Calculus Legacy: A Ludo Didactical Learning Experience for Mathematics in Engineering Education

Workshop Recommended citation: Chen, M., Ramesh Kumar, S., Phillips, G., Schneider, K., & Boussé, M. (2025). Calculus Legacy: A Ludo Didactical Learning Experience for Mathematics in Engineering Education. 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.17631264. 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. CALCULUS LEGACY: A LUDO-DIDACTICAL LEARNING EXPERIENCE FOR MATHEMATICS IN ENGINEERING EDUCATION M. Chen a, S. Ramesh Kumar a, G. Phillips b, K. Schneider c, M. Boussé d, 1 a FSE, Maastricht University, Maastricht, the Netherlands b FSE, Maastricht University, Maastricht, the Netherlands, 0000-0003-4443-0822 c Department of Advanced Computing Sciences, FSE, Maastricht University, Maastricht, the Netherlands, 0000-0001-6250-9011 d Department of Advanced Computing Sciences, FSE, Maastricht University, Maastricht, the Netherlands, 0000-0003-2090-0682 Conference Key Areas: 3. Teaching mathematics and physics in engineering education, 12. Curriculum development and emerging curriculum models in engineering Keywords: Ludo Didactics, Game-Based Learning, Student Engagement, Mathematics Education, Problem-Based Learning ABSTRACT Calculus is a key subject in engineering education but is often experienced as abstract and demotivating by students. Calculus Legacy, a narrative-driven, legacy-style board game, was designed using Ludo Didactics principles to create an active, learner-centered environment. By aligning the game with Problem-Based Learning, the game transforms calculus into an engaging, contextualized, and learner-driven experience. In this workshop, participants will engage with a curated version of the game, assume unique roles, and solve real-world-inspired calculus problems, simulating how students collaborate in small teams. Calculus Legacy provides a concrete example of how Ludo Didactics can enhance mathematics education within engineering programs. Participants will gain insights into implementing similar game-based strategies in their own courses to promote student-centered, active learning and increase motivation in STEM education. 1 Corresponding author M. Boussé [email protected] 1 BACKGROUND AND RATIONALE 1.1 Calculus in Engineering Calculus is a cornerstone of engineering education, essential for modelling, analyzing, and solving complex problems in domains ranging from mechanics and thermodynamics to systems control and data science. Despite its fundamental role, calculus remains one of the most challenging and often demotivating subjects for first-year engineering students (Tall, 1993; Lim-Teo et al., 2007). Many learners experience it as abstract, technical, and detached from practical applications, often leading to surface-level learning and disengagement. One key issue is the dominance of teacher-centered, lecture-driven formats that emphasize procedural proficiency over conceptual understanding (Thompson & Harel, 2021). These traditional methods often neglect the potential benefits of active learning paradigms such as Problem-Based Learning (PBL), which promote engagement and critical thinking through real-world problems. In response, there is a growing call within the engineering education community to reimagine how we teach calculus, moving towards student-centered approaches that are collaborative, contextual, and engaging (Mokhtar et al, 2013; Maastricht University, 2024). Embedding calculus instruction in such frameworks is crucial not only to improve understanding of mathematical principles, but also to enhance students’ confidence and motivation. In this context, game-based learning emerges as a powerful pedagogical tool. By leveraging the motivational affordances of games, such as narrative, competition, feedback loops, and role-playing, educators can facilitate deeper learning and make abstract mathematical concepts more tangible and engaging (Bayeck, 2020; Oliveira et al., 2023). Calculus Legacy, the board game showcased in this workshop, embodies this vision by blending Ludo Didactics with PBL principles to create an active, immersive, and learner-driven experience for engineering students. 