Dyslexia has specific difficulties in writing and spelling problems and sometimes a specific problem in mathematic included (British Dyslexia Association, 2002). Traditionally, dyslexia has concentrated mainly on literacy – the learning of the reading and spelling processes. But some dyslexic difficulties also transmit into the learning of mathematics. Research results, based on initial studies, claim that about 60% of dyslexics have some problems with school maths (Chinn & Ashcroft 1998).
Of the 40% of dyslexics who don’t seem to have maths difficulties, about 11% of dyslexics do well in mathematics and the rest (29%) do as well as children of the same age, who have no learning difficulties. Surveys say that between 2-4 per cent of people may have severe dyslexia about one in each classroom – and more may have milder forms (Yeo, 2003). It is therefore significant that all teachers are aware of methods to help dyslexics. Many dyslexic children and teens have problems in some fields of maths, particularly the multiplication tables, fractions, decimals, percentages, ratio and statistics.
A dyslexic student usually requires extra teaching, particularly as new concepts are introduced. With this subject, it is important to grasp each concept completely before moving on. If not instructed appropriately in maths, it will become yet another thing to load down their self-esteem. Although research has indicated that difficulties in language experienced by dyslexic people frequently go hand in hand with difficulties in mathematics, there has been too little emphasis on expert study for those having problems with maths (Henderson 1989a).
With the help of specialist teaching and the introduction of significant strategies into their learning, these people can be assisted to get higher levels of mathematical understanding and functioning. In this paper we will examine how dyslexia can affect the learning of mathematics and how cognitive weakness can affect mathematics learning for dyslexic learners then explore how to assess and diagnose the mathematics difficulties for student with dyslexia I will also consider how to facilitate mathematical learning in children with dyslexia. Maths and dyslexia:
The International Dyslexia Association characterises dyslexia as a learning disability distinguished by difficulties in expressive or receptive, oral or written language. Problems may arise in reading, spelling, writing, speaking or listening. Changes have recently occurred in the definitions of dyslexia. The change is a return to the application of the word dyslexia. The term specific learning difficulty used to be equivalent to dyslexia in the UK. This is no longer the case as other specific learning difficulties have been defined, for instance dyspraxia, attention deficit disorder, Asperger’s syndrome (Riddick 1996).
In the last decade following the seminal and tireless work of Tim Miles, Steve Chinn, Ann Henderson and others it has also been increasingly accepted that many dyslexic children do, indeed, have at least some difficulties learning maths, and that there are, in fact, a number of quite identified maths problems which seem to be quite widely associated with dyslexia. Difficulties with mathematics are recognised as a possible result of dyslexia. It is likely that dyslexia causes difficulties in at least some fields of mathematics, most particularly in numeracy.
Although dyslexia is a life condition, the influence on potential depends largely on educational intervention. What may be very hard to discriminate is where an individual’s difficulties with maths are rooted. The learning of maths is very dependent on teaching being appropriate to the person. People do not all learn in the identical way and, as maths is a very sequential subject in that each new idea builds on previous learning, failure can be cumulative. To put right difficulties with maths it may be essential to go back to maths themes, which were learnt well before any difficulty, was identified (Riddick 1996).
How can dyslexia affect the learning of mathematics? Most people consider the rules of maths are consistent, some more consistent than the rules of spelling (Riddick, 1996). In fact there are many inconsistencies in mathematics, which are often invisible. Maths has more exclusion to the rules than many people believe (Riddick 1996). These incompatibilities can especially hinder the dyslexic child in that they challenge the security of learning. Many of these inconsistencies happen in numeracy and in that way the seeds of disorder and failure are sown very early (Henderson 1989b).
This is one reason why endeavours to deal with problems in maths have to move back a long way in the individual’s learning history. For instance in fractions, which are considered as problematic by many learners, we write 1/5 + 3/5 = 4/5 and merely the top numbers are added. Yet in 3/5 x 2/5 both top and bottom numbers are multiplied. We carry sums and decompose in subtraction sums, yet both are trading actions, trading ten ones for one ten and trading one ten for ten ones. We expect absolute exactness in answers and then expect students to abandon this strict regime and estimate.
