Data Handling

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Data Handling
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Qualifying to Teach Standards
Standards reference 2.1, 2.3.
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Website
http//www.standards.dfes.gov.uk/numeracy/publicat
ions/
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Introduction
Graphs, charts and tables have become
increasingly important in our society. They are
used to organise information and present it to
others in a way that is useful and accessible.
They do, however, need careful interpretation.
Work on representing and interpreting data begins
in Key Stage 1 and is built on in Key Stage 2.
Reports from QCA on Standards in mathematics
continue to stress that children need more
opportunities to extract, interpret and discuss
information presented in a variety of ways.
NB - Too often, children spend time collecting
and presenting data with little attention paid to
specifying the question and to interpreting
information to answer the question.
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In the past handling data has been mentioned by
OFSTED as a weakness in mathematics in Key Stage
2 The good attainment in Handling Data at Key
Stage 1 is not maintained there is too little
progress at Key Stage 2.
Note - Children often represent data that they
have collected directly from their friends or
families, or from experiments that they have done
in school. Secondary sources of information are
used much less, although these too provide a
range of useful data.
TIP - Look out for ready-made collections of data
that children can refer to, such as prepared
databases, including those on CD-ROM, in
reference books, newspapers, registers,
magazines, census data or tables of weather and
climatic conditions.
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Graphs, Charts and Tables
Graphs, charts and tables provide ways of
displaying data that has been collected together
for a purpose.
Remember!!! - The way that the data is
represented and interpreted should reflect that
purpose.
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Discrete

• Quantities that can be measured precisely by
  counting are called discrete.

e.g. children's favourite story, or their current
shoe size. Discrete data can be displayed in a
block graph, bar chart, tally chart, pictogram,
or pie chart.
Continuous

• Quantities such as length, weight, capacity,
  temperature, time, and so on, are called
  continuous.

A measurement of height, for example, can never
be exact. In growing from 155 cm to 156 cm, every
possible value between has been reached at some
point. Continuous data is displayed in a line
graph or can be grouped and displayed in a bar
graph.
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You can use graphs, charts and tables
productively in many subjects but particularly in
mathematics, science, history and geography. They

• often provide a wealth of information in a small
  amount of space

• represent information at a glance, e.g. a price
  chart, a bus timetable

• replace the need for lots of words in a given
  context.

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Five aspects of data handling

• Specify the problem formulate questions, decide
  who might want to know, and why.

• Plan decide what data should be collected,
  including sample size and data format, and what
  analysis needs to be carried out.

• Collect data obtain data from appropriate
  sources, including experiments and surveys,
  primary and secondary sources.

• Process and represent reduce the data into
  summary information that provides insight into
  the problem.

• Interpret and discuss relate summarised data and
  analysis to the initial questions, report
  appropriately.

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Activities in lessons may incorporate from one to
all five of these aspects. A balance should be
maintained.
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Points to note about progression in graphs and
charts

• Only discrete data is used in Key Stage 1.

• Continuous data is introduced in Key Stage 2, in
  Years 5 and 6.

• Children should be able to use and interpret
  symbols representing more than one unit in
  pictograms.

• There is progression in the scales used, from
  ones to twos, fives, tens . . and larger numbers.
  Reading numbers from scales, especially
  intermediate divisions, is an important skill
  that links to work in measurement and number.

• Line graphs can be used in Key Stage 2 to
  represent trends as well as relationships.

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Think of a story for this graph
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This graph represents the water level in a bath
At first both taps are on and the bath is filling
quickly. For a while the cold tap is turned off
the water gets too hot so the cold tap is turned
on again. A short time is taken to remove
clothes. The person steps into the bath and lies
down a period of relaxation follows. The person
sits up, gradually lowering the water level as
they do and stays sitting for a while. The phone
rings. They get up suddenly and step out, leaving
the water level lower than when they got in
because some spills out as they get out. After
the phone call, the water is let out.
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Chocolate graphs
Look at the chocolate graphs. Think up, for each
graph, three questions that could be asked about
it. Bear in mind the age group for whom this
might be a suitable activity.
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Possible questions

• How many thousands of tons of beans were
  produced in Brazil in 1994 and in 1997?

• On average, how much chocolate did each person
  in the UK eat in 1995?

• Look at the graphs 'Where do beans come from?'
  and 'Who eats the chocolate?' What conclusions
  can you draw? Estimate how much chocolate you eat
  in a year.

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Give children regular opportunities in
mathematics and other subjects to

• formulate and clarify questions - the purpose of
  the enquiry, who might need to know and why

• interpret a range of graphs and charts,
  especially those from secondary sources, e.g.
  magazines, newspapers, reference books and CDs

• interpret and analyse data in ways that foster
  speculation on their part

• justify their interpretations, analyses and
  conclusions.

