Learning
Support
Service
Dyscalculia and
Specific Difficulties
in Mathematics
Guidance
Document
Learning Support Service
January 2015
Contents
1. Introduction
2. Identification and Assessment
3. Identifying Pupils with Specific Learning Difficulties in Mathematics
4. Circles of Inclusion
5. Barriers to Learning and Strategies to Support
6. Self Esteem
7. Supporting your Child at Home
8. References
Learning Support Service
January 2015
Dyscalculia and Specific Difficulties in Mathematics
Guidance Document
The purpose of this document is to increase the knowledge and
understanding of teachers and teaching assistants when working with pupils
with specific difficulties in Maths.
What is Dyscalculia?
Dyscalculia is described as an ‘unexpected’ difficulty that some people have
in dealing with mathematical problems (Tony Attwood).
‘Dyscalculia is a condition that affects the ability to acquire arithmetical skills.
Dyscalculic learners may have difficulty understanding simple number
concepts, lack an intuitive grasp of number, and have problems learning
number facts and procedures. Even if they produce a correct answer or use a
correct method, they may do so mechanically and without confidence.’
Guidance to Support pupils with Dyslexia and Dyscalculia
Ref: DfES 0512/2001
It is most helpful to see dyscalculia as at the severe end of a mathematical
learning difficulties spectrum.
Key researchers into dyscalculia including Butterworth, Dehaene and Miles
have described dyscalculia as a deficit in the ability to represent numerosities.
In particular they refer to an inability to subitise (state the number of objects in
a group without resorting to a counting in one’s approach) and a weakness in
comparing the number magnitude or value of individual numbers.
When looking at identifying dyscalculia Thambirajah (2011) has suggested
that the following four key points should be considered:
1. Difficulties with understanding quantities or carrying out basic
arithmetic operations inconsistent with the person’s chronological age,
educational opportunities or intellectual abilities.
2. The severity of the difficulty is substantial as assessed by standardised
measures of these skills (at the 5th percentile of achievement) or by
academic performance (two school years behind peers) and is
persistent.
3. There is significant interference with academic achievements and the
activities of daily living that require mathematical skills.
4. The arithmetic difficulties are present from an early age and are not
due to visual, hearing or neurological causes or lack of schooling.
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January 2015
There is a growing acceptance within the research world that there are some
pupils who present:
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Dyslexic characteristics
Dyscalculic characteristics
Aspects of both conditions
Aspects of both conditions, but are actually experiencing the side effects of
dyslexia, rather than ‘pure’ dyscalculia.
Purely dyscalculic learners who have difficulties only with number will have
cognitive and language abilities in the normal range, and may excel in non
mathematical subjects. It is more likely that difficulties with Numeracy
accompany the language difficulties of dyslexia.
Professor Brian Butterworth proposes that the current (2001) best estimates
indicate a prevalence of between 3% and 6% of the population. These
estimates are derived from the proportion of children who have special
difficulty with maths despite good performance in other curriculum areas.
Understanding of the nature of Dyscalculia and its implications in the
classroom is some way behind research into other Specific Learning
Difficulties such as Dyslexia and Dyspraxia.
Difficulties with some Mathematical concepts can also be found in students
with Dyslexia, with Specific Language Difficulties and in students with low
cognitive ability. Therefore it is sometimes hard to separate what is at the
root of the problem and allocate a single label to explain the difficulty.
The SEN Code of Practice (2014) emphasises the need for early identification
and for the use of well founded interventions. Anne Dowker’s publication
‘What Works for Children with Mathematical Difficulties’ highlighted the
following evidenced based maths interventions and approaches:
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Training in Metacognition
Using Derived Fact Strategies
Mathematics Recovery (www.mathsrecovery.org.uk)
Other evidence based maths interventions include:
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Accelerated Math (www.renlearn.co.uk/accelerated-maths/)
FASTT Math (www.teacher.scholastic.com/math-fact-fluency/fasttmath-next-generation/)
Catch-Up Numeracy
Numicon
Numbers Count
Rapid Maths
Other maths interventions, without, at present, accompanying robust research
to validate their efficacy include:
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January 2015
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Nippy Numbers
Beat Dyscalculia
Dynamo Maths
Max’s Marvellous Maths
Schools will develop systems through effective provision planning to ensure
that pupils with difficulties in maths are supported by:
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a whole school approach
an appropriate curriculum
flexible support
opportunities to celebrate success
close links between home and school
opportunities for the student to increase their understanding of the
nature of their learning difference and the opportunity to say what
works for them
targeted interventions
These targeted approaches/interventions should be organised in schools in a
variety of ways including:
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the use of teaching techniques to maximise inclusion and access to
the curriculum i.e. a dyslexia friendly classroom environment (Wave 1)
targeted small group work delivering support for areas of weakness in
the learning profile (Wave 2)
one to one sessions to provide intensive time limited intervention
programmes (Wave 3)
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January 2015
Identification and Assessment of Pupils experiencing Specific Learning
Difficulties in Maths
A variety of methods should be used to collect and gather information about
the barriers to effective learning experienced by a pupil with this type of
learning difficulty.
