3 The role of playfulness in supporting creativity in mathematics
Playfulness is considered important to support creativity because in play you explore many possible solutions in a spontaneous way. The word playfulness is often associated with young children, but it should not be restricted to them. Play is about exploring and experimenting which anyone, at any age, can and should do. Simply watching children play can be a good reminder of children’s creativity.
In the process of exploring and experimenting it is important that students have choices – the choice to approach a problem in different ways, the option to make mistakes, the choice to come up with their own conjectures and test whether they are valid or not. In order to encourage students to adopt a playful way of thinking in the mathematics lesson it helps to use examples that are light-hearted, and even funny.
The next activity presents the students with an image of an extremely large shoe and asks them to imagine how big they would be if the shoe fitted them. By exploring possibilities, making their own choices about how to go about working out the mathematics and no doubt getting things wrong in the process, the students will develop their proportional reasoning skills.
Activity 2: Make it BIG
Preparation
This task works well for students working in pairs. However, make sure they also have some opportunity to work through the sums and do some thinking on their own. You may want to have a look at the key resource ‘Involving all [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] ’ to help you prepare for this activity.
The activity
Tell your students that Figure 2 shows the world's largest pair of shoes. The shoe is 5.29 metres (17.4 ft) long and 2.37 metres (7 ft 9 in) wide. It is said to be equivalent to a French shoe size of 753. The French shoe size of 34 is equivalent to the Indian shoe size of 6.
If your students have access to the internet, they could use a search engine to find more photographs and information about this pair of shoes. This might arouse their curiosity even further! If you have access to a printer, you could print out some larger photographs to share around the class or to help create an exciting wall display of the students’ work after the activity.
If this was your shoe, how tall would you be? Tell your students to talk about how they would solve the problem. After a few minutes, share ideas with the whole class and agree which ideas should be explained further.
Did all your students participate? If not, how can you encourage more participation next time?
 Video: Involving all |
Case Study 2: Mrs Mohanty reflects on using Activity 2
I did this activity with my Class VIII students. I thought it would be nice to start with an open discussion with the whole class so I decided to show them the picture and then passed it around the classroom so all the students could have a close look. They all laughed when they saw the shoe and I could feel they got curious about what this shoe was doing in their mathematics lesson!
I wrote down the measurements of the shoe on the blackboard and asked them the question: ‘If this was your shoe, what would be your height?’ Then Ranu shouted out (shouting out is normally not allowed in my lessons but I let him get away with it this time) with heartfelt emotion: ‘How on earth would they know what the height would be?’ Manisha raised her hand and then said that they could try by comparing their own shoe size and height.
Bharat wondered if that would always be true, as he argued that sometimes people with the same height have different shoe sizes. So he wanted to ask each student what their shoe size and height was. I thought that was a lovely idea but thought having my 86 students measuring their height and the length of their feet, and sharing that data there and then in the classroom, would result in chaos!
I shared this fear with the students and they came up with the suggestion to get some measuring sticks and rulers ready at lunchtime and then everyone could find out their measurements then and write them on the blackboard. Two students volunteered to oversee this happened in a good manner.
We continued with the activity after lunch. I asked them first to work in groups of four to see whether heights always matched the same feet length. Then work out individually what the proportional relationship was between their height and the length of their feet and to check with each other that they had done their calculations right. This way they would already get a lot of practice in working out proportions and ratios and they would get to know about different ways of working it out.
I then asked the whole class about that big shoe and the question ‘If this was your shoe, what would be your height?’ Different suggestions were made on how to work this out such as:
- comparing their own shoe size with the big shoe and then using that ratio to multiply their height
- using the ratio they had worked out earlier of feet length to their height and multiplying this with the big shoe length.
I told them they could use any of the suggested methods and it would be interesting to see whether different methods gave different results – in which case I wanted them to start thinking about why this would be, and discuss this with each other in their groups. Not many students thought about this in the end, but even so, I was pleased I asked the question because it might have planted a little seed for them to think about. We ended the lesson with a discussion about the various things in life that you could observe in nature that are in proportion and those that are not.
 Pause for thought
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Activity 2 used the question starting ‘If this …’ to trigger students to play, explore and investigate the proportional relation between shoe size or length of feet and the students’ height.
Having the choice of how to go about this – to work out a method themselves and make mistakes – together with the funny example of the huge shoe, enthused the students and encouraged them to engage with the task.
2 Creativity in learning mathematics