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.
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.
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.
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.
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’.
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.
Butterworth’s test for dyscalculia will deal with early identification. Some children may then progress beyond the levels of concern.
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.
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
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.
The second question, on using a teaching assistant effectively, relates, of course, to the first question. Obvious benefits are: