Early indicators will be problems dealing with sequences, problems with long-term retention of basic facts, no sense of number, an inability to see patterns in information.

Certain difficulties, for example, reading and comprehending the unique language and vocabulary of mathematics, may ‘click in’ after a relatively successful start in the subject. A child may excel at mental arithmetic and fail when required to document (or vice versa). Different areas of mathematics may well evoke different reactions from different pupils.

It is often useful to analyse a mathematics task in terms of, for example, vocabulary, basic fact knowledge, understanding of the four operations, memory (short and long term), sequencing ability, generalising, documenting, spatial awareness, and then to identify which area creates a difficulty for the learner.

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Q2: How do I recognise a child who has dyscalculia? What are the symptoms and how does this differ from dyslexia with numbers?

A2:

As a basic indicator, the child will be performing below expectations (primarily yours, the teacher’s) with no obvious reason such as emotional state or an illness such as, say, glandular fever. This underachievement may manifest itself in specifics such as problems with knowing the value or worth of numbers, in realising than 9 is one less than 10, for example, or in being able to rapidly recall (as the NNS requires) basic number facts - or perhaps in a totally mechanical application of algorithms (procedures) with no understanding of why or what the result means or how to evaluate the answer.

Some children with good memories and good general abilities may not present as underachievers within a class, but may be dramatically underachieving in terms of their true potential. Some children just get stuck in the counting-on phase of development.

So recognition goes back to Butterworth’s test, which should back your subjective conclusions with standardised information. This should also identify the symptoms.

The (part) question as to how dyscalculia differs from ‘dyslexia with numbers’ will depend on the interpretation of ‘dyslexia with numbers’.

Over the past twelve or so years a number of specific learning difficulties have been identified, labelled and researched. These include Asperger’s syndrome, ADD, ADHD, dyspraxia, semantic pragmatic language disorder and dyscalculia. A child may exhibit the characteristics of just one of these, but there is a strong chance that more than one ‘condition’ will apply. Difficulties often occur together and this may be causal, independent or due to similar underlying aetiologies. This may be of theoretical interest to the teacher, but the manifestations of the difficulties in the classroom should be more pertinent.

My guess is that the interventions used for one disorder may very well impact on all disorders and their various combinations. This is not to say that one programme of intervention will help all children. It is far more subtle than that, but the basic principle, stated by workers such as Dr Harry Chasty in the UK and Dr Margaret Rawson in the USA, is ‘If the child doesn’t learn the way you teach, can you teach the way he learns?’

You have to ask: is there such a child as a ‘pure’ dyscalculic or a ‘pure’ dyslexic (difficulties only with literacy) or are there cases where the two conditions occur together for whatever reason? My guess is that the answer may be ‘No’ to the first question, and a simple ‘Yes’ to the second. It may be that one difficulty is dominant, but that does not mean that the other difficulty is totally absent.

My experience of working with pupils who have been diagnosed as severely dyslexic is that most, if not all, have difficulties in at least some areas of mathematics (most commonly in number). The key word here is ‘difficulty’. For example, I always mention a severely dyslexic young man who obtained a degree in mathematics, but could not give an instant correct answer to 7 x 8. Some dyslexic learners will exhibit very few mathematical difficulties, but mathematics is made up of many topics and my experience is that many dyslexic learners will experience difficulty in some areas of number but may very well shine in other areas.

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Q3: Is there a test which identifies a child as being dyslexic/dyscalculic?

A3:

The standard ‘tests’ for dyslexia are going to be focused on literacy.

There is a test for dyscalculia, written by Professor Brian Butterworth and recently published by NFER-Nelson.

For testing for numeracy difficulties, it is not a bad idea to set up your own informal diagnosis. Sutton LEA have done this, based on Chinn’s suggestions in Chapter 3 of Mathematics for Dyslexics: A Teaching Handbook (Whurr). Use the basic ideas, the content of the NNS and your own expertise and knowledge for this task. Good teachers are natural diagnosticians. Think what the child needs to know, including the prerequisite knowledge, and construct your test accordingly. One of the most revealing diagnostic questions is ‘How did you do that? Talk me through your work.’ And remember, the errors are more revealing than the correct answers. The end result of a mathematics test should be a lot more than just a number. As Alan Kaufman, the leading authority on the WISC (a very widely used intelligence test) says, ‘Be better than the test you use’.

