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Dyscalculia: What It Is And Other Maths Problems

An explanation about Dyscalculia and how we can help!

Date : 06/01/2013

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Anne

Uploaded by : Anne
Uploaded on : 06/01/2013
Subject : Special Needs

Dyscalculia: What it is and other Maths problems . Abstract: `Men experiencing poor numeracy skills are two and a half times as likely to be unemployed` Butterworth (2009). This statistic alone is enough to set alarm bells ringing. But the problems start to arise in a child`s early years of education. Dyscalculia is an example of a specific learning difficulty in mathematics which can often go undiagnosed. This article examines what Dyscalculia is, and the impact it can have. Along with other mathematical difficulties, I will look into the important task of how children learn to count (for numerosity or cardinality) and at what is available to help schools intervene in a child`s struggles with number.

Dyscalculia is a specific learning disability in mathematics. It is a word you use to describe when people have significant problems with numbers - but still have a normal or above normal I.Q. The term dyscalculia comes from Greek and Latin and means "counting badly". "Calculie" comes from the Latin "calculare", which means "to count". The word "dys" comes from Greek and means "badly or difficulties" although various other explanations have been given for the same word: severe difficulty in making simple mathematical calculations, due to cerebral disease or injury [C20: from dys- + Latin calculare to calculate] . Whether the manifestations of dyscalculia are developed from birth (Developmental Dyscalculia), or as the dictionary definition above suggests, caused through illness or injury (Acquired Dyscalculia), can have an impact on the severity of experiences and how and what interventions are administered but are classified under the umbrella term of dyscalculia.

According to Geary 2005: "A score lower than the 25th or 30th percentile on a mathematics achievement test combined with a low average or higher IQ score are common criteria for diagnosing Mathematical Difficulties" of which dyscalculia is the extreme. Even though Geary et al are using their preferred Americanisation for their criteria to describe a maths disability, which can differ from the British, the essence of a person`s difficulties is offered succinctly through this statistic. The Rose report of 2009 presents a much simpler descri ption: Lacking a sense of number. The British Dyslexia Association (BDA) refers to the Department for Education`s descri ption of dyscalculia as: `A condition that affects the ability to acquire arithmetical skills`. Dyscalculic learners may have difficulty understanding simple number concepts, lack an intuitive grasp of numbers, and have problems learning number facts and procedures. Even if they produce a correct answer or use a correct method, they may do so mechanically and without confidence.` It is these definitions that will help me to explore further the difficulties a dyscalculic person experiences with their learning and experiences of maths education. This will also give us some clues to how we can provide what dyscalculic children require as well as considering other factors such as the levels of anxiety felt and the impact maths education can have on their self esteem and levels of confidence.

Adler 2008 says: `Children with dyscalculia usually have normal intellectual capabilities, but often display spectacularly uneven results in intelligence tests. The causes of these difficulties are not emotional or psychological, but can be traced to problems with certain specific (cognitive) thought processes.` This distinction between general mathematical difficulties and dyscalculic signs is essential to the correct diagnosis of the condition and indeed to the interventions used to combat the difficulties associated with it.

Adler highlights the following points as those suffering mathematical difficulties or dyscalculia, he doesn`t however distinguish between the experiences of those with the learning disability and those that suffer similar difficulties but who aren`t as such actually suffering from the condition of dyscalculia, as commented upon previously. Suggesting that other causes for mathematical difficulties need to be considered and maybe addressed as a primary need, for example poor educational experiences can lead to similar gaps in a learner`s abilities but yet with the correct intervention distinctly different outcomes can be obtained.

`. Being slow or unable to recognise numerosities without counting them (otherwise known as subitising), such as being able to automatically read the arrays of dots on dice or dominoes (arguably seen as an innate ability) up to the value of four and learnt to seven. . Poor sense of number size - in number comparison tasks where they are asked to select the larger of two numbers their reaction time compared to controls is significantly longer. . Reliance on laborious strategies for arithmetic - counting on their fingers, continuously resorting to counting in ones rather than steps even for larger 2 or 3 digit numbers, . Poor memory retrieval of arithmetical facts . Inability to grasp and remember basic mathematical concepts such as addition, subtraction, place value and in more advanced teaching; using and applying rules, formulas, sequences. . Their mathematical conclusion or answer are often inconsistent. . Arithmetical laws (such a + b = b + a) have to be learned by rote and not in an intuitive way. . Difficulty with time and direction. May be chronically late or early for appointments. . Poor with money and credit. Cannot do financial planning or budgeting. They may have fear of money and cash transactions. May be unable to mentally figure change due back, the amounts to pay for tips, taxes, etc.`

However, the British Dyslexia Association reports that forty to fifty percent of dyslexics show no signs of dyscalculia, with about ten percent achieving at a higher level than other children in their age group. The remaining fifty to sixty percent do suffer problems with mathematics but the BDA suggests that it is has its origins in the difficulties in decoding the mathematical symbols that numbers represent (as is the case for reading letters experienced by dyslexics) rather than an actual understanding of the numerosities of the number itself. It is an important point to note in the education of children suffering from mathematical difficulties as it gives again evidence of the distinction between Dyscalculics and Dyslexics. The importance of the diagnosis and correct intervention for a child suffering from mathematical difficulties becomes even increasingly more important when considering the warnings issued by important figures in politics and education; Brian Butterworth states in his article for Foresight that Gordon Brown in 2007 announced that `24% of 11 year olds failed to reach the expected level in mathematics`. Brynner & Parsons (1997) offered the findings with: `Evidence showed people without numeracy skills left school early, frequently without qualifications, and had more difficulty getting and maintaining full-time employment.`

The introduction of Every Child Counts (ECC), a government funded programme for 5 to 7 year olds with very low numeracy is the one of the governments contributions to combating these statistics. Though ECC doesn`t target dyscalculia specifically, it is delivered in the form of a Wave 3 intervention called Numbers Count. As a result of significant teacher professional development and the implementation of the intervention, children showing significant signs of poor mathematics achievement (usually in year 2) receive a 30 minute, one to one numbers lesson every day for a school term. The impact, not only on academic levels, but on the child`s self esteem can be, and from my experience as a Number`s Count Teacher, has been at times astonishing.