In entire numbers the succession of words from left to right of the decimal points are units, tens, hundreds, and thousands. For decimals, the succession from right to left of the decimal point is tenths, hundredths, thousandths. There are some factors, which can affect the learning of mathematics. These may happen in seclusion or may interact to make a possible learning difficulty. Each person is an individual and will have a personal mixture of various levels of severity of these factors.
With proper help most of the difficulties connected with these factors can be lessened. Here are some main areas that dyslexia learner may have difficulties in mathematics: 1. Language. Mathematics has its individual vocabulary, for instance, algebra is only a maths word. But maths also shares words with other activities; so “take away” connect with food as well as subtraction (Riddick, 1996). In numeracy there is a series of words used to mean the same maths operation, so we could use add, more, and, plus to mean add.
But we can also use more to imply subtract as in “Nick has three more pens than Ann”. Nick has ten pens, how many pens does Ann have? ” Maths word questions often use a special mathematical form of the English language. It is not enough just to be able to read the words; the students have to understand the meaning that is pertinent to maths. Thus it is not unexpected that people list word difficulties as one of the most difficult fields of maths, even if they are not dyslexic (Miles, Haslum & Wheeler, 2001). 2. Short Term Memory.
Most dyslexic people have poorer short-term memories than their non-dyslexic peers (Chin & Ashcroft, 1998). The results of this are that they can lose track in the middle of doing a multistep intellectual arithmetic problem or fail to realise a sequence of instructions. For instance, in adding 234 + 93 in mind, the learner may try to add mentally using a written method, so starting with the units, there is 4 + 3 = 7, then the tens, 3 + 9 = 12, carry on the 1 to end as 2 + 1 = 3, then reverse these numbers (7, 2, 3) to give 327.
It is improbable that dyslexics can retain by rote learning basic number facts especially times table facts (Chinn, 1998) or it may be that they can not remember the succession of steps needed to finish a long division sum, particularly if the process has no sense or logic to confirm memory. 3. Direction. This tendency for learners to look for logicality (and thus patterns, rules and connections) in what they learn.
There are much more inconsistencies in direction in maths than many people understand, for example the teen numbers, fourteen, fifteen (14, 15) and so on are discordant with other two digit numbers such as forty six, fifty six (46, 56, where the digits are written in the same order as the words). Any inconsistency can affect an uncertain learner and many maths learners are insecure. 4. Visual. This may be a difficulty with recognising differences between symbols, such as + and x; or + and ч or the plan of work on the page of a book can be reason of difficulties, for example if the distance between examples are very close.
5. Speed of Work. One of the odd things about maths is the need to do it quickly. This requirement tends to increase disquiet and thus decrease precision. Dyslexics usually are slower in maths with many factors furthering to this, such as slow recall of basic facts. In a classroom study (Chinn & Ashcroft , 1998) found that dyslexic pupils took about 50% more time to finish a set of arithmetic questions than their non-dyslexic peers. It is difficult for dyslexic children to concentrate on high numbers and this highly slows their work.
This is a perfect example of an area where by choosing proper techniques of work with dyslexic children, simple awareness and adjustment can reduce stress and help learning. 6. Sequencing. Maths needs sequencing capabilities. These might be the ability to count on, or back, in eights or sixes or they might be the complex sequence of the steps in the long division procedure. This problem can connect with language problems in questions such as ‘Take 17 away from 36” which presents the numbers in the reverse sequence for calculation to “26 minus 16” which presents the numbers in the sequence in which the subtraction is computed.
The succession of negative numbers can be bewildering as in negative co-ordinates (-3, -6). Going from coordinates which are positive to coordinates which are negative can make a very high anxiety level or understanding problem for some dyslexics. 7. Anxiety. Maths can make anxiety in most learners (and some teachers) (Henderson & Miles, 2001). For example, fractions often are reason of disorder. It is a feature of dyslexics (and probably other learners, too) that if they pre-judge a question as too difficult to solve then they escape failure by not begin to try to solve the question.
