### ABSTRACT

This project suggests briefly about the "Dyscalculia" and the possible biological bases of dyscalculia and about the people who is suffering from the dyscalculia and also mentioned about the problems that are facing by the dyscalculic people in different fields of areas in their daily life. Coming to this case of Dyscalculia it is defined as the mathematical and arithmetical inability while coming to the brief description it is named as "Number blindness". Here in this project we focussed only on arithmetical addition and briefly describing problems facing by the dyscalculic people while doing mathematical addition and counting of numbers. And secondly we are going to describe how does dyscalculia comes from and the reasons and explain the relationship between "Dyslexia and Dyscalculia" as there is a chance to acquire dyscalculia from dyslexia.

The main aim of the project is to teach the mathematical addition rule to the People with "Dyscalculia" would struggle in doing arithmetical addition. Before starting to teach the mathematical addition rule to the dyscalculics I already studied briefly about the dyscalculia and how does it occur and what are the "Types of dyscalculia" that occurs to the dyslexic people and the deficits intended in dyscalculic people as they expressing while doing mathematical addition.

Now a day's Dyscalculia is the main problem that are affecting people up to some extent. But not as much this is the problem mainly occurs which is connected with "Dyslexia". However one thing should remember that all the Dyslexics are not Dyscalculics although 40% of dyscalculia occurs from dyslexia.

### Introduction

First of all before starting of my project this document reflects and introduce about the project from its advanced stage to the conclusion in a simple and briefly explanation on which concept that I am doing my project. I started my dissertation on a special concept of human disabilities which is known as "Dyslexia" and its further effects on human life prospectus. Especially this discuss about the defect on humankind that are suffering with mathematical and arithmetical difficulties known as "Dyscalculia". The effect of dyscalculia mainly refers the lacking of mathematical skills and concepts such as addition, subtraction, multiplication and division.

"Dyscalculia" is the major problem that is affecting the human life in our daily activities mainly focuses on inability of basic mathematical concepts of adding and counting of things which performs vulnerable and inefficient out coming result while doing calculations and normal counting in our daily life

The main aim of the project is to help the people who are suffering from "Dyscalculia "and its deficits. To perform the activities that can help to understand the mathematical concepts and to overcome the deficits of dyscalculia that is affecting the people in their real life.

The way of designing and the implementation of the project can be able to pave the way for finding the right solution to solve the problems of dyscalculic people with which they are suffering and to overcome their deficits with which are having individually and its total scope is to enhance the possible ways of teaching methods of addition particularly for the dyscalculic in an understanding and in a possible way which can be capable by the dyscalculic.

The whole project is designed as user friendly and can be able to the dyscalculic people who are suffering with learning difficulties particularly in arithmetic addition that is adding of numbers starting from the adding of single digit to the higher level addition. In the advanced stage of the project we introduced the design with colourful Cuisenaire rods with attractive colours so by introducing attractive features into the design so that the dyscalculics can show their interest on learning addition very faster and can show the efficiency to get the output result correctly with satisfaction.

The entire work of the project is based on teaching of mathematical addition in an understanding way to the dyscalculic people with learning difficulties in mathematical addition. Particularly in adding and counting of numbers according to the situations in their daily life.

The possible steps in designing the project which is very useful to dyscalculic;

1. The simple way of designing the project can be easily to understand by the dyscalculic people.
2. Operation is user friendly to dyscalculics
3. Introduction of special features can attract the dyscalculics towards the learning process.
4. They can show their interest on mathematical addition and can learn easily by understanding.

### What is Dyscalculia;

Dyscalculia is mainly defined as difficulties with numbers it is identified as the difficulty in counting the numbers and things fast and fluently with lack of grasping power.

### Why the people with dyscalculia are different?

Individuals with dyscalculia have specific difficulty with numbers, despite exhibits good results in other areas. They may have great difficulties with counting and adding the numbers.

1. The example of an arithmetic addition2+4 or 4+2
2. Prices in the shops like tendering the money and taking the change correctly.
3. Normal identification of numbers and what those represent, e.g. which is bigger, 2500 or 2770? Does 100+100 = approximately 200 or2000.
4. Judging of numbers instantly for example 'seeing' there are 5 glasses on the table normal people can count immediately and respond quickly where as the dyscalculic need to count them and to respond slowly.
5. Phone numbers, seeing of dates , time etc,.

It shows that people having dyscalculia has to struggle to achieve successful goals in the field of employment than having disability.

Dyscalculia is the main learning problem that affecting many individuals and it is termed as the learning of mathematic disability by the disabled. It states that dyslexia is identified as the difficulties in reading written text fast and fluently with lack of grasping capacity. On the other hand dyscalculia refers the difficulties with handling and carrying out specific mathematical operations such as addition, multiplication, subtraction, division.

### Relation between dyslexia and dyscalculia:

Here the relation between dyslexia and dyscalculia is very obvious. However, there are some points of overlap. There is a variant of dyscalculia that could be called as dyslexic dyscalculia. This problem involves primarily difficulties in reading which leads to mathematical problems for the people and these are the problems that arise with reading numerical symbols or difficulties with reading with multi-digit numerals so that 14 becomes 41. If the error happens like this in the reading of a task then obviously the solution becomes incorrect.

On the other hand dyscalculia can be recognized in the lack of mathematics concern the ability to quickly retrieve numerical facts such as adding small digit numbers like 4+5=9 from the memory. There are several indirect similarities between difficulties with reading and mathematics. A poor working memory is one of the more obvious. Dyscalculia is defined as the mathematical problems caused by working memory or evident in the tasks that must be solved mentally, in the head. In the time of calculation the student may run into great difficulties keep various numbers in the memory. The other case is problem of remembering longer instructions and commands. May be they can remember a short what was supposed to be done. The rest is forgotten, because the information was never stored in the memory.

The earlier researches shows that people with dyscalculia also have dyslexia most of the people with dyscalculia can have only mathematical difficulties. And they have a highly specific form of a learning difficulty and many are good in reading. Nowadays the occurrence of both dyslexia and dyscalculia at the same time is diagnosed as icd-10.

The most common thing in dyscalculia is the difficulty with the number order. Difficulties involve understanding and use of mathematical operations and concepts. People of large proportions with dyscalculia display problems with following calculations to reach a correct solution. They easily lose their strategy and therefore run into difficulties with complex mathematics.

