# What is Dyscalculia?

DYSCALCULIA is a specific learning difficulty with mathematics, primarily arithmetic. It was defined in a UK Government document in 2001 as: 'Dyscalculia is a condition that affects the ability to acquire mathematical skills. Dyscalculic learners may have a difficulty understanding simple number concepts, lack an intuitive grasp of numbers, 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.'

It is defined in the USA (Diagnostic and Statistical Manual of Mental Disorders, 2013) as:

'Difficulties in production or comprehension of quantities, numerical symbols, or basic arithmetic operations that are not consistent with the person's chronological age, educational opportunities, or intellectual abilities.'

Research into dyscalculia has lagged far behind research into dyslexia, but this is beginning to even out. The new powerful neurological tools are shedding new light on this difficulty. Despite this, our understanding of dyscalculia lags behind our knowledge of dyslexia. However, researchers agree that there is no single profile. There are many contributing factors. It is described as a heterogeneous problem which is compounded by the constellation of demands made by maths.

Bearing this in mind, the estimate of people who are dyscalculic is around 5%. There will be a spectrum of maths difficulties. A UK survey into young adults suggests that about 22% are functionally innumerate. My own research suggests some startlingly depressing statistics of success rates for basic problems in a wide range of topics, for example, multiplication and fractions. Again, the research is not definitive, but it some research suggests that the occurrence of dyscalculia is the same for girls and boys, and may even be more prevalent in girls.

#### Impact

Whilst it is socially acceptable to say, 'I'm hopeless at maths' and for people to accept that statement without criticism, it doesn't mean that there are no everyday problems that are a consequence of those difficulties with maths. Obviously, there may be problems with finances and money, time management, remembering sequences of numbers (for example, phone numbers, pin numbers), reading timetables, correctly diluting medicines, speed of calculating and achieving the maths qualifications needed to enter many professions and jobs.

Maths, more than any other subject, causes anxiety and that anxiety usually amplifies problems. I think one of the key contributors to this situation is the fear of being wrong, the fear of negative evaluation. Much of maths is very judgemental, for example, whilst saying 7 plus 8 is fourteen is close to the right answer, the answer is wrong. Children rarely get credit for being almost right.

There is now neurological evidence to confirm a link maths anxiety to a fear of physical harm.

#### Primary Age

Introduction.

There is substantial research about the lasting influence of early experiences in learning about number and arithmetic and the two key skills of classification (closely linked to generalising) and seriation (putting things in order of size and/or value). The two skills are critical to the foundations of maths. They develop the abilities to see patterns and organise information and data.

Brian Butterworth, the UK's leading expert on dyscalculia, emphasises the importance of 'subitising'. This is the ability to see a small quantity of randomly organised dots and simply know how many are there and of 'numerical Stroop'. This is the ability to identify the digit symbol that represents the bigger numerical quantity whilst ignoring the font size, for example, to identify 6 as representing the bigger quantity when shown a pair of digits such as, 6 4.

The ability to count forwards is a sequencing (seriation) task as is the, frequently, more challenging task of counting backwards. Young children are expected to rote learn number facts, such as 5 + 8 or 2 x 6 and quickly retrieve them from long term memory. These are not easy tasks for many children and can be a source of frustration for all involved, children, parents and teachers.

A key issue in learning is that first learning is dominant. So, if a child learns that 6 + 8 is 15, it will be difficult to 'unlearn' that and replace it with 6 + 8 = 14. The child has to be able to inhibit that incorrect first learning. These problems will be exacerbated by the demand to answer quickly. My, by now, extensive informal survey of teachers at my lectures around the world tells me that many children are giving up on maths around the age of 7 years old.

We need to get the correct information in there first time and we need to constantly revisit to check that it is still there.

#### At home (in general/ doing homework).

The input at home needs to generate success and be low stress and purposeful. So, for very young children work on subitising, that is, identifying consistently and accurately small quantities, linking these to the symbols/digits. Try sequencing objects in size. use seriation and classification games. Counting forwards and backwards, in ones when young and later in twos and tens is a key skill and sets the foundations for addition and subtraction. Demonstrate the counting with objects such as chunky counters and link quantities to the symbols. Use lots of appropriate vocabulary such as, 'add one more, take away one' and the key question, 'Is it bigger or smaller?'

Be careful about demanding that children do these tasks quickly. A key problem is speed of processing. remember that failure rarely motivates, so ensure that children are challenged appropriately.

Try to find the maths in everyday life, so that it is seen as a normal activity and skill. 'How long does it take to walk/drive to school?' 'How many chocolates in a packet/box?' 'How many steps to climb?' 'How many leaves on a tree?'