This is the hidden factor that have connection with above. The dyslexic pupils demonstrate a much higher proportion of “no attempts” in the arithmetic test, which is they determine they are unable to get the question accurate, so they avoid failure by not trying the question. Learning needs the learner to take a risk and get inveigled in the learning process. Dread of default can stop the learner taking the risk necessary for learning. 8. Conceptual Ability. There is just a usual spread of conceptual ability in maths for dyslexics and they can reach at or above this potential with proper teaching and motivation (Henderson & Miles, 2001).
Unfortunately the speed of working and the other factors included here can imply that they do not get the experience and practice necessary to develop skills and concepts. Another significant factor is the problem that an early misconception and initial wrong practise of an idea may create a dominant memory. For example, if pupils write 51 for 15 when they first meet this number, then unless the correction comes immediately, that will be a dominant memory. It is important to make sure that each new idea is practised accurately. 9. Thinking Style.
Dyslexic strengths and difficulties share the same source – the dyslexic thinking style. Dyslexics tend to think originally through pictures and images rather than through the internal monologue used by verbal thinkers (Yeo,2003). Nowadays researchers have identified two thinking styles (Yeo, 2003). Basically one style is pattern and sequential and the other is intuitional and entire. Most learners lie somewhere on a continuum between the two extremes of style and indeed this mixture is likely to be the most successful style as success in maths tends to need flexibility in thinking.
Understanding a learner’s thinking style can be one of the most important pieces in the jigsaw of realizing the learner. Each style needs sub-skills, but this does not mean that the learner chooses to use the style more appropriate to his own sub-skills. 10. Notation. Some dyslexic children may have problem if a new piece of notation is introduced, for instance an algebraic symbol, such as “x”, a geometric term such as “obtuse angle”, a trigonometric term such as “cosine”, the use of a colon to express ratio, or the use of the symbols > and < to mean “greater than” and “less than”. Fractional and decimal notation may also prove confusion.
11. Understanding place value. Some dyslexics do not readily understand the idea of place value, especially when there are zeros in a number (20,040). They may also take longer to understand the patterns of multiplying and dividing by 10, 100, 1,000 etc. How cognitive weakness can affect mathematics learning for dyslexic leaner? An important proportion of dyslexic students have difficulty-learning maths (T. R. & E. Miles, 1992). Some dyslexic students are held back by surface aspects of numeracy – difficulties in remembering orally encoded maths facts, such as multiplication tables, for example.
Others have more severe problems. In students with severe maths learning difficulties: 1. Basic counting development is delayed. Students learn to repeat oral counting sequences later than their peers, and also control the demands of enumerating specific objects later than their peers (Chin & Ashcroft, 1998). 2. These students also seem to understand the main principle later than other students. On the other hand, however, as their counting skills evolve, dyslexic children with important basic maths difficulties do not seem to develop basic “number sense”.
In other words they fail to develop a “feel” for numerosities, and a “feel” for abstract numbers (Henderson & Miles, 2001). In addition, we know that individuals with dyslexia may have difficulties with the language of mathematics and the concepts connected with it. These include spatial and numerical relations such as before, after, between, one more than, and one less than. Mathematical terms such as numerator and denominator, prime numbers and prime factors, and carrying and borrowing may also be difficult (Miles, Haslum & Wheeler 2001). Children may be bewildered by implicit; multiple senses of words, e.
g. , two as the name of a part in a sequence and also as the name of a set of two objects. Difficulties may also happen around the concept of place value and the role of zero. Resolving word problems may be particularly challenging because of problems with decoding, comprehension, sequencing, and understanding mathematical ideas. In understanding the complex nature of dyslexia, Ansara (1996) made three general assumptions about learning, especially, for individuals with dyslexia. These assumptions affect the way one needs to provide instruction. They are: 1.
Learning involves the understanding of patterns, which become bits of knowledge that are then arranged into larger and more significant units. 2. Learning for some dyslexic learners is more difficult than for others because of deficits that intervene with the ready recognition of patterns. 3. Some students have difficulty with the organization of units into wholes, due to a disability in the handling of spatial and temporary relationships or to sole problems with integration, sequencing or memory. It is important to be aware of the child’s learning style (inchworm or grasshopper).