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Informal observation of the student in the learning environment on a
daily basis using Assessment for Learning and Assessing Pupil
Progress.
Discussion with the pupil, the parents or carers, teacher, teaching
assistants.
Individual Diagnostic Assessment e.g. Wave 3 Numeracy Materials,
Diagnostic Interviews, Sandwell Assessments, MaLT (Mathematical
assessment for Learning and Teaching)
Dyscalculia Screener
Brian Butterworth 2003
This is a computer based assessment tool that indicates Dyscalculic
tendencies by measuring pupil response times as well as the accuracy of the
answers. It can be used with pupils aged 6-14 years and takes approximately
30-35 minutes to administer. The screener has been developed based on the
hypothesis that pupils with dyscalculia have deficits in even the simplest
number concepts. Butterworth feels that this should help to distinguish pupils
with dyscalculia from those who are simply weak at maths for other reasons.
However, it is worth keeping in mind when considering the use of this
screening test that:
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Screening tests are a starting point and should not be used in isolation
The results of this type of test should be considered in conjunction with
all other formative and summative assessments recorded over time
and should be used to add to the profile of strengths and weaknesses
to help build up a picture of the learner
A poor score on this assessment in itself does not provide sufficient
evidence to state categorically that an individual has dyscalculia
You will also have to think about:
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How you will share the results of the test
What action will be taken after the screening
Whether there are resources available to support the action
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January 2015
Barriers to Learning in Maths:
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Visual Difficulties
Directional Difficulties
Sequencing
Short Term Memory
Working Memory
Long Term Memory
Vocabulary of Maths
Language of Maths
Organisation
Speed of Working
Thinking Styles
Structure and Style of the Curriculum
Anxiety/ Stress
Motivation
Learning Support Service
January 2015
Indicators of Dyscalculia
(Taken from www.unicornmaths.com )
Indicators of dyscalculia can be seen as specifically mathematical and also as
life skill difficulties brought on by lack of mathematical proficiency and the
weakness of underlying skills needed for the development of mathematical
understanding.
Specifically mathematical difficulties would include:
 Inability to tell which of two numbers was larger
 Frequent difficulties with arithmetic – confusing operation signs + - x ÷
=
 Reliance on ‘counting on’ strategy and using fingers rather than more
efficient mental arithmetic strategies
 Times table difficulties
 Mental arithmetic difficulties
 Difficulties mentally estimating measurements of an object or distance
 Inability to grasp or remember mathematical concepts, rules, formulae
and sequences
Generally observed life skill difficulties would include:
 Difficulties in activities requiring sequential processing, from the
physical, such as dance steps, to the abstract, reading, writing, and
signalling things in the right order.
 Difficulties with everyday tasks like checking change and reading
analogue clocks.
 Inability to comprehend financial planning or budgeting such as
estimating the cost of items on a shopping list or balancing an account.
 Difficulties in conceptualising time and judging the passing of time.
 Problems differentiating between left and right.
 Having a poor sense of direction and difficulties navigating or ‘mentally’
turning a map to face the current direction rather than common north.
 Difficulty keeping score during games.
These difficulties may lead to a phobia of mathematics and mathematical
devices.
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January 2015
A checklist for Identifying Pupils with Specific Learning Difficulties in
maths (including Dyscalculia)
Use this checklist to identify areas of difficulty and how it has been observed.
