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How Stern’s structural apparatus breaks
down the barriers to learning maths
The Structural Arithmetic programme was developed by mathematician and child psychologist, Dr Catherine
Stern. Structural materials are described by Bristow et al (1999) as a bridge into knowing and understanding
number.
Cognitive Learning Systems
Difficulties in learning mathematics
arise from one or more deficits in the
following cognitive learning systems:
• Discrimination ability
• Spatial ability
• Working and long-term memory
• Inter-sensory organisation
• Perceptual processing – both visual
and auditory
• Speech and language ability
• Sequencing ability
• Sustaining attention
During the spring term Highview
School in Kent began to use the Stern
maths programme with their Y6 and
Y7 classes. Whilst attending a Stern
Training Day the maths co-ordinator
was able to see and envisage the
impact the system could have on the
pupils in his particular educational
setting how Stern could be more than a
maths tool.
With a particular Year 7 pupil in
mind, student A, who has severe spatial
and visual discrimination difficulties,
was introduced to the Stern programme
with dramatic results.
“In the year 7 class I have been
focussing attention on the evident
support that the apparatus can give to
one child who has severe spatial and
visual discrimination delay. Initially he
was unable to place the blocks in the
correct ‘channels’ and later was unable
to copy the pattern boards and certainly
not with left/right completion.”
“When the materials were first used
with this pupil, I asked his art teacher
to also monitor his progress in this
subject in order to see if any changes
were noted. Over the course of the 2
spring terms he was able to sort the
blocks into their correct ‘channels’ and
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also master left/right sequencing and
accurate copying up to the ‘6’ pattern.”
An improvement in other curricula areas
has been demonstrated through the
development of this particular child’s
cognitive learning systems.
“This pupil’s art has shown
considerable progress so much so
that he won the end of term Senior Art
Award for the most progress shown
during the spring terms. Progress is
also being shown with his reading, for
obvious reasons, and he is currently
doing much to overcome ‘on/no’
reversals.”
“This I think is part of the benefit of
the materials and the activities namely
their cross curricula support because
as this pupil’s global discriminatory
skills increase these will feed back into
supporting his mathematic abilities.”
“As for the year 6 class they have
been using the materials at a ‘higher’
level to support 2 digit place value and
staff have been very pleased with the
children’s enjoyment of the equipment
and progress it has brought.”
Ken Pollock – Maths Co-ordinator
Typical barriers to learning, but
specifically prevalent in the acquisition
of maths skills, are:
• High levels of anxiety
• Emotions such as panic, switching
off, feeling stupid
• Being teased by their peers
• Avoidance tactics
• Frustration – when older pupils
realise that their peers are able to
do what they cannot.
materials too soon. This in turn, causes
further barriers to learning leading
to a catch twenty-two situation. All
pupils require a means of accessing
information in a non-threatening and
fun way to build levels of confidence
and self-esteem. Stern’s manipulatives
can take away the pressure pupil’s
experience – possibly every day in their
maths lessons?
Sensory experience is essential in
forming the imagery needed for
internalisation of learning. While we
are already familiar with VAK (visual,
auditory and kinaesthetic) as separate
learning styles, Prof. Usha Goswami’s
(Cambridge University), research
has shown that creating a learning
environment incorporating all three
produces the optimum impact for
learners.
Impact Learning – four routes
to transfer information from working
memory to long term memory
• Visual elaboration route
• Auditory route
• Kinaesthetic route
• Repetition route
Stern’s structural apparatus provides
unforgettable imagery,
therefore has visual
impact. There is
also sensori-motor
impact through
manipulation. The
The abstract nature of our number
system means that many children are
unable to access the maths curriculum
when moved away from concrete
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MATHS
activities provide progressive repetition.
There is opportunity for auditory and
visual input through the teacher’s
explanation; modelling; the child’s own
commentary to peers; the incorporation
of role play. This strengthens the child’s
own developing mental strategies
providing multi-sensory experience
from the formation of imagery, building
concepts and enhancing storage and
recall.
