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Data handling is one of the central activities in which real
mathematicians engage: they are frequently analysing data that they
have gathered in various contexts and looking for patterns and
generalities within them. In schools we often undertake tasks in
which we encourage children to collect data about themselves and
their friends but the emphasis tends to be on presenting data in a
variety of forms such as bar charts or pictograms. Analysis is
often confined to identifying the most popular or least popular
item. These limitations tend to restrict the interest and variety
of the contexts that are explored, and fail to engage children in
any significant mathematical thinking. Here are some alternative
suggestions taken from the NRICH website that offer a broader view
of data and ask some tricky questions about it.
Let us start with a simple question which would be suitable for a
group of children to tackle at Stage 1:
This question offers children some raw data that they have not had
to collect themselves. This has some advantages: the teacher knows
that everyone has the same information without worrying about the
accuracy of their recording methods. So, we have a data handling
problem that focuses on analysis rather than collection. Now the
children need to begin to make sense of the situation. It is
probably helpful to ask them to think about the pictures and to
talk to each other about whatthe problem means. Offer them plenty
of opportunities to think without insisting on quick answers. After
they have had this chance, find out their ideas and, if need be,
they can be encouraged to focus by asking them:
How many ladybirds does each child have?
From this point the question concentrates on how the data could be
represented to show how many ladybirds the different children have.
Be prepared to consider a variety of responses: the solutions do
not need to be bar charts or pictograms. Their suggestions will
provide insight into the children's own methods of recording.
Engaging in conversation with them about their representation may
be essential and is a great way to probe their previous experiences
of handling and recording data. On the website we post children's
solutions to our problems and we received an interesting
from one pupil as a way of representing the data.
The Pet Graph
is a question that has the representation of the
data done already.
This time the question is asking the children to work out how the
graph should be labelled. This type of task is often regarded as
being trivial by teachers and yet it involves crucial aspects of
To be successful pupils need to understand what the graph is saying
and relating that to the information they have been given. This
requires high level thinking, especially if you ask your pupils to
justify what they have done by asking questions such as:
"How do you know that ...?"
"Why can't the yellow bar represent ...?"
Which bar was the easiest to identify and why?
Later on in secondary school children often leave out the labels on
axes so rendering the representation meaningless. This question
would help children to realise the significance of the labels. It
also involves working with unknown quantities that are the
precursor to algebra. Once again the key approach involves
discussion and thought, and children should be encouraged to think
about the question and talk about it in pairs before a class
is another question with very different data, not
statistical this time, and appropriate for use with children at
Timetables are tricky things and they sometimes needcareful
thinking to make sense of them. As adults we often forget how many
conventions are involved in their presentation and we need to help
children to unpack the meanings in them. Once again the role of
thinking quietly and discussing the meanings in pairs before
voicing suggestions to a wider audience is vital. The teacher may
find it helpful to ask children about what is going on and how they
might represent the information in different ways. How about some
pictures of the buses on the road from A to B? At 0600 there are
just two buses starting off but what about at 0620, 0640, 0700 and
so on? What understanding do the children have of the
representations of time on the 24 hour clock? The
to the problems suggests that the children should:
"Draw a diagram of all the coaches on the road when this one sets
Once again there is a
from children posted on the website and they have
explained their reasoning as well as given the answer:
"The 10am coach will see the 8.40, 9.00, 9.20, 9.40, 10, 10.20,
10.40, 11, 11.20 coaches on its way to Betaville. Therefore it sees
9 coaches. We know this because they are travelling at the same
speed and on the same path."
Now for another question in a totally different context appropriate
for children at Stage 2.
is a very challenging problem and should stretch
even the highest attainers in the class. At the same time it is an
engaging scenario and should provoke some good discussion. This
time the data is in the form of a description.
So what exactly do we need to do? The problem is asking us to fill
in the letters of all the family members on the family tree. The
clues in the question are sufficient to do so. How could we
encourage children to start working on a solution? Once again
encouragement to think quietly, make jottings and discuss things
with a partner before embarking on class discussion will help to
raise the quality of mathematical thinking and reasoning. One of
the pitfalls is the tendency to think of the mathematicians as male
which obviously addresses issues of gender stereotyping.
Trying a similar problem with a group of children recently provoked
so much enthusiastic participation that they found it hard to wait
for a turn to write on the board. The kind of logical reasoning
that this requires is central to mathematical thinking and
reasoning and yet we tend to offer few opportunities to tackle
logical puzzles like this in school mathematics. The data handling
involved in this problem is easy to relate to and the
problem-setting engaging. These problems offer interesting contexts
in which to explore data handling and there are plenty more on
offer on NRICH from football results to codes.
This article first appeared in
Maths Coordinator's File issue 19, published by pfp publishing. To
find out how to subscribe to the Maths Coordinator's File,