1.2 Ludo Didactics as a constructive, collaborative, contextual, and self-directed (CCCS) teaching and learning approach Maastricht University’s educational vision revolves around PBL, promoting active learning through four core principles (EDLAB, 2017): ● Constructive learning encourages students to build upon their existing knowledge by actively integrating new concepts. ● Collaborative learning promotes co-creation of knowledge through teamwork, fostering communication and collective responsibility. ● Contextual learning situates academic concepts in authentic, real-world scenarios, increasing relevance and transferability of knowledge. ● Self-directed learning empowers students to plan, monitor, and evaluate their own learning trajectories, promoting autonomy and ownership. The CCCS principles have been linked to greater student satisfaction and deeper learning (Dolmans et al., 2005; Bergman et al., 2012). They have also been linked to improvements in critical and creative thinking, preparing students for real-world problem solving (University of Illinois, 2019). One way to operationalize CCCS principles in innovative learning environments is through Ludo Didactics. Developed by the Utrecht School of Arts (HKU), Ludo Didactics is a pedagogical framework that designs learning behavior and education around game principles (Renger & Hoogendoorn, 2019). It shifts focus from traditional, content-driven teaching to learner-centered approaches, in a similar spirit as PBL. At its core, Ludo Didactics integrates methodologies from game design to create learning experiences that are inherently engaging and meaningful. This is achieved, e.g, by using the Mechanics, Dynamics, Aesthetics (MDA) framework, which guides the design of the learning experience (mechanics and dynamics) and its emotional impact on the learner (aesthetics). Also, the Epic Epistemic Canvas ensures alignment between game design and intended learning outcomes (Renger & Hoogendoorn, 2019). Ludo Didactics naturally aligns with the CCCS principles: ● Constructive: Learners actively build knowledge as they engage with evolving challenges embedded in game scenarios. ● Collaborative: Many Ludo Didactical designs emphasize team roles, cooperation, and shared decision-making. ● Contextual: The narrative-driven nature of Ludo Didactics often situated learning within authentic contexts and real-world scenarios. ● Self-Directed: Games inherently give players agency, enabling students to explore, strategize, and reflect on their actions and learning progress. Building on previous efforts to align assessment on teaching and learning activities in our programs with CCCS principles (Boussé et al., 2023), Calculus Legacy represents a tangible realization, applying Ludo Didactics to promote active, student-centered learning experiences. It enhances the learning process and addresses the pedagogical challenges associated with teaching calculus, such as perceived abstraction and lack of engagement, by transforming them into motivating, collaborative, and authentic learning experiences. 1.3 Calculus Legacy board game Calculus Legacy is a narrative-driven, legacy-style board game developed to enhance student motivation and engagement in calculus through a Ludo Didactical learning experience. It promotes a lean-forward learning attitude by immersing students in an active and collaborative environment where they tackle real-world inspired challenges. The game, financed by Comenius Teaching Fellow 2024. is designed to transform the learning of calculus from a traditionally passive, abstract exercise into a meaningful and interactive journey that sparks curiosity and deepens understanding. The game consists of six, 90-minute sessions aligned with six weeks of course content, where students work in small teams, each assuming unique roles, see Figure 1. Using an event-card deck system, students are confronted with decision-making scenarios, applied calculus tasks, and narrative twists that foster collaboration and critical thinking. The legacy mechanics ensure that choices made in one session impact subsequent sessions, scaffolding mathematical concepts progressively across the course. The game evolves and changes over time depending on how players interact with it, offering a one-of-a-kind gameplay experience for every group. The evolving narrative, paired with role-playing and problem-solving, encourages continuous engagement, collaboration, and authentic learning experiences in line with CCCS and Ludo Didactical principles. To assess its impact, we conducted a playtest with BSc Circular Engineering students, see Figure 2. The game session created a lean-forward and collaborative environment for the students to explore solutions for a real-world, calculus-based problem. Each of the Calculus Legacy sessions are designed based on specific calculus-related concepts that are traditionally included in first-year engineering curricula. These include topics such as functions, limits, derivatives and their applications, integrals and their applications and differential equations. To integrate these concepts into the game, we have introduced a layer of engaging, relatable and unique narratives for each. For example, application of derivatives are explored through a vegetable garden optimization task where students aim to calculate the optimal temperature, cost and fertilizer usage. Students explore integrals by decoding a recipe, where the quantities of the ingredients have been encoded in various integral types. As for integral’s applications, student teams have to design their own chalice-shaped beer glass by computing its volume and areas whilst adhering to constraints introduced by the event cards. Fig. 1. Conceptual illustration of the Calculus Legacy board game, showing the key components such as event cards, player role and goal cards, and a collaborative team workspace, designed to enhance motivation, collaboration, and communication in an educational setting. Note that a tutor is always present as a guide on the side. 1.4 Relevance for engineering education The integration of PBL and the CCCS principles can be highly beneficial for effective engineering education, especially in mathematics instruction (Dolmans et al., 2005; Mokhtar et al., 2013). Ludo Didactics offers a practical, creative, and playful design methodology to translate these principles into engaging, meaningful, and authentic teaching and learning experiences that resonate with engineering students. In this workshop, we showcase Calculus Legacy as a tangible example of how PBL, CCCS, and Ludo Didactics can be integrated to improve mathematics education by fostering deeper conceptual understanding and student motivation. These methods align with the pedagogical approaches in Education for Sustainable Development (UNESCO, 2017; Guerra & Holgaard, 2013), the vision described in the SEFI annual report 2023-2024, precisely with the Leonardo da Vinci medal winner, Professor in Engineering Education and PBL, Anette Kolmos (Ferdová, 2024), and the vision of the European Higher Education Area (European Commission, 2024, Chapter 5.3). By offering participants a curated experience of this board game, we provide a practical blueprint for integrating student-centered, game-based learning into engineering curricula. This contributes to broader curriculum development efforts that call for active and meaningful learning experiences (Bayeck, 2020; Oliveira et al., 2023). Ultimately, this workshop aims to inspire educators across disciplines to apply these design principles in their own courses and contexts. This workshop also supports the growing emphasis in engineering education on developing transversal skills, such as teamwork, problem-solving, and reflective thinking. By fostering collaboration and contextual learning, Calculus Legacy equips future engineers with both technical expertise and the ability to apply knowledge creatively in real-world, project-based settings. Fig. 2. Real-life playtest of the Calculus Legacy board game, featuring students actively collaborating to design a chalice-shaped beer glass. In this session, students brainstorm how to compute the volume and surface area of the glass. Each student has a distinct role and hidden personal goal, adding an extra layer of strategy and engagement. 2 WORKSHOP OBJECTIVES 2.1 Target audience The target audience for this workshop are educators from all fields within engineering. This workshop does not require any specialised knowledge in calculus to participate because it is a curated experience from the original board game. 2.2 Expected learning outcomes The goals of this workshop are two-fold: 1) to familiarise participants with the core concepts and educational rationale of Ludo Didactics by engaging them in a curated play experience of Calculus Legacy, and 2) to inspire and empower educators from diverse engineering disciplines to critically reflect on and explore how Ludo Didactics could be adapted and implemented within their own teaching contexts. The intended learning outcomes (ILOs) of the workshop are: 1. Describe the ludo-didactical principles within the context of constructive, contextual, collaborative, and self-directed (CCCS) learning principles. 2. Explore the ludo-didactical approach in their own teaching practices. We aim to achieve this through an interactive game session - which will comprise most of the workshop, followed by a short post-discussion to share experiences and insights. This will provide the participants a first-hand experience of Ludo Didactics. 2.3 Transferability Although Calculus Legacy was created for calculus, its underlying structure is highly transferable across STEM disciplines. Ludo Didactics provides an adaptable design methodology for other contexts and learning objectives. The game’s role system, event-card mechanics, and legacy format are content-neutral, making them suitable for other fields such as physics, computer science, or interdisciplinary courses such as sustainability and product design. By modifying the narrative and task structure, educators can craft engaging, game-based learning environments tailored to their specific domains. Such adaptability supports broader adoption of student-centered, active learning approaches within engineering education. 