Pupils with specific processing
deficits have been shown to benefit
significantly from being immersed within
the Stern programme.
“I started using Stern’s Structural
Arithmetic with two boys in January
2008. One boy has severe global delay
and very little expressive language and
the other is severely autistic. They are
aged 9 and 8. Previously both boys
would join in number rote counts and
join in number rhymes with help but
had no basic understanding of abstract
mathematical concepts.”
“Since the introduction of the
scheme there has been a marked
improvement in both boys
understanding. In the first case the boy
is able to manipulate the blocks and
place them vertically in their assigned
place (At first they would be placed
horizontally and it took a good month
to teach him to do it correctly). He
recognises the order they should be in
and can match them to their twins.”
“With the autistic child who is
a visual learner, he has moved very
quickly through the first level (Stern)
and has developed an understanding
of ‘before’, ‘after’, ‘bigger’, ‘smaller’,
‘ordering’, ‘patterns’ and using
blocks to make 10’s. He has now put
number names to the blocks and
has developed an idea of addition
to 5. Modelling activities to learn
the language, which for him
is particularly difficult, and through his
actions rather than the use of language,
we can monitor his progress.
progress.”
“Both boys are developing
a fundamental understanding of
arithmetic concepts, which were lacking
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previously. It has also helped with their
fine-motor and thinking skills.”
Cynthia Jacobs - Kisheron Day School
London.
Stern has proved to be effective at any
age, or stage of development. It has the
ability to engage the learner’s interest,
adding to long term memory storage
effectiveness. It has the intrinsic
capacity to display relationships
between numbers clearly. The built-in,
self-checking element of the apparatus
automatically reinforces learning.
Overview of the Stern System
What is Stern Structural
Arithmetic?
Stern’s multi-sensory maths system was
designed to develop a child’s emergent
number sense by building-up number
knowledge and number facts and by
facilitating the understanding and use of
the four number operations. Since the
system is based on two tangible sets
of number representations, the blocks
and patterns promote a clear image
of number in the concrete enabling
pupil’s to discover for themselves all
of the attributes on a physical level.
When numerals are introduced they
correspond to the blocks and patterns
by embodying the intrinsic qualities and
values of those numerals.
Stern is an inclusive system
with proven success in early years
and AEN. It aids the development of
spatial thinking and reasoning, whether
children are measuring blocks or
working with patterns of cubes, they
are applying spatial thinking to help
them reason. Each experiment leaves
a mental picture to turn around in their
minds to explore new relationships.
Hand-eye coordination and oneto-one correspondence increases;
unfamiliar maths vocabulary can be
clarified by the practitioner through
concrete demonstrations and further
reinforced by the child’s actions with
the apparatus; by following spoken
directions children are able to develop
receptive language; this is a means of
assessing the child’s receptive
language acquisition and auditory
memory; a system of errorless learning
where misconceptions in the child’s
understanding will be seen immediately
and acted upon through further
demonstration and practice.
Catherine Stern had the vision to
develop a maths system ahead of its
time through tasks designed specifically
to be SMART.
• Specific progressive steps which
strengthens learning
• Measurable progress intrinsic to the
teaching methodology
• Achievable with built in elements for
success
- actively engages the child as
a learner
- promotes the interest of the
learner
- encourages expressive and
receptive language
- enhances short and long-term
memory
- develops opportunities for
speaking and listening
• Realistic concrete small stepped
programme incorporating scaffolded
learning
• Time related – level of progress
determined by individual
The ease with which practitioners are
able to administer Stern’s system and
speed of results, coupled with the
immediate engagement and genuine
enjoyment experienced by children is
testament to the effectiveness of this
maths programme. s
Vikki Horner and Libi Patterson
For Stern INSET Training Days, Talks and Demonstrations please contact Vikki at Maths
Extra on 01747 861 503 or E: [email protected] W: www.mathsextra.com
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