Dyscalculia From Detection to Diagn

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E-BOOK SUMMARY

Dyscalculia: From Detection to DiagnosisGaurav R. Wankhade

1*

ABSTRACT

The article is an examination and illustration of the most common reasons behind the occurrence of learning difficulties in

mathematics, medicinally termed as Dyscalculia. When the basic emotion i.e. Fear dominates over thoughts; a central

equilibrium for learning mathematics, Danger Alert System of the body,perceiving any real or imaginary threat puts the defence

reaction on backseat activating the defeat reaction, which is one of the main causes of Dyscalculia. Assessment of Dyscalculia

contains three main types viz: Neurological, Neuropsychological and Neuropediatric assessments. Diagnosis Dyscalculia is a

help measure which provide the exact environmental framework for the treatment of Dyscalculia by distinguishing in between

Dyscalculia and other forms of learning difficulties in mathematics i.e. Acalculia, General learning difficulties, Pseudo-

Dyscalculia and ADD (Attention Deficit Disorder). The paper concludes by taking an overview of Management of Dyscalculia

which includes Remedial measures such as mathematical screening, tests and Help.

I. Introduction:The article is related with a specific cognitive process in action (operations) where the brains logical

application is being implied to understand Mathematics. The basic purpose of this article is to analyse &

interpret learning Mathematics as a subject and the consequences of difficulties thereof. Though an

important part of our everyday life, the way, the subject is taught is uninspiring and unfortunately

irrelevant, mounting the basic fear of mind and questioning the self esteem of many peoples especially

childrens and youngsters. When the basic emotion i.e. Fear dominates over thoughts, Danger Alert

System of the body, perceiving any real or imaginary threat puts the defence reaction on backseat

activating the defeat reaction, which is one of the main causes of learning difficulties in mathematics. Theresult is repeated failure leading to disliking and complete denial to the further learning of the subject.

Dyscalculia is the medicinal term reflecting the basic problem of Learning Difficulties in mathematics

which is the main reason behind the creation and which forms the core of this article.

II. Development of Mathematical Ability: The process (How Does Mathematical AbilityDevelops?)

Understanding of Numbers (logical symbols and specific mathematical characters), which are the

representation of visionary objects already exists in an elementary format in every childs mind, by birth.The entire learning process of the subject of mathematics passes through many stages before it gets fully

developed and a child gets fully aware of it. Here is the depiction of the process which helps a child to get

into the world of mathematics.

1*E-Book, What is Dyscalculia?, by Dr. B. Adler, published online by Kognitivt Centrum Sweden, 2001, summarized by

Gaurav R. Wankhade, Research Associate, ICFAI Research & Publication Centre, IBS - Mumbai.


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Table I: Mathematical Learning Process of a Normal Human Being

Sr.

No.

Age Stage Characteristics

1. At Birth Rudimentary Grouping; Formation of

categories and prototypes (Size, colour,

forms etc.)

Development of feelings, reln-ships

(instead of faces, mamma, daddy comes

into picture)

2. 1 years Understanding of existence of objects

irrelevant of the sight & vision of the

observer

Replacement of concrete objects by

numbers for e.g. no. 3 replaces three

oranges etc.

3. From 1

years 2

years

Questioning; Understanding and

classification based on characteristics of

the object

Child understands that every object has

some special characteristics

4. From 2

years 4

years

Ability to distinguish properly Ability to analyze quantities with

variances in shape and size

Counting and sequencing

Learning of orderly and correct

sequence of numbers

5. 4-6 years Strategic understanding For the purpose of counting child

extracts data from memory instead of

actual count

6. 6-7 years Learning of basic parameters for e.g.

Scale, distance, time etc.

Understanding of little-big, high-low,

long-short etc.

7. 7 & after Working with numbers starts Automatization

8. 8 years Deeper understanding of numbers & the

particular number system

Number system: In which each digit is

separated from the adjacent no. by 01.

9. 9-10 years Learning of counting (principles of

number constancy) without remembering)

e.g. 20 coins are same whether grouped

or spread-out

10. 10-12

years

Understanding that numbers are symbols

of concrete things with further knowing of

multiplication & division

Understanding of a number as different

parts which can be divided. (no. 25 as

25 separate parts divisible as 7 parts of 5

each

11. 12 years &

above

Dealing with Higher (complex)

Mathematics which includes Diagrams,

graphs and tabular forms of number

Reading out figures from table, charts,

drawing diagrams, understanding

direction etc.


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system; visualization of things;

development of problem solving and

planning ability

More logical acting rather than the

mechanical way.

Source: Compiled by Author from What is Dyscalculia?, Dr. B Adler, 2001, Kognitivt Centrum Sweden (An e-book).

This is a normal process through which mind of every child has to pass without any major difficulties but

things may become problematic at any of the above listed stage. Generally the basic problem starts at or

after the age of 7. In many cases the beans of the problem already sown in early (premature) stages of

Age. Someone may neglect them by terming them as normal difficulties which are the parts and parcel of

learning course. So in many cases such problems (difficulties in learning mathematics) do not get their

due recognition and care (corrective measures) at the stages of occurrence and over the period of time

they take a shape of severe difficulties.

How do we recognize Dyscalculia?

