Cards on the Table: Playing with Linear Algebra Concepts

Linear Algebra is a core mathematics course in numerous undergraduate programs, yet students often struggle with its abstract nature and with recognizing key connections between topics. This lack of conceptual coherence motivates the need for innovative teaching approaches that make linear algebra more accessible, engaging, and meaningful. We developed a Linear Algebra card game grounded in ludodidactical principles and aimed at fostering conceptual understanding through collaborative learning. The game is not intended to trivialize mathematical content, but to elicit meaningful interaction and explanation among students. It is played in groups of 2 to 6 students and invites players to strategically place and connect concept cards representing key topics in linear algebra (such as systems of linear equations, vector spaces, eigenvalues) by explaining the mathematical relationships between them. Players earn points for correct and meaningful connections, shifting the emphasis from computation to explanation and reasoning.

The game was implemented in a variety of educational settings and evaluated using end-of-course student surveys focusing on engagement and learning outcomes. Preliminary results indicate increased student engagement, improved understanding of relationships between linear algebra concepts, and positive perceptions of learning through peer interaction. In addition, multiple playtesting sessions with colleagues in mathematics education were organized to iteratively refine both the game mechanics and its pedagogical focus.

Our findings suggest that well-designed ludodidactical tools can play a valuable role in supporting conceptual learning in abstract mathematics. The Linear Algebra Card Game is adaptable across different course levels, and all materials are shared as open educational resources.