Students with dyscalculia can be able to solve mathematical tasks but with in a average time frame they are unable to retrieve numerical facts from their vulnerable memory and must expend a lot of energy doing

The word dyslexia comes and originated from the Greek word 'Dys' means impaired and 'lexia' is a word. Dyslexia ranges from easy to severe conditions. There exist various forms of this disease. Therefore there are different types of symptoms of this illness. The individual features of every type are specified for every human being separately. In general there is no such a typical type of dyslexia. Dyslexia refers to be a learning disability of the brain especially difficulties in reading or writing and spelling and it is the disability of neurological disability. Due to dyslexia the main drawback is that the people with dyslexia failed to remember the name of the things or to connect the name of the item with the definition. Recent surveys revealed that girls are less dyslexic than boys.

### Genetic

1. Acquired

Genetic transfers with the genes and the second one that is acquired occurs to brain damage in the left hemisphere that is responsible for language areas.

### Possible causes of dyslexia;

Dyslexia is widely recognised as having a genetic component for example if a one kid of a pair of twins is dyslexic and the other twin is more likely to be dyslexic in the areas specially in language processing dyslexia links with brain differences. Possible causes of dyscalculia;

It suggests by evidence that dyscalculia may have a genetic component. If there exists dyscalculia in one identical twin most possibly there is a chance of around 70% to become dyscalculic characteristics in the other twin. For non identical twins there is a less possibility of getting dyscalculia around 55% only. Research facts of "Dyscalculia";

"Brian Butter worth" an expert in dyscalculia research facts;

Simply Brian butter worth done some research on a particular person who has dyscalculia and he is describing about the situation of the particular person and his name is Charles.

Brian Butterworth met Charles when his (Charles) age was 30 years old Charles is a good professor in psychology and getting psychology degree is an achievement for Charles. But entries to the university in the first place even though he is best he failed to normal condition for entry into the maths GCSE.

Charles is intelligent and very hard-working. But he is very poor in number skills that always have been a severe handicap and shopping is a constant embarrassment he doesn't understand the product prices and unable to grasp the idea of the total cost of the shopping basket. When he comes to the till, he has no idea about the money how much to tender and to get correct change. At that time immediately he use to add and multiply his fingers, and he is unable to do the two digit arithmetic problems such as 47-19. The real surprise thing that Butterworth found here about Charles is he couldn't tell that which is bigger or which is smaller in a numbers list which were given for suppose 9 or 5 and to find the difference suddenly he started to count his fingers to work in out.

Charles is an example and this condition is known as "dyscalculia" and this mainly affects the ability of acquire the skills in mathematical and arithmetical skills. Dyscalculic learners may face the difficulties in understanding the basic and simple arithmetical concepts like adding of single digit numbers. For simple arithmetical concepts they may face severe anxiety and they struggle to understand what is obvious to all their friends and classmates.

Dyscalculics even if they produce a correct answer or use a correct method they may do so mechanically and with lack of confidence. This captures what many dyscalculics like Charles feel about maths it is incomprehensible.

Dyscalculia is not only a problem for the individuals but also it is one of the effect to the nation and for some especially as from the published report of the basic skills agency shows that poor math skills is a bigger handicap to getting a job by having that poor numeracy the employee will transport the wrong number of goods and fails in the money transactions such as receiving or paid out the money. And due to this poor efficiency in calculations affects the particular company.

The current estimations suggest that about 5-6% of average to the superior intelligence children will have a real deficit in doing maths. Dyscalculia seems to be particularly found in dyslexics around 40% of the people who struggles with reading difficulties also having difficulties in learning maths and the remaining 60%have no problems than normal. It was found already that there is link between dyslexia and math learning difficulties although the latter can occur alone.

It is worth noting that learning about numbers is different from learning to read in an important way. We are born with basic numerical abilities. Infants, even in the first week of life, are sensitive to changes in the number of things they are looking at. We know this because they will look longer at a display when we change the number of things, but often will not when we change one of the things but keep the same number. Babies also seem to be able to do very simple arithmetic. If the baby sees a doll place behind a screen, and then another doll placed behind it, it can be shown that the baby expects there to be two dolls (1 + 1) when the screen is removed. Babies look longer at things they don't expect, and will look longer at one doll or three dolls in this situation. So there is evidence of an innate capacity for numbers. One hypothesis to explain dyscalculia is a lack this innate capacity.

However we don't have a specialised capacity in reading by birth. Reading is a complex skill made up of various brain systems set up automatically to do the other tasks like language recognising visual patterns, sequencing, and so on. And some of these used to learn maths in school and deficits in them may also affect learning in mathematics.

What we need urgently is a way of diagnosing dyscalculia, and separating it from all the other causes of maths problems, including inappropriate teaching. Once we can identify these children reliably, we can begin systematic research on how best to help them. Charles was not diagnosed as dyscalculic until he came into our lab, and, like many other dyscalculics, felt himself first to be incredibly stupid for not being able to do what all his friends could do easily. This was not good for his self-esteem, of course. After that he came to realise that there was something wrong, but he was completely immersed in the dark as what it could be. Better for his self-esteem, but of little practical help. We don't know there are how many cases like Charles, but we are slowly reaching there. Difference between dyscalculic and ordinary people in arithmetic calculations;

### Ordinary people;

For suppose if there is a four dots or four things on a screener the ordinary people(without dyslexia) can identify the things which is on the screener and they can give instant reply with respect to the situation. So therefore the normal people can react very quickly and they can respond very quickly comparing to the dyslexic people. The grasping capacity is very good in the normal people.

### Dyslexic people (Dyscalculia);

While coming to the dyslexic who suffers from dyscalculia cannot give the quick responses with respect to the situations like ordinary people. So to overcome this type of situations in dyslexic people we need to train them in such a way so that they can give their responses slowly in a particular way as the trainer and the people can understand a bit.

In order to train the dyslexic people to overcome the problem of arithmetical difficulties we should introduce some specific designs which is very user friendly and comfortable to hold by the dyslexic people particularly who is suffering with dyscalculia. And the designing aspects should be able to overcome their deficits.

### Mathematical grasping capacity;

This describes the mathematical ability of the dyslexic people and their mental ability of doing the mathematical calculations mainly the people who is suffering with dyscalculia.