3 WORKSHOP DESIGN 3.1 Time plan This workshop is divided into three parts consisting of an introduction, a play experience, and a post-discussion, along with preand post-workshop materials, see Table 1. Materials for all activities can be downloaded via the link in the footnote2. Table 1. Workshop time plan Run time Activity Description 5 min Short introduction Brief introduction to the workshop. 30-35 min Play experience Participants play a curated version of Calculus Legacy in small groups. 15-20 min Post-discussion Participants engage in a guided discussion to explore opportunities, challenges, and contextual adaptations to their fields. In the pre-workshop material, we provide explanations about the main principles of Calculus Legacy and the rules of the game. Reading the pre-workshop content prior to the onsite workshop is recommended and beneficial to the progression of the game session but completion is not mandatory and does not limit participation. During the workshop, the short introduction ensures all participants understand the basic rules of Calculus Legacy. In the interactive playtest, the provided game session is inspired from the final board game but shortened and tailored to a wide audience without prior knowledge. The post-discussion will be guided by a set of structured reflection questions, encouraging participants to link their gameplay experience explicitly to CCCS principles and reflect on how Ludo Didactics could be applied in their own teaching. Participants will also be prompted to share potential barriers and enablers for implementing game-based learning in their contexts. Examples include: implementation for large cohorts, adaptation to other subjects, and integration with existing curricula or assessment strategies. The discussion aims to generate actionable insights and inspire participants to experiment with Ludo Didactics and game-based learning in their courses and curricula. After the onsite workshop, post-workshop material will be provided via a download link consisting of: a concise Ludo Didactics primer with some examples 2 Workshop material link https://surfdrive.surf.nl/files/index.php/s/NxU65YekyfZaDhS and a guide to run the curated game session at their home university. This will further disseminate our ideas and enable participants to adopt similar strategies. 3.2 Interactivity The workshop design ensures a high level of interactivity: 1) participants engage directly in the game-based learning activity (“learning by doing”), 2) the game is designed to promote small-group discussion and teamwork, 3) the design also creates an immersive, shared learning experience, 4) because of the role system, every participant/player brings unique game abilities to the table, and 5) in the post-discussion of the workshop participants share their personal game experience. 4 WORKSHOP RESULTS The workshop attracted 8 participants involved in engineering education and coming from different backgrounds, mainly mathematics and physics educators. Immediately following the workshop, participants completed a brief evaluation, using the interactive tool Wooclap, to evaluate the effectiveness of the workshop and assess the extent to which the intended learning outcomes (ILOs) are achieved. To assess ILO1, which focuses on participants’ understanding of Ludo Didactical principles in the context of CCCS learning, we included Likert-scale based and open-ended questions. The results of the Likert-scale were generally positive, see Table 2. Table 2: Results of the post-workshop survey with Likert-scale rating from 1 to 5 (1= I strongly disagree and 5 = I strongly agree). Statement Average rating The workshop was useful to me 4.0 I learned something about Ludodidactics and CCCS 3.9 I am interested in implementing Ludo Didactics in my teaching 3.6 In the open-ended questions, the audience expressed the challenges and opportunities with the implementation of Ludo Didactics in engineering education. In terms of opportunities, the participants mentioned the modularity of the approach given the adaptability of the narrative alongside the increase in learner engagement through enjoyable and interactive sessions. As for the challenges, they highlighted the time constraints in developing effective yet non-demoralising exercises fitting the Ludo Didactical approach, hardships with engaging passive students and time taken to understand the problem. Additionally, the audience indicated that they especially appreciated the interactiveness, collaborative and fun hands-on experience. To evaluate ILO2, concerning participants’ ability to explore the applicability of Ludo Didactics within their own educational practice, participants were invited to provide written reflections on potential applications within their field. The reflections included the interest for implementation of PBL, defining an assortment of exercises suited for Ludo Didactics and even inclusion of real-life data. 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