According to Geary (2005) 5-8% of children have some form of Mathematical disability, whereas from a British sample Butterworth (2009) estimates it to be between 3.6% and 6.8%. Butterworth continues with the knowledge that Men aged 30, with poor numeracy are: . 2 ½ times as likely to be unemployed . 3 ½ times as likely to be depressed . Nearly twice as likely to be arrested

Again these statistics do not differentiate those with dyscalculia, dyslexia with mathematical issues and those that have more general learning difficulties. It does however give us an insight into the need to improve provision for these children and the continued professional development of class teachers in this area. It is the work of programmes such as those through Every Child Counts that give hope that such figures will be reduced in the future. It is commonly accepted that dyscalculia has had considerably less research in comparison with the investigations into dyslexia that spread the previous 30 years. However, the work of Brian Butterworth, Sashank Varma, Diana Laurillard as well as Geary and others are pushing it to the front of the agenda both in education and scientific research. A recent article in Science by Butterworth et al also offers the hope that as a result of learning strategies that compensate for their mathematical difficulties, a dyscalculic`s `cognitive and neural functioning will actually come to resemble that of their non-dyscalculic peers` ! Adler in his article What is Dyscalculia takes the practical approach of considering how children learn the fundamentals of mathematics and numerosity and how this is affected by dyscalculia. He refers to the principles that Gelman and Gallistel apply to learning to count. They note 5 steps that a child has to go through to grasp the important concept of cardinality (numerosity of a set of objects):1-1 Principle-assigning a count word to each item. From my experience children with mathematical difficulties sometimes develop poor 1-1 correspondence. At this stage the numbers don`t have to be applied in the correct order, (in fact theoretically they don`t have to be number words at all), but the tags do have to be used just once.

The next principle takes this a step further insisting that the order of the tags (preferably number tags) are of a stable-order. This Stable Order Principle, focuses on the tags being the same each time a child counts, at this stage it is still not essential to have the conventional number names or order, as long as they are applied individually to each object in the same order. The numerosity of a group of objects becomes more essential in the learning to count process with Gelman and Gallistel`s third-Cardinal Principle. Children need to establish that the last number name they apply (in a consistent order) to a set of objects is the total number of objects, for the child counting goes from being a process they undertake with little purpose to something they actually achieve a product from. At this point counting has a whole new meaning for the child and I would suggest that from here, mathematics can really begin to take off, suddenly everything can be counted, compared and thought about in new terms. The correct number word to object soon develops for the child as they realise the why of their practice not just the how. The fourth of Gelman and Gallistel`s principles takes place when a child realises they can count any group of objects, they do not necessarily have to be classified into a particular group first. In fact Gelman and Gallistel would state that this Abstraction Principle supports the idea that children are willing to count anything, including non-physical things. The final principle is the order-irrelevance principle: This is the significant step to realising that number names are `arbitrary and temporary designations rather than inherent properties of the countable items. ` The significance of these 5 principles to dyscalculics is in the difficulties they experience when realising numerosity (or cardinality) perhaps because these Principles haven`t been adhered to. The application of this in teaching children to count may improve the chances of children with mathematical difficulties as those educators would perhaps resist the temptation to experienced and taught assume a child understands numerosity and cardinality before moving onto more abstract mathematics. It is interesting to note that Bermejo et al (2004) `maintain that counting and cardinality are not the same and that.counting is one means of evidencing cardinality (as indeed are subitising and estimating);` three of the fundamental struggles of a dyscalculic. Again we see the importance of early mathematics intervention for these children and by following this guidance we can start to see a possible way in to helping children who suffer the mathematical difficulties experienced not only by Dyscalculics and Dyslexics but those experienced generally.

I would suggest however that the need to determine the underlying cause of persisting mathematical difficulties in order to concentrate the interventions appropriately is where the need for a good dyscalculia screening test. An example has been devised by Brain Butterworth for Granada Learning; http://www.gl-assessment.co.uk/. It looks at: Simple reaction time, dot enumeration, number comparison and arithmetic achievement (addition and multiplication). The results of this could be an important step to helping children and adults who suffer from this learning difficulty to receive the appropriate help they require. Unfortuntately the screening is aimed at children 7 years and above, however the Sandwell Early Numeracy Test is designed to give a standardised score, number age and national curriculum level for children working within P levels, up to 2A. This test has been widely used with the implementation of Numbers Counts and the Teaching Assistant led 1st Class @ Number. Edge Hill University are continuing to develop Wave 2 & 3 interventions for children throughout their primary education; a positive step to fill some of the gaps in mathematics education and intervention.

This was published in the Winter 2012 edition of Education Today Vol 62, No. 4.

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