Connecting Linear Algebra Concepts Through Play: An Educational Card Game for Linear Algebra in Undergraduate Mathematics

Linear Algebra (LA) is a core mathematics course in STEM programs, yet students often struggle with its abstract and densely interconnected nature. Students may learn procedures such as computing determinants or eigenvalues, while still finding it difficult to explain how these concepts can relate to each other. This can lead to fragmented understanding, especially in topics where many concepts interact closely and densely and where deep understanding often depends on recognizing key relationships rather than applying isolated procedures. For example, understanding why a non-invertible matrix must have an eigenvalue equal to zero, requires students to connect several ideas at once. Such conceptual links are central to higher-level reasoning in LA but are often difficult for students to articulate explicitly.
To address this, we developed the LA Card Game (LACG): a physical educational card game designed using ludodidactical principles. In the game, students place cards containing concepts, theorems, and examples from LA in a shared grid in the middle of the table and explain how their card connects conceptually to the surrounding cards. Peers can ask questions, challenge explanations, and then collectively decide whether the reasoning is accepted. The game shifts the focus from procedural calculation towards explanation, relational thinking, retrieval practice, and collaborative discussion. The project was developed collaboratively by a team of LA teachers at Maastricht University and implemented in tutorials across multiple engineering and computing science programs.

The game is intentionally simple in its core mechanic but tends to generate rich mathematical discussion. During gameplay, students continuously negotiate meaning, refine explanations, and collectively construct conceptual “maps” of LA topics. In this sense, the game can support relational understanding rather than isolated procedural fluency. The game can be played competitively, collaboratively, or in hybrid forms, depending on the educational setting and goals of the teacher.

Initial playtesting and classroom experiences suggest that the game creates a highly interactive learning environment where students actively discuss and negotiate conceptual links in LA. Interestingly, several playtesting sessions with mathematics educators and researchers also led to discussions about how the game could function as a diagnostic tool: discarded or avoided cards often reveal which concepts students perceive as difficult or disconnected.

For this contribution, we want to organize a group activity consisting of three phases: First, we introduce the game and its design rationale. Next, participants will be able to play the game in small groups. Finally, we reflect on learning interactions, discuss opportunities and challenges of using game-based learning in concept-dense mathematics courses. We hope that this session can enable us to connect with researchers and educators across the Dutch mathematics education community who are interested in game-based learning approaches to mathematics education across educational levels.

All game materials are available as an open educational resource through www.linearalgebragame.eu.