The Recreational Mathematics Colloquium (RMC), organized biennially by the Ludus Association in Portugal, is a premier international gathering dedicated to the study and dissemination of Recreational Mathematics. What makes RMC so special is its multidisciplinary nature. It attracts mathematicians, educators, historians, artists, games and puzzle lovers from all over the world, each bringing their own unique perspective.

We are incredibly grateful to Jorge-Nuno-Silva, president of the Ludus Association for organizing such a great event. We leave with new inspiration, new challenges to explore and most importantly, the firm belief that mathematics, games and puzzles should always be a source of wonder, joy and endless curiosity.

Recreational Mathematics is often perceived as a lighter, more accessible side of mathematics, but its significance extends far beyond entertainment. Historically, it has catalyzed scientific discoveries, influencing key developments. It also plays a critical pedagogical role, providing alternative methods for engaging students and the general public in mathematical reasoning.

RMC successfully reinforced these perspectives by showcasing research that connects recreational problems to serious mathematical inquiry. The presentations demonstrated how puzzles, games, and paradoxes can serve as powerful tools for both formal education and informal learning, bridging the gap between theoretical mathematics and applied problem-solving.

The 2025 Colloquium embraced the “Show and Tell” spirit. The format allowed for an engaging exchange of ideas, with a balance of theoretical rigor and practical application. Every speaker had something fascinating to share, and every participant left with a renewed sense of wonder.

One of the most striking aspects is how Recreational Mathematics makes mathematics accessible to diverse audiences. It is not confined only to research papers and theoretical arguments. It thrives in puzzles, games and magic tricks. This ability to engage people of all backgrounds, from schoolchildren to professional mathematicians, is what makes it so powerful. Because mathematical insight often emerges from playful exploration.

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If you want to find out more about What is Recreational Mathematics and how does it relate to chess? join our next Discussion Group Meeting on 26 February 2025 with the amazing Thiago Hirth. Register here

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Presentation by John Foley from ChessPlus (London):

Teaching Games in Primary School

I’m deeply involved in chess education, working with the European Chess Union’s Education Commission and I’ve spent years teaching chess in schools. But my background wasn’t always in chess. I’ve worked in mathematical modeling and operational research. Also as a philosophy lecturer and even as a barrister. Yet, about 20 years ago, I was drawn back to chess because I saw something powerful in it. Something bigger than just the game itself.

Today, I want to talk about why games, particularly strategy games, are a vital tool in education. And when I say “games,” I mean playable strategy games, not gamification, which is often just a sprinkle of engagement over an otherwise tedious task. Nor am I referring to mathematical game theory. I’m talking about games that challenge the mind, develop thinking skills, and transform the classroom into an arena for critical thought.

The Role of Games in Education

Children love games. They are drawn to play naturally, and through that play, they learn. As educators, our job is to harness that enthusiasm and channel it into meaningful learning experiences. But what is the real goal of teaching games in school?

If I had to sum it up in one phrase, I’d say it’s to cultivate critical thinking.

I’ve heard the term “critical thinking” mentioned often at this conference, but let’s break it down. Let’s test the room.

• Who here thinks they’re good at mathematics? (Show of hands.)
• Keep your hand up if you think you’re good at logic. (Most hands stay up.)
• Now, what about critical thinking? Who considers themselves skilled in critical analysis? (Fewer hands remain.)
• And finally—philosophy? (Even fewer hands.)

This is fascinating because it highlights something crucial—there are different layers of thinking. And if we want to develop well-rounded, analytical thinkers, we need to start early. That’s where games come in.

Games and Cognitive Development

One of the most essential skills for learning is concentration. Yet, in a world of constant distractions, how do we train children to focus?

The answer lies in structured play. When children engage in games, they enter a psychological state of deep focus—far longer than they would in traditional lessons. And within this focus, something remarkable happens:

• They analyze situations.
• They think ahead.
• They recognize patterns.
• They make decisions.

But there’s something else at play: metacognition—the ability to think about thinking. Are they solving a problem? Remembering a pattern? Testing a hypothesis? Understanding how they think is just as important as thinking itself.

And let’s not forget the social element. Games are inherently interactive. Unlike passive learning, where students consume information, games require them to engage, adapt, and respond to others. This fosters confidence, collaboration, and resilience—all essential life skills.

The Challenge of Implementing Games in Schools

If games are so powerful, why aren’t they a staple in every school? The reality is that integrating games into education comes with challenges:

1. Time Constraints – A typical lesson lasts 30 to 60 minutes. Many games take longer, making classroom integration tricky.
2. Teacher Confidence – Most educators aren’t trained to teach chess or strategy games, leading to reliance on external tutors.
3. Classroom Management – Games can create noise and excitement, which, if not structured well, can disrupt learning.
4. Competition Bias – While competition is a natural part of gaming, overly competitive environments can discourage students who struggle.

The solution? A structured approach to game-based learning.

How to Teach Strategy Games Effectively

1. Minimal Direct Instruction – Let children explore the game rather than overwhelming them with rules. They learn best by playing.
2. Guided Discovery – Teachers should act as facilitators, offering insights when needed rather than dictating play.
3. Peer Learning – Once a child learns a rule or strategy, they naturally spread it to their peers—creating a viral learning effect.
4. Balanced Competition – Recognize achievements without overemphasizing winners and losers. The goal is engagement, not just victory.
5. Resource Management – Schools need well-maintained, easily accessible game sets to ensure seamless implementation.

Chess vs. Other Strategy Games

Chess is often the default strategy game in schools and research suggests it positively impacts academic performance. However, chess alone is not enough.

Why? Because traditional chess instruction tends to focus on a select group of talented players, leaving others behind. And, as brilliant as chess is, it primarily develops deductive reasoning—the ability to logically analyze information based on set rules.

But critical thinking is more than just deduction.

The Missing Piece: Games of Hidden Information

The scientific reasoning model teaches us that true critical thinking involves both deduction and hypothesis formation. Most strategy games—chess included—rely solely on perfect information: all players see everything. But real-world problem-solving often requires dealing with uncertainty.

So, how do we train children to think critically in an uncertain world? We need to introduce games with missing information.

Examples of Effective Hidden-Information Games:

• Battleship – Players must hypothesize the opponent’s ship placement based on limited clues.
• Stratego – Players see only their own pieces, requiring both deduction and deception.
• Kriegsspiel (Blindfold Chess Variant) – Players don’t see their opponent’s moves directly but must infer them from limited data.

Or, we simplify things even further:

• Secret King & Queen – Each player hides the identity of their king and queen using draught pieces.
• Latako – A game where players move hidden pieces, trying to deduce their opponent’s strategy before making a move.

These games force players to form and test hypotheses, a key skill in critical thinking and scientific reasoning.

The Future of Game-Based Learning

If we truly want to develop critical thinkers, we need more than just chess—we need a variety of strategy games that develop different cognitive skills.

• Chess sharpens deductive reasoning.
• Hidden-information games build hypothesis formation.
• Fast-paced strategy games develop decision-making under pressure.

Games are not just recreational activities—they are powerful educational tools. They teach logic, strategy, concentration, and social skills. But to unlock their full potential, we must:

Expand beyond chess

• Incorporate hidden-information games.
• Train teachers to integrate games effectively.
• Create an inclusive environment where all students can engage, not just the best players.

By doing this, we can transform classrooms into hubs of critical thinking, creativity, and lifelong learning.

Thank you.