For suppose if we introduce any four kinds of things in front of the dyslexic people they cannot give the quick response by counting the things so they will take time to count one by one and starts 1,2,3,4 and will give the response very slowly as 1+1+1+1=4

So people suffering with dyscalculia unable to do bigger calculations like adding numbers which is in big units like 234+432 so therefore we need to train them in such a way from the earlier stages of addition like adding single digits 1+2=3 so we need to begin from the earlier stages of addition. And after that by observing their progress we should train them to the further stages like adding double digits and then 100's and 1000's and so on.

It's very important to train them with respect their progress by observing their progress we can easily calculate their mental ability of doing the calculations and thereby we can implement the teaching techniques which can very easily and comfortable to the dyslexic people. So by introducing the new and comfortable techniques of teaching the people (dyslexic) can easily do the mathematical addition.

### Teaching of mathematical addition rule;

To teach the Mathematical addition rule to the dyscalculia we need to train them in specific way.

1. The mathematical symbol (+) is to be fix in their mind strongly.
2. And to make them to learn its importance and its rule.

### Developmental dyscalculia;

It is referred as mathematical and arithmetical dysfunction in individuals with normal mental functioning, that results and occurrences of brain anomalies at the time of prenatal development. Discrepancy occurs between the mean mental age and math age there exists a neat and clear retardation in mathematical development.

### Problems encountered by pupils with dyscalculia;

The will recognised and the observable things that generally we can find in the peoples with "Dyscalculia" are the learning and remembering difficulties in mathematical concepts like addition, subtraction, multiplication etc,. In this project especially we are focussing on the mathematical addition particularly and the difficulties which are the dyscalculics are facing in their real life in the fields of employment and in the living society and we had discussed the problems with dyscalcilia which they are facing in all the areas of everyday life prospectus.

Leaving that matter about what we are talking above and coming to the point of the problems that are encountered by people about the problems of dyscalculia.

The well recognised problems of dyscalculics;

1. Difficulty in learning and remembering of mathematical concepts such as used in our daily life in our activities Ex; Addition
2. In the time of interviews with teachers.
3. Difficulty in remembering even up to the number bonds to 10 is the worst problem that pupils struggling with maths were up against.
4. Difficulty in executing mathematics calculations procedures.
5. In 1984 Russell and Ginsburg found a dyscalculic group of people struggling on both written calculation and arithmetical fact retrieval.
6. In 1992 Yamashita and Aram found dissociation absence between arithmetical fact ability and procedural ability with numerical processing difficulties in pupil.
7. In 1993 Geary suggests that procedural problems are likely to improve with experience and also suggests the retrieval difficulties are less likely to do so. And he proposes that the emerging of procedural problems is due to lack of understanding concepts. Problems of retrieval difficulties are the result of general semantic memory dysfunction.
8. In 1999 Ostad has noted that the dyscalculia people use fewer procedures and often apply their smaller repertoire in the situations where they are not appropriate.
9. Even the counting of simple and single digits were shown to be vulnerable in dyscalculic people
10. Geary, Bow-Thomas and Yao in 1992 found that dyscalculic people are less likely to detect the counting errors than normal people.
11. However, all these deficits occur by the lacking of the conceptual understanding of the basic ideas of the numerosity and arithmetical concepts.

Good memory for arithmetical facts depends and can be able to convert and organise them into meaningful patterns.

And coming to the poor memory it can arise when the fact make little sense to the people.

The known information from the dyscalculic people was heard badly by themselves is that they can't remember what the teacher is saying about the mathematics.

Even some simple tasks like counting and adding single digit numbers dyscalculic people show a kind of rigidity.

Geary, Bow-Thomas and Yao in 1992 found that counting should do perfectly from left to right without skipping around. From all these we can find right thing from all these authors' observations and description we should note very important thing here is that these people ( Dyscalculics) can't understand the conceptual things in mathematics. Coming to the normal people can understand quickly that objects can count in any order.

### Underlying processing deficits;

It is one kind of the approach to study about developmental dyscalculia and this involves trying to see it as a consequence of cognitive deficits based on the understanding of the mathematical and arithmetic concepts. And all of these proposals have included.

### Weak phonetic representations

An advantage of this approach is there is a possibility of finding exactly the co-morbidity between dyscalculia and dyslexia, as we can find that dyslexics known to suffer from these conditions.

Geary and colleagues suggested that semantic memory difficulties are the main cause for the problems of developmental dyscalculics which they are experiencing in number facts. As well as the co-morbid reading difficulties frequently found with dyscalculia.

It shows the evidence particularly the argument is based that dyscalculic people have the difficulties in learning and remembering arithmetic facts that this deficit occur by lacking of understanding of math concepts. Empirical evidence for a general semantic deficit in dyscalculic people is thin.

In 2002 temple and Sherwood recognises that a group of dyscalculic people are suffering with arithmetical difficulties were slower at colour and object naming than controls. This comes to know their speed and accessibility is very low. However the authors argued a casual relationship between the arithmetical ability and the speed of access

It shows that People may be slower especially dyscalculics while the time of processing information in 1997 Jordan and Montana showed that the dyscalculic people can do the mathematical calculation on being unlimited time but they can't perform like the normal people whereas normal people can do significantly in case of time limit

In 1999 Mclean and Hitch compared the dyscalculia between the younger and the older people and found that the older people is performing the accuracy than the younger people in the time of solving the arithmetical and mathematical calculation. It reveals that the performance of the older people acquired due to the experienced things which they faced before in their daily life which is continuing from their early starting from the childhood.

In 1989 Siegel and Ryan found that people with dyscalculia showing their weak performance only in the fields of arithmetic and mathematical fields such as counting and adding of numerical things but not in the fields of non-numeric. On the other hand that found the spatial working memory and some aspects of central executive function were poorer in the dyscalculic people.

Moreover, in2002 temple and Sherwood tested dyscalculic people and controls on forward and backward digit span, word span and corsi blocks (a non-verbal test of working memory). This study reveals there is no difference between groups and no correlation between the working memory measures and arithmetic ability measures.

### SUBTYPING DYSCALCULIA;

The study of developmental dyscalculia has evolved to its new division of approaching to identify dyscalculic subtypes according to the presence or absence of other disorders, in an attempt to highlight the underlying processes that are contributing to the co-morbidity of the disorders. One of the things that we should note is the important correlate of mathematic disability is reading disability. It is estimated that at about 40% who is suffering from the dyslexics also have dyscalculic problems with learning difficulties in mathematics. The one of the most common ways of dyscalculic sub typing is according to whether or not they have a co-morbid reading disability.

