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T1628 Dyscalculia
in Schools: what it is and what you can do Sample Pages Contents 1:
The concept of dyscalculia 2:
Maths and dyscalculia: is
dyscalculia a side-effect of dyslexia? 3:
Why are some children bad at maths? 4:
The best ways to teach children who appear to be dyscalculic 5:
Overcoming dyscalculia: the
systematic approach and the holistic 6:
The systematic method of approach: the
3 steps to solving the 7:
Policy documents on dyscalculia 8:
The inchworm and the grasshopper: how
dyscalculic children learn maths 9:
Strategies adopted by dyscalculic children when faced with maths
problems 11:
Multi-sensory approaches to overcoming dyscalculia 12:
Self-esteem as a method of overcoming dyscalculia 13:
Check to praise – a method of motivating dyscalculic children 14:
The maths and self-esteem special group:
raising self-esteem and 0vercoming
dyscalculia together 15:
Self-esteem, maths and behavioural problems 16:
Information for parents 17:
Information for governors and members of staff Other Resources for Teachers and Parents of Children with Dyscalculia
Dyscalculia is the name given to the problem suffered by people whose ability to handle mathematical concepts is significantly lower than we might expect it to be, when taking into account that individual’s age and intelligence. This definition makes it clear that dyscalculia is not a
term intended to be used for everyone who is poor at maths.
But as we will see later, many of the methods of teaching that have been
devised for helping pupils who are dyscalculic will work with all pupils who
have difficulties with maths, irrespective of the cause of the problem. However just because the best ways of working with children
who have difficulties with maths are almost always the same, this does not mean
that we should be too ready to use the word “dyscalculia” in cases where it
does not apply. It is obvious that everyone sits somewhere on a continuum
of mathematical ability, which we might arbitrarily number from 0 to 100.
Anyone at position 100 is a mathematical genius.
A person at position 0 has no mathematical ability whatsoever.
A person at point zero has no concept of number and therefore no ability
to see how a number such as “2” relates to “4”. From this point it is possible to devise a spread of
mathematical ability for all age groups.
If (for the sake of this exposition) we accept that the level
mathematical ability in each age group is a normal curve then we will have most
people with an ability rating of 50 and ever smaller numbers of people as we get
further and further away from position 50. Even if reality doesn’t quite match the standard pattern
suggested above, we would expect to have a small number of people at each end of
the curve, and we might choose to give a special name (such as dyscalculia) to
the people who are at the low end. The
giving of a name in this way will inevitably have the appearance of separating
out this low achieving group, but the name does not of itself signify that there
is anything particularly different about these people, other than the fact that
they are at the lower end of the spectrum. The most likely factor that binds together those who fall towards the end of our 0 to 100 scale at any particular age is intelligence. It seems reasonable to start from the belief that at any given age, the lower the level of intelligence, the lower the level of mathematical ability. If the match between intelligence and mathematical ability
were perfect there would be no need for a concept such as dyscalculia.
However, what we do find is that there are some children who appear to
have a mathematical ability which is much lower than we would expect given their
intelligence. From this finding we
can begin to see that there might be a specific learning difficulty which some
children have in relation to maths. If dyscalculia represents a specific learning difficulty
one might expect that some people who appear at the bottom of the ability range
in mathematics might well be at or near the top of the ability range in other
areas of study. From such a
view we might speculate that some of those people who are at or near the bottom
of the scale in mathematical ability within a certain age group suffer some sort
of genetic dysfunction which makes it difficult or impossible for them to learn
mathematics in the way that others of the same age will do. At first sight this seems very reasonable.
Belief in such an approach has been heightened by the belief among
researchers into dyslexia that dyslexia itself is genetic in origin.
The definitions and ideas above make dyscalculia seem like a mathematical
version of dyslexia. We might also
be encouraged by a body of neuropsychological research which has shown that
mathematical ability is particularly associated with specific areas of the
brain. What’s more, we also know that there is a link between
higher levels of ability in maths and a particular ability in music – and this
suggests that a particular part of the brain might well be responsible for the
ability to handle specific types of abstract activity, in this case mathematical
and musical concepts. A failure in
this area of the brain can then lead to a much lower than expected ability in
maths. Thus we might expect to find that a percentage of the
population is significantly worse at maths than we might otherwise expect when
IQ score and age is taken into account.
Dyscalculia becomes the behavioural outcome of a genetic disorder.
We might note that those involved in working with children who have
dyslexia speak on occasion of 10% of the population being dyslexic, and we might
assume that a similar figure applies with dyscalculia. However we must also note that for every ten children who
are diagnosed as dyslexic there is probably only one for whom the term
dyscalculia is applied. Does
this suggest that our opening hypothesis is wrong?
