Dyslexia and Mathematics by Tricia Gardner

DYSLEXIA PARENT SUPPORT GROUP Dyslexia and Mathematics by Tricia Gardner Background In the 1970s it was common to diagnose dyslexia by identifying ch...
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DYSLEXIA PARENT SUPPORT GROUP

Dyslexia and Mathematics by Tricia Gardner Background In the 1970s it was common to diagnose dyslexia by identifying children who had reading difficulties but average or good mathematical ability. These children may have had some specialist remediation. If a child had poor reading and poor maths then they were classified as being slow learners. These children would not have been given any specialist help. They would have been seen to have general learning difficulties and have been placed in a group of slow learners. It was not until the Bangor dyslexia test (Miles 1983 and later 1993) identified 11 core difficulties discovered by diagnosticians that the link between dyslexia and mathematics was made. These 11 difficulties were: • Reading • Digits & Numbers • Sound Symbol Correspondence

• •

Writing Memory

• •

Spelling Sequencing



Orientation



Polysyllabic Words

• •

Speech Alphabet & Sequence

The latest theory regarding dyslexia is that it is essentially caused by or results in an underlying difficulty in phonological processing of auditory information in at least two thirds of all observed cases. All 11 difficulties are related to mathematics and all are underpinned or dependant on phonological processes. Why does dyslexia affect mathematics? Dyslexia is a syndrome which manifests itself in a variety of different ways. So for some children their mathematical ability will not be affected at all whilst the effect on others will range from mild to severe. Some of the current theories as to why dyslexia affects mathematics are: Language Learning Weaknesses This makes it difficult to learn all the codes used in maths. For example, the meaning of all the different symbols, place value, how fractions and decimals must be treated differently. A difficulty with vocabulary e.g. “product”, “minus”, “subtract”, “takeaway”, “times”, “multiply”, “share”, “fraction” etc. would lead to difficulties in understanding many concepts and instructions. Consider how the vocabulary of mathematics uses many terms when talking about quantities: Big Some Light Lot More

Same Different Small Great Many

Amount Difference Product Largest Fraction

Portion Plus Minus Less than More than

Mathematical language is often quite complex and ambiguous. For Example, by Tricia Gardner 1

Miles (2004) shows how the words right and write can cause confusion because of their many meanings: Write it down. You haven’t got it right. Put the one right at the top. Now make that right. Put it on the right. Right, now we’ll do another one. (2004 p 56) Commercially Produced Schemes (text books and work sheets) The reading level of the text in a question may be too high. It is also very difficult to pick out meaning from the text in a question because of the language used. Processing speed is also affected so it may take them longer to understand the problems e.g. “Take away double the number you started with” or “Half it four times” Many texts contain beautiful illustrations and look highly attractive and colourful and really appealing for children. However lots of illustrations and cartoons and small disjointed text make it extremely difficult to know what to focus on. This can cause overcrowding as it is very difficult for the dyslexic child to pick out the relevant information. Short Term Memory Weaknesses It is now accepted that most dyslexic individuals have difficulty with short term memory. Memorising (days of the week, months of the year, multiplication tables etc.), mental calculations, remembering procedures such as algorithms, remembering which direction to work a sum out, mistakes in calculator procedures are all problematic. Organisational Weaknesses This will affect their grasp of timetables and their ability to set their work out clearly and systematically. If they have handwriting difficulties it may make their work very difficult to read and follow. Maths and the Hemispheres There is now evidence that the brains of some dyslexic individuals may be “wired” differently to the brains of non dyslexics and that they experience different hemispheral dominance. It is believed by many (such as Shaywitz) that dyslexics have less lateralisation so that they have different hemispheral processing capabilities. The left hemisphere is responsible for logical sequential thought needed for such things as number sequencing and arithmetic calculations. The right is more concerned with spacial abilities and has been found to be the dominant hemisphere in many dyslexic individuals. Dyslexia is Developmental The old theory that dyslexic individuals were somewhat bizarre, in their spelling for example, is being replaced by the theory that they are not. Dyslexic spelling has been by Tricia Gardner 2