Try to include estimating as well as precise answers to encourage that important skill. Estimating is a less judgemental activity in that answers are 'close, bigger, smaller, not that close' as compared to 'right' and 'wrong'.

On the individual (socially/ emotionally/ behaviourally) and in education (on learning / Attainment / behaviour) Good teachers and parents watch and notice, they pick up the non-verbal information that makes communication empathetic. To para-phrase a remarkable pioneer, 'You teach the maths as it is to the child as he is.'

Maths seems to be a subject that generates anxiety in more people than any other subject in school and life. Some people become maths phobic, which may or may not be a consequence of dyscalculia, but a consequence of too much experience of failure. That is a personal judgement for the individual. The avoidance of maths is very common. Low achievers in schools avoid being wrong in maths by avoiding maths. This avoidance can be total, or maybe restricted to certain topics, for example, 'I don't do fractions'. A child will withdraw from involvement in maths if he or she does not experience success at a level that is both meaningful and encouraging for them as an individual. Teachers and parents have to provide opportunities for the child to experience meaningful successes. Complementary to this is that intervention should not solely be asking a child to do what he or she can't do.

Not every teacher in primary school is confident when teaching maths. Their memories of their own school experiences may contribute to that. Early experiences are a dominant influence unless counter-balanced by more positive experiences. Anxieties and attitudes to maths can be passed through families and classrooms.

In the early years (and, I would argue later, too) meaningful manipulatives and visual images will help learning attitudes. More on this in the next section. Also of help to children who are unable to organise their work on paper, for example, to line up columns of numbers, is the use of squared paper where the squares are sized to suit the individual.

#### Strategies

Strategies to help learning start with a pro-active recognition of the potential barriers to learning. Children may have very weak short term memories so they do remember instructions or sequences of information. Information should be presented in chunks that are manageable for the child … and repeated. Short term memory does not store information. When it is lost not amount of concentration will bring it back.

One of the counter-productive beliefs of maths is that computations should be done quickly. This is especially so for mental arithmetic tasks. One of the often-found characteristics of maths learning difficulties and dyscalculia is a slow speed of processing information. It takes a little longer for some children. The expectation of quick responses can be very demotivating. Give more time, but do this discretely and creatively so that the child doesn't feel singled out as 'slow'.

Wipe-clean boards are a useful tool for reducing the impact of negative evaluations on motivation. It is easy to make wrong answers vanish. Encourage sub-vocalising, repeating information almost silently to help in holding that information for enough time to do what it asks. Research I did back in the 1980s with Colin Lane confirmed the efficacy, for many, but not all children as is ever the case, of using self-voice for rote learning.

Having a good working memory is strongly related to being good at maths. For young children this is especially apposite for mental arithmetic. A weak working memory will dramatically reduce a child's ability to perform mental arithmetic. There will be children with weak working memories, so they cannot hold information for long enough to perform the steps in a calculation. Teachers and parents should know the stm and WM capacity of their children. Long term memory stores facts and procedures. A child's long-term memory capacity may be poor for maths facts whilst being good for, say, spelling. This is part of the specificity of the specific learning difficulty of dyscalculia. An approach that will help with facts and also have the benefit of strengthening an understanding of maths is to encourage and teach the connections between facts, to develop strategies that use what you know to work out what you can't remember. It is an approach that encourages meta-cognition, that is, thinking about how you are thinking.

Examples are working out 6 + 7 from 6 + 6, which in turn is related to 5 + 5. This starts with visual and/or manipulatives, alongside symbols and is progressed to just the symbols.

..or working out 7 lots of 6 (7 x 6) from adding 5 lots of 6 (5 x 6) and 2 lots of 6 (2 x 6), that is 30 + 12 = 42 (which infers that the child has been shown that multiplication is adding together 'lots of' the same number.

For many children the secure facts are for 1, 2, 5, 10 and later for 20, 50, 100 and so on. Build on these. Build on strengths. A key concept to understand is place value. It is a sophisticated concept and is absolutely critical to understanding maths. (Note: Many more of these methods are available as video tutorials on my website: www.mathsexplained.co.uk)

#### Useful sites / resources

- www.mathsexplained.co.uk (Tutorials that address the core topics in maths in a dyslexia/dyscalculia friendly way)
- www.stevechinn.co.uk
- www.wordshark.co.uk/numbershark.aspx
- www.dynamomaths.co.uk

