2 Essential characteristics of good games for mathematical learning
There are plenty of number games to be found in books and on the internet, but are they all good and effective for learning mathematics? To help in deciding which games offer good mathematical learning for use in the classroom it is helpful to first think about the characteristics of good educational games in general. Gough (1999) identified that a good game needs:
- an element of competitiveness; this can be achieved by having two or more players who take turns to achieve a ‘winning’ situation of some kind
- an element of choice and decision making about the next move throughout the game
- an element of interaction between the players in that the moves of one player affect the others.
Activity 2 presents some games that help to develop an understanding of number relationships. Many such games can be found freely in books and on the internet. Activities 1, 2 and 4 of this unit are adapted from the NRICH mathematical resources website.
Activity 2: Being strategic about numbers
Preparation
This game asks the students to think about place value and is enjoyed by students of all ages. For younger students the size of the boxes can be reduced.
Several variations to the game set-up and scoring systems are suggested. Once the students understand the set-up you can also ask them to come up with more variations and scoring systems of their own, as these will also require mathematical thinking.
For this activity students will need six-, nine- or ten-sided dice (with numbers 1 to 6, 1 to 9 or 1 to 10) or spinners with ten segments numbered 1 to 10 or 0. You can find templates for spinners in Resource 3 These resources can be used again in Activity 4.
Game 1 below describes how to set up the basic game, and Games 2 to 6 describe variations and developments from Game 1.
Playing the games
Game 1
This game is best played in pairs, or with two pairs playing against each other.
Each player draws a set of four boxes, as shown in Figure 2.
Instruct the students as follows:
- Take turns to roll the dice, read the number and decide which of your four boxes to fill with that number. Do this four times each until all your boxes are full. Read the four digits as a whole number
Whoever has the larger four-digit number wins.
Here are two possible scoring systems:
- One point for a win. The first person to reach 10 points wins the game.
- Work out the difference between the two four-digit numbers after each round.
The winner keeps this score. First to 10,000 wins.
Game 2
Whoever makes the smaller four digit number wins.
You’ll probably want to change the scoring system from Game 1.
Game 3
Set a target to aim for. Then the students throw the dice four times each and work out how far each of them is from the target number. Whoever is the closer to the target number wins.
Here are two possible scoring systems:
- One point for a win. The first person to reach 10 points wins the game.
- Work out the difference between the two four-digit numbers and the target number after each round. Keep a running total. First to 10,000 loses.
Game 4
This game introduces a decimal point. The decimal point will take up one of the cells so this time the dice only needs to be thrown three times by each player. Choose a target number. The winner is the one closest to the target.
Two possible versions:
- Each player decides in advance where they want to put the decimal point before taking turns to throw the dice.
- Each player throws the dice three times and then decides where to place the digits and the decimal point.
Again, different scoring systems are possible.
Game 5
This game really requires strategic thinking and can be very competitive! Tell your students the following:
Play any of the games above. This time you can choose to keep your number and put it in one of your cells, or give it to your partner and tell them which cell to put it in. It’s really important to take turns to start each round if this game is going to be fair.
This variation of the game becomes even more challenging when you play it with more than two people.
Game 6
This is a cooperative game rather than a competitive one – to be played by three or more people.
Tell your students the following:
- Choose any of the games above. Decide in advance which of you will get the closest to the target, who will be second closest, third, fourth, etc.
- Now work together to decide in whose cells the numbers should be placed, and where.
(Source: adapted from NRICH, http://nrich.maths.org/ 6605 [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .)
 Video: Planning lessons |
Case Study 2: Mr Mehta reflects on using Activity 2
From reading through the instructions for this activity I could see some of the learning opportunities it could offer, but I was not sure to what extent this would be a ‘good’ game. I discussed this with a colleague and we decided to first try it out ourselves in the staff room. And oh my, is it fun to play! We could hardly stop, and other teachers had a go as well.
I was a little bit worried about making up teams of younger and older students as I teach mixed-age groups, so when we first played the game I made students of similar age play in pairs against each other. We played game 1 and then game 2, each one a couple of times. Since then we have used these and other games regularly, sometimes at the beginning of the lesson to energise the students (especially good after lunch), and sometimes at the end of the lesson. It also works well as a reward, telling the students if they finish their work quickly we can play ‘being number strategists’.
I have used game 6, the ‘cooperative’ version of the game, with mixed-age groups and it is lovely to see how most of the older students support the younger ones. I initially thought it would help the older ones in their learning because they would have to help and communicate their mathematical thoughts with the younger students, and that has indeed been the case. At the same time I realised I made the assumption that the younger ones would be reluctant to talk with the older students – but that has proved wrong! The younger students are very happy arguing with the older ones about the mathematics involved.
Because we do not have dice in the school, I made the spinners myself. I made them on cardboard and they have now been used often, so it was worth the effort. I would like to make one big dice that I can roll and then all the students would have to work with the same numbers – just as a variation on the game.
It was good to read about the characteristics of a ‘good’ game. I had never really thought about it in detail. From watching the students play I think that much of the excitement and thinking that happens comes from having ‘an element of choice and decision making about the next move throughout the game’. And the characteristic of ‘an element of interaction between the players in that the moves of one player affects the other players’ seems to trigger them into strategic thinking behaviour – thinking beyond the next step. This strategic thinking really helped them to develop their understanding of place value because they had to think very carefully about the value of each digit.
 Pause for thought In the case study, Mr Mehta was positive about the interaction between the older and younger students in his class. What strategies might he have used to support the students’ learning if the younger students had been more reluctant to talk or the older children had dominated the discussion? Reflect about how your own lesson(s) went using some of these questions:
Make some notes of your thoughts and ideas in response to these questions and discuss them with the teachers in your school or at a cluster meeting. |
1 Using games for developing number sense