Count your cards and do your maths!
By designing a card game, maths tutors at the Department of Advanced Computing Sciences increase their student’s engagement with linear algebra.
Linear algebra, a branch of mathematics, is an abstract and sometimes tedious course to take. In general, students manage to understand individual mathematical concepts. Seeing how these concepts fit together is a lot harder. So, keeping students up to speed is a tough job for everyone who teaches mathematics at a university. Monica Salvioli and her colleagues wondered if a mathematical card game could improve their student’s engagement with linear algebra.
Gameplay
Linear algebra is widely used in science and engineering. “Therefore, it is not just students at our department who take the course”, says Monica, assistant professor at the Department of Advanced Computing Sciences. “We teach the course in many programmes, such as Circular Engineering or Business Engineering.”
The game consists of cards each showing a mathematical concept. Players place cards next to each other on the table and explain how the concepts on them relate. The more connections they make, the more points they earn.
“If you walk into our lecture room, you will see small groups of 2-6 players discussing mathematics, even more than I expected beforehand”, says Monica. Players end up having deep, lively discussions about math. Everyone adds insights or levels of detail, and students do not necessarily agree. The tutor judges and by doing so gets a feeling of concepts and interconnections not yet fully understood. “We can then decide to discuss these topics with the whole group.”
Homework
Playing the game has another positive effect. “In general, we notice that by the end of the course, concepts covered during the first weeks are already a bit out of mind. This hinders the students in seeing the connection between topics. But after introducing the game, students come prepared by revisiting course materials at home.”
The developers kept in mind that some people are by nature shy or uncomfortable talking about topics they do not fully grasp yet. “The game can be played by just two players, where you can have one-on-one discussions about the mathematical concepts”, Monica explains. No matter if played by 2 or 6 players, the game fits perfectly in Maastricht University’s Problem Based Learning approach, where learning by discussing problems is key to the educational system.
The ultimate question, of course, is whether the game improves grades. “We don’t know yet”, says Monica. “At first our research was aimed at designing and improving the game. As of next academic year, we will do more quantitative research into the effect of the game on, for example, grades. In part we will do this with our partners at Delft and Twente universities.
Multidisciplinary use
Early 2025, Monica and her teammates started working on the game. At first with simple cards, cut out of a printed sheet of paper. “We tested the game with groups of students as well as colleagues. Each time we collected experiences and advice, improving the game. Students pointed out that the game could need some strategy, so we added a system that allows for choosing more challenging paths between cards, which require you to explain harder-to-understand interconnections which will get you higher scores at the same time.”
Meanwhile, the card game attracted international attention. “We have been invited to present the game during the 27th Conference of the International Linear Algebra Society in May.” In future, Monica foresees more applications than just linear algebra: “You can adapt the game for other purposes. The game is about finding and explaining connections. This could just as well be connections between historical events, molecules in chemistry or maths at a high school level.”
The game is free to print and use, so anyone can benefit. Soon, a polished version will be available for purchase, and a pocket version is in the making, helping students everywhere to see the big picture in linear algebra.
EDULAB Grant
Monica Salvioli and her colleagues Martijn Boussé, Phillipe Dreesen, Ralf Peeters, Marieke Musegaas, and Max Sondag developed and evaluated the game, together with many volunteers who were willing to play it. Their work was supported with a € 5000 EDULAB grant. “That enabled us to ask a professional to design the final version of the game, so it no longer has a homemade feeling”, says Monica.
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