#### The 'What to do when you can't ….' series of maths books by Steve Chinn

- Chinn, S. 'Maths learning difficulties, dyslexia and dyscalculia.' British Dyslexia Association
- Emerson, J and Babtie, P (2014) The Dyscalculia Solution, Bloomsbury
- Hornigold, J. 2017, 'Understanding Maths Difficulties', Oxford University Press
- Hornigold, J, 2013 'Dyscalculia Lesson Plans' Nottingham . Special Direct
- Chinn et al (2017) 'Numicon: Big Ideas.' Oxford University Press. Suitable for: Schools with pupils in Upper Key Stage 2 or Key Stage 3 (aged 10 upwards) who need a more secure understanding of key concepts within the primary maths curriculum.
- Dyscalculia Screener - Dynamo Assessment (6-9y) www.dynamomaths.co.uk
- Council for the Registration of Schools Teaching Dyslexic Pupils (CReSTeD): http://www.crested.org.uk

#### Secondary Age

**Introduction.**

Many of the problems experienced in Primary school will continue into Secondary school. These will often be exacerbated by a more formal approach and a change in surroundings and ethos. We should be aware of the strong influence of, and need for, consistency in many aspects of learning.
When collecting the data for my standardised test (see, More Trouble with Maths, 2nd edition, 2017, Routledge) I recorded a dip in achievement levels across the whole sample at age 12 years, a dip that seemed to be overcome by 13 years.

I noticed with my students, all severely dyslexic, that any work that is not constantly refreshed is often lost. This is just one reason why it is so important to revisit the pre-requisite knowledge and skills for any new topic. For example, a sound understanding of the four operations (add, subtract, multiply and divide) is an essential pre-requisite for algebra. One of the basic cognitive (thinking) skills for algebra is the ability to generalise and see patterns. That was a key skill for young children and just one illustration of the need to take interventions back to the basics, even if just for a brief refresher.

Topics such as word problems and fractions become more prevalent at secondary level. These present many children with overwhelming challenges and withdrawal is the most likely coping strategy. Students will often choose not to answer a question rather than get it wrong. The classroom ethos is critically important to minimise this behaviour.

Note: It may be helpful to read the previous section, irrespective of your age

#### At home (in general/ doing homework)

There are some reasons that might interfere with parents helping their children with maths. These include the parent's own anxieties and insecurities about maths or that the methods used in schools now are different to those used when they were in school or that some children do not want to 'see' their parents as teachers.

One of the practices I try to encourage in schools regarding homework is that pupils are given the homework before the lesson ends so that they can try the first two questions. This will help teachers identify the pupils who are likely to fail in the task. Again, I refer to the research that found that getting something wrong in the first stages of learning is harmful to future attempts to get it correct. Speed of working is a common problem so parents may have to be advocates (as is so often necessary) and ask the school to set fewer examples for their child, again without drawing attention to different treatment.

Creating the right environment for doing homework is often important. Children who are easily distracted may benefit from what Americans call a 'vanilla environment'.

Beware of setting expectations. This is a very complex skill, often simplified to 'Do your best'. If pupils do their best, they do not want to achieve low scores. If parents under expect, for example, 'It doesn't matter, I was never any good at maths', then they facilitate failure. I like the ungrammatical phrase, 'unanxious expectations'.

#### The individual (socially/ emotionally/ behaviourally)

There is a danger of creating learned helplessness if failures, however small, are not managed. I have long been an advocate of attributional style (by Martin Seligman) and used it with great success in my school (see, Burden, 2005, 'Dyslexia and Self-concept')

One of the biggest issues I have found, both from working with dyslexic and dyscalculic children and my research is withdrawal. At the classroom worksheet level, this is revealed as a 'no answer'. If the pupil predicts failure then they will not commit to paper. The lack of engagement, of risk taking is, of course, a major barrier to learning.

Feed-back, obviously, has a significant impact on attitude. This can be as simple as a mark, 1/10, a comment, 'You are not trying' or a facial expression or tone of voice. Teaching is an incredibly complex and skilled activity and involves as much about the affective (emotional) domain as it is about cognition.

There is a questionnaire on maths anxiety in 'More Trouble with Maths' (Chinn, 2017) which can help identify some of the main issues. Although (Western) social attitudes to maths condone poor abilities with maths, the reality for young people now is that career options will be dramatically reduced if they fail to achieve an acceptable qualification/examination result in maths. Peer pressure can be a significant factor at this age and can work at two extremes (and in between). There may be pressure not to be good, which could be seen as 'geeky' or pressure to be correct, quick and high achieving.

#### Strategies in education (learning / attainment / behaviour)

One of the most useful strategies is the appropriate use of the question, 'How did you work that out?' or 'Can you tell me how you did that?' Listening to the pupil is so important and informative. There is currently a great interest in meta-cognition, which is 'thinking about how you are thinking', for example, when seeing 99, some students are literal and see just that number as an isolated piece of information rather than seeing 99 as 1 less than 100. So much in education depends on effective communication, teacher to pupil and pupil to teacher.

