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Mathematical problem-solving and chess

Four soccer players on a pitch and one soccer ball
It’s not a mistake. Why is a story about chess illustrated with an image about soccer? Because both involve mathematical problem-solving

Playing a competitive game is all about solving problems – which involves a surprising amount of maths. Lanella Sweet explains why playing chess builds students’ maths capabilities.


The score is 2-2 in the dying seconds of the Girls’ Firsts Soccer match, and Wesley’s star forward Matilda is fouled inside the box and awarded a penalty. She knows she’s more accurate shooting to her right – but, she reasons, the goalkeeper is surely aware of this as well. What are the probabilities – or the payoff – if Matilda shoots right, with the goalkeeper covering that direction? She, and the goalkeeper, have to figure out the optimal tactic.

Matilda and her teammates have a quick discussion, a mixture of competitive passion, problem solving and not a little mathematical thinking. Matilda, who also plays competitive chess, decides to shoot left. Her calculation? Her chance of scoring is greater.

The benefits of chess

There’s plenty of mathematical calculation in most competitive games, not least in chess. While researchers continue to debate the transfer of learning from chess to maths, studies have found that learning chess has a positive impact on students’ ability to tackle novel problem-solving tasks and even maths tasks. Farhad Kazemia and colleagues found that chess significantly improves students’ mathematical problem-solving ability, while Giovanni Sala and colleagues found that even short-term chess practice enhances students’ mathematical abilities.

Students who experience thinking through the many facets of a chess game use a variety of critical thinking tools along the way. Chess requires students to collect data on the different positions on the chess board during a game and analyse the many alternatives for their next move, anticipating the probable consequences of their move, including the probable responses of their opponent – essentially planning ahead. Chess also offers a context in which students can develop their meta-cognitive ability to ‘think about thinking’ and use this to examine options and analyse their consequences.

Wesley’s chess program

Chess taught as a ‘subject’ one period a week ignites student interest and general foundational teaching of the rules and how pieces move on a chess board is beneficial. Teaching the game essentials is a starting point but doesn’t develop students’ complex real problem-solving techniques. As Sala and colleagues observe, understanding the basic rules of chess is not sufficient to develop students’ cognitive skills. It’s the more complex approach to the game that does this, by exposing students’ to opportunities to analyse and abstract in a competitive situation where the better their analysis, the more likely they are to play well. Chess, somewhat like video games, encourages players to learn ‘what works’ and rewards them when they find solutions, as Steven Coshutt observes in ‘Video games, social media and the brave new world of online learning.’ [article yet to be published]

The more students practise chess, collecting and mentally sorting complex data, the more they develop their ability to focus, analyse and choose between multiple options.  While the skills and attributes students develop by playing chess transfer across the curriculum, Sala and colleagues note that they transfer particularly strongly to mathematics problem solving.

Attitudes

Students who play chess develop not only important skills that can be applied to other curriculum areas like mathematics and problem solving, but also important attitudes. When students are able to think about thinking they develop positive attitudes about themselves and their abilities – described in education literature as self-efficacy.

This self-efficacy can be seen particularly in the calm approach chess-playing students take to problem solving. This may be in part because they have played in multiple chess competitions and tournaments, but it’s also because they have developed the skill of using the chess clock appropriately to analyse data and consider their options. Unlike many maths ‘games’ that are really just computation sessions that reward – or punish – students on the basis of their speed of recall in identifying correct answers, chess creates genuine, often novel, problems and values the process of thinking, regardless of whether the player wins or loses a particular game. In fact, according to Cathy Seeley in Faster isn’t Smarter, fast number fact recall at the expense of problem solving and conceptual experiences often gives students a distorted idea not just of mathematics but also their ability to do mathematics. In chess, students learn to take ‘enough’ time before they make their next move, ‘enough’ being that amount of time necessary to have considered the data and the options.

Problem-solving approaches

The skills and attitudes of chess players prompted me to observe the problem-solving approaches to a mathematical problem by chess-playing and non-chess-playing students, and I found that Seeley is right: faster isn’t necessarily smarter. I noticed that the chess-playing students were more likely to:

  • expect they could understand the problem
  • fully interrogate and comprehend the problem to be solved
  • sort through data to identify information necessary to solving the problem
  • analyse abstract information
  • identify whether further information or clarification of supplied information was necessary, and
  • undertake these steps before tackling the actual problem.

The non-chess-playing students, in contrast, were more likely to:

  • respond quickly, often without fully understanding the problem
  • form a superficial understanding of the information necessary to solving the problem
  • identify possible solutions before fully understanding the problem to be solved, and
  • make inadequate estimations that their solution effectively solved the problem.

It was evident that preparation, analysing, and identifying the key information relevant to the problem were fundamental strategies for the chess-playing problem solvers.

Students who have more than foundational experience in playing chess and extensive experience in managing themselves in chess competitions and tournaments seem to approach problem-solving tasks using skills and attitudes that enable them to fully examine and solve mathematical problems. Not only this, the stronger the chess-playing skills of the students, the better they seem to be at understanding and solving mathematical problems.

And what of the final score in that Girls’ Firsts Soccer match? Wesley won 3-2. Checkmate.

Lanella Sweet is an enrichment teacher at Wesley’s Elsternwick Campus.

Elsternwick Junior School students take a chess class for one period a week for one term. Students can also join Elsternwick’s Chess Club for after-school coaching, as part of the Community College program.

Interested in reading more on maths in sport? Try ‘When to take the two’ on optimal tactics in Rugby League; or ‘What is the absolute limit for human athletes?’ and ‘What it will take to run a sub-two-hour marathon?’ on the maths and science of improvements in athletic performance.