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Q4: What do I do as a teacher to help a child with these problems? How can I use my teaching assistants effectively?

A4:

The first question would need a long answer. The AMBDA teacher training course is three Masters’-level modules plus 30 hours of teaching with two individual children, but as a start:

Ten Tips for Teachers

One of the most frequently occurring problems for dyslexic learners and dyscalculic learners is not being able to (rote) learn the times tables, so a possible alternative is to use the facts the child knows to work out the facts they don’t know. This has an additional bonus of teaching further understanding of numbers and number relationships.
The facts that can be learnt (and the child does have to have some facts) are 1x, 2x, 5x and 10x. Other facts can be derived from these, a strategy advocated in the NNS for 4x, for example:
5x can be obtained by halving 10x facts (also useful for percentage work)
4x facts are done by using 2x twice as in 4 x 7 as 2 x 7 = 14 and 2 x 14 = 28
9x facts are derived from 10x facts using the pattern n x 9 = n x10 – n as in 7 x 9 = 7 x 10 - 7
3x facts are done by doubling the number and adding the number as in 3 x 6 = 2 x 6 + 6 = 12 + 6 = 18
6x facts are similar but using 5xn and 1xn as in 6 x 8 = 5 x 8 + 8 = 40 + 8 = 48
7x facts are computed from 5x and 2x facts as 5n + 2n, for example 7 x 3 = 5 x 3 + 2 x 3.......................
and if you teach the commutative property (e.g. 4 x 3 = 3 x 4) then there is only 8x8 left, which can be done by a triple sequence of doubling, starting with 8.
Use the same interrelating strategies with addition and subtraction facts, for example compute plus 9 as add 10 then subtract 1. The nearness of 9 to 10, 99 to 100 and so on is a very valuable concept for mental arithmetic.
Use known facts as reference points for other facts as in using 5+ 5 to access 5+6.
Add 7 as 5 then 2 or 2 then 5
Teach the addition and subtraction facts for 10 and then extend them to the facts for 100 and so on.
Build confidence. Encourage the pupil to take risks. Guard against the pervasive and permanent attitudes of ‘I’m no good at maths. I never will be.’
Mark the first two or three questions before an error pattern can build up.
Use easy numbers when introducing new procedures, so the pupil can focus on the method, not on yet another numerical challenge. Also, easy number examples can be used to check procedures, for example adding ½ + ¼ illustrates much about adding fractions, and the child has the security of knowing the answer is ¾ so can rationalise the mathematical procedure that takes him there.
Teach that much of mathematics is inter-connected (which can be a negative concept if the child doesn’t understand the basics so never underestimate how far back an intervention must go to address the root of the problem). For example, you can teach that division is the opposite of multiplication and show how this is of benefit in actual work. For example 180 divided by12 can be rephrased as 12 x ? = 180, then try 12 x 10 = 120 as a first entry to the question. Division and multiplication are easier for many pupils if done as addition in chunks or subtraction in chunks (1x, 2x, 5x, 10x, 20x, 50x, 100x and so on in a repeating pattern of easy multiples). Remember that our coins and notes are in these values and we make any value from them.
Go back to what the pupil knows and understands. This will almost certainly be further back than you think. It is important to build on a firm base.
The concepts of mathematics start early and should transfer upwards. For example, algebra uses all the rules of number and is often easier for dyslexic learners than number. Calculating the perimeter of a triangle of sides 37, 56 and 88 may be more difficult than the algebraic triangle with sides a, b and c…if the pupil knows the principle and can move to the abstract concept of a, b, c, x and y’s.
Look for the links, for example 7 + 3 =10 develops to 70 + 30 = 100 to 700 + 300 = 1000 to 0.7 + 0.3 = 1.0 to 7a + 3a = 10a. But do not be surprised if a progression which usually creates no problem does seem to create a disproportionate difficulty. It may well be due to that firm base mentioned in 6.>
Encourage the pupil to relax and overview the problem before starting. Help pupils to estimate and strengthen their sense of number values. Encourage them to use the facts they truly know (not the ones they think they know!). For example, the number facts for 10 are extremely useful. The pupil may know them but may be slow and possibly inaccurate under pressure. It takes very little time for them to write two lines of numbers to create a memory jogger:

0 1 2 3 4 5 6 7 8 9 10
10 9 8 7 6 5 4 3 2 1 0
Note the 5 + 5 check, useful in itself, but also a good habit to instil in the uncertain learner.
Help pupils to learn the skill of rephrasing questions until they make sense to them. Perhaps use drawings to help the understanding.

The second question, on using a teaching assistant effectively, relates, of course, to the first question. Obvious benefits are:

At the start of the lesson, getting children organised to start work and making sure they have any homework at the end of the lesson.
Helping them read the question.
Reminding and possibly showing them how to rephrase the question until they understand it.
Demonstrating an ‘easy’ example.
Making sure they start the questions (avoiding avoidance).
Providing spare basic fact sheets (they will be lost quite frequently!). Providing answers to some basic facts so this deficit does not stop the child learning a new procedure.
Checking the first two examples to ensure that any errors are not internalised.
Being aware of the child’s learning style (inchworm or grasshopper) and helping appropriately (see Mathematics for Dyslexics: a teaching handbook by Chinn and Ashcroft and an article in the Journal of Special Education, vol 28, no 2, June 2001, p80–85). Basically, Inchworms are step-by-step, formula learners whilst grasshoppers are intuitive, big-picture learners.

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Q5: What do you say to a teacher who says their pupils with dyslexia are unable to work independently?

A5:

To help an included dyslexic pupil work independently there will have to be some differentiation. Dyslexia is a ‘hidden’ disability and, even after twenty years’ work with dyslexic pupils, I am still stunned by the disparity between their oral work and the way they present, and the actual work they produce on paper. It is hard to relate the pupil to the work.

Different mathematics tasks will demand different levels of support. The levels of support may differ for each dyslexic child, but there are some generally useful hints that may help. These adjustments are not overly burdensome.

Obviously a teacher may have to make arrangements for word problems to be read aloud to the pupil by an adult or another child (a ‘study buddy’).

There may be a short-term memory (STM) difficulty which prevents the pupil from remembering all the instructions, so there will be a need to repeat instructions, probably in separate chunks rather than in one long string. Short-term memory also impacts, for some, on mental arithmetic skills.

There may be a problem with retrieving basic facts such as times tables, so giving the pupil a small tables square may be useful.

If a pupil judges a task to be over-demanding or beyond his capabilities, the classic reaction is not to try, so adjust the presentation or content of the task.

There are many other suggestions (see Q 6), but the basic principle is to remove the barriers which stop the pupil working independently. It is not that dissimilar in principle to providing a ramp for wheelchair users so they can access the library to use the computers.

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Q6: What research is available on dyslexia in mathematics and dyscalculia?

A6:

The flippant answer is ‘Not a lot.’ Compared to the body of research on reading, the research on mathematics difficulties associated with dyslexia is slight, and on dyscalculia as a separate difficulty the research is minimal (though there is a 2002 paper published by Wiley in Dyslexia, volume 8, no. 2, pp 67-85).

Prof Brian Butterworth of the University of London is currently involved in research in dyscalculia. Workers on the mathematics difficulties experienced by dyslexic learners include Richard Ashcroft, Steve Chinn, Ann Henderson, Elaine and Tim Miles, Mahesh Sharma, Julie Kay and Dorian Yeo. Jan Poustie has written a book specifically on dyscalculia.

There is a reasonable list of references in Mathematics for Dyslexics, by Chinn and Ashcroft (published by Whurr), but their second edition was published back in 1998. Miles and Miles Dyslexia and Mathematics (Routledge) is about to go into its second edition and Butterworth’s book, The Mathematical Brain ( Papermac) is worth considering. Sharma’s work is available in the UK from Berkshire Mathematics (trish@chazey.tele2.co.uk).

A truly comprehensive literature search was created by the Swedish worker Magne in 1996: Bibliography of literature dysmathematica, Didakometry, School of Education, Malmo, Sweden.