Or could it be that there are other factors at work here?
Or does dyscalculia simply affect fewer people than dyslexia?
Or is it simply that we are less open to the notion that failure in maths
is a sign of a specific learning difficulty? Certainly far fewer educational psychologists are
administering tests for dyscalculia than there are administering tests for
dyslexia. A review of the
literature shows that there are only a handful of books on the subject of
dyscalculia, as opposed to thousands of texts on the subject of dyslexia.
Even as we put this book together the Times Educational Supplement
carries a front page story about a supposed “cure” for dyslexia.
Such claims, such stories simply do not exist for dyscalculia. In part this might be explained by the impact being
dyscalculic has on a pupil, as opposed to the impact of being dyslexic.
A dyscalculic pupil fails at maths – but this may have no impact on the
child’s ability in history and geography, where the use of number is very
limited. But a dyslexic pupil will
fail at history and geography because written English is the very medium of
those subjects. It is therefore
possible that there has simply been less pressure for support for dyscalculic
pupils because their disability affects the teaching and learning in a smaller
number of subject areas. Issues relating to the impact of dyscalculia, and the
publicity that it gains in the educational and national press, are quite
possibly part of the explanation for the lack of awareness and action taken on
behalf of dyscalculic pupils. But
these pointers do not help us understand what dyscalculia really is.
Is it a specific learning difficulty?
Is it genetically based? To
answer these points we now turn to the link between dyscalculia and dyslexia. 2: Maths and dyslexia: is dyscalculia a side-effect of dyslexia? Some esteemed writers on dyslexia have suggested that the
genetic disorder which leads to dyslexia also leads to failure in maths.
They put forward a number of reasons as to why this is likely. Firstly it is suggested that a number of the problems associated with dyslexia (for example difficulty with short term memory, and difficulty with sequencing) are as likely to affect the ability to cope with mathematical concepts as they are to affect the ability to handle the written word. Clearly there is a logic in this. Issues such as understanding multiplication tables which are at the heart of mathematics are sequencing issues. Numbers are dealt with as sequences – it is logical to see dyscalculia as a dyslexia problem. A child who has particular difficulty with multiplication tables often expresses the view that she can’t remember where she was in the table – a clear indication that there might be a short term memory issue at work. Secondly it is noted that in the UK we have traditionally
taught and tested mathematics in a way that leaves the subject surrounded by
written English. Many mathematical
questions are posed as written questions, requiring the student to be competent
in English before he or she can handle the maths. Maths is not just a question of knowing what symbols such as
+ actually mean. It is also a case
of being able to read and understand and remember the meaning of “sum of”,
“add”, “total”, and “equals”. From arguments such as these we might begin to believe that
a dyslexic child is also a dyscalculic child.
Once a child has been diagnosed as dyslexic then support should be given
in maths as well as written English. Reviewing the
evidence Unfortunately there is some evidence to suggest that the
link between dyslexia and dyscalculia is not as straightforward as we might
hope. A few studies have suggested
that instead of all dyslexic students being poor at maths, about 25% of dyslexic
students are apparently above average at maths. This suggests that contrary to the above argument dyscalculia
is a separate issue from dyslexia. In the light of this evidence we might feel more inclined
to say that dyscalculia and dyslexia are separate, but that some pupils –
perhaps the majority of pupils – suffer from both dyslexia and dyscalculia. Unfortunately the evidence which might translate these
views which appear to be reasonable, into views supported by experiment and
data, is hard to come by. Genetic
science is not far enough advanced to give definitive answers and, where tests
have been carried out on dyscalculic pupils, the number of people tested has
often been extremely small. This latter point is particularly worth remembering as it
has bedevilled testing in relation to dyslexic students as well as dyscalculic
students. The number of pupils and
students examined in the research which is reported is often no more than a
dozen or so – a very small sample indeed and one from which it is very hard to
draw serious implications. But such evidence as there is does seem to keep coming back to the fact that while many dyslexics do also show signs of dyscalculia there is this sizeable minority (the 25% figure is regularly quoted) which, far from being way below the expected level in mathematical ability, is actually considerably above that level. However we should also note that although some research has
revealed this figure to be correct in surveys on dyslexic pupils, this is a
figure which has now started to be handed down as if it is an absolute proven
fact – when it is not. Again this
is a problem that afflicts dyslexia as much as dyscalculia.
It is commonplace for organisations that seek finance or support for
dyslexics to quote “facts” such as the view that Einstein was dyslexic.