found not to be bizarre but to resemble the spelling of younger non dyslexic individuals. In the same way their mathematical understanding in some areas takes longer to develop and resembles that of younger children. Younger children very much need to work in the concrete for example when working with fractions they need to see the fraction. They cannot move to the abstract until they have reached that stage of development (Piaget). Telling a dyslexic child something does not mean they will “get it” the auditory channel is the weakest. They need to see it and they need to do it. They therefore may need concrete apparatus for working out a problem or understanding a concept. They need to complete their learning in the concrete before moving onto the abstract. For this reason they need multi sensory mathematical experiences. When they are young they are given these experiences but often the apparatus is removed from the classroom too early for dyslexic children. An example of a multi-sensory learning experience linking the maths to the language. Fractions (the real nasties)

Example of how to get children to “see” how the fractions are equivalent A little girl (Bee) was in year 6 at primary school when I worked with her. After a revision of the last lesson I gave Bee the algorithm 2/3 +1/6 and once again she added the denominators to produce 3/9. I asked her to show me this with the eggs and egg boxes and at once she saw how it was not possible to do so. I gave her two exercise books and a few sheets of paper and asked her to add them together. She was able to comprehend how she could turn the books into paper but that she could not turn the paper into books by Tricia Gardner 3

and we discussed how she could take the cover off the books and then count them which she did. This took some time but hopefully she will remember doing it and think about what she discovered. She was able to link the books to the egg boxes and by trail and error realised that when dealing with fractions it is impossible to make something smaller, bigger but that there is a way of making something larger smaller. The biggest difficulty for Bee is realising that 1/12 is smaller than 1/6 because 12 is a larger number than 6. That is why it is so important to be able to show her. She was able to perform the algorithms and make ones of her own from situations I presented her with. She did this all by manipulating the eggs and exchanging for example 1/3 for 2/6 when she needed to. I acted as the banker and she told me what she needed for each transaction and explained why. In this way we were able to practice the mathematical language she will come across such as numerator (the number of eggs) denominator (the number of boxes). Dyslexia in the Classroom Dyslexic individuals will very often get by by masking their difficulties for example by copying other children’s work (they are skilled at it). As processing speed is slow instructions take longer to be assimilated. They often won’t ask for constant clarification they will copy. It is not cheating, it is a survival strategy. Their workbooks may hide any difficulties they really have. They will often learn an algorithm by the recipe approach with no understanding of the mathematical processes involved so when they forget the algorithm (which they often do) they are completely lost. Examples of Common “Dyslexic” Errors 83 +

49 1212

35 +

67 912

43 +

72 115

The student has started on the left as one would for reading. He/she has failed to understand the notion of regrouping, is simply following a recipe with no understanding of place value and is unfamiliar with setting the algorithm out vertically. 83 +49 1212 This child has no understanding of place value. They are also confused with the vertical presentation. They need to be taken back to basics with concrete apparatus. They have learnt a process but forgotten it.

Some of the difficulties dyslexic children may have with maths are: Sequencing the days of the week Sequencing the months of the year. Multiplication tables. Specific difficulties with the passage of time and time related problems. by Tricia Gardner 4

