Catch a falling bar chart
The recent introduction of data handling as a key component of the mathematics curriculum led to a realisation that many teachers were ill-prepared and this was felt most acutely in the primary schools. What is data handling? How does it relate to statistics? and why are we being asked to teach it?
In many ways "data handling" is just a new name for "statistics". The term data handling with its clear emphasis on activity is a practical subject devoted to the obtaining and processing of data with a view to making statements, called inferences, which often extend beyond the data.
Listen to these three children: "I really thought that all children had the same ability to cross the road - but they don't do they?" "This has made me realise I must be much more careful in Cambridge and Royston."
"Children from busy city schools are not the best at judging the speeds, distances and times of oncoming traffic . . . they are over confident."
A group of primary pupils did a project on how long it took pupils to decide if it was safe to cross a road and how long it took them to cross. They timed pupils from different backgrounds (rural, city, small town) in different road situations. They were handling data. They were doing statistics.
These primary school pupils had to ask clear questions, obtain appropriate data, analyse the data with a view to answering the questions, and draw useful inferences.
It may be helpful to follow Alan Graham, author of Investigating Statistics, and use the acronym PCAI to spell out the four main stages of data-handling.
P - Posing the question This must be done in such a way that you can see what needs to be observed, measured or counted to give an insight towards an answer. Usually the first question tends to be too general and needs to be made more specific.
The primary school pupils in our example started with the vague "Is the Green Cross Code good enough?" and then focused in on "Are children from city areas better able to estimate whether it is safe to cross a road than children from other schools?" National curriculum documentation and schemes have been weak on this aspect of the process. Without some purpose it is easy to fall into the trap of collecting data for its own sake.
C - Collecting the data The pupils measured how long it took children to decide whether it would be safe to cross, how long it took the vehicle to travel from the corner when it first came into sight to where they were standing, and how long it took pupils to cross the road. To collect the data they had to design a data collection sheet.
A - Analysing the data This will include calculations and graphical and pictorial representation. It should be remembered that graphs can have two purposes - to explore the data (analysis) and to display the data (reporting). The pupils counted how many city pupils would not have had time to cross the road, and how many rural pupils would not have crossed when there was plenty of time to do so. The analysis was done using frequency tables, bar charts, pie charts and simple calculations.
I -Interpreting the results What insight into the original question do the results give? These pupils were quite surprised to find that the children from a city school were over-confident; those from a quiet rural school were over-cautious.
The PCAI cycle Although the PCAI cycle starts with posing questions and ends with interpreting results, fresh questions often arise and the cycle repeats.
Why teach data handling?
To think statistically, to deal with statistics and not to be misled, are important skills needed by all citizens. Data handling is an important aspect of the decision making that we all have to do. Our decision as to whether it is safe to cross the road is based on estimates of the speed of the car, the probability of making a mistake, and the likely consequences of such a mistake.
Take a tuck-shop problem investigated by some Year 2 children in the Midlands. During break-time, favourite flavoured drinks sold out quickly and some children missed out. How often did this arise? A daily count was made: Children made a list of their favourite flavours and compared it to the tally chart. Some children drank lime but preferred cola, and so on. After keeping a tally for two weeks, patterns began to emerge, providing enough information to ask the secretary to order more boxes of certain flavours and less of others. This gave opportunities to experience frequency tables, question posing and the practical application of data handling activities.
Data do not have to be collected directly by the pupils. When the data are collected by those who are to analyse them the term primary data is used. When data have been collected by other people the term is secondary data. The children doing the Green Cross Code investigation could have used secondary data from the local authority or other sources on the number of road traffic accidents and the ages of the people involved. Secondary data raise important but difficult questions such as "Who collected them?" "How?" "Why?" and "When?"- all part of learning how to handle data.
National curriculum documents perhaps inevitably stress data handling as a set of techniques to be taught. This obscures the real value of enabling pupils to think statistically. There are techniques but they need to be taught and used in the context of investigating problems.
All this may seem difficult but it need not be. "Which canned drinks are most popular at school?" could be investigated very quickly and simply by a show of hands and a tally chart. Or it could involve a thorough discussion of what the question really means and what questions to ask. It might lead to a carefully controlled term-long school-wide project involving the monitoring of canned drink consumption and pupil opinion. It might even include periodically delving into the school bins.
o The information in this article is based on the introductory chapter of Data Handling by David Green and Alan Graham (eds), Scholastic Practical Guides. 0 590 53145 X. Pounds 9.99 from The Mathematical Association, 259 London Road, Leicester LE2 3BE. Tel: 0116 270 3877 Also recommended: o Practical Data Handling by Glyn Davies, Hodder. Book A (for KS12) 0 340 55389 8, Book B (for KS34) 0 340 55390 1 o Investigating Statistics by Alan Graham. Hodder 0 340 49311 9