‘Evidenced by’ key:
CO Classroom Observation
WS Work Sampling
IDA Individual Diagnostic Assessment
Impact on Life Skills
Evidenced
by
High level of anxiety around maths
Lacks confidence in working with number
Left /right confusion
A problem with all aspects of money
A marked delay in learning to read a clock to tell the time
An inability to manage time in their daily lives
Slow processing speeds when engaged in maths activities
A tendency not to notice patterns in number
Inability to master timetables and manage time in their daily
lives
Difficulty in remembering to work in the same unit of measure
within a question
Impact on Self Esteem
Finds it difficult to ask questions even when he or she does not
understand
Slow in working in comparison with others
Lacks confidence in their own answers
May adopt avoidance/ learned helplessness strategies
Dislikes whole group interactive sessions
Number
Difficulties with mental calculation
Uses fingers to count simple totals
Inability to subitise (see without counting) even very small
quantities
Inability to estimate whether a numerical answer is reasonable
Needs to continue to use concrete materials as is unable to
work in the abstract
Finds it difficult to count on
Difficulty copying numbers accurately (reverses or inverts
digits)
Difficulty with place value (misreads numbers 36/63)
Inability to count backwards reliably
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January 2015
Difficulty writing numbers that contain zeros e.g. 4021
Lack of ability to make ‘one to one’ correspondence when
counting objects
Not ‘see’ immediately that, for example, 7+5 is the same as
5+7
Finds it difficult to count fluently less familiar sequences such
as 1,3,5,7,9etc
Fail to see the relationship between addition and subtraction
and multiplication and division
Uses maths procedures mechanically without understanding
Language of Maths
Finds it difficult to explain mathematical processes
Has problems choosing the right strategy to unpick a word
problem
Has sound technical reading skills but fails to understand the
mathematical language
Difficult to generalise learning from one situation to another
Makes mistakes interpreting a word problem
Confuses mathematical terms e.g. total, sum, equals
Memory Difficulties
Finds it difficult to learn and retain basic number factsincluding times tables or can only recall the x2, x5 and x10
table facts
Finds it difficult to learn and retain what basic maths symbols
mean, including Maths rules, formulae and abbreviations
Loses track of the ‘sum’ when completing a longer word
problem
Forgets previously mastered procedures
Difficulties with Sequencing
Has difficulty sequencing the order and the value of numbers
Loses place/ track when counting
Difficulty reciting the times tables
Difficulties with position, spatial organisation and visual
perception
Confuses numbers and uses them interchangeably e.g. 12 and
21
Confuses basic symbols e.g. + and x
Poor setting out of work and calculations on the page often
resulting in errors
Does not see the difference between 6-4 and 4-6
Takes the smaller number form the larger regardless of
position
Finds estimating and rounding numbers difficult
Finds telling the time on an analogue clock difficult and may
have poor understanding relating to the passage of time
Is easily distracted/overloaded by worksheets full of maths
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January 2015
Copies inaccurately
Confuses the axes on graphs and co-ordinates
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Dyscalculia Lesson Checklist (Based on the British Dyslexia
Association’s lesson checklist)
Planning
Resources made available to use as appropriate e.g. squared paper, table
squares, number lines, procedural examples, counters, money, Numicon,
Cuisenaire Rods, Base ten materials, Stern blocks.
Classroom layout purposefully planned taking into consideration factors such
as:
 Style of lesson
 Use of buddies
 Use of ICT
 Use of minimum distraction areas
Classroom
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Displays are relevant, recent and not over-cluttered
There is a low distraction area available
A range of concrete apparatus is made available for children to use
The Lesson
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Content of previous lesson is reviewed
Objectives for the lesson are outlined
New vocabulary is displayed and explained
The number of instructions given is limited
Adaptations made to support children with memory problems such as
flow chart reminders or sticky notes
Greater response time given to help slower processors and the use of
personal whiteboards to show rather than shouting out answers
If written work is required, worksheets are modified to acknowledge
different working speeds
Children are encouraged to discuss and verbalise their thinking and
decision making
ICT is available and its appropriate use is encouraged
Lesson objectives reviewed
Homework and Marking
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Worksheets and text books are not over-cluttered
Pupils do the first two questions of any homework sheet before taking it
home to check understanding and ensure that they do not go away and
practise wrong methods
Marking is constructive and diagnostic wherever possible
Marks are not read out to the whole class
Learning Support Service
January 2015
Strategies to Address key Difficulties
Strategies to address the difficulties
Link mathematics to familiar and
relevant contexts
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Avoid moving a child onto higher level 
tasks before easier levels have been
fully understand
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Give pupils explicit instructions in
strategy and then guide/support their
practise
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Use a variety of objects, images and
models
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Learning Support Service
Practical ideas for the classroom
Practical activities e.g. class shop,
measuring for cooking
League tables e.g. football
Use of both indoor and outdoor
resources e.g. playground
Locate number problems in real
situations that have meaning for
the pupil, e.g. “two more toys”
rather than the abstract “two
more” or the unimaginable “two
more metres per second”
Give plenty of time at the early
stages before moving on.
