Recording and Presentation in Mathematics
– some guidance from the Leicestershire Numeracy Team
The introduction of the National Numeracy Strategy has raised many issues about
children’s recording of mathematics, particularly in relation to the progression
from mental to written calculation. For some people the move away from
workbooks and worksheets has posed questions about what, when and where
children should be recording.
It’s worth considering the idea that mathematics is foremost an activity of the
mind and written calculations are an aid to that mental activity. The Numeracy
Strategy aims to develop children’s mental strategies alongside written methods
that derive from and support these mental methods. Learning written methods is
not the ultimate aim: the aim is for children to do mathematics in their heads and,
if the numbers are too large, to use ‘pencil and paper’ to help them keep track of
where they are in the calculation.
The OFSTED document ‘Inspecting Subjects 3-11: guidance for inspectors and
schools’ says;
‘At Key Stage 1, much of the learning involves oral, mental and practical work with
less emphasis on written recording. Consequently there may be little written
evidence for the youngest pupils. As pupils develop their mathematical skills, it is
important they record and use mathematical vocabulary, terminology and
symbolism. At Key Stage 1, you might find further evidence about progress…in
teachers’ records and by talking to pupils in each age group. At Key Stage 2, pupils
formally record mathematics more regularly.’
The same booklet also suggests the following questions to consider when analysing
children’s written work.
 Does the work show an appropriate use of personal recording and jottings to
aid calculation and problem solving?
 Do the pupils achieve appropriate accuracy?
 Is the work well presented?
 Are explanations clear?
The QCA booklet ‘Teaching Written Calculations’ suggests several reasons why
written methods may be useful. To illustrate the range and types of recording we
have used examples from the QCA booklets ‘Teaching Written Calculations’,
‘Teaching Mental Calculation Strategies’ and ‘Standards in Mathematics’.
There are many more examples of children’s recording in these booklets.
These give ideas about appropriate presentation and neatness.
Written methods can:
 represent work that has been done practically;

support mental calculations; (often in the form of jottings)

record and explain mental calculations;
5009+2476

help in observing patterns;
communicate ideas and information;


establish connections between practical experiences, symbols, language
and patterns;
Investigate ways of
arranging 36 cubes

help keep track of steps in longer tasks;
Have I been alive for a
million seconds?

develop mental imagery;

work out calculations which are too difficult to be done wholly mentally;

develop efficiency in calculation.
Efficient methods
Inefficient
methods
When do children need to start recording?
Children should be encouraged to see mathematics as a written as well as a spoken
language. Children will need to be introduced to the following aspects of recording
in relation to number.
 Developing the use of pictures and a mixture of words and symbols to present
numerical activities;
 Use of standard symbols and conventions (e.g. numbers 0-9, the equals sign,
operations signs);
 Use of jottings to aid a mental activity;
 Use of expanded forms of recording as a step towards standard pencil and
paper methods;
 Use of compact forms of recording;
 Use of a calculator.
From QCA
Teaching
Written
Calculation
It is important to encourage children, at all ages, to look first at the problem and
get them to decide which is the best method to choose – pictures, diagrams,
mental calculation with or without jottings, structured recording or calculator (in
years 5/6 for calculation purposes).
Some questions and thoughts you may wish to consider and discuss in your school.
What type of maths book do we/should we give children to record in? Will
this differ for different age groups?
You will need to consider whether squared books are the most appropriate books to
use in the light of the range of recording required by the strategy. There is a
danger that the use of squared books can cause children to focus on digits rather
than numbers as a whole. They are often less appropriate for recording
horizontally (particularly when the one square one number/letter rule is applied!)
and can encourage formulaic recording as well as restricting creativity. It is
interesting to note that none of the above examples of children’s recording are on
squared paper and all QCA and SATs questions are completed on plain paper.
Where else might children be recording?
Both in the mental and oral starter and the main part of the lesson children may be
recording on whiteboards, individual sheets of paper or large shared
boards/sheets. These recordings will often not be kept but do form a valuable part
of the children’s recording experience. This type of recording helps to reinforce
the very important link that children need to make between oral, mental and
written work. If a record is needed a simple copy of the main ideas can be
recorded in their books.
How neat does the work have to be?
While worksheets and workbooks may look ‘neat’, structured and ordered they
often require a limited use of mathematics, particularly when children simply fill in
an answer in an appropriate space. If this has been the predominant form of
recording children may find it difficult to develop their own recording methods as
they move through school. However through recording independently they are
developing their mathematical thinking and to help this a range of ways of
recording needs to be modelled by teachers. Overall presentation must fit in with
your school policy but shouldn’t be at the expense of including a range of recording
models such as jottings, which may or may not be understandable to the reader.
To facilitate this some schools divide pages in their book to provide a jotting area.
It is better to do this than have a separate book that removes the jottings from
the calculations/problems. Obviously teachers should expect children to be as
neat and careful as they can but this should not be at the expense of the
mathematics.
Now would be a good time to discuss the presentation of mathematics in your
school. The following questions may help you think about and justify your whole
staff decisions.
Should everything be dated and titled? What do you do in other subjects?
(Objectives make good, helpful titles).
When should pens, pencils, rubbers and rulers be used?
Is there a school policy for the layout of expanded and compact recording?
Is there appropriate paper for different types of graph/diagrams?
Have you got or do you provide photocopies of generic tables and charts for when
it is important to avoid unnecessary ‘drawing time’?
When should the method of recording be left to the children?
When should the teacher model a method of recording?
What do parents expect? Why? Who creates the expectation? How do we inform
them about methods within the strategy?
Do we need to reconsider the books we are using?
Where does the use of worksheets fit in?
Leicestershire Numeracy Team