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Q7: What sources of support are there for teachers who teach children with these difficulties?

A7: Teachers need support at three different levels of intervention. First, an awareness and understanding of the difficulties will help them react appropriately. Next, adjustments to aspects of each lesson such as addressing short-term memory problems by restricting the number of instructions given at one time, or ensuring that new vocabulary is explained carefully, or adjusting the design of worksheets so that the reading level is accessible and that layout is uncluttered. Third, knowing and using alternative methods of presentation and explanation.

In terms of training for teachers, there is a new course leading to a Certificate of Professional Studies (3 M-level Masters’ modules) and an AMBDA (Associate Member of the British Dyslexia Association) in Numeracy. Obviously the course demands a lot of extra work from already busy teachers, but Advisers from three LEAs have now been trained and are ‘cascading’ the work to many teachers. This may prove to be an effective way of disseminating this knowledge. At present the course is only available at Mark College, Somerset, to a limited number of teachers.

The Dyslexia Institute (DI) runs a shorter course, which is often oversubscribed, which qualifies the teacher to use the DI mathematics programme (DIMP). The British Dyslexia Association (BDA) has a list of speakers/trainers on mathematical difficulties.

Resource books include:

Chinn, S. J. and Ashcroft, J.R. (1998). Mathematics for Dyslexics: a teaching handbook, 2nd edn. Whurr.
Chinn, S.J. What to do when you can’t add and subtract (1999) and What to do when you can’t learn the times tables (1996). Egon.
Grauberg, E. (1998) Elementary Mathematics and Language Difficulties. Whurr.
Henderson, A. (1998) Maths for the Dyslexic. David Fulton.
Henderson, A. and Miles, E. (2001) Basic Topics in Mathematics for Dyslexics. Whurr.
Miles, T.R. and Miles, E. (eds) (1992)) Dyslexia and Mathematics. Routledge.
Poustie, J. (2000) Mathematics Solutions: an introduction to dyscalculia. Next Generation.
Yeo, D. (2002) Dyslexia, Dyspraxia and Mathematics. Whurr Resource videos by Mahesh Sharma are available from P Brazil, trish@chazey.tele2.co.uk.
The National Numeracy Strategy has published guidance on dyslexia and dyscalculia as part of a file called Guidance to support pupils with specific needs in the daily mathematics lesson (Reference DfES 0545/2001).
Leaflets on mathematics and dyslexia are available from the British Dyslexia Association’s website www.bda-dyslexia.org.uk
Most LEAs have a special educational needs or pupil support team able to give advice on appropriate intervention for pupils with mathematical difficulties.
Nationally there is one school, Mark College in Somerset, which has Beacon status for its work with mathematical difficulties (centred on dyslexia) and offers in-service training and the AMBDA Numeracy course.

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Q8: When do you realise that number reversal is part of a bigger problem?

A8:

Well, of the many severely dyslexic GCSE pupils with whom I have worked, only a handful still reversed numbers. So number reversal is not often a permanent difficulty. In itself it is not a great problem, as a 4 written backwards still looks like a 4, for example. The only real problem is if the pupil writes a loopy 2 and reverses it when it can look like a 6.

So that’s a positive start.

However, with younger pupils a persistent tendency to reverse numbers may alert a teacher to the need for further investigation. Please refer to the question and answer (Q3) on recognising dyscalculia or mathematics difficulties.

There are also number transposals, that is writing 15 for 51. You could speculate that our vocabulary for the ‘teen’ numbers, the first two-digit numbers pupils encounter, contributes to the problem. So we say ‘fifteen’, that is, ‘fiveten’, and write ‘ten five’, 15. Numbers from twenty onwards are less irregular, but by then the confusion may be set in place.

This is a good example of an application of some research from the 1920s which said, basically, that what you learn on first exposure to new knowledge is what you are most likely to remember. So if pupils write 51 for 15 when they first meet this number, then unless the correction comes immediately, that will be a dominant memory.

See Dorian Yeo’s book, Dyslexia, Dyspraxia and Mathematics (published by Whurr) for more advice on mathematics in the early years.

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