in a sequence of discussions. The two researchers were themselves the main organisers of the CWP in 2021/2022 and 2023/2024, respectively. As such, they drew on their personal experiences to contextualise student answers. The organiser from 2023/2024 was also a participant in the 2021 CWP. Both have several years of teaching experience to draw upon. Following Braun and Clarke (2022), we point out aspects in the data analysis where we believe those personal experiences inform the interpretation of students' statements and internal evaluations. Thus, the following not only constitutes an analysis of (student) feedback, but also a personal reflection on past and current teaching practices. 3 RESULTS AND DISCUSSION In the following, we discuss the six categories we generated from the data. Category 1: Satisfaction & Motivation Many students denoted variations of “CAMMP was great, I would do it again!”, as well as that their expectations were met, they enjoyed the group work and they liked their challenges. When students gave reasons for their satisfaction, they often noted the large autonomy they had in structuring their work, getting insights into current research topics and doing actual research themselves. Teamwork was also frequently mentioned as a clear positive. Previous research has found both students that are in favour of teamwork (Sekhar et al., 2022) and those that prefer working independently (Lingard & Barkataki, 2011). Apart from a selection bias, the fact that some students stem from lecture-heavy traditional Bachelor’s engineering programs may contribute to their positive attitudes. Category 2: Informal Socialising These are a major reason why students partake in CWP. One student explicitly noted “some beer in the afternoon” as an expectation, and socialising with others was expected by students before the week: “A holiday :)”. Most students also felt social events and interactions were positive, with few students complaining about their frequency. From an organiser's perspective, we found social events to be more popular at the beginning of the week than at the end, as students are more stressed to finish their reports/presentations then. Category 3: Organisational Matters For the years in Voeren, students routinely complained about the food and accommodation quality. This was one reason to switch to a different youth hostel eventually, starting in 2024. Students also complained about insufficient internet access. Since 2022, we preemptively bring USB storage devices, ethernet cables, backup laptops, hard copies of all code, data and software required, and if necessary our own router(s) and switches. Some students felt that challenges and materials on the challenges should be made available earlier, i.e., a few weeks instead of days before the CWP. In internal debates amongst the organizers, this issue was raised several times. It was not changed based on the assumption that students often do not do preparatory work or do not do it properly. For example, Felder & Brent (2024) point out that pre-class assignments are only effective, in that students actually do them and learn something from it, if students are provided with quality, visual content, not just reading exercises. Doing so would put significant additional time burdens on the case organisers, as well as the students, which we try to avoid. In the two-week CWP, students overwhelmingly criticised two weeks as too long, while still arguing that an “extra day or two would give opportunities to consider separate options or refine the main approach further”. Furthermore, during the week-long in person CWPs, students experienced stress mostly as a challenge to be overcome: “more stress than expected, but it feels like that was part of the experience”. In comparison, for the two-week remote CWP, students indicated that this is “too long and exhausting”. We conclude that one week is an appropriate duration. Category 4: Comments on Individual Cases Students approve of the real-world relevance of their cases. However, one insight from the analysis is that the level of scaffolding in CWP sometimes varies, and that students' expectations may be misaligned if that happens. Consider those two statements: “The project was not mature enough and we had to formulate it ourselves. It would have been better if the tasks were clearer and already established.” and “The topic was okay, the execution was not so much. It was more like we were given a problem and the solution and were expected to do only the implementation and debugging.” The first quote indicates a misunderstanding of the reasons for why the challenge steps were not pre-defined, as the openness of the challenge is a key part of CBL, allowing students to gain agency over their own learning process (Johnson et al., 2009; Gallagher & Savage, 2020; Doulougeri, 2024). Indeed, the internal advisor guidelines explicitly state “Important: Please do not structure the learning and working progress of your group in advance. Your problem should allow the students to come up with their own ideas and models.” The second quote indicates that this recommendation was not followed for the respective group. Hence, we plan to explicitly include the openness of a problem as an item in the initial presentations, and provide some input on CBL and the reasons for doing so to students at the beginning of the week. This aligns with previous research that indicates that openness and ill-defined nature of challenges may create uncertainty and sometimes resistance in students (Doulougeri, 2024). This also links to Category 5, as it underscores the need for CBL training for advisors, which has been advocated for in research (Doulougeri, 2024). Category 5: Supervision Many comments praised advisors, some students would have liked more help from advisors and others note that “outcome depends heavily on group / problem / supervisor”. While it is possible to remotely advise students, without being at the CWP location in person, especially for the first and second day, we found students that did not have an advisor in place to feel less confident and to struggle more to understand problems that are outside their previous fields of expertise. This is supported by ample evidence that supporting students in their group creation process is a crucial success factor for CBL (Doulougeri, 2024). An important issue that links to the next category was close interaction