Basically, Inchworms are step-by-step, formula learners whilst grasshoppers are intuitive, big-picture learners. The learner differently makes sense of the world and their experiences (Chin 1998). This can be done sequentially or holistically. Unfortunately, many numeracy teachers tend to limit themselves to providing sequential experiences and logical explanations. The grater part of dyslexics is seeking a holistic understanding. Without it they can’t understand the purpose of the activities, lose control of the experience and cannot remember the “bits” of information.
Some learners are greatly intuitive in the way they learn and do maths. For example, if asked to find three consecutive numbers, which add up to 33 they will divide 33 by 3 and arrive at 11, then quickly conclude the trio with 10 and 12. Other learners are pattern and step by step in their style. They would approach the 33 question algebraically, probably by inferring the equation x (x + 1) (x + 2) = 33, which resolves to x = 10 (Chin & Ashcroft 1998). Learners require drawing on both these learning styles. An over-dependence on one style is in some way a disadvantage.
Dyslexics will often choose the style, which they consider as most reliable, the formulaic style, even though it may not be the best way for them to solve the difficulties. Assessment for diagnoses of the mathematic troubles for dyslexic leaner: There are at least two ways in which a student may be identified for assessment (Chin & Ashcroft 1998). The first is that the education institution recognises the presence of a learning or behaviour problem and asks the student’s parents for permission to assess the student individually.
The teacher has to identify if the child has scores too far below his or her peers and to present tests in a particular grade. Alternatively, the student’s classroom teacher may identify that there is some problem – possibly the student’s work is below anticipations for his or her grade or age, or the student’s behaviour is shattering learning – and so the teacher directs the student for assessment. The student’s parents can also call or write to the school or to the director of special education and ask that their child be evaluated.
They may suspect that the child is not progressing as he or she should be, or notice special problems in how the child learns. If the institution suspects that the child, indeed, may have a disability, then it must conduct an assessment (Riddick 1996). The SEN Code of Practice (2002) requires schools to provide appropriate support so that all dyslexic children have the opportunity to benefit from an education (Karp & Howell 2004). In line with the Code of Practice, the SENCO will made an Individual Education Plan, setting out the steps which the school will take to provide appropriate support for the child’s needs.
If local education authority does not think that the child has a disability, they may refuse to assess the child, but must apprise the parents in writing as to their reasons for refusing. If parents feel mightily that their child does, indeed, have a disability that needs individual education, they may request a due process hearing, where they will have the opportunity to show why they think their child should be evaluated. While all students are different from each other in very many ways, they may also share something in common.
Each may be a student who has dyslexia that will require special education services in the school setting. Before decisions may be made about what those special education services will be, each student will require an evaluation conducted by specially trained educational personnel, which may combine a school psychologist, a speech/language pathologist, special education and standard education teachers, social workers, and, when appropriate, medical personnel. Assessment in educational settings serves five fundamental purposes (Miles, Haslum & Wheeler, 2001):
1. Screening and identification To screen children and identify those who may be experiencing protraction or learning difficulties. 2. Eligibility and diagnosis To decide whether a child has a disability and is eligible for special education services, and to diagnose the peculiar nature of the student’s problems or disability. 3. IEP development and placement To present detailed information so that an Individualized Education Program (IEP) may be evolved and appropriate decisions may be made about the child’s educational.
4. Educational planning To develop and design instruction appropriate to the child’s special needs. 5. Evaluation To evaluate student’s progress. A major issue seems to be identifying dyslexia across the population. There are problems within the school system of proper and early identification. Within higher education, a good idea would be a wider screening system for dyslexia, although this is already being used in some further and higher education institutions. One system is a fifteen-minute computer-based screening test.
It is an easy thing to do, and it is preferable to do this early on to avoid situations where students have been underperforming on their degree courses. For testing for numeracy difficulties, it is not a bad idea to create your own informal diagnosis. Think what the child needs to know, combining the prerequisite knowledge, and build your test accordingly. One of the most revealing diagnostic questions are “How did you do that? Talk me through your work. ” And remember, the mistakes are more revealing than the right answers.
The end outcome of a mathematics test should be a lot more than just a number. There is a test for dyscalculia, written by Professor Brian Butterworth (1987). He devised DfES (the Department for Education and Skills) tests which involve a sequence of simple maths questions, combining counting dots on a computer screen, or comparing two sets of images and indicating which is the larger. Children are classed according to the time they take to answer the questions, with different response times expected for different groups.
