Approaches to Recording in Calculations in the Primary School
– informal to formal methods
To ensure continuity and consistency it is recommended that your school decides on a
policy for teaching written methods.
The Primary National Strategy stresses the need for children to develop sound mental
calculation strategies and the approach that the Framework for mathematics takes to
recording is based on making a smooth transition from these to standard written methods.
The mental methods in the Primary Framework for Mathematics should be taught
systematically from Reception onwards and pupils need to be provided with regular
opportunities to develop the necessary skills. However, mental calculation is not at the
exclusion of written recording and should be seen as complementary to and not as separate
from it. There is an element of mental processing in every written method and it is important
that these links are made. It is crucial that written recording helps children to clarify their
thinking and supports and extends their development of more fluent and efficient mental
strategies.
This policy concentrates on the introduction of standard symbols, the use of empty number
lines to aid mental calculation and the introduction of other pencil and paper procedures.
Children should not abandon jottings and mental methods once other more formal methods
have been introduced. Children need to be encouraged to look at a calculation or problem
and then decide which is the best method to choose: pictures, mental calculations with or
without jottings, formal methods or use of a calculator.
The following whole school policy is only an example of what your school’s approach to
teaching calculation might be. It is very important that the approach taken is discussed
and agreed by the whole staff to ensure continuity and progression throughout the
primary phase.
You can begin the process with this sample policy, which will allow you to adapt, amend
adjust it to the needs of your school.
There are certain points that will need particular consideration:
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Will work in books reflect the school’s calculation policy? Is there an appropriate number
of calculations, and care taken not to give too much ‘drill and practice’?
Will calculations be presented horizontally so that children can make a choice about which
is the most effective and efficient method of calculation?
Will there be evidence that children have had opportunities to make informed choices
about methods of calculation?
Is your school going to teach expanded recording of addition? How and when? When will
you move on to compact recording?
Are you going to teach decomposition? Are you going to introduce it by teaching
expanded deposition first? If so, when will you start? When will you begin to teach a
compact method?
Will you begin to teach multiplication by partitioning? Will you teach the ‘grid method’?
When will you begin to teach the compact method and will you record as an expanded
method first?
Will you teach recording for division by repeated addition or subtraction leading on to
‘chunking’ as outlined in the sample policy? Will you teach the common standard method
of recording (which isn’t in the Framework)?
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How will you inform the teacher who takes the children the following year which methods
of recording different children were able to do effectively, efficiently and appropriately?
Through records passed on? Through pupils’ work?
What are the strategies employed to ensure that the children continue to develop mental
skills and use them as a method of first resort?
How are the needs of the less and more able children catered for?