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.

Learning Support Service January 2015 There is a growing acceptance within the research world that there are some pupils who present:

 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:

 Training in Metacognition  Using Derived Fact Strategies  Mathematics Recovery (www.mathsrecovery.org.uk)

Other evidence based maths interventions include:

 Accelerated Math (www.renlearn.co.uk/accelerated-maths/)  FASTT Math (www.teacher.scholastic.com/math-fact-fluency/fastt- math-next-generation/)  Catch-Up Numeracy  Numicon  Numbers Count  Rapid Maths

Other maths interventions, without, at present, accompanying robust research to validate their efficacy include:

Learning Support Service January 2015  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:

 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:

 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)

Learning Support Service 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.

 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:

 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:

 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

Learning Support Service January 2015 Barriers to Learning in Maths:

 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.

Learning Support Service 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

Learning Support Service January 2015 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 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 facts- including 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

Learning Support Service January 2015 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 Copies inaccurately Confuses the axes on graphs and co-ordinates

Learning Support Service January 2015 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

 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

 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

 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 Practical ideas for the classroom Link mathematics to familiar and  Practical activities e.g. class shop, relevant contexts 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”

Avoid moving a child onto higher level  Give plenty of time at the early tasks before easier levels have been stages before moving on. fully understand  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.

Give pupils explicit instructions in  Chunking instructions strategy and then guide/support their  Scaffolding activity practise  Visual support/use of STC  Help box with resources e.g. number square,  Interactive white board to demonstrate

Use a variety of objects, images and  Numicon models  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

Learning Support Service January 2015 Strategies to address the difficulties Practical ideas for the classroom Encourage children to discuss and  Group work explain in order to support  Pupils explain/demonstrate the development of their mathematical steps they took to the class understanding  Prompt questions e.g. what is the question asking you to do?  Visual display of the process  Brain storm ideas

Encourage them to make choices  Discuss learning styles about methods used  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 Use peer tutoring  Mixed ability groups  Partner work  Collaborative approaches e.g. snowball

Support accurate recording by  Provide grids, graphs etc providing squared paper/prepared  STC format to support recording formats  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,

Learning Support Service January 2015 allow him to highlight key areas

Strategies to address the difficulties Practical ideas for the classroom Establish a routine of ‘estimate –  Make this normal classroom calculate – check’ practice  Classroom display of process  STC symbol prompt on table  Regular reminders  Use peers to demonstrate

Display maths terms and symbols  STC to support vocabulary  Interactive whiteboard display  Vocabulary walls  Games e.g. matching symbols to meanings

Take time to explain vocabulary and  Pupils explain to each other/class check understanding  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 Provide time for practice and  Booster groups consolidation at each stage  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

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;

 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:

 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.

Learning Support Service January 2015 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

Learning Support Service January 2015