with the advisors: “Before, I was afraid of going beyond my comfort zone. And working together with professors always felt intimidating to me. But after this event I feel more confident about working on new topics and working together with professors. While I still prefer to stay in my lane and focus on the topics that I am good at in the future, I am less anxious about tackling new problems.” Students also reported (and the organisers remember) using the CWP for personal academic career advice, as researchers from different career paths are present and can be interacted with in an informal setting. Category 5: Personal development Students' narratives centered around being challenged and overcoming those challenges. This includes dealing with stress, or engaging with a hitherto unknown challenge: “At first we were all lost on how to approach solving the project. At the end everybody participated as they could.” Or as one student put it: “Throughout the work we did, everything seemed difficult. But as we kept working on them and putting them into presentations, they became simple to grasp.” This underlines the inherent potential of CBL to foster self-efficacy (Michel & Förster, 2025). Students especially point to this regarding research that after the week “[...] actually seems doable - sure, we only got a small look at it, but things always seem scary from the distance“. Similarly, the open problem nature is seen as an opportunity. To quote another student: “it was even better than expected. I could steer the project in the direction I wanted.” Often, students also actively reflect on their role as learners during CWP. To quote one comment: “I think this is as much of an opportunity for new experiences and personal development as for academic achievement.” In some cases, that leads to them reflecting on their studies and their roles, as well: “I learned a lot and it lifted me out of a slump (that I was experiencing, as a normal engineering student would). Your feedback during the week and on the report was truly valuable, it made me think more deeply about the topic.” That specific quote is from a student who also sent a follow-up email to one of the organisers. For her, the course reaffirmed her desire to study engineering, which had been on the decline after a year of theory heavy lectures and average grades. Notably, for CAMMP fostering excitement for STEM subjects is part of the project's core philosophy 3 . Considering the high dropout rates in STEM subjects (Gao et al., 2024), we consider this a significant benefit. Several students reported overcoming stress and issues with time management: “it's amazing what you can achieve in one night”, which also links to the next category. 3 CAMMP website: https://www.cammp.online/english/85.php , last access: 2025-03-24 Category 6: Prior and developed skills Which skills students have, did not have and learned was frequently discussed. In 2021-2024, there were very few references to technical skills, such as using Python or the technical workings of fuel cells. Instead, students put a strong emphasis on the development of professional skills. Often, this is linked to personal development, as students for the first time identify skill gaps they have, especially regarding professional communication: “Communication is hard - I am not used to working in a team to that extent and noticed that often I struggled formulating ideas and sometimes we could have saved a lot of time by communicating better.”. Generally, they report a positive development over the course, e.g. that they got “more group work experience than [experience on] the actual topic, and I learned a lot from the topic.” In 2020, students reported more issues with technical skills. We believe this to be due to lack of inperson access to advisors and team mates. This points to an advantage of the narrow interdisciplinarity of CWP. Due to sharing knowledge paradigms (Kolmos et al., 2024), students can effectively collaborate and make use of peer learning in inperson environments. All students are expected to know how to code before the course. However, we found that while students tend to know how to code for themselves, they tend to have little to no expertise in collaborative software development. Thus, students learn, e.g., that “best practices for code are there for a reason”. Both organisers vividly remember multiple students and student groups worrying whether they would get a mathematics major in their team, for fear of having insufficient mathematical depth to address a problem. However, there is not a single statement about lack of mathematical skills in any of the feedback surveys. This likely is due to the fact that students tend to overestimate the mathematical skills required to effectively work on their problems, especially compared to professional skills. At the same time, the mathematics majors feel that “it can be a bit frustrating, since other group members are already familiar with the concepts being used and you're not, which results in time issues.”. As a result, we are setting up a small teaching unit on good collaboration practices for the first day of CWP. 4 CONCLUSIONS AND IMPLICATIONS In summary, the CWP uses challenge-based learning to successfully foster both students' motivation for their studies and their professional skills. For students, interdisciplinary collaboration constitutes a valuable learning opportunity. We saw that supporting students during that process is critical to its success. That includes general input on technical (good coding practices) and professional skills (teamwork). When given two weeks instead of one to complete their challenges, students ended up being more stressed and less happy, while still asking for more time. This indicates that a single week is enough and that the real challenge lies in learning time management. We found that course evaluations should include items on students’ perception of their role as students, as part of the group and of the role of advisors, as we found those to be important to students, however, the data we had did allow us to delve deeper into those issues. What we did find is that advisors not only play a technical role, but also contribute to team dynamics and career advice. Finally, on a curriculum level, domain projects such as CAMMP need to be followed by courses where students can experience interdisciplinarity in a broader sense.