Butterworth’s test for dyscalculia will deal with early identification. Some children may then advance beyond the levels of concern. Early indicators will be problems dealing with sequences, problems with long retention of basic facts, no sense of number, an inability to see prototypes in information. Certain difficulties, for instance, reading and comprehending the unique language and vocabulary of mathematics, may “click in” after a comparatively successful start in the subject. A student may excel at mental arithmetic and fail when needed to document (or vice versa).
Different fields of mathematics may well produce different reactions from different students. It is often helpful to analyse a mathematics task in terms of, for example, vocabulary, basic fact knowledge, realising of the four operations, memory (short and long term), sequencing ability, generalizing, documenting, spatial awareness, and then to identify which area makes a problem for the learner (Miles, Haslum & Wheeler 2001). As a basic indicator of maths disability is when the student will not be showing expectations in studies with no obvious reason such as emotional state or an illness.
This underachievement may manifest itself in specifics such as difficulties with knowing the value or worth of numbers, in realising than 8 is one less than9, for example, or in being able to quickly recall (as the NNS requires) basic number facts – or probably in a absolutely mechanical petition of algorithms (procedures) with no understanding of why or what the result implies or how to reckon up the answer (Karp & Howell 2004). Some students 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 students just falter in the counting-on phase of development. The (part) question as to how dyscalculia differs from ‘dyslexia with numbers’ will depend on the explanation of “dyslexia with numbers”. Often, a primary part of the assessment process comprises examining a student’s work, either by choosing work samples that can be analyzed to identify academic skills and deficits, or by conducting a portfolio assessment, where folders of the student’s work are investigated (Karp & Howell 2004). When collecting work samples, the teacher chooses work from the areas where the student has difficulty and regularly examines them.
The teacher might identify such elements as how the student was instructed to do the activity (e. g. , orally, in writing), how long it took the student to finish the activity, the pattern of mistakes (e. g. , reversals when writing, etc. ), and the pattern of right answers. Analyzing the student’s work in this way can yield useful insight into the nature of his or her difficulties and advise probable solutions. Sustaining portfolios of student work has become a popular way for teachers to track student success.
By collecting in one place the body of a student’s work, teachers can see how a student is advancing over time, what problems seem to be re-occurring, what concepts are being understood or not understood, and what skills are being developed. The portfolio can be analyzed in much the same way as choice work samples, and can develop the basis for discussions with the student or other teachers about difficulties and successes and for determining what modifications teachers might make in their teaching. Facilitating mathematics learning for dyslexics: Using of calculators
The proper use of calculators can be very helpful. As with every equipment there can be disadvantages and cautions. The calculator can be used to carry out sums which would take a long time on paper, for example 522 ч 11. 72. Calculators are also source of information in advance provided by log tables and sliding rules. They can also compute hard statistical data and present data graphically. For dyslexics, there needs to be some attention over right keys and correct order of keys, which again can be verified by pre-estimations (Yeo, 2003). So if we ask for “5.
3 divided into 607” we key in the numbers in reverse order 607 ч 5. 3, seeking an answer just over 100. If the keys are used without error and in the correct order, the calculator can be used to show up or develop patterns. Software for maths Software should be able to offer the dyslexic learner an effective learning input. Voice output, graphics, symbols and text can all be included to give a multisensory experience to the learner and, where appropriate, a diagnostic element can be incorporated as well. Notwithstanding some programmes are near to this, most are not. Existing programmes are fallen into three groups:
1. Games which present practice (Perfect Times – online games to practice the multiplication tables). The biggest problem with these is that the appearance and design can be somewhat age peculiar to the level of maths in alike way that books with a reading level appropriate for poor readers are often far too young in essence. Some have built in progressive maths construction which enables the user to target the level of maths is required. Sometimes the games can be frustrating in that they slow up the maths or take an immortality to complete and achieve the goal. 2. Programmes such as Excel and plot graphs.