Pupils may not know all the times table facts, but they do tend to know the 1x, 2x, 5x and 10x facts. This can be the cause of failures when doing calculations rather than the concept that is being tested. I find that error patterns are very illustrative for teachers. It takes a reaction from, 'Wrong' to 'Here is where you made the mistake'. Error patterns can be used to reveal misconceptions.

The questions that generate a 'No answer' response from the pupil are also a guide to the problems and perceptions of the pupil. The 'No answer' response is an emotional issue and may come to be the dominant behaviour, the pupil no longer engages with any maths.

Being pro-actively aware of students' short term and working memories can help maintain their engagement in maths. For example, to address stm problems, repeat a question or a chunk of information, break the information down into stm appropriate chunks. As a real-life example, notice how the 16 digit credit card numbers are broken down into chunks of 4 digits.

Working memory influences much of maths, especially mental arithmetic. For example, if the question involves four steps to achieve a solution and the pupil's working memory can only handle three steps, then he will fail. Thus, the failure may not be conceptual, but a consequence of poor working memory. It is worth noting that reversing any sequence of procedure challenges working memory.

It is rare to see visual images and maths manipulatives used a secondary level. The appropriate use of these can help in teaching pupils to understand maths topics. They can link the maths vocabulary to the symbols and to the procedures and enhance conceptual understanding. For example, cutting (dividing) squares of paper can show what fractions mean. Cutting a square into three equal parts shows it being divided into three thirds. Combining this with the symbols, 1/3, shows that the / means division, the 3 means 3 equal parts and that the 1 shows that this is 1 of 3 equal parts. As recommended for use with younger pupils, it may continue to be of help to children who are unable to organise their work on paper, for example, to line up columns of numbers, to use squared paper where the squares are sized to suit the individual. As with any accommodation, the pupil and peers must not perceive this as treating them specially and giving them an advantage.

#### Useful sites/ resources

- R. Ashlock (2010) 'Error Patterns in Computation' 10th edn Pearson
- Chinn, S. (2017) 'The Trouble with Maths' 3rd edn. Routledge
- Chinn, S. and Ashcroft, R. (2017) 'Maths and Dyslexia and Dyscalculia: A Teaching Handbook' 4th edn. Wiley
- Henderson, A. (2012) 'Dyslexia, Dyscalculia and Mathematics: A Practical Guide' 2nd edn. Taylor and Francis
- www.mathsexplained.co.uk (tutorials that address topics in a visual and non-age specific way)

#### Further Education

**Introduction**

There are students who will be re-taking maths to achieve the maths exam result and qualification that enables them to apply for jobs. There will be students who find that their chosen course has aspects of maths as a vital and important component of the topic they are studying. Obvious examples will be courses in engineering or construction. Less obvious examples will be psychology and hairdressing.

Some students will have a long history of low achievement in maths, so regaining motivation will be a big issue. These students will not be motivated by 'more of the same'. The time span for studying is relatively short and expectations may be high, as in, trying to achieve a 'pass' grade in maths in one year, having spent the last 10 years of schooling not understanding the topic at a level that generates exam success.

Thirty years ago it was hard to find books and materials for English that were at the correct level of intellectual challenge, yet age-appropriate in appearance. That has been addressed, but the same has not yet happened for maths. This is exacerbated by the culture in maths teaching that views manipulatives, such as base-ten blocks, as unnecessary for older students (and that often applies in secondary schools, too).

Alternative qualifications to GCSE may have maths set in a more functional and practical way, but they are often much more wordy, so that the challenge is as much about reading and interpreting the paper as it is about the maths content.

Worksheets need to be both age and level appropriate and set up to generate success. Motivation is more likely to come at any age, but especially this age and after a history of failure, if meaningful success can be experienced. Worksheets should also have enough content to provide experience, but not over-face the student and create avoidance.

Note: It may be helpful to read the previous sections, irrespective of your age.

#### At home

Key issues, as the perception of students as independent learners increases, are likely to be personal organisation, especially time and timetables. Some useful apps are listed under Resources in the HE section. Negotiating extra time for assignments may help, but it is important to remember that time is finite and that life needs balance.