Revisit basic activities often.
Use appropriate visual/concrete
materials
Start by doing something
concretely, before recording the
maths in writing
Remember that work with
concrete materials should come
before diagrams, and that pictures
and diagrams are the transitional
stage between concrete and
abstract work.
Chunking instructions
Scaffolding activity
Visual support/use of STC
Help box with resources e.g.
number square,
Interactive white board to
demonstrate
Numicon
Resources appropriate to the
activity e.g. 100 square, bead
string
Consider different learning styles
Help box on each table as part of
normal classroom practice
January 2015
Strategies to address the difficulties
Encourage children to discuss and
explain in order to support
development of their mathematical
understanding
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Encourage them to make choices
about methods used
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Use peer tutoring
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Support accurate recording by
providing squared paper/prepared
formats
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Learning Support Service
Practical ideas for the classroom
Group work
Pupils explain/demonstrate the
steps they took to the class
Prompt questions e.g. what is the
question asking you to do?
Visual display of the process
Brain storm ideas
Discuss learning styles
Demonstrate how to solve the
problem using different methods
Encourage alternative strategies
Use a range of teaching methods
Have a range of resources
available for pupils to choose from
Ask, “How would you approach
this?”
Interactive displays
Problem solving
Mixed ability groups
Partner work
Collaborative approaches e.g.
snowball
Provide grids, graphs etc
STC format to support recording
Try squared paper of variously
sized squares until a suitable one
is found
Offer a worksheet where the
writing demands are minimised
Raised line paper
Talking Tins
Providing plastic numerals/cards
so pupil does not have to write
Although the pupil opportunities to
talk through his methods so he
can show his abilities
When copying from the board,
offer notes, allow him to photocopy
the notes from a student who
produces good notes
If the materials is in a text book,
allow him to highlight key areas
January 2015
Strategies to address the difficulties
Establish a routine of ‘estimate –
calculate – check’
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Practical ideas for the classroom
Make this normal classroom
practice
Classroom display of process
STC symbol prompt on table
Regular reminders
Use peers to demonstrate
Display maths terms and symbols
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STC to support vocabulary
Interactive whiteboard display
Vocabulary walls
Games e.g. matching symbols to
meanings
Take time to explain vocabulary and
check understanding
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Pupils explain to each other/class
Vary the mathematical vocabulary,
e.g. use ‘subtract’, ‘less than’,
‘decrease’ or ‘minus’, as well as
'take away’
Displays
Barrier games
Word walls
Personal vocabulary books
Games
Booster groups
Regular 5 minutes practice time
Use of plenary
Real life scenarios to enable
pupils to link ideas and
consolidate
Collaborative activities e.g.
carousel, cocktail party
‘Jog your memory’ cards
Provide time for practice and
consolidation at each stage
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Learning Support Service
January 2015
Self-esteem, Confidence and Maths
Confidence is a critical ingredient for successful learning. This is especially
true for young people with difficulties in maths where it can quite simply mean
a difference between success and failure.
Supporting learners to feel good about themselves and to appreciate their
pattern of strengths and weaknesses is a building block of effective classroom
management.
(Neil Mackay ‘Removing Dyslexia as a Barrier to Achievement’ 2005)
Teaching methods’ which create effective learning environments;
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value the contributions of all pupils
ensure pupils feel secure and able to contribute appropriately
are appropriately paced and planned and monitored so that all pupils
have a chance to learn effectively and achieve success.
allow for different learning styles, encouraging children to demonstrate
what they know through different means
provide positive feedback
allow time for the pupil to engage with the learning
are planned to engage all children with easily achievable goals
Confidence
Pupil’s confidence in maths will only come through the experience of success.