The conditions that have been associated with dyscalculia are stated below.

• attention deficit hyperactivity disorder (ADHD) (Badian, 1983;Rosenberg, 1989; Shalev, Manor and Gross-Tsur, 1997);
• poor hand–eye co-ordination (Siegel and Feldman, 1983);
• poor memory for non-verbal material (Fletcher, 1985);
• poor social skills (Rourke, 1989)

In 1993 shalev and gross-tsur examined a group of seven people with developmental dyscalculia and not responding to intervention. All the group of seven people were suffering from additional neurological conditions, up to dyslexia starting from petit mal seizures and is mentioned as ADHD.

### Phonological processing in dyslexia

In the main case studies of dyslexia phonological processing takes an important role compare to other disorders like sensor motor disorder. This survey was again confirmed by the recent survey shows the 100 percent of samples for dyslexia was affected. This survey had an argument is that theory of phonological processing was the tautology compare it as an explanation. That phonology and the reading of the dyslexia are the two sides of the same coin. That means this awareness was explained more by the reading skill. If the phonological deficit was Leeds to a problem along with the phoneme awareness.

The main problems of dyslexics of the phonological problems are rapid naming and the verbal short term memory. This is related to reading. In this we can understand that phonological awareness and the rapid naming deficits are the relatively independent. Phonology does not reduce to the awareness of naming and memory. Some of the aspects for the phonology dyslexics remain to be investigated.

Attention-Deficit/Hyperactivity Disorder is presented in the children's. This is to cause the neurodevelopment disorder. This also most studied part for the people. ADHD public health dimensions are received relatively little interest. According to the survey of epidemiologic the distribution of ADHD around the population by the age, sex, and race and according to the socio economic status. The origins of the risk factors are preventable.

In this scenario we are going to discuss few of the independent concepts those having independent case of definition for ADHD. Summarizing the epidemiologic data regarding prevalence. In the literature key gaps were identified and ended with few suggestions for the epidemiogic research.

### Magnocellular deficit

Due to the perceptual deficits of the dyslexia reliability is the one of the problem. With this performance Macarthur proposed the theory. This is one of the heterogeneity dyslexic samples. Mainly the magnocellular is made link with the cerebella dysfunction. These measures are become very hard to incorporate into the routine assessment of the reading. Cerebella hypothesis applied to the dyslexia. Those agree the phenotype. It is the research of phenotypes. With that we can clearly as showed the symptom complex.

### Auditory deficits;

Auditory deficit is defined as the deficiency in one or more behavioural phenomena listed below for suppose deficit in.

1. Auditory discrimination
2. Auditory performance with degraded signals
3. Auditory performance with competing acoustic signals
4. Sound localization and lateralization

These mechanisms lead to nonverbal as well as verbal signals and may affect many areas of function. Including speech and language and auditory deficit can delay the maturation in the development of the important auditory centres within the brain. The deficits are related to maturity differences in the developing stages of the brain. And usually auditory deficits represents more static types of problems and these deficits can be caused by tumours, trauma, degenerative disorders, viral infections, surgical compromise, lead poisoning, lack of oxygen auditory deprivation, and so forth.

Prevalence of auditory deficits is estimated to be between 2 and 3% and we can observe more in males is often co-exists with other disabilities. And they include speech and language disorders or delays, learning disabilities or dyslexia, attention deficit disorders with or without hyperactivity.

### Learning memory deficits in children;

Children having learning disabilities such as dyslexia and dyscalculia. These are tending to may experience the core skills of the reading, writing and the arithmetic operations. These problems are raised at the first days of school. Even if we pass an instruction it needs to special requirements while understanding. These methods will affect the growth of the schools. Mainly concept of dyslexia concept is defined by the development of the reading skills. The concept dyscalculia is the special question of mathematical skills. Some of the approaches are developed while avoiding the numerous problems. International classified solution for these systems. According to the internationally classified systems learning disorders are present at the individuals of the domains those are reading, spelling, or arithmetic are expected potential at the respected age. According to the world health organization 7% of the people affected by the dyslexia problems. After a long time they found that dyslexia is caused by the visual deficits. Those deficits currently specified as phonological information processing. These are demonstrated to be responsible.

Considering this situation from the recent years there was particular deficits in the memory, mainly that memory is working memory. This working memory is the responsible for the processing and short term storage of information. Various models are developed on the method of working memory. This model developed by the Baddeley. He proved the particular theoretical tool in numerous studies on learning disabilities. These models make differentiate between the components of the working memory. The first component is the modality free central executive system. This system was used to control and regulate the most advantaged system which has limited capacitance of salvage systems. This method is useful while retrieving the representations threw the long term memory.

Two components of phonological loops are proposed. Those methods are phonological store and the sub vocal rehearsal process. This sketch pad is mainly working with the remembering and processing the visual and spatial information. This is for the visual cache is for the outer part and inner scribe for the dynamical process. Mainly this research provided the number of indications. These indications

Re associated with the methods in the working memory. Children with the specific disabilities have main deficit problems in phonological processing. The evidence reveals that main deficit is the central executive functioning. A few relatively reports of disabled children.

Some arithmetic learning disabilities are also available for all the domains of the working memory. These types of working memory show the deficits. In these deficits central executive seems to be mainly impaired. Some people are invented that the children's with the main deficits are found in the phonological working memory. But the research studies of bull no impairments were found. McLean and Hitch tell the theoretical concept is that deficits in the phonological loop do not define the characteristics of children's with the more arithmetic learning disabilities. After that Bull find that arithmetic disabled children and normal achieved peers should same and delivering the same output.

Some research findings in the working memory are the heterogeneous. Especially for this results made potential results which made positive result among the selection criteria which instruments are used. Only few studies are considered for this achievement remains in the children and also the previous reports reveal that the learning disorders are defines above. In the various functions working memory only few of them are functionalized. The precluding differentiated analysis of individual components of the working memory.