#### The individual (socially/ emotionally/ behaviourally)

(Much of the advice for secondary age students applies here). Maths in the context of the subject being studied, for example, carpentry or hairdressing, is now real and has consequences if it is wrong. Not in appraisal via a score or a tick or cross, but in the success of doing the task. Being able to estimate before and after the task helps set up the task and then appraise it. This needs to be in addition to any precise calculations. For example, a painter may need to estimate how much paint to buy for a specific job or how much time the job may take in order to provide an estimate of the cost. A hairdresser will need to calculate the correct dilution for a hair colouring. Not surprisingly, the standards required, and tested, for calculations in nursing are very high. This can raise the levels of debilitating anxiety. The use of estimations in combination with precise calculations can provide some level of reassurance. In education (on learning / attainment / behaviour)

When a student has to gain a maths qualification in order to access and pursue a career and that student has a track record of failing to achieve this, then it will not be surprising if there are emotional consequences. Individuals will show different behaviours, but creating motivation will have to deal with that range of behaviours. As with so many issues in maths, there will not be one approach, one solution. I am always wary of the person who advocates a teaching strategy because 'It worked for me'. As with the comments in the Secondary age section, attributional style may provide some helpful strategies. In some respects, I find that source broader than Mindset and thus more useful across a range of situations. There is a (free) maths anxiety questionnaire on this website. The questionnaire in my book 'More Trouble with Maths' is only standardised to age 16 years, but may still offer useful and pertinent information. Often, initiating relaxed conversations about affective issues is far more revealing than simply an 'anxiety score'.

#### Strategies

The key goal for those re-taking GCSE or Functional Skills will be to restore motivation. It is likely that that will mean a different approach combined with providing experiences of success. This may well include discussing what the student's goals are and why he thinks these have not been reached and what he remembers as something that did help. It is a constant theme in this section on dyscalculia that visual images, linked appropriately to the pertinent vocabulary and the symbols has a strong chance of success. However, there are rarely 'quick fixes' so it may be a case of finding the relevant strengths, the topics that are best understood by the student and focusing on those rather than attempting to master the whole syllabus. It is likely that input for maths test anxiety will help. Students may need to learn exam techniques and strategies. They may need to jot down key information before starting to answer questions. This can help direct the mind to the maths and may give a secure source of information that stress might block as the test/exam progresses.

As with any age of learner, asking them to explain how they are trying to solve the problem (meta-cognition) encourages understanding and success. Asking if the student can see another way of solving the problem may help, but make sure this doesn't create stress. It is important to always keep in mind that no one approach works for all. The goal is to make this routinely automatic for students to do for themselves. It is important to refresh the memory for strategies that access basic facts, so that the access becomes as close as possible to automatic. For example, 15% can be calculated by working out 10% (divide by 10), halving that 10% to get 5% and adding the two percentages. This is an example of an approach that uses two (or more) easy steps to replace one impossible step.

There is often a need to go back to the basics to ensure that they are secure. Maths is a very developmental subject and the foundations must be sound and automatically accessible.

#### Useful sites/ resources

- dyscalculia-screener.co.uk/ , which claims to be, 'the World's only post 16 screener'.
- Mathematics Pro – a GCSE revision app.
- Moorcraft, P. (2015) 'It Just Doesn't Add Up: Explaining Dyscalculia and Overcoming Number Problems for Children and Adults' Original Paperback
- www.mathsexplained.co.uk (tutorials that address topics in a non-age specific way)
- stemreader.org.uk is a Windows application with tools to help read and explore equations. With STEMReader you can hear equations read aloud and see the transcript on screen, break down equations into simple chunks to make them easier to understand and check the meaning of unfamiliar symbols.

#### Higher Education

##### Introduction

Recent research which I carried out with Clare Trott of Loughborough University revealed that a significant number of students applying for University courses are not aware of any, or the extent of, maths in the courses. The questions to ask of the University are, 'How much maths is there in this course? What maths should I know?' and maybe, 'What support can I get?'

The research illustrates the prevalence of maths in HE and the situation where students think they have left maths behind after achieving the necessary grade of GCSE at 16 years old. Some achieve that success by cramming just before the exam, but the knowledge is not retained long term. Support at University can be significant. The DSA, Disabled Students' Allowance (see www.yourdsa.com for comprehensive information) can lead to provision of assessment, equipment, assistive software and general support. It may be that students may be wary of asking for help. Parents and friends may have an important role to play here.

Lectures may present a number of problems, often around note-taking. Among the Apps that can help with this is the (free to download) Soncent App which enables students to make high quality recording and mark up key information as they listen. Students may ask for PowerPoints or notes prior to a lecture, reducing the need to take notes. At this stage in their education and as an adult there will be the reasonable expectation that students will take on at least some of the initiative to seek appropriate help. Sites like yourdsa.com will be a great help. This initial help is impersonal and anonymous. Note: It may be helpful to read the previous sections, irrespective of your age.