Reading numbers accurately. Telling the time. Simple computation (addition, subtraction, multiplication, division). Naming numbers e.g. 4 read as five. Counting forwards and backwards. Matching the correct name to the mathematical symbol and then remembering what symbol or process represents. Mental calculations. Using money. Trouble with left/right, forwards/ backwards, before/after, above/ below. Noticing when the mathematical symbol has changed i.e. + to – Shifting from one topic to another. Keeping columns straight, e.g. the tens and units in the right columns. Spatial difficulties causing confusion due to untidy presentation. Dyspraxic problems making the numbers difficult to read. Language difficulties having an influence on any reading and writing connected to mathematics. Putting the correct numbers in a calculator. Pressing the correct symbol key on the calculator. Decimal point i.e. difficulty with place value. Great difficulty with fractions. Remembering the right algorithm. They memorise the wrong method. Maths phobia and anxiety. Maths is a subject which induces anxiety as there is a right answer and a wrong answer. Therefore the risk of failure is increased. It is a subject that requires an amount of risk and confidence. Children cannot be afraid of getting the answer wrong. Children are less likely to take risks if they do not feel secure and confident. The imbalance of skills often witnessed in dyslexic children is often seen in their mathematical ability. Mathematics calls for a wide range of abilities which draws on both hemispheres. Dyslexics may therefore be slow to learn their multiplication tables, perform computation and learn algorithms. However, in other ways they can show profound understanding and ability. For example, they may have very good visual spacial skills needed for such things as recognising large scale pattern and visualising three dimensional configurations. Many dyslexics have gestalt thinking (the ability to see the bigger picture - Thompson, 2002), which is needed for creative mathematical thinking. The dyslexic child should therefore never be seen as a slow learner and treated the same way because unlike a slow learner development they may not be slow in all areas which will make their needs different. Many can and do have exceptional abilities. by Tricia Gardner 5

What can I do for my child at home? Helping with homework can be difficult as often processes for mathematics teaching have changed since the Numeracy strategy was introduced and the vocabulary used can be different. It is very confusing for a child if you try to teach them a different method (even if you think your way is better). Very often the best way will not be yours or maybe not even the teacher’s. The best way could be the one the child works out for themselves. Encourage them to keep a scrap of paper with them to write numbers down rather than trying to hold them in their head. Younger children may find a number line invaluable they can also use the numbers on a ruler if they haven’t got a number line. Make a multiplication square (or download one from the internet) to use at home, keep it at the back of their book and encourage them to use it if they need to. Do not teach them to chant their tables by rote if they find this difficult unless they understand what multiplication is i.e. repeated addition. Dyslexic children do not unconsciously always make the connections so if they learn the tables and have no understanding of what they are chanting like parrots they will have no strategies to work them out them when they forget them (which they will!). Teach them short cuts such as gipsy calculations (nine times tables on their fingers) anything which helps them. Makes mathematics fun! The chances are if your child has a difficulty in maths they may not enjoy it. No one likes doing things that they find difficult and things they think they will fail at. The greatest motivation to succeed in a subject is confidence that you can. Maths is everywhere. Classroom maths is only one aspect of mathematics learning. Play games. With younger children snakes and ladders, ludo or anything which practices their counting skills. Bingo is excellent and they love it. For older children card games, darts, anything which encourages keeping score. Lots of boys love football, get them to work out aggregates (whatever they are). Badminton and tennis are great for keeping score too, any ball games. Chess is excellent for concentration and memory (dyslexics are often very good at chess) For learning about conservation and measurement, cook. Take them shopping, let them handle money, let them pay for things and check the change. Let them work out their pocket money and how much they have to spend etc. Time. Time how long it takes them to get dressed or eat their dinner. Time everything to make them aware of time intervals. Practice telling the time with them. Ask them frequently to tell you what he time is. When is their favourite TV programme on? How long is it on for? When does Brownies start? How long is it on for etc.? Give them a calendar to keep on their bedroom wall and record important events birthdays, holidays. When are they? How many days do we have to wait? For older children encourage them to use their homework agenda to write down all important information such as submission dates for assignments. If they like the computer and the internet exploit it. There are some excellent games such as “Maths Adventures” and great internet sites. One excellent one is www.mathsisfun.com. If you look on the national numeracy site which is there are often activities on there for teachers but they are all free.

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http://www.standards.dfes.gov.uk/primaryframework/cpd/mathematics/developing_langu age/ This is a popular website: www.mathsyear2000.org This site provides games, puzzles, and activities for all students. Mathsmagnet, Number Land, and Puzzle of the Day allow students to work with numbers, patterns, and problem solving situations. Further Reading and References Chinn, S. 2005 The Trouble with Maths RoutledgeFalmer Deutsch, G and Springer, S. 2001 Left brain, Right Brain San Francisco: W H Freedman and Co. Henderson, A. and Miles, E (2004) Basic Topics in Mathematics for Dyslexics. Whurr Kibel, M. (2004) “Linking language to action” in Miles, T.R. and Miles, E. (2nd Ed) 1992 Dyslexia and Mathematics London: Routledge Loviglio, L. 1981 “Mathematics and the brain: A tale of two hemispheres,” Massachchusetts Teacher Jan/Feb. p. 8-12 Shaywitz, S, E. (1996) “Dyslexia” Scientific American November 1996 pp 78-84

