Teaching number skills and concepts with Numicon materials
Tony Wing and Romey Tacon
This paper discusses the use of Numicon number teaching materials with children with Down syndrome. The theory underlying the design of the materials is discussed, the teaching approach and methodology are described and evidence supporting effectiveness is outlined.
Wing T, Tacon R. Teaching number skills and concepts with Numicon materials. Down Syndrome Research and Practice. 2007;12(1);22-26.
Number ideas are very abstract, and children need to have these presented to
them in a wide variety of ways. In the Numicon approach we offer children
multi-sensory activities with patterned shapes, rods, number lines, and a broad
range of everyday experiences and contexts so that their understanding of number
ideas is very richly varied. We do not believe that any single approach or sets
of particular apparatus can be adequate in themselves, nor that children will
understand numbers just by working with 'figures'.
Figure 1 | Numicon number shapes representing
Very importantly in Numicon activities, children can physically combine all
patterns, rods, and everyday objects representing numbers with each other in
order that their calculating is made 'real'. For example the Numicon patterns
themselves physically fit together so that when combining numbers children can
physically 'do' the calculations that we want them to 'think'. As they
physically combine and compare these patterns they simultaneously 'see' the
effects of their actions, and as they speak about what they do and see, their
ability to internalise their actions, i.e. 'think with number ideas' gradually
becomes secure. In using the Numicon 'feely bag' children learn to relate their
physical handling of patterns to their visual impressions, and incorporate both
into their growing mental understanding of what number words and figures
actually mean; feeling, seeing, thinking, speaking, reading, and writing all
Figure 2 | Part of the Numicon
It is essential that children experience number in a wide range of ways and
situations because the wider their experiences the more they will be able to use
their understanding in new situations. And connecting their experiences with
each other always deepens their understanding greatly. Because children with
Down syndrome are relatively strong in their visual thinking, the Numicon
approach appeals to their strengths and relies much less on their auditory
capacities, with which they generally have more difficulty.
Again essential to Numicon is the belief that because number ideas are so
abstract and complex, most children will need to develop them in very small
steps. As adults who encountered these ideas long ago, most of us have forgotten
just how many times we felt puzzled or simply lost before we gave up and just
learned 'how to do sums' without having much of a clue as to what it all meant.
The Numicon programme of activities has been developed from innumerable
experiences with children in which they have shown us exactly how small many of
the steps need to be.
Finally, central to the Numicon approach is the conviction that when children
truly feel they understand numbers through physically doing and seeing
calculations, their personal self confidence with the ideas will be a key
support to them through increasingly difficult later learning. Confidence will
encourage perseverance, and perseverance brings success.
Figure 3 | Numicon pegs grouped to
show 16 as 1 ten and 6 units.
It is important that every child meeting Numicon for the first time learns the
Foundation activities. As the name suggests, these help children to establish
the foundation for success in number. All the materials needed for teaching the
Foundation activities are included in the Numicon Foundation Kit, including
twelve double-sided, illustrated activity cards which explain the teaching
activities. The activities are designed to build up children's skills in small
steps. In her recent book, Nye gives helpful suggestions for adapting the
activities to the specific needs of children with Down syndrome. Nearly all the
activities are designed as games so there is lots of opportunity for turn taking
and naturally showing the child what to do when the adult takes a turn;
helpfully this means that the activities play to the social strengths of
children with Down syndrome. Mathematical language is difficult for all
children, so the language that can be developed through each activity is shown
clearly on the cards. Of course Numicon is only part of the child's experience
with numbers, so on each of the activity cards there are suggestions for making
connections with other activities that reinforce the learning and help the child
to use and apply the new understanding. Importantly, from the very beginning,
children need to be learning and practising their counting alongside all Numicon
The Foundation activities fall into eight broad stages from the earliest
familiarisation with Numicon shapes and patterns to practical arithmetic. The
first activities are designed to introduce the Numicon shapes and for children
to learn to recognise the patterns without using number names or numerals,
although they may use number names independently. We suggest that this is
encouraged by displaying the Numicon number line which has pictures of Numicon
images linked to each number. Several parents have this up permanently where
their children can easily reach it. We suggest that children as young as
eighteen months can start to become familiar with Numicon, indeed some parents
have strung Numicon shapes on ribbons to hang on their children's pushchairs!