#### At home

Assignments may create problems and make demands on time that seem overwhelming. The support staff at the University will offer help and advocacy. Some Universities have Mathematics Learning Support Centres, most have Learning Support Centres. The individual (socially/ emotionally/ behaviourally) and in education (on learning / attainment / behaviour) Among the problems that may be experienced are those around the many manifestations of organising. This may be organising notes and records, organising time or organising tasks. There are some Apps (see below) that may help. Again, the Support Centres are there with expertise and contacts that can source help from other agencies if required. Ideally students at this stage have learned self-advocacy.

#### Useful sites/ resources

- Moorcraft, P. (2015) 'It Just Doesn't Add Up: Explaining Dyscalculia and Overcoming Number Problems for Children and Adults'. Original Paperback
- www.mathsexplained.co.uk (tutorials that address topics in a non-age specific way)
- dyscalculia-screener.co.uk A screener for post-16
- Swipes app An intuitive to-do list which gives the fastest way to organise any list of tasks into priorities, scheduled events and history of accomplishments
- www.todoist.com. Another App for organising.
- www.mathscentre.ac.uk Resources for learners in HE and those applying for HE
- stemreader.org.uk is a Windows application with tools to help read and explore equations. With STEMReader you can hear equations read aloud and see the transcript on screen, break down equations into simple chunks to make them easier to understand and check the meaning of unfamiliar symbols. untimeapp.com A timer app that shows how much time is left in a visual way

(I am grateful to Pete Jarrett of Tutorum.co.uk for his assistance in suggesting resources for FE and HE sections. Note: Pete does assessments for dyscalculia.)

#### Identification:

**Introduction**

Initial note: There is a difference between:

- informal identification of the possibility of dyscalculia/maths learning difficulty,
- a screener,
- and a full diagnosis.

Each will have its place and appropriate circumstances. A diagnosis has to take note of the lack of an agreed definition, though the USA does have the DSM-V version. I consider this to be an appropriate definition.

There is also the nature of dyscalculics. Key researchers have described them as heterogeneous, that is, there is not one profile. This is compounded by the nature of maths itself. It is a subject with many facets which challenge a range of abilities and skills. However, that does not mean a thorough diagnosis of the components of maths difficulties and their cumulative severity is not possible.

Of course, many people who seek a diagnosis of a problem want to know not only what that problem is, but what can be done to address it, so for me, a diagnosis should lead to and include advice on addressing the issues. As with dyslexia, this will not be a cure, but advice on how to deal with as many issues as possible and how to cope with the others. Always beware of the snake oil purveyors. For a broad and balanced approach to identifying and diagnosing maths difficulties which looks at many of the factors involved, refer to 'More Trouble with Maths: A complete manual to Identifying and diagnosing mathematical difficulties' 2nd edition, (Chinn, 2017). The tests and procedures are not restricted to psychologists.

#### Who can diagnose dyscalculia? What qualifications should the assessor have?

At this time with the general understanding of dyscalculia, there are few people who specialise in diagnosing dyscalculia, partly due to lack of experience and appropriate training. There will be a connection between why the diagnosis is needed and the qualifications necessary for the person who carries out the diagnosis. For example, to have a diagnosis that will help access the Disabled Students Allowance or accommodation for examinations the assessor will need to have an APC, an Assessment Practising Certificate (for more information see www.patoss-dyslexia.org/SupportAdvice/.../DSAInformationforStudents). A more informal diagnosis may be enough for a school to provide appropriate intervention, though something far more comprehensive may be needed to access funding and/or an Education and Health Care Plan (EHC).

A list of psychologists is available from the British Psychological Society (www.bps.org.uk). The psychologist should also have current HCPC (Health and Care Professions Council) registration. Assessments can also be carried out by an appropriately qualified specialist dyscalculia teacher with an APC. Usually the teacher will hold an AMBDA. The British Dyslexia Association (www.bdadyslexia.org.uk) can award an AMBDA to people who have completed comprehensive training, for example, Edge Hill University's PGCert-dyscalculia (www.edgehill.ac.uk/courses/education-dyscalculia)

#### How is Dyscalculia identified? (children and post 16)

For children, the first step is likely to be a realisation that the child is not making appropriate progress in maths compared to their peers. This may be a consequence of classroom observation and perceptions or poor performance in examinations and tests. Usually teachers and parents are comparing performance in maths with that in other subjects. It is that contrast in performance coupled with the persistence of the difficulties that is often leads to the first suspicions of a specific learning difficulty.

For adults, it is often the challenges that come from a promotion or a change of job that expose the difficulties that have been previously concealed. Adults (and indeed children) can become very skilled at disguising their dyscalculia. Society's norms collude to some extent in that it is socially acceptable to confess that you are 'not good' at maths, but not that you are 'not good' at reading and spelling. (I have never understood the irresistible compulsion some good spellers have to correct an incorrect spelling).