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Other Questions What is dyscalculia and how is this related to dyslexia? Dyscalculia is a relatively new term and because of this research is still in its infancy. There is still much debate about what it is and questions such as: “Can you be dyscalculic and dyslexic?” or “If you are dyslexic then is it not dyscalculia you have but dyslexia?” It is very complicated and no one has really seemed to have decided yet. As there is debate about what it is exactly. At the moment it seems to be the label given to individuals who have very specific difficulties with mathematics for example: a) Kosc’s definition of dyscalculia: Developmental dyscalculia is a structural disorder of mathematical abilities which has its origin in a genetic or congenital disorder of those parts of the brain that are direct anatomico-physiological substrate of the matural of the mathematical abilities adequate to age, without a simultaneous disorder of general mental functions. [Kosc 1970a, p.192] b) Word summaries of the six categories of dyscalculia: i. Verbal Dyscalculia Individuals with Verbal Dyscalculia would have great difficulty understanding the language of mathematics and are also unable to communicate the meaning of mathematics verbally even if they are able to understand. They may be able to write down a number or a mathematical symbol which is presented to them verbally (motor –verbal dyscalculia) but they may not be able to express it verbally; name it. If they are unable to communicate in this way but can show understanding using concrete apparatus for example by showing that number on their fingers; this it is called (sensory-verbal dyscalculia.) ii. Practognostic Dyscalculia An individual with Practognostic Dyscalculia is unable to manipulate everyday objects in order to show mathematical comparisons. For example, they may have difficulty with translating the notion of money into notes and coins. They would not know how much money to give or how many coins they should receive in change. They would be unable to work out which pile of coins would be worth more. They would not be able to identify equivalences for example that the two halves of a pizza presented to them was equal to a whole pizza. They may be unable to understand how the passing of time is related to a clock. An individual would be unable to estimate the length of an object or measure it with a tape measure. iii. Lexical Dyscalculia An individual with Lexical Dyscalculia will have difficulty with reading and understanding the symbolic language of maths. This could include, for example the basic number notations (+ - ÷ x % < > =) and numbers themselves. Similarly shaped numbers could be confused. For example, confusing a 9 with 6 or reversing two digit numbers e.g. reading 36 as 63. Multi-digit numbers would by Tricia Gardner 8

be very difficult to read and ones which contain zeros would be more problematic. Numbers written in a horizontal rather than a vertical line could cause difficulty. Individuals would also have difficulty with decimals and fractions. Lexical Dyscalculia is also known as Numerical Dyslexia. iv. Graphical Dyscalculia An individual with Graphical dyscalculia will have difficulty with the writing of the symbolic language of maths. It exists alongside Lexical Dysgraphia and individuals will often experience Dysgraphia and Dyslexia. In the most serious cases individuals will not be able to write or copy any numbers. In less severe cases individuals may write individual numbers in reverse and be unable to write larger numbers in the right order. He/she may have great difficulties with zeros and not be able to write down any mathematical symbols. Graphical Dyscalculia is also known as Numerical Dysgraphia. Lexical and Graphical Dyscalculia is often referred to as Numerical Dyssymbolia. v. Ideognostical Dyscalculia An individual with Ideognostical Dyscalculia will experience difficulty with understanding mathematical concepts. The severest of cases will not be able to carry out the simplest of mental calculations. The individual may be able to read and write numbers but have no idea as to what they represent. vi. Operational Dyscalculia An individual with Operational Dyscalculia will have difficulty carrying out mathematical operations. For example they may confuse multiplication with division. They may be unable to choose the best operation to solve a problem and choose a very complex method (or do not have one) and so choose an inappropriate one. It is difficult to follow their logic in problem solving if they cannot explain their rational.

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