Algebra game helps students get to grips with the subject

At Maastricht University, linear algebra seminars now end with a game of cards. The idea is that this helps students retain the material better and see the connections more clearly.

TEXT: MARLIES TER VOORDE

For readers who are engineers or have otherwise studied science subjects: can you still remember the linear algebra lectures from the first year of your degree? And if so, did you understand the connections between concepts such as linear equations, rank, invertibility, null spaces, equivalence and eigenvectors?

You can test your knowledge with the resit exam on page 64, but chances are you relied on algorithms – the ‘recipes’ that told you how to solve the various algebra problems. At least, that is the experience of a group of researchers from the Department of Advanced Computing Sciences at Maastricht University, who teach linear algebra to various groups of students. ‘We see that students focus primarily on the procedures to be followed,’ explains Martijn Boussé, a mathematical engineer and algebra lecturer. ‘They know exactly what to do when using Gaussian elimination and how to calculate an eigenvalue. But ask them about concepts or interconnections, and it becomes too complicated for them. Yet that is precisely where the power of linear algebra lies. That’s where it gets interesting!’

Making connections

To help students understand and master this branch of mathematics, the team from Maastricht – consisting of Boussé and his colleagues Monica Salvioli, Philippe Dreesen, Ralf Peeters, Marieke Musegaas and Max Sondag – developed the Linear Algebra Card Game. The game consists of square cards, each featuring a concept, example or theorem from linear algebra.

The aim is to take turns placing a card on the table, which must match the cards already there. Think of it as a game of dominoes – except that in this case, ‘matching’ means there is a connection between the terms on the cards. The student who places the card explains what that connection is and tries to convince the other players of it. If they succeed, the student scores points. The first player to reach thirty points wins the game.

The Linear Algebra Card Game has been designed in accordance with didactic principles. ‘The game offers students proven learning strategies,’ says Boussé. ‘They have to retrieve information from their memory, formulate definitions in their own words, make connections and convince their fellow students by explaining things clearly. All of this falls under effective learning behaviour.’ It ties in with the problem-based learning approach favoured by Maastricht University, in which collaborative problem-solving takes centre stage.

Half an hour of cards

The idea for the game arose when Boussé attended a summer course on Ludo didactics at the University of the Arts (HKU) in Utrecht, which focused on designing teaching and learning behaviour based on game design. ‘It was initially a more complicated card game,’ explains Dreesen. ‘We’ve tweaked and refined it over the past two years, together with lecturers and students.’ Thanks to an EDLAB Education Innovation Grant from Maastricht University’s Centre for Teaching & Learning, the mathematicians were able to engage a professional designer for the final product.

So now, every linear algebra seminar in Maastricht ends with half an hour of card games. The group of around fifteen students is then split into three, and the lecturer walks round to offer help if needed. It works perfectly, says Boussé. ‘It’s a six-week course. For the first two weeks, the students were really struggling with the game and I had to constantly explain things to them. But then something changed; they became more independent and figured things out for themselves. To my surprise, by week six they were even making connections that hadn’t even occurred to me. Some groups were having really in-depth discussions. That was exactly what I’d hoped for, even though no cards were being played at all in those groups.’

Daring to be a nerd

A better understanding of the subject matter isn’t the only aim, says Gavin Phillips, programme director of the circular engineering programme at Maastricht University’s Faculty of Science & Engineering, who was involved from the start of the project.

‘Students often take linear algebra in the early stages of their degree, when they still need to learn to come out of their shells.’ It takes a certain amount of self-confidence to have in-depth discussions about maths with fellow students rather than just talking about last weekend’s football results, notes Phillips. ‘You have to dare to be a bit of a nerd, rather than, as we say in England, “too cool for school”. This game removes that barrier.’

Boussé, Salvioli and Dreesen have all already used the game in their seminars. ‘It was well received,’ says Salvioli. ‘If only because it’s finally something different from just doing exercises. And we have the students to thank, because they made a huge contribution by testing the game and providing feedback.’ ‘There’s a difference between game-based learning and gamification, ’emphasises Boussé. ‘Gamification is making an activity more fun by adding a game element to it, similar to handing out stickers to those who get the exercise right. What we have done, however, is to build effective learning behaviour into the mechanics of a game. This not only makes learning more enjoyable, but also makes it more effective.’

Digital version

The researchers have been awarded a Scholarship of Teaching & Learning Grant to investigate learning outcomes with and without the game. ‘The problem with understanding concepts is that students have very few opportunities to practise them,’ says Peeters. ‘They find questions on these topics the most difficult part of the exam. We can give them examples, but once they’ve worked through those, that’s it. With this game, they can keep practising.’ He therefore expects better exam results from now on.

Meanwhile, a digital version of the game for multiple players is also in the pipeline. Phillips: ‘Then students all over the world will be able to play it together.’ Peeters believes the game’s concept lends itself to other subject areas. ‘In fact, it can be used for any course where the connection between different topics is important and students need to learn to recognise networks.’