Figure 4 | Numicon shapes showing 3 plus 4 equals 7.
The next stage is for children to start to put the shapes in order, again
without using number names or numerals. To start with only the first four or
five shapes are ordered, gradually building up to ordering all ten. Ordering is
such an important activity for mathematical understanding that we suggest also
ordering a wide variety of objects so that children can learn the difficult
language of size, order and position while playing these activities.
The third stage is to give number names to the Numicon shapes, specifically
counting the holes in each shape, filling them with pegs and learning to
recognise the numerals. Children then move on to stage four where they order the
shapes and the numerals together. This is a huge step for many children and can
take some time to master; children are connecting their counting and ordering
skills, and as they match the appropriate numeral to each Numicon shape they are
learning to order numerals and shapes in relation to each other.
Stage five is really designed to consolidate all the learning achieved up to
this point. The activities are designed to help children to confidently
recognise Numicon shapes, use number names, recognise numerals, and make
connections between their varied counting experiences and the Numicon shapes.
Children are also encouraged to consciously visualise the shapes in their minds'
eye, preparing for the time when they will cease to rely on actual Numicon
shapes because they have a clear mental picture of number that they can use in
Children are now ready to begin to understand the structure our 'place value'
system so in stage 6 Numicon patterns are used to show how grouping counters
into patterns is an efficient way to find out and see 'how many' objects there
are in a collection. For instance, 16 objects can be arranged in a Numicon
ten-shape pattern and in the Numicon six-shape pattern.
Understanding place value is essential for later work when children learn to add
and subtract two and three digit numbers, decimals, money, percentages,
multiplication and division. All of which are important for basic numeracy life
Children now have a firm foundation for understanding the sizes and order of
numbers, and how numbers relate to one another. They can now begin to relate
addition to combining two or more Numicon shapes and learn to use the vocabulary
involved in adding.
In this seventh stage children meet their first mental arithmetic strategies: In
'One more' children can see with the Numicon shapes that if you add one to any
number it becomes the same as the next number; 'Doubles' are also introduced as
special combinations of two numbers.
Subtraction is introduced in the eighth and final stage of the Foundation Kit.
It is introduced first as taking away but as you can't actually 'take away' from
a piece of Numicon we use the idea of hiding a part of the Numicon shape. The
language involved in subtraction is also introduced on these cards. For instance
children see that when 1 is taken away from any number the preceding number is
always the answer. The tricky 'comparison and difference structure' of
subtraction (for example, what's the difference between 8 and 3?) is easily seen
by comparing two Numicon shapes.
Children are now ready to move on to Numicon Kit 1 which relates to the English
National Curriculum Levels 1 and 2 and the Primary Numeracy Strategy. To check
their children's progress and follow through the teaching programme parents can
refer to the Numicon Assessment Signposts and Record of Progress, available from
Numicon at a cost of £12.50. It is in Numicon Kit 1 that children begin to gain
sufficient mathematical understanding to start to understand money and work with
simple measures. In Kit 2 children start to work with higher numbers and so are
ready to work on measuring in metres and centimetres, litres and millilitres.
The Kit 2 work on introducing fractions and multiplication builds the skills
children need for learning to tell the time with understanding.