Diagnosis will focus on identifying the levels of mathematical knowledge, usually in arithmetical tasks, such as recall of times table facts. This may be coupled with examining key factors such as short term and working memories, mathematical vocabulary and speed of processing. The following sections give more detail.

#### Screeners

A screener may the next step after informal recognition of classroom or workplace concerns. They have a purpose, but obviously are not a full diagnosis. Comparing a screener and a diagnosis:

- Screeners can be used with a large number of students whereas a full diagnosis in for an individual.
- Screeners can be used to identify students who might be at risk whereas a diagnosis is to find the realities and details of a problem (dyscalculia) and to confirm dyscalculia/maths learning difficulties.
- Screeners are of relatively low cost compared to a diagnostic procedure.
- Both screeners and full diagnoses should be intelligible to those involved.

So, a screener should flag up a potential problem. It will not attempt to offer advice on addressing the problem. That would be a subsequent process. Some of the screeners available are:

- dyscalculia-screener.co.uk - suitable for post-16
- www.gl-assessment.co.uk/products/dyscalculia-screener-and-guidance - for ages 5y to 14y
- The Dyscalculia Checklist (in 'More Trouble with Maths' Chinn, 2017) - for any age
- (The Dyscalculia Checklist can provide guidance and information for constructing an individual's maths intervention programme)
- www.dynamomaths.co.uk - for 6y – 9y
- The Dyscalculia Assessment. Emerson, J. and Babtie, P. (2010). Continuum Publishing - for Primary and Secondary.

#### It is more than a screener. What do they look at?

It is the nature of a screener to focus on what the authors consider to be key issues. For example, the GL screener has a focus on subitising (quickly recognising and quantifying small numbers of randomly organised dots) and numerical stroop (knowing which digit symbol represents the bigger value number despite relative font sizes as in 2 and 7). They will often look at basic arithmetic skills such as place value and basic fact recall.

#### Full Diagnostic Assessment

Introduction

I would expect a full diagnostic assessment to include:

Pertinent background information (where available). For example, any information on IQ, school reports, a (maths) teacher report, text books used by the student, exercise books.:

Core skills, for example, subitising, place value, counting forwards and backwards, maths vocabulary and associated symbols:

Core knowledge, for example, basic facts (recall and strategies), the four operations (add, subtract, multiply, divide):

Cognitive skills, for example, short term and working memory, cognitive style (and flexibility), estimation:

Affective issues, for example, anxiety:

Word problems:

A standardised maths score showing how the student's performance compares to his/her peers.

I would expect to see data, often comparative (standardised) alongside clinical observations. (see 'More Trouble with Maths' 2nd edition (2017) by Steve Chinn, Routledge for more detail and a range of tests) For me the process is not just about finding what can and cannot be done, but how it is done and that includes attitudes, strategies and error patterns. Much depends on the relationship established between the assessor and the subject (person). The key is the clinical approach and thus investigating why the subject is doing what he is doing. The assessor should know the tests and procedures completely so that he/she can focus on what the subject is doing, noting all those non-verbal behaviours that make an assessment human.

I would also expect the assessment to identify performance levels, cognitive strengths and weaknesses, explanations as to why these are as they are and, most importantly, advice on interventions.

**How long does it take? **

Children and adults who know they are not successful at maths may well have a low time tolerance for any activity, which includes testing, for doing maths. In my experience, and using some 40+ years of teaching experience, I can get around one hour of peak attention. This is helped by using a mix of formal and informal procedures. I consider it a professional responsibility to get the best out of the adult or child so that I know what is the optimum performance.
Where the assessor has continual access to the subject, for example, as a teacher, then the testing can be done in stages. Where the subject is with an assessor especially for diagnosis then this is usually for one session only. Then the relationship between assessor and child/adult becomes critical.
When assessing children, I insist on a parent being present, but invisible, so that they can see all the behavioural clues that are an essential part of any assessment. Screeners tend to be on line and all that important behavioural information is unavailable.

**Who can request an assessment? (school EP, private ST or EP) **

Essentially anyone who has a legitimate concern can request an assessment. It is helpful to have evidence to back up the request. There are an increasing number of SENCos (Special Educational Needs Coordinators) in schools who can carry out assessments, but do check that they have an APC (see next section). Psychologists are often in short supply.

Many decades of experience as a provider for special needs coupled with all the experiences of being a parent of a child with special needs have taught me that parents need to have extremely effective advocacy skills … and persistence. Where can you find private assessments if needed?

