2 Moving from physical representation to recording data

One of the things that is often forgotten when interpreting the representation of data is that the bars of the bar chart or the sections of a pie chart represent the number of people (usually people, but it could be other categories) that have a particular characteristic. So in counting the number of sisters in Activity 1, the height of the bar labelled ‘6’ shows the number of students in the class who have six sisters.

Some students can get very confused between the number of people shown by the bar and the number of – in this case – sisters. Exposing them to activities like this will help them to be able to reason out problems such as how many sisters altogether are shown by this chart or that table.

Having physically made bar charts and pie charts with their bodies, it would be useful to challenge the groups to have a go at recording their charts on paper. This will help them make connections between their activity and work in textbooks later. If your class has access to a computer and handling data software, it would also be useful to get some or all of the children to produce their charts on the computer. Computer software can process data into accurate and colourful graphical representations instantly. This can be very helpful, but it may also get in the way of students thinking carefully about what a chart actually represents. The link with their physical activity will give greater meaning to the charts that students produce on the computer.

Moving from the bar or pie charts that they have made themselves to inspecting and interpreting bar or pie charts in a book, or constructing written descriptions of bar or pie charts, the students will benefit from their memories. For example, of how they all lined up, how they made sure that the spaces between them were equal, so that it was easy to tell which bar or sector was the biggest, and so on.

As discussed at the start of this unit, bar charts and other representations of data are used widely in newspapers and magazines, on television programmes and on the internet. The next activity will help the students in your class to see that this is the case, but it will also help them to understand the need for rules and conventions when dealing with data. The activity also aims to get students thinking about whether the representations are as effective as they might be in representing data, or whether the representations are constructed in such a way that hides something or emphasises something unfairly.

Activity 2: Bar charts and graphical representations of data in the real world

Preparation

A few days before this lesson ask the students to look for bar charts and other graphical representations of data in newspapers and magazines that they have at home, or by searching on the internet. Ask them to bring in any examples they find.

This activity works well if done in groups of four students, because more examples are then available for them to examine.

The activity

Instruct the students along the following lines:

• You were asked to bring examples of bar or pie charts you have come across. Put these on a desk to share with your group.
• Sort quickly through the charts and decide which you think you understand without spending too much time examining them (the ‘easier’ pile) and which ones you think you will need to examine more carefully to understand (the ‘harder’ pile).
• Compare the two lists. What is the same, and what is different about these two lists?
• Use your answers to write a list of ‘good things to do when constructing bar charts’ or ‘good things to do when constructing pie charts’.

Case Study 2: Mr Rawool reflects on using Activity 2

This activity did not get off to a good start: I had asked students to bring in examples of bar charts – and they managed to bring in … none. Perhaps it was lack of motivation to make the effort, or perhaps they did not know where to look to find charts. To motivate them I told them what I had read in this unit so far, and also asked them to think of examples where charts are used in real life.

To give them an example I showed them the magazines and newspapers that I had brought in with examples of charts, so they could see where they could find them. By the next lesson most students had brought in several examples – some even managed to download some charts from the internet.

The students worked in groups of four. They found the charts they regularly saw on the TV easy, especially those related to games and advertisements, and decided this was because the information it represented was simple. They did notice however, that some of these ‘easy’ charts used scales were not clear, and the labels on the axes were also not always correct. They had more problems with charts representing medical and economic information. They found it hard identifying what was represented on each axis and interpreting what exactly was shown in each chart.

I collected the charts to use for later exercise problems and told the students to bring in more if they could, so that we could have a whole library of charts to use for years to come.

 Pause for thought What do you think about the way Mr Rawool responded when his students did not bring in any examples of bar charts? How might he have anticipated this potential situation in his preparation for the lesson? What do you think are the advantages of asking children to bring in this kind of resource, and can you think of any difficulties that might arise from the kind of examples they might bring in?

3 Discrete and continuous data