Parents and teachers often ask 'how long will it take to do the Foundation
activities?' and of course this will vary hugely from child to child, depending
on age and previous experiences as well as aptitude. Older children coming to
Numicon for the first time will sometimes move through the stages quite swiftly,
some very young children may take three years or more to cover them. What is
important to remember is that learning is not a race, every step is significant
and is to be celebrated and practised so that children build confidence and
positive attitudes. When children enjoy what they are learning they are very
likely to be successful. Parents of children with Down syndrome support one
another in the use of Numicon through their local associations and there is also
a very helpful international discussion group where parents share their
successes and questions firstname.lastname@example.org . Numicon has five training
consultants who specialise in Down syndrome, and full details of the training is
available from email@example.com .
The Numicon approach first began to be developed in 1996 (with UK government
funding) by practising teachers in mainstream schools as an approach that would
support children of all ages and abilities, and success was quickly shown in
dramatically improved SATs scores across the whole ability range
Devon Education Authority's Primary Maths Team later undertook their own
research project into the use of Numicon in mainstream schools during 2003-4,
and based upon the success of their findings published a booklet of guidance on
the use of Numicon for all Devon primary schools
. Apart from this original
work in mainstream schools however, several other local education authorities
(LEAs) have seen a particular advantage in using Numicon to support children
with a range of special educational needs, and have undertaken their own
research to test whether the approach really can help children who are finding
number work difficult.
Between 2001 and 2006, supported and scrutinised by their educational psychology
, and Brighton and Hove
 LEAs have all
independently undertaken teaching programmes based upon the Numicon approach for
children who were not succeeding with their school mathematics. Using standard
psychological tests to measure results, all studies showed notable improvements
in both children's scores and also very importantly in their personal confidence
and attitudes to number work. Currently Cambridge and Doncaster LEAs are also
trialling the Numicon approach with children with special educational needs, and
are reporting very encouraging initial feedback (including again, significantly
increased personal confidence in children) informally.
In the Wiltshire project the Numicon approach was used to support specifically
children with Down syndrome, and there the reporting educational psychologists
"..results to be extremely pleasing in view of the fact that (these) children do
not normally make one month's progress per month, yet the average gain exceeds
this, and many individuals have improved their skills at a much faster rate than
the average." (REF 4, p.4)
Down Syndrome Education International has been working with the Numicon approach
[6-14]. There have also been a number of reports about Numicon in the
national journal of the Association of Teachers of Mathematics, Mathematics
Jo Nye has recently reported
 on a carefully conducted research project
undertaken with 16 children with Down syndrome in Portsmouth, UK. The detailed
results from the first year of this project show that all children following the
Numicon approach made better progress than other children with Down syndrome not
using the system, whilst some children made considerably more progress than
their counterparts who were not using the Numicon approach. Other conclusions
were that, "[Numicon] enables teaching staff to 'see' what the child is
thinking, which is important for identifying both successes and confusions in
the child's understanding" (REF 1, p.3), and "Children are motivated to engage
with the materials as they are so attractive, and they develop confidence in
maths work as they can succeed with the materials" (REF 1, p.3).
A multi-sensory approach to arithmetic teaching that uses patterns that are
structured to encourage the understanding of number and number relationships.
The statutory teaching curriculum in England for pupils up to the age of 16. It
determines the content of what will be taught and sets attainment targets for
Primary National Strategy
A strategy to support teachers and schools to raise standards set out for
England by the UK government.
National Curriculum – Key Stages and levels
The English National Curriculum Key Stage 1 is for pupils aged 5-7 years, Key
Stage 2 for 7-11 years, Key Stage 3 for 11-14 years and Key Stage 4 for students
aged 14-16 years. The programmes of study also map out a scale of attainment
within the subject. In most Key Stage 1, 2, and 3 subjects, these attainment
targets are split into eight levels. By the end of Key Stage 1 (aged 7), most
typically developing children will have reached level 2, and by the end of Key
Stage 2 (aged 11), most will be at level 4.