A search on the web for dyscalculia assessors produces few results. Unfortunately, there are still only a handful of assessors who specialise in this task.
Organisations that may help in suggesting assessors include:

www.educational-psychologist.co.uk/services-and-fees

www.patoss-dyslexia.org

A useful source of background information about qualified assessors (particularly the APC) for special needs is at www.sasc.org.uk/FAQ.aspx

#### Myth buster: The biggest misconceptions about dyscalculia

Recognition of dyscalculia is relatively recent in education. Research is only just beginning to take off. One of the exciting innovations we have now compared to the pioneering days of research into dyslexia is having increasingly sophisticated technology to study the brain. It's hard to deny evidence obtained from brain scans.

Myths arise from ignorance. Hopefully as our knowledge grows and becomes widely dispersed, myths will hold less and less credibility. The website: https://www.understood.org/en/.../dyscalculia/5-common-myths-about-dyscalculia lists five common myths about dyscalculia. I have added my comments for each myth.

**Myth #1: All children with dyscalculia have the same difficulties with maths.**

There are many factors that contribute and combine to create difficulties, each at its own level of severity, for example, working memory and anxiety. The extra layer of complexity comes from the interactions, for example, anxiety can reduce working memory capacity, a slow retrieval of basic facts needed for a calculation can overload working memory so that there is not enough left to perform the calculation.
This complexity has been recognised in research and has led to the observation that the problem is heterogeneous.
This doesn't mean that there will not be a core of main contributors to the problems of dyscalculia and it doesn't mean that a diagnosis cannot be done. What is does mean is that the diagnostic protocol has to include all the critical factors.

**Myth #2: Dyscalculia is another name for maths anxiety**

Maths anxiety is one of the contributing factors. Although anxiety can be facilitative, for children and adults with dyscalculia it is going to be debilitative. It will exacerbate the problems, as in the working memory comments above, but it will also lead to a fear of maths and a complete withdrawal from anything that is perceived as mathematical. So, the outcome of extreme anxiety may look like an inability to do maths.

**Myth #3: Dyscalculia is basically dyslexia for maths.**

There are similarities in the factors that contribute to these difficulties and the two specific learning difficulties can occur in the same individual, but that is not always the case. Certain difficulties apply to both dyslexia and dyscalculia, for example, the prevalence of symbols and poor working memory.
My early work (in the 1980s and 1990s) was about dyslexia and maths difficulties. There was less awareness back then of the term 'dyscalculia'. For example, the ratio of research papers on dyslexia to those on dyscalculia in the decade 1986 – 1995 was 22:1. Although the schools where I was Head or Principal were for (severely) dyslexic students, the majority had difficulties with maths as well as language. The difficulties and the prognoses covered a wide range.

**Myth #4: Dyscalculia isn't very common.**

One of the reasons people might believe this particular myth is lack of awareness. There is little doubt that people know that maths difficulties are very common. I firmly believe that maths learning difficulties lie on a spectrum and that dyscalculia lies at the extreme end of that spectrum. So, dyscalculia affects around 5% of the population, but the maths learning difficulties affect around 25% of the population. The statistics for 2016 for GCSE maths (a national exam for England and Wales, usually taken at age 16y) is that 39% failed to get a grade that was considered to be a 'pass' grade.

**Myth #5: Kids with dyscalculia can't learn maths.**

I could parallel that to the myth that dyslexic children can't learn to read. Both myths are very wrong. Pupils with dyscalculia may not be able to learn maths when taught inappropriately, but back to Margaret Rawson's wise words, 'Teach the subject as it is to the child as he is.' In my specialist school, we took on children at 10 and 11 years old who were 3 or 4 years behind in maths and taught them according to their learning profile. The National 'pass' rate in regular schools in those days was just under 50%. We were getting over 75-80%, with most of the rest only one grade away from that 'pass' grade.
I could, and indeed have in a recent (May 2017) article, argue that traditional teaching methods for maths discriminate against dyscalculics.

#### Frequently Asked Questions

**1. What is the difference between dyscalculia and dyslexia when it comes to maths as both SpDs can result in maths difficulties? How do you discriminate between the two?**

Dyslexia is about language, as in reading, writing and spelling. Dyscalculia is about maths, particularly arithmetic. They can occur together in an individual (comorbidity). Both language and maths use symbols, both rely on working memory and (specific) long term memories and on speed of processing. For these reasons alone the two specific learning difficulties might be present in the same individual. They differ in the subject matter they affect.

**2. Can you have both dyslexia and dyscalculia?**

Yes. However, the outcomes, in terms of dealing with them, may be different.

**3. Is there a special way of teaching dyscalculics?**

Yes, but it is important to note that those ways may often help many other children too. I am a great believer in learning from the 'outliers'. Certainly, avoid the 'more of the same, but slower (and definitely NOT louder)' approach. At any age!