These working memory deficits in the children may be in higher order of learning disabilities. Some studies of numerous studies reveal the comparability between the dyscalculia and dyslexia. Lewis proposal theory reveals that children face the problems in both reading and arithmetic. So previous examinations reveal two disorders separately. The mixed disorders with scholastic skills. examination reveals that children's with reading disability or arithmetic disability in one hand children with the both disabilities in another hand shows that later group has more particular deficits in the working memory functions. Recent studies revels the children classified as according to the disability criteria reading or spelling or both. But some children did not show the difference between the intellectual ability and the achievement. Characterise pattern defects had no evidence found in the children. So this method remains unclear it applies to the children relevant learning difficulties in both the domains.

The main aim at present is to find the functioning of the three components of working memory in the children who met the ICD-10 criteria. This criterion belongs to the relevant specific learning disorders. The specific components of working memory revels the there are specific deficits in individual components of the working memory.

### Developmental dyscalculia:

It is important to note that not all dyscalculic people show difficulties in the areas named above. And that many orders and many of the authors made specific subtypes of cases in developmental dyscalculia. Indeed the known subtypes of dyscalculia could lead to the clarification of symptoms the current lengthy list of characteristics might be a mixture of various subtypes. In this section briefly review major subtype proposals that have been subject and based on several research and continual studies.

A research was conducted early by Rourke and co, (see Rourke, 1993, Rrourke & Conway, 19997 for reviews), they argued for two kinds of subtypes of disabilities in mathematics and a verbal type that is associated by left hemisphere impairment. They grouped dyscalculic children based on whether the reason that they had concurrent capacity of reading and deficits such as spelling mistakes that is stated as reading and spelling deficits (RDSD), and or stated as isolated arithmetic deficits (MD). It reveals a double dissociation of Neuropsychological tests on all these groups. The RDSD children performed better on Visio-spatial tests, and worse on verbal tests, whereas MD children already showed an opposite pattern (Rourke & Finlayson. 1978). It comes to know that MD children also showed the deficits in psychomotor and tasks in tactile-perceptual, and on the complex non-verbal abstract reasoning tasks (Rourke & Strang, 1978). However for these two subtypes of dyscalculia there exists no independent studies been had been found, for example share et al. (1988) found this pattern in boys only not at all in girls, and shalev et al. (1997) failed to find it.

Recent studies by Jordan and his colleagues (Jordan & Hanich, 2000; Jordan et al., 2003; Jordan and montani 1997) have focussed of grouping children on mathematical and reading disabilities (MDRD) and those have only with mathematical disabilities (MD). However, unlike in the previous studies, these authors measured performance on basic mathematical and numerical tasks. In general it reveals the results of a single dissociation. In an exact calculation MD children are consistently better than MDRD children, and capable of solving story problems. However, there are no tasks at which MD children are worse than MDRD children. Leaving open the possibility due to the difficulty of the tasks the differences are very simply. Furthermore comes to the other researchers using core numerical cognition tasks have failed to find the variation between the performances of MDRD and MD children (e.g.Landerl, Bevan, & Butterworth).

### NEUROANATOMICAL CORRELATES OF DEVELOPMENTAL DYSCALCULIA;

In the present days mathematical skills are becoming increasingly more critical for achieving academic and professional success. While comes to dyscalculia it is a learning deficit estimated to have a prevalence of about 5-6% as the estimations revealed by Brian Butterworth (2005) a master in the field of dyscalculia research and some other experts in this field of research named cohen Kadosh and Walsh (2007), Rubinsten and Henik (2009). Developmental dyscalculia (DD) can be defined as "a disorder of numerical competence and arithmetical skill which is manifest in normal intelligence who does not have acquired neurological injuries". The prevalence of arithmetical difficulties arising from the non-specific attentional, working memory and reading disabilities has a higher prevalence rate the range of estimation from 5% to 20% of the young children depending on the precise criteria. The rate of prevalence of dyscalculia is at least as high as dyslexia and reading disabilities. It shows that dyscalculia and its related mathematical disabilities have received much less attention from developmental neuroscientists.

Lack of arithmetical and mathematical abilities can affect academic and career opportunities. The Neuroanatomical basis of DD(developmental dyscalculia), is a specific learning deficit with a rate of exceeding Prevalence up to 5%, that understood poorly. Fo this We used MRI structure and diffusion tensor imaging (DTI) to examine macro- and- micro structural impairments in 7- to 9-years Children with DD, by comparing with a group of typically developing (TD) children matched on age Intelligence, gender, reading abilities and working memory capacity. Voxel-based morphometry (VBM) revealed reduced grey matter (GM) bilaterally in superior parietal lobule, intra-parietal sulcus, fusiform gyrus, parahippocampal gyrus and right anterior temporal cortex in children Developmental Dyscalculia. It shows reduced white matter in VBM analysis as well and presence of (WM) volume in right temporal parietal cortex. In this WM region was revealed by fractional anisotropy pointing to Signify can't right hemisphere micro-structural impairments. FA in this region was correlated with numerical operations but not in verbal mathematical reasoning or word reading.

### Standardized neuropsychological assessments;

(CBCL) the child behavioural checklist was leading all the participants to exclude the children linked of later psychopathology and with the relating behaviours. Participants were administered a demographic questionnaire. Wechsler abbreviated a scale of intelligence in Wechsler in his individual achievement test and working memory test battery for children. While was provided a standardised measure of full scale IQ, and measures of reading ability yielded by WIAT-2. (Word reading and comprehension scores), and math ability (Numerical Operations, Math reasoning scores and derived from them Math composite score). To obtain several measures of working memory a shortened version of WMBTC was also administered. (Digit recall, Block recall, counting recall, Counting recall and Backward Digit recall subscales). A composite working memory score was calculated the standardize across the obtained measures of WMBTC. The tests of neuropsychology were administered by trained research assistants by using multiple rater's.

### NETWORK ANALYSIS;

Based on the deterministic tractography the exploratory classification analysis to test network level connectivity differs in children with DD (Developmental dyscalculia) and TD (Typical developing) children culled pathways (2 mm diameter "fascicles") in each individual were first classified to 58 AAL labels according to their projection target, each pathway contributing two targets. And these two projections were contributed by AAL for each pathway and its labels pathway origin and termination points and then performed a classification analysis with the help of a support vector machine (SVM) algorithm using sparse logistic regression with the help of L1 and L2norm regularization. The number of pathways connecting each pair of ROIs was used a pairs of ROIs and feature vectors that contains no pathways in any participant were excluded. The pathway counts Were transformed to z-scores to control differences in sizes of the ROIs. A grid search was performed to find the optimal L1 and L2 norm regularization parameters to maximize 10-fold cross validation accuracy across 50 iterations.