This like many other such claims is based on virtually no evidence but is
handed down from one speaker to another along with many other urban myths. Steeves 1983 cites a boy who in a few seconds could
calculate the number of squares on a piece of squared paper, but who was
profoundly dyslexic and this is often cited as “evidence” of the separation
of dyslexia and dyscalculia. Along
similar lines Griffiths in a paper in 1980 cited the issue of a university
lecturer in physics who in his 50s could not repeat his six times table.
In this case the suggestion is that dyscalculia is therefore a separate
concept from difficulty in understanding scientific principles and formulae. Indeed I could add my own contribution to this type of
debate. One of my daughters has
been diagnosed as profoundly dyslexic by suitably qualified educational
psychologists on two separate occasions. She
suffered the traditional problems of having difficulty with maths, but it was
perfectly evident when one spoke with her on a one-to-one basis that she had a
perfect grasp of mathematical principles. What she had was some difficulty with sequencing, and a
significant amount of difficulty reading the text of the maths questions she was
given. Because of these
difficulties she was placed in a group at secondary school that was entered into
maths GCSE to take papers which could at best only give the pupils a Grade C
pass. Such was her grasp of
the subject that she was awarded the rare distinction of a B from the marks
gained on these exams. Meanwhile it
was considered that her dyslexia was so bad that in other subjects she was
allowed a reader in the exams who would read her the questions! I cite the case of my own daughter not to prove that
dyscalculia is separate from dyslexia, but rather to show the dangers of
accepting much of the “evidence” that currently surrounds the subject.
Evidence from individual cases cannot be used as proof that there is
independence of dyscalculia from dyslexia for with the simple use of two
observations the opposite can be argued: Firstly, we may note that a number of people who are
dyslexic are drawn in their work and interests to activities which use the
written word. It is not at all
unknown for dyslexic children to select for A level study the very subjects that
we might expect them to seek to avoid, such as English and history.
It is not unknown for people who are writers by profession to show all
the signs of being dyslexic. It is
not at all impossible for my own interest in maths to have impressed itself on
my daughter, and that she determined to sort out her maths problems with me. In other words she was dyscalculic, but through the
application of good teaching and learning techniques, she overcame it. Which brings us to the second point: just as there are methods of teaching dyslexics which can be highly effective and which can remove almost all signs of the disability from people who have undergone the training, so there are methods of dealing with dyscalculia which can remove all the effects of dyscalculia. Put these two points together and we could, despite the evidence above, argue that dyscalculia is a side-effect of dyslexia – that is, all dyslexic pupils also suffer from dyscalculia. But we may also note that some pupils have a strong desire to work with mathematical concepts, and have become particularly successful at overcoming the dyscalculic part of dyslexia, to such a degree that they become above average in their mathematical ability. This over achievement may have been caused by good teaching, home support or an interest in a topic that relates to maths, or requires a mathematical ability to engage in it. In exploring this possibility, one interesting field of
research has looked at the specific problems that supposedly dyscalculic pupils
reveal when undertaking maths tests. In
some cases it was found that pupils had particular difficulties with mental
maths tests, as might be expected through the suggestion that dyscalculia is
related to sequencing difficulties. But
other pupils did better than expected in this field – almost as if the
opportunity to do mental maths was a liberation (for them) from the tyranny of
the written word and symbol. In other research some pupils were found to be
mathematically able in terms of concept awareness and understanding. But some of
these pupils suffered from particular problems with addition and subtraction.
Indeed this latter scenario is one that often crops up in reports about
dyslexics with mathematical problems. What is clear however is that a considerable number of
writers on this topic have failed to spot that this is an issue which often
reoccurs in reports on dyslexic pupils. It
is not so much the fact that dyscalculic pupils cannot “do” mathematics or
understand mathematical concepts as such, but that they simply find addition and
subtraction confusing. Obviously
any inability to handle any of the four basic functions of maths is bound to
disrupt all attempts to solve mathematical problems.
But such a fundamental failing can be easily misread as an inability
to understand all types of mathematical issues rather than a specific
problem relating to one or two of the fundamental concepts of maths. Therefore we are now left with three possibilities: Firstly we can argue that dyscalculia is a separate issue from dyslexia, but it is a specific learning difficulty that affects a significant number of dyslexics. Secondly it can be argued that dyscalculia is a side-effect
of dyslexia, but that some dyslexics do not show the symptoms because they have
worked to overcome the problem. Thirdly it can be argued that dyscalculia is nothing other
than a failure of learning in relation to the basic functions of maths.
This may be due to short-term memory problems, to sequencing
difficulties, or simply due to poor teaching or poor learning.
Once remedial teaching has been undertaken the child will be able to
undertake work in maths which is as expected, given the child’s age and
intellectual ability. All three arguments are sustainable given the current state of our knowledge. Fortunately, as we will see later, whichever theory one accepts, the way of overcoming dyscalculia remains the same. |
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