### 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.

In this project to overcome “Dyscalculia” particularly in the arithmetical addition and to teach the mathematical addition to the dyscalculics I designed application software in “Flash” with visual graphical design with the help of a colourful Cuisenaire rods. By studying about the previous sources that are useful to teach the maths addition which were designed by some experts in dyscalculia studies such as Brian Butterworth and some other experts on dyscalculia the teaching designs like Phonological loop, Visio spatial sketch pad etc,. Hence by following some of that specific designs in my view and I designed an understanding design to teach mathematical addition rule to dyscalculia people. This includes brief understanding and attractive designs that can impress the dyscalculic and make them enthusiastically towards to the learning of mathematical addition from the basic adding to the high level digits adding that means starting from single digit adding to higher level adding. For this we need to train them on the Cuisenaire rods and the colours and values which was assigned to them and then we need to teach them first by running the application software automatically and I designed the whole process of addition in this software from the advanced stage to the stage of getting result. After that I am conducting a quiz to test their ability and grip on addition after teaching by using the designed application. I hope this design can help the dyscalculia to overcome arithmetical addition inability up to a greater extent.

### 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;

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

### Back ground;

### Dyscalculia;

### 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.

- The example of an arithmetic addition2+4 or 4+2
- Prices in the shops like tendering the money and taking the change correctly.
- Normal identification of numbers and what those represent, e.g. which is bigger, 2500 or 2770? Does 100+100 = approximately 200 or2000.
- 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.
- 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.

### There are two kinds of dyslexia

### Genetic

- 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.

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

### Types and sub-types of dyscalculia;

### 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;

- Difficulty in learning and remembering of mathematical concepts such as used in our daily life in our activities Ex; Addition
- In the time of interviews with teachers.
- Difficulty in remembering even up to the number bonds to 10 is the worst problem that pupils struggling with maths were up against.
- Difficulty in executing mathematics calculations procedures.
- In 1984 Russell and Ginsburg found a dyscalculic group of people struggling on both written calculation and arithmetical fact retrieval.
- In 1992 Yamashita and Aram found dissociation absence between arithmetical fact ability and procedural ability with numerical processing difficulties in pupil.
- 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.
- 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.
- Even the counting of simple and single digits were shown to be vulnerable in dyscalculic people
- Geary, Bow-Thomas and Yao in 1992 found that dyscalculic people are less likely to detect the counting errors than normal people.
- 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.

### DEFICITS OF DYSCALCULIA;

### 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.

### ADHD:

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.

- Auditory discrimination
- Auditory performance with degraded signals
- Auditory performance with competing acoustic signals
- 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.

### Dieted by the reminder of the hypothesis.

### 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