Children may be confident of their ability in other areas but this does not
necessarily transfer into others.
The links between confidence and motivation are strong. It is easy to spot
confident children who begin a task straight away whilst the children with low
self-confidence will more often be low in motivation and application.
Stress in maths
It has been suggested that 80% of learning difficulties have been attributed to
stress. Stress in turn may be caused by a fear of disapproval, failure from a
past experience, and fear surrounding tests and exams.
Success in maths requires controlled, orderly and sustained thinking which is
unfortunately quite vulnerable to disruption by anxiety. Pupils with dyscalculia
are at high risk of anxiety related learning difficulties. This can only be
exacerbated if the child becomes anxious about failure.
Learning Support Service
January 2015
Supporting your Child with Maths at Home
It is important to talk to your child’s teacher about the methods that are used
in school and the terminology being used, so that if you help your child with
school maths you are working along the same lines as the teacher and not
confusing your child.
General help at home- use Maths in everyday activities such as:
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Encourage your child to use money when shopping
Ask your child to estimate the cost of buying items such as milk or
bread
Measure ingredients when cooking
Talk about different ways of measuring e.g. measuring the materials
required for model making, filling the bath-estimate how many litres of
water in the bath etc.
Sing counting songs and rhymes, chant times tables.
Talk about number in everyday life, e.g. when driving look at road
signs, in restaurants look at the menu, calories in food, names of solid
shapes e.g. cube, cone, sphere.
Try to encourage the use of mathematical language such as more,
less, greater, smaller, lighter, heavier.
Becoming familiar with telling the time and being aware of the passage
of time e.g. using clocks, timetables, calendars so that the children
understand the concept of a day, week, month, year. Use TV
magazines to look at the times of their favourite programmes.
Writing/drawing numbers, playing with shapes through games and
activities.
Use objects, coins and counters to help your child practically with
counting.
Use computer software/Ipads/Apps such as ‘Wuzzit Trouble’ and
‘Motion Math’ and games from websites such as
www.mathbreakers.com
When you watch a sport programme talk about the scoring, league
tables etc.
Be patient and allow your child plenty of ‘thinking’ time.
Try to make maths fun!
Learning Support Service
January 2015
References
Bird R. (2007) The Dyscalculia Toolkit. London: Paul Chapman Publishing
Butterworth, B (2003) Dyscalculia Screener. London: NFER Nelson
Butterworth B and Yeo D (2004) Dyscalculia Guidance London: NFER Nelson
Chinn, SJ (2004) The Trouble with Maths: A Practical Guide to Helping
Learners with Numeracy Difficulties. London: Routledge Falmer
Chinn, S. (2012) More Trouble with Maths, Oxon: Routledge.
Chinn, S. (2012) Maths Learning Difficulties, Dyslexia and Dyscalculia,
Bracknell: British Dyslexia Association
Clayton P. (2003) How to Develop Numeracy in Children with Dyslexia
Cambs: LDA
DCFS(2001) Guidance to Support Pupils with Dyslexia and Dyscalculia.
0512/2001
DCFS – Supporting Children with Gaps in their Mathematical Understanding –
1168-2005 G
Dowker, A.(2004) What Works for Children with Mathematical Difficulties,
DFES
Emerson, J. & Babtie, P. (2010) The Dyscalculia Assessment, London:
Continuum International Publishing
Gifford, S., & Rockliffe, F. (2008) ‘In search of Dyscalculia,’ in Joubert, M (ed)
Proceedings of the British Society for Research into Learning Mathematics,
28 (1), 21-26
Hannel G.(2005) Dyscalculia Action Plans for Successful Learning in
Mathematics: Oxon: David Fulton Publishers
Henderson A, Came, F and Brough M. (2003) Working with Dyscalculia
Recognising Dyscalculia, Overcoming Barriers to Learning in Maths. Wiltshire:
Learning Works
Kroeger, L., Brown, R., & O’Brien, B. (2012) Connecting Neuroscience,
Cognitive and Educational Theories and Research to Practice: A Review of
Mathematics Intervention Programmes, Early Education and Development,
23, 37-58.
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Thambirajah, M.S. (2011) Developmental Assessment of the School-aged
Child with Developmental Disabilities, London: Jessica Kingsley.
Yeo, D. (2003) Dyslexia , Dyspraxia and Mathematics, London: Whurr
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