Figure shows the representation of fractional anisotropy in groups and the growth of developmental dyscalculia merging with typical development. These tell us about the estimations of the WM roi groups and DD and TD VS standardised FA.

As the figure below represents the graph is the estimation of the WM roi VS numeric operations. Characteristics of the Developmental dyscalculia and typical development.

Fractional anisotropy (FA) within right temporal-parietal regions that showed white matter deficits in DD children. FA was significantly reduced in children with DD, compared to TD children. (B) Across the two groups, FA was significantly correlated with the Numerical Operations sub score of the WIAT-II.

### BEHAVIOURAL PROFILE;

The table below represents demographic and neuropsychological profiles of DD and TD groups. And these two groups differed significantly on the strengths of mathematics as assessed by the WIAT-2, but not on is age, reading ability, or working memory.

### GREY MATTER VOLUME

Compared to TD children, children with DD showed decreased GM volume in several posterior brain regions (Figure 1, Table 3).Within the ventral visual stream, differences were found bilaterally in the cuneus/precuneus, lateral occipital cortex, lingual gyrus, and the fusiform gyrus. Within the dorsal visual stream, children with DD showed GM deficits bilaterally in the superior parietal lobule (SPL) and right posterior IPS. They also showed deficits in the medial temporal lobe, within the right entorhinal cortex and, bilaterally, within the parahippocampal gyrus, and the hippocampus.

### GREY MATTER DEFICITS IN CHILDREN WITH DD (developmental dyscalculia);

Children with DD showed prominent GM defi cits in both dorsaland ventral visual streams as well as the anterior temporal cortex. Unlike Rotzer et al. (2008) we found no evidence for defi cits in the anterior cingulate cortex, the inferior frontal gyrus and the dorsolateral prefrontal cortex, perhaps because of our use of more stringent criteria for matching the groups on IQ, working memory and reading. The dorsal visual stream regions that showed GM deficits included most prominently the posterior aspects of the IPS and the SPL. Similar to Rotzer et al. (2008), we found that children with DD showed defi cits in the right IPS, but we also observed differences in the adjoining SPL as well as the left IPS and left SPL. The IPS is a core parietal lobe region implicated in the development of number sense and magnitude judgment (Ansari, 2008). Functional imaging studies have also shown that the IPS region plays a crucial role in arithmetic calculations, independent of other processing demands such as working memory

### WHITE MATTER VOLUME

Children with DD showed reduced WM in the posterior brain, primarily within WM regions adjacent to the right temporal- parietal cortex Roughly two-thirds of the voxels within this WM region overlapped with WM tracts included in the JHU white matter tract atlas Prominent right hemisphere WM tracts included the inferior front-occipital fasciculus (t = 4.16; 30, -26, -4), the forceps major of the selenium of the corpus collossum (t = 3.76; 6, -36, 14), the inferior longitudinal fasciculus (t = 4.16; 30, -28, 4), the corticospinal tract (t = 3.56; 20, 36, 46), the superior longitudinal fasciculus (t = 3.90; 22, 36,42), and the anterior thalamic radiation (t = 3.54; 22, -32, 32), as shown in the left hemisphere, defi cits were observed in the superior longitudinal fasciculus (t = 3.40; -36, -30, 44), forceps major (t = 3.39; -16, -46, 8), and the anterior thalamic radiation (t = 3.42; -18, -40, 2). No clusters showed greater WM volume in DD compared to TD children.

### Developmental dyscalculia and cerebral locations;

In both Cerebral hemispheres if there is a presence of developmental abnormalities can lead to DD (Developmental dyscalculia) the difficulties understanding the properties of quantities, spatial learning happens due to the presence of the right hemi sphere Ys function

Problems (for example, understanding and using place value) can be useful for arithmetic for the solution of the real life problems. Due to the dysfunction of the Left hemisphere dysfunction lay cause the difficulty in comprehension and abstract meaning of numbers and sequencing math matical and numerical operations

It should note that due to conditions such as epilepsy, the abnormalities can occur and there is a chance of abnormal maturation of lag development

We can find damage to late myelinating neural tissue, or disorders of lateralization.

In 1995 It has been explained from Shalev, Manor ,Amir and Co Left and right hemispheric dysfunction occur with approximately equal frequency in primary students with DD and that leads to greater arithmetic difficulties.

### Right hemispheric immaturity;

One type of DD has been linked with nonverbal reasoning disabilities. With the Characteristics of Developmental right hemisphere deficit syndrome (DRHS)

• reading, spelling and strong verbal skills including inadequate social interactional and Paralinguistic abilities,
• Due to right hemispheric immaturity it happens severe graphomotor problems; performance IQ is lower than verbal IQ, impaired visuo spatial skills.
• Presence of neurological indicators on the left neurological "soft signs" of right cerebral dysfunction
• Dyscalculia and emotional as well as interpersonal difficulties;

It shows a sign of higher verbal than visual organisational reasoning ability in students whose learning ability minimises to arithmetic frequently.

Left hemispheric dysfunction: The angular gyrus and calculating;

It includes right side soft neurological signs on the left hemisphere dysfunction and performance IQ less than verbal IQ, dyslexia and intact.

Difficulties of visuo spatial functions in one key area.

### Gerstmann's syndrome' is as follows:

• Finger agnosia, observed using finger differentiation or naming tasks,
• agraphia or dysgraphia, observed in poor handwriting, difficulty copying writing from blackboard and poor spelling,
• Right left disorientation, shown in directional confusions,
• Dyscalculia,
• Constructional dyspraxia and
• Emotional problems.

