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Article by Jenni Way# Learning Mathematics Through Games Series: 1. Why Games?

### What is a mathematical game?

### Benefits of Using Games

### Hints for Successful Classroom Games

### References

Links to the University of Cambridge website
Links to the NRICH website Home page

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Age 5 to 14

Published 1999 Revised 2011

We all know that children enjoy playing games. Experience tells us that games can be very productive learning activities. But ...

- What should teachers say when asked to educationally justify the use of games in mathematics lessons?
- Are some games better than others?
- What educational benefits are there to be gained from games?

This article supplies teachers with information that may be useful in better understanding the nature of games and their role in teaching and learning mathematics.

When considering the use of games for teaching mathematics, educators should distinguish between an 'activity' and a 'game'. Gough (1999) states that "A 'game' needs to have two or more players, who take turns, each competing to achieve a 'winning' situation of some kind, each able to exercise some choice about how to move at any time through the playing". The key idea in this statement is
that of 'choice'. In this sense, something like Snakes and Ladders is NOT a game because winning relies totally on chance. The players make no decisions, nor do that have to think further than counting. There is also no interaction between players - nothing that one player does affects other players' turns in any way.

Oldfield (1991) says that mathematical games are 'activities' which:

- involve a challenge, usually against one or more opponents; a
- are governed by a set of rules and have a clear underlying structure;
- normally have a distinct finishing point;
- have specific mathematical cognitive objectives.

The advantages of using games in a mathematical programme have been summarised in an article by Davies (1995) who researched the literature available at the time.

- Meaningful situations - for the application of mathematical skills are created by games
- Motivation - children freely choose to participate and enjoy playing
- Positive attitude - Games provide opportunities for building self-concept and developing positive attitudes towards mathematics, through reducing the fear of failure and error;
- Increased learning - in comparison to more formal activities, greater learning can occur through games due to the increased interaction between children, opportunities to test intuitive ideas and problem solving strategies
- Different levels - Games can allow children to operate at different levels of thinking and to learn from each other. In a group of children playing a game, one child might be encountering a concept for the first time, another may be developing his/her understanding of the concept, a third consolidating previously learned concepts
- Assessment - children's thinking often becomes apparent through the actions and decisions they make during a game, so the teacher has the opportunity to carry out diagnosis and assessment of learning in a non-threatening situation
- Home and school - Games provide 'hands-on' interactive tasks for both school and home
- Independence - Children can work independently of the teacher. The rules of the game and the children's motivation usually keep them on task.

Few language barriers - an additional benefit becomes evident when children from non-english-speaking backgrounds are involved. The basic structures of some games are common to many cultures, and the procedures of simple games can be quickly learned through observation. Children who are reluctant to participate in other mathematical activities because
of language barriers will often join in a game, and so gain access to the mathematical learning as well as engage in structured social interaction.

These tips come from Alridge & Badham (1993):

- Make sure the game matches the mathematical objective
- Use games for specific purposes, not just time-fillers
- Keep the number of players from two to four, so that turns come around quickly
- The game should have enough of an element of chance so that it allows weaker students to feel that they a chance of winning
- Keep the game completion time short
- Use five or six 'basic' game structures so the children become familiar with the rules - vary the mathematics rather than the rules
- Send an established game home with a child for homework
- Invite children to create their own board games or variations of known games.

Future articles in this series will cover types of games and creating your own games.

Aldridge, S. & Badham, V. (1993). Beyond just a game. Pamphlet Number 21 . Primary Mathematics Association.

Davies, B. (1995). The role of games in mathematics. Square One . Vol.5. No. 2

Gough, J. (1999). Playing mathematical games: When is a game not a game? Australian Primary Mathematics Classroom. Vol 4. No.2

Oldfield, B. (1991). Games in the learning of mathematics. Mathematics in Schools. January