Remember - Keep a balance across the five aspects
of data handling.
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The implications for teaching
Most teachers -

• recognise the need to provide opportunities for
  children to interpret a range of graphs and
  charts.

• they are aware of the usefulness of secondary
  sources of material.

• they understand that the skill of interpreting
  data is a powerful tool.

But, as was highlighted earlier - In spite of
this, too much time in mathematics is spent on
data collection and presentation.
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Teachers therefore need to provide more
opportunities for children to interpret and
explain data presented in different forms.
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Some possible problems
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Key messages

• Try to maintain a balance across the five
  aspects of data handling.

• To achieve that balance, you may need to give
  more time to interpreting and analysing data, and
  less to collecting and presenting it.

• Use ready-made collections of data, and graphs
  and charts in newspapers and magazines.

• Allow plenty of time for discussion so children
  can explain their reasoning and write their
  explanations.

• Give children regular practice in reading scales
  of increasing difficulty as they get older.

• Overcome difficulties through careful planning
  and anticipation.

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Some activities
These seven activities are about interpreting
data. They have been adapted from 'Handling data'
- a booklet which is part of the training pack
'Using ICT to support mathematics in primary
schools'.
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Using a Venn diagram to sort numbers
Where will these numbers sit in the Venn diagram?
31 77 67 86 32 47 93 42 3 21
Describe what properties numbers would have if
they were to sit in the place where the two
circles overlap. Which numbers would you put in
this section? Why? How could you use this
activity with your Key Stage 1 children? What
criteria would you give them for sorting numbers?
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Sorting shapes with a Carroll diagram
Sort these shapes into the correct section of the
Carroll diagram.
How many shapes will there be in the 'not
triangle', 'not yellow' section? Add three more
shapes of your own and add these to the Carroll
diagram. How could you use this activity with
your Key Stage 1 children?
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Presenting data using a pictogram
This chart shows the favourite flavours of boiled
sweets of a group of children in a school.
Which flavour is the most popular? Which
flavours are the least popular? Which flavour is
twice as popular as raspberry? How many children
preferred citrus fruit flavours? How many
children were there in this sample? Would these
findings be true for a whole class in the school?
Explain your answer. What data might you collect
and present using a pictogram with your Key Stage
1 children?
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Using a branching database to sort numbers
Where will each number finish? Three of the
numbers will end at the same letter on this
database, what are they? Think of another two
questions to add to the database which will
separate these three numbers and allow every
number in the list to be individually identified.
How would you use this activity with your Key
stage 2 children?
Use this branching database to sort each of these
numbers 38 47 25 80 32 24
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Calculating the mode, median and mean of sets of
data
This chart shows how the children in one class
travel to school each day.
How many children are there in this sample? If
you need to look at page 117 in the Framework to
help you work out the answers to these questions.
What is the mode of this sample?
Now look at this table of midday temperatures for
the week.
What is the median? What is the mean? What other
sets of data might you ask your Key Stage 2
children to collect, present and analyse using a
bar chart?
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Mean, Mode and Median
Mean Average number of different amounts. Add
up all the amounts and divide your total by how
many amount there were.
Mode A type of average. The mode is the one
that occurs the most.
Median A type of average. The middle value of
an ordered set of values.
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Understanding line graphs

• Labels for graphs
• Favourite colours of children in a class
• Room temperatures taken over a morning
• Conversion graph for kilometres to miles
• Scores on a dice rolled 50 times
• Look at these four graphs and write the
  appropriate label under each one.

Look at the graph which shows room temperatures
taken over a morning. Explain the changes in
temperature that you see. How would you use this
activity with your Key Stage 2 children?
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Using pie charts to display data
This pie chart shows the ages of people living in
a village. Each segment represents the
percentage of the whole population of the village
that is made up by the particular age group
represented in the key.
Approximately what fraction (percentage) of the
population is 16 or under? Approximately what
fraction (percentage) is aged twenty-five to
sixty? How would you describe the population of
this village? Is this most likely to be an
old-established village or a newly developed
village? Why? What other data might you ask your
Key Stage 2 children to collect, represent and
interpret using a pie chart?
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Reading
Chapter 19 from Mathematical Knowledge for
Primary Teachers by J. Suggate, A. Davis and M.
Goulding.
Chapter 17 from Mathematics Explained for Primary
Teachers by D. Haylock.
Chapter 6 from What Primary Teachers Should Know
About Maths by A. Duncan.