They can be very helpful for dyslexic children with bad presentation skills and slow speed of producing. 3. Some programmes are just books on screen making use of the potential of the computer to do so much more than just show print (Language Shock – Dyslexia across cultures). Nevertheless, for a dyslexic learner these programmes may be easier to trail through than a book. The child can read E-Books on ordinary computers, PDAs and some special e-book readers. A large screen is more comfortable and clear then printed text. Dyslexic child may also be able to listen to the text.
DAISY format can give e-books which the student can listen to, but also search and move around. Using ICT for self-governing working and learning Software can permit the learner to work independently. Certainly the success of this depends on the design of the programme. For example, it is important that the learner can move easily around the programme. It is good if there is clear voice output and that the programme uses good images. Many dyslexics consider view on the screen overdone. There seems to be a striving among some designers to put everything from their design collection onto the screen.
Preparing the proper balance is hard as learners are very individual. Multiplication and division Multiplication and division are the hardest for the child to master. It will make it easier for the dyslexic to learn if they actually understand the concept. The following may assist: take 5 pairs of items, gloves, socks, shoes, toy animals, anything as long as the pairs are identical. Lay out the pairs before the child, demonstrate her that there are two items in each pair, one pair has two items, two pairs have four items, etc (Miles 1992).
When the child can see the five pairs have ten items, clarify as you write it down, that is what 5 x 10 signifies. This exercise can be reiterated with each of the different pairs until he or she understands what the “2 times” implies. When the child is familiar with the 2 times table, they should start to work on all the tables in the following order: 2x, 10x, 11x, 5x, 3x, 4x, 9x, 6x, 7x, 8x, then eventually 12x, which they should know from the other tables. When we first use worksheets, utilise pictures of known animals or items for students to count.
If a student has problem with one special fact we have to show them how to use these facts in order to help them to remember. Games act particularly well Games work particularly well with dyslexic children as they seem to have a dislike to plain work sheets (Riddick, 1996). Children like playing Bingo. This multiplication Bingo game is a big hit within most children (Henderson & Miles 2001). Bingo type card can be made on a piece of paper with the answers to all the multiplication facts, up to 6 x 6 with regular dice, 9 x 9 and 12 x 12 (or with the polyhedral dice available at school supply stores).
You have to take it in turns to roll the dice and multiply the two numbers rolled and mark it off on the players’ Bingo sheets. Without making it too evident, let the child win some games to set up their self-confidence. We have to teach the child to talk through maths problems, saying it carefully to them, without disturbing others. This will employ ear as well as visual memory abilities. Explain to them how this will assist because the brain can store different types of memories. Real coins
When teaching about money it is better to use real coins instead of plastic, this is far more fun and exciting for the children (Karp & Howell 2004). Children are excited as they are given real coins to sort. They make good progress in their knowledge of the values of the different coins. It is not always essential to spend a fortune on items for tactile use; change from your pocket, pieces of cereal, simple circles clipped out of coloured paper are perfect for whole number and fraction work. Conclusion: Dyslexia is a learning difficulty involving problems in acquiring literacy skills.
However, dyslexia often involves specific difficulties in acquiring arithmetical skills. Building a solid foundation in math involves many different skills. The overall evidence suggests that all or most dyslexics do, indeed, have difficulty with some aspects of mathematics, but that in spite of this a high level of success is possible. Progress is often slow and frequent revision is necessary. The same ground may need to be covered many times. However, I think that a teacher should provide children with appropriate strategies and a framework they can relate to.
This will help the dyslexic children to grow in confidence, become independent in their learning of mathematics and, above all, to succeed. The concept of different learning styles, though relevant in the case of all pupils, is particularly relevant to the teaching of dyslexics. The diagnosis and subsequent remedial programme offered, and even the subsequent mainstream programme, should acknowledge that not all children process numbers in the same way and that children have different batteries of skills and knowledge.
The typical dyslexic problems of difficulty in rote learning, short-term memory deficits, and weakness at arranging symbolic material in sequence are likely to make many standard methods and basic facts difficult to learn. I believe that the relationship between teacher and pupil has to exist. This needs to be a partnership in which both are actively involved. It is understood in particular that they will talk about the pupil’s difficulties and try to discover their source. This cannot be done unless both of them are fully a