SATs - Standard Attainment Tests
UK National Curriculum teacher assessments and Key Stage tests at the end of Key
Stages 1,2 and 3. These give parents and school information about how children
Relationship to UK Primary National Strategy
Since the Numicon approach was originally developed at the same time as the
introduction of the Primary National Numeracy Strategy, both Numicon and the UK
government have drawn upon the latest research available on mathematics learning
and teaching. Consequently there are key similarities between Numicon and the
approaches currently being undertaken in schools (not just in the UK), and this
has important implications for parents who wish their children with special
educational needs to be included as far as possible in mathematics work with
their classmates in schools.
Numicon activities are all cross-referenced to the number objectives of the
current Primary National Strategy, and both approaches address the number
requirements of the National Curriculum for Mathematics. (Incidentally, in
physically manipulating and combining the Numicon patterns children address many
of the 'shape and space' objectives as well.) The 'Problem Solving' activities
in the Numicon approach closely relate to the categories of problems in the
National Strategy, and also to the 'Using and Applying' sections of the National
Very importantly, both the Numicon and Primary Strategy approaches place great
emphasis upon the use of visual 'number lines' as central to all children's
understanding of number, as well as encouraging as wide as possible a variety of
other 'models and images' for numbers. This means that children working with
Numicon and its distinctive number lines are developing a mental imagery for
numbers that is closely related to that offered in schools for all children.
Interestingly also, as many teachers begin to realise that what works with
children with special educational needs is also usually good mathematics
teaching for all children, a rapidly increasing number of schools are
introducing Numicon and making it part of the normal everyday classroom scene
A further vital connection between the Numicon and Primary National Strategy
approaches is the shared emphasis upon mental arithmetic and how to write down
the answers to sums. Because we nowadays ask children to first do sums in their
heads (using their mental images), then to say how they did them, and finally to
learn how to write down what they have done, children learn first to say, and
then to write what are called 'number sentences', e.g.
13 + 5 = 18
This is very different from the Victorian approach most of us learned in
schools, called 'tens and units' column recording. 'Tens and units' work was
based on a 19th century approach to arithmetic, well before electronic
calculators were envisaged, and when every child had to do calculations with
paper and pencil from the beginning of their schooling. Modern teaching is based
upon children learning mental arithmetic first, and only later learning to do
complicated calculations on paper. Consequently, our ways of writing out 'sums'
has needed to change to reflect our modern emphasis upon mental arithmetic.
Background of developers and trainers
The developers of the Numicon approach are all graduate (and post-graduate) UK
qualified teachers with between them some 85 years experience teaching
mathematics to children and students of all abilities, from nursery settings
through to university level. Until very recently, all were full time teachers
working in schools and university implementing the National Numeracy Strategy
with children of all abilities – which of course is the challenging context in
which the Numicon approach was first developed.
Five of the team of Numicon consultants who undertake training in the use of the
approach are experienced in teaching children with Down syndrome and three of
them are themselves parents of children who have Down syndrome. All the Numicon
consultants are, like the authors, formally qualified teachers with a great deal
of successful experience teaching mathematics in schools, with one exception –
Dr Joanna Nye (formerly at Down Syndrome Education International) is a practising
research psychologist at the University of Bristol, UK.
Box 1 | Materials required and costs
To begin with an individual user would need to buy the Numicon Single User
Foundation Kit @ £86 + VAT. As the child begins to make progress with this first
stage, it would be helpful to buy also a set of Number Rods @ £30 + VAT.
The Numicon Kit 1 Plus Pack then supports the middle phase of the Numicon
programme, and this currently costs £76 + VAT.
The current final phase of the Numicon programme is supported with the Numicon
Kit 2 Plus Pack @ £64 + VAT.
Thus the current whole Numicon programme, taking the learner from the first
introduction to basic number ideas through addition, subtraction,
multiplication, division, and problem solving, would cost £256 + VAT to support
an individual learner.
The cost to a school for the equivalent whole class kits would be:
Foundation Class Kit @ £120 + VAT
Kit 1 Class @ £160 + VAT
Kit 2 Class @ £180 + VAT
A set of Number Rods £30 + VAT.
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Received: 2 February 2007; Accepted 14 February 2007; Published online: 30