### Assigning Numerical Value to the rods;

The next step in using the rods is to assign numerical values according to colours to each of the rod.. Rather, I encourage only a numeric value according to these values: white= 1, red= 2, light green= 3, purple= 4, yellow= 5, dark green= 6, black= 7, brown= 8, blue= 9, and orange= 10. We do, however, express relationships by colour orally, simultaneously with numeric value. Some suggestions for helping students learn the numeric value for the rods are:

1. Place a drawing chart with the colourful Cuisenaire rods in the front of the children in a room with each numeral from one to ten written in the colour of the corresponding Cuisenaire rods. That is the numeral one would be written in white, the two in red and three in green and so on up to the ten with its colour in orange. It is also helpful later on to have the eleven written in orange and white, twelve in orange and red and so on. Gather the students and instigate them interestingly towards to the staircase structural picture of colourful Cuisenaire rods close their eyes and. Oral games can be played, like what you see after red, or before pink.
2. From three different rods, a student with eyes closed, tactically identifies the longest and shortest and guesses the name-- yellow or five. A student could also be handed one rod and just by feeling it behind his/her back correctly tell what number it is (+/- 1). With eyes closed, the students can try to find a specified rod from within the carton. The one, two and ten rods are usually the first ones learned.
3. After that make the students to measure the difference between longer and shorter rods and to remember the assigned values to the corresponding rods.
4. Allow them to make trains of lengths after measuring the lengths of the rods.
5. So after learning how to make trains corresponding to the length of different colour they can make many different trains that equal the orange rod, placing each below the succeeding one. Then take one car off a train and have the student tell which one has been taken away. This is good practice for learning which two numerals make ten or any other value for suppose nine or eight.
6. Make the students to practice and to consider staircases in which mistakes have been made. Make them to correct the mistakes by conducting oral discussion.
7. By providing worksheets that can make the student with experiences other than oral ones. Students can colour the rods drawn on paper to their appropriate colour, and write the corresponding numerical value under a picture of a rod. They can trace around rods to represent a specified numerical value or colour shapes or a picture labelled with the numbers 1-10 with the corresponding colours.

### Relationships Study

Coming to the next area we need to cover that is the relationships study. The student starts to see and know the lengths of rods that which rod is bigger than another and by how much. Some activities include:

1. Make the student to find a rod that is longer than green but shorter than orange. This involves oral work, with the teacher first giving the specifications, and then students can give the whole group or specifications of partner. First of the entire colour and after the numeral name are used.
2. Find a rod which is 3 times as long as the white, red, or white.
3. Find a rod longer than light green by the same amount as the yellow is longer than the red, and so on.
4. Know the relationship of the red, white and light green rods to the others. White is 1/3 of green, 1/2 of red, and 1/5 of yellow.
5. Match trains of two different colours to the same length of another bigger value of any other big rod.
6. Using of work sheets such as less than, greater than and the equal symbols are used for independent activities.
7. Make number families. For example, show how many different ways there are to make trains which equal 8 or brown. Discuss combinations. Those who are ready to, write equations.

### Beyond Operational Mathematics Activities

I have found the use of the rods helpful beyond aids in computing math problems. They can be used as concrete aids in many other ways:

1. Oral Word Problems: When given an oral word problem the student uses the rods to represent the story elements. For instance, in the story, "I had three pennies and lost one. How many do I have now?" The student can use three white rods to represent the pennies. By removing the lost one from the group, s/he clearly sees that two are left.
2. The rods help to build a left to right progression as all work with them moves in a left to right direction.

### The specification & design;

The design process of the application which is made for the teaching of addition to the dyscalculics is very user friendly and in a possible way of understanding and is comfortable to handle and operate the application in a desired way with direct operation without any involvement of complex introduction methods and formats. The response of the system will be possible according to the user operation and the user interface is designed in an outstanding which can be capable to understand for dyscalculics. The user interface design is very comfortable and can give good responses to the user. The user can operate the system very easily as such that this is designed with formal and simple operating methods.

The system is designed by using the flash software and introducing the Cuisenaire rods for the mathematical addition. The introduction of colourful Cuisenaire rods for mathematical addition can attract dyscalculic to participate in doing and learning arithmetic calculations. Introduction of the flash software is a better choice and can give very efficient and desired result. Designing of the application using flash software is very convenient and it consists of easily and effective applications which are very flexible to the user and are useful that can twist the design into our favour in any way. The dynamic representation of the system using flash software is very comfortable and can make any changes after completion of the application also if we need any change or any modification in the middle of the project or after completion of the project. We can do it very comfortably and without being disturb the whole application in the sense with the dynamic representation we can make changes at any time without disturb or collapsing the application. So that can manage the application in our way as we wish and conveniently.

The designed process of the system is very dynamic and can do the operation very easily so the user from the beginning of the operation while doing can understand the process from starting to the end of the operation. If the user (dyscalculic) starts the application to-do the addition he can understand the application step by step from the beginning. The application is designed in such a way that the user can easily understand and hold the application with much interestingly. The fact included in this is that the design of the application using flash with much easier to operate by the dyslexic people who is suffering with dyscalculia.

The application is described with the related data that can be very useful for the dyscalculia and its features. The information which is used in this is totally that can be useful for the dyscalculia and the characteristics of the people who is suffering from dyscalculia besides arithmetical addition

### The information related to dyscalculia;

2. Characteristics of dyscalculia and behaviour
3. How the dyscalculia occurs and the relation between dyslexia and dyscalculia.
4. Dyscalculia and its deficits
5. Working memory deficits in adults and children.
6. Developmental dyscalculia.
7. Teaching of mathematical addition to dyscalculia and implementation of teaching to dyscalculic.

The design of the software application and its features are very realistic and sub-divided into the different partitions such that it is framed from its reality.

1. The design starts with static and briefly arranged stages with explanation
2. The design starts with adding of Cuisenaire rods to get the result
3. After the result we will ask the question relating to the result of addition which exhibits
4. And we will give the answers to select the right answer by choice
5. If the user answers right or wrong we designed the symbolic expressions relating to the selected answers with special and interesting effects like multimedia.

With special and interesting features designed in this application can attract the dyscalculics towards to the learning of mathematical addition interestingly and improve their efficiency in arithmetical addition and can overcome their difficulties in addition.

### Implementation;

Before we are going to discuss about my design implementation I need to explain the teaching sources which they had used for the teaching to the dyscalculic people and i am not going to discuss about them very briefly and i can tell a short story about the teaching sources which were used by the experts in the past.

The sources of teaching which were used for the teaching to "Dyscalculia";

1. Phonological loop
3. Brian Butterworth's Dyscalculia screener for teaching dyslexia

So what I mentioned below are the sources which were used for teaching dyscalculia and by reading about the working functions which i mentioned above and by following those working functiosns and procedures I designed and make the implemantations for teaching to dyscalculia by introducing new technical software FLASH.

