Dyscalculia and Specific Difficulties in Mathematics
Guidance Document
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
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.
There is a growing acceptance within the research world that there are some pupils who present:
Ø Dyslexic characteristics
Ø Dyscalculic characteristics
Ø Aspects of both conditions
Ø 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:
· 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)
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
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
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.
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 byHigh 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
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 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
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
Strategies to Address key Difficulties
Strategies to address the difficulties / Practical ideas for the classroomLink mathematics to familiar and relevant contexts / · 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”
Avoid moving a child onto higher level tasks before easier levels have been fully understood / · 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
Give pupils explicit instructions in strategy and then guide/support their practise / · Chunking instructions
· Scaffolding activity
· 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 models / · 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
Strategies to address the difficulties / Practical ideas for the classroom
Encourage children to discuss and explain in order to support development of their mathematical understanding / · 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
Encourage them to make choices about methods used / · 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
Use peer tutoring / · Mixed ability groups
· Partner work
· Collaborative approaches e.g. snowball
Support accurate recording by providing squared paper/prepared formats / · 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
· Allow 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
Strategies to address the difficulties / Practical ideas for the classroom
Establish a routine of ‘estimate – calculate – check’ / · 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 / · STC to support vocabulary
· Interactive whiteboard display
· Vocabulary walls
· Games e.g. matching symbols to meanings
Take time to explain vocabulary and check understanding / · 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
Provide time for practice and consolidation at each stage / · 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
Self-esteem, Confidence and Maths