The implementation in this project was done by introducing flash software. Because it is very convenient and very flexible such that we can make lots of twists and turns with respect to the changing ideas according to the design patterns. The main advantage of the flash software is convenience due to this benefit we can make changes at any stage from the beginning to the completion while designing the application. The designing of this application with flash is not only for the reason of convenience but also for the execution of the output with much efficiency with our desired aspects.

The fact that should tell really is I can perform the application in flash in the beginning I decided to design the application on asp .net but it is not a convenient and very much supportive to my ideas and implementation. So I really changed the mind and turned towards flash software to implement the application. Why because flash software is very supportive and easy to design according to my intension.

Using other applications like java, asp, etc for designing this application can execute the output but to evaluate the output some complexity has to face with that application but we can execute the output. But by using the flash we can design easily what we expected. With flash execution of output also done in step by step in detailed process that can be easily understand by the dyscalculic. And we can expect the efficient output from them.

### Results and evaluation;

Mathematics is typical concept to understand even for the normal people. So while coming to the mathematical addition it is a simple thing to do for the normal people not for the dyscalculic people. So the normal people can feel difficult in the advanced stage of learning and after that within a short period of time the normal people can learn it easily and can do their performance very best at any time in every situation. Coming to the point of dyscalculics they use to struggle while learning if we are teaching as usual and making them to teach in a classroom environment on a normal black- board as of the normal people. Because the dyscalculics can't remember the concept for a long time as of the normal people they use to forget the concept within a short period of time so to overcome these defects in them we need to introduce a special kind of teaching to fix the mathematical addition concept in their minds forever.

So for this special kind of teaching we need to introduce some effective methods of teaching like adding of attractive and interesting things like colourful Cuisenaire rods with the effects of multimedia and some other kind of interesting methods of teaching.

The main aspect and the goal of this project is to present an invincible design of application to solve the arithmetical calculation particularly addition. So to achieve this up to greater extent I introduced and design the application in all the possible way as I can. And very confident about this application that I can be able to present to the people especially who is suffering with dyscalculia (lacking in mathematical calculations) especially in doing addition.

I preferred and selected special software flash to perform the application and to demonstrate in an understanding and possible fluent way

The selection for designing of this project is in a new way as already we know that we can teach the mathematical concepts by introducing the colourful Cuisenaire rods by assigning numerical values to them. As we know that the teaching can do by showing the pictures of colourful Cuisenaire rods to the dyscalculics and can train them by adding rods in pictorial representation. So by taking a few advantages from them we developed the things by adding more special features to them with attractive features that can turn the dyscalculics interestingly towards to the mathematical learning of addition.

So by introducing the same Cuisenaire rods we designed the application with some effects of multimedia with the help of flash software. So by introducing flash I implemented the way of teaching with dynamic representation that automatic adding of rods assigned with different individual values to the rods starting from the single digit values and gives training to them and observe the results of the persons whether they approach the correct standards in doing so. If we observe and extract the correct output from them and after that we can move to the further stages of addition to teach the next double digits adding. So after observing the efficient output from them we can train and teach them by extending the digits of addition.

I have lots of confidence on my design that this can train the dyscalculia in a perfect and in an understandable manner and turn them into the positive attitude in learning mathematical addition up to complete extent the effects which introduced in this application is very helpful and dyscalculics can easily operate the system with much interest.

In future my application can fill the confidence in dyscalculic people that they can learn the addition much easily in their desired way and they can overcome the arithmetical difficulties any where according to the appropriate situations in different places and in different fields.

The future work;

The designing of mathematical addition for the dyscalculia is done and expecting that this design of the project can become a good evaluation to perform the addition for the dyscalculia. With this design the dyscalculics can understand the addition how to do and they can learn the addition from the advanced stage of adding single digits to the bigger level digits very easily. This application is designed especially for them (dyscalculia) to grasp the mathematical calculations and counting in their daily life. After learning the addition by this design of application they can overcome the dyscalculia particularly in the field of addition. So after following the current designed application the dyscalculic people can perform the mathematical addition sharply without facing any difficulties in their daily life especially in the areas of doing jobs on the till like counting money and tendering of money and taking and giving change etc,.

If possible I have some ideas and lot of interest to perform the applications on flash as similar to this addition may be in future have a plan to do the applications on subtraction, multiplication, division as well as how to solve the equations, if we design the applications which we mentioned above. That could become a great advantage to overcome the dyscalculia in arithmetical operations and can perform like normal people in the society.

1. If I get any chance for further development on dyscalculia. I can develop the applications such that the dyscalculic people can overcome the dyscalculia completely in any standards.
2. I can present the designs with suitable applications which are capable of doing all the mathematical and arithmetical calculations by the dycalculics.
3. The other thing that I can make the applications which is convenient and easily to teach the mathematical concepts to the dyscalculia as well as in a detailed and in an understandable pattern.
4. I think this provides convenience and feel the self confidence in dyscalculia and can hold the determination towards arithmetical calculations which is very useful to their daily life aspects.

### Conclusion;

So far after searching and studying about the "Dyscalculia" and its areas of research I can conclude that this whole information that which I gathered relating to the dyscalculia can be useful for the people who is suffering with basic learning of mathematical and arithmetical concepts particularly in doing mathematical addition Because in this project we had specially focussed on addition and about the difficulties of the dyscalculic people while performing addition with simple numbers and therefore we have confirmed that by studying and researching about dyscalculia I came to know that how they are facing the problems with dyscalculia in doing mathematical addition.

So that is the main reason to make me respond to do some favour for the dyscalculic people and I decided to make the application which is going to be user friendly and supportive to the dyscalculic people and I tried my level best and prepared a new application as far as I can do.

So to shape this application I have been studied thoroughly and meeting my supervisor and some the professors which are experts in our university especially the dyslexic supportive team. So by studying and taking suggestion from my professors and following the directions of my supervisor I referred about dyscalculia and how is occurs and its causes and the deficits of dyscalculia and its subtypes and everything. After keeping all these in my view I had prepared a new application in flash with the help of the attracting and colourful Cuisenaire rods and implementation of addition with the help of these Cuisenaire rods. So I introduced interesting new way of teaching methods in addition with some with the effects of multimedia to teach addition to the dyscalculic and I hope this can attract the dyscalculic towards the learning of addition from basic stage of addition to the higher level addition and keep remember for a long time why because they forget early after learning the concept. I hope this project can present an outstanding result in the area of "Dyscalculia

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