The word Dyscalculia is a combination of two different words i.e. Latin word dys meaning a form of

special difficulties and the Greek word calculus which means counting stone. Thus the word literally

refers to the special difficulties with counting. In more proper words it means specific (particular) or

special difficulties with learning Mathematics. The basic difference between Dyscalculia and General

Learning Difficulties is that in the later one need extra time to complete the learning process. Another

important difference is that General Learning Difficulties are characterized by even performance i.e.

students with such difficulties perform very slowly and evenly over the time. But in case of Dyscalculiathe uneven performances (students excel at one point of time and suddenly dispel at the next moment) are

the main problem.

Origin of Dyscalculia:

Small initial difficulties for e.g. writing down any number or deriving specific value (fixed amount) from

each number of the Numerical System occur with some children at the beginning of their school. Either

they take very long time or simply lack continuity when asked to perform a mathematical task. This may

be because of cognitive resistance or emotional blocking in the mind of a child arouse out of the childsoverall attitude towards the subject. This further leads to repeated failures creating knowledge gaps at the

initial stages. These initial special learning difficulties in mathematics often develop into more general

learning problems by the end of primary education.

The learning process of mathematics showing the beginning of learning difficulties is depicted below.


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Fig I: Origin of the Learning Difficulties in MathematicsSource: Compiled by Author from What is Dyscalculia?, Dr. B Adler, 2001, Kognitivt Centrum Sweden (An e-book).

But Dyscalculia indicates specific or special learning difficulties in mathematics which differs from

General learning difficulties.

One can detect or recognize Dyscalculia from some important symptoms shown by the student as given

below_

i) Lack of continuity in handling same or different mathematical tasks,ii) Lack of implementation of skills (misunderstood as disinterest of the student) instead of having

the basic knowledge of mathematics,

iii) Inability of easy access and fast retrieval of stored information from the long term memory whenrequired which gets severe with the passage of time,

iv) Because of some difficulties whole subject of mathematics seems impossible to solve to the childcreating a sense of stupidity within.

v) Problem with certain cognitive thought processes for e.g. telling correct time with analog clock,problems with temporal orientation, problems with planning and remembering etc.

Pedagogical Signs:

Further recognition could be obtained from the pedagogical signs or characteristics displayed by the

person with Dyscalculia. The list is provided below. The list is not a complete analysis, but representation

of common examples.

Early Stage

Blossoming,

Later stage Difficulty No Difficulty at all

Early stage difficulty,

Later Stage

Blossoming

Early stage

difficulties

developing into

Dyscalculia

Mathematics

LearningDifficu

lties--


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Table II: Pedagogical signs with their respective examples

Sr.

No.

Pedagogical Signs Examples

1. Difficulties with reading and

comprehension

Difficulty in Reading directions, maps, diagrams,

tables, space comprehension and recognizing symbols.

2. Difficulties with writing Difficulties in recalling, copying, calculating or simply

writing down in order the numbers & the symbols

(geometric shapes & figures).

3. Problems with understanding concepts

and symbols

Difficulty in understanding and implying concepts of

amount, weight, space, direction (sequencing), time etc.

and mathematical symbols (+, -).

4. Problems with number sequence and

mathematical facts

Difficulty in sequencing, calculation, reverse counting,

arranging numbers in their mathematical order.

5. Problems with complex thinking and

flexibility

Rigid or concrete level thinking, restricting childrens

to choose strategic options wisely, following specified

steps, ability of making reasonable judgement and

difficulty in planning.


It is most important to first examine & discover the causes of the childs difficulties and then apply the

appropriate remedial methods. For that examination the above listed pedagogical signs are of very much

importance as they clearly describe most commonly occurring symptoms of the disorder.

Below given is a simple check-list detailing dyscalculia. To determine conclusively whether a child really

suffers from dyscalculia, a thorough assessment in collaboration with an informed psychologist or doctor

is necessary.


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Table III: Detailing Dyscalculia

Dyscalculia: Characteristics in everyday life-

Difficulties with temporal orientation (time planning ability)

Inability to make rational and reasonable judgements calculating values.

Lack of logical understanding caused by poor working memory.

Tracing Existence of Dyscalculia-

Dyscalculia have been observed to be existed

for more than 100 of years

Theories put forward in this regards_

-Gerstarms (German scientists) first used the

term Dyscalculia

-L Koscs theory of developmental Dyscalculia,

based on

-A lurias theory of Brain and its 3 functional

blocks namely Regulating, Analysing and

Ruling block

Population*2

having Dyscalculia-

E,62.5

A,6.4 B,

4.8

C,20

D*,6.2

A B C D* E

Can Dyscalculia be cured-

Definitely, Yes and with a course called asDiagnosis Dyscalculia.

The Diagnosis Dyscalculia is a course ofmaximum of 1 year and it is the current

stage developmental descriptive framework

which is available today.

Value of a Diagnosis-

Value to

The Child The Parents The Teachers Psychologists and Doctors Society

Difference in Between Dyscalculia and Dyslexia-

Dyslexia mean Difficulties in reading written text fast and fluently, while Dyscalculia meanshandling out specific mathematical tasks

There is a variant of Dyscalculia which is called as Dyslexic Dyscalculia, meaning primaryreading difficulties leading to mathematical problems

Automatization difficulty i.e. lack of flow in readingSimilarities-

A poor working memory Recalling inabilitySource: Compiled by Author from What is Dyscalculia?, Dr. B Adler, 2001, Kognitivt Centrum Sweden (An e-book).

*Where, A- Problem in Counting, B- Problem in Reading, C-Other types of Mathematical Difficulties, D-

Childrens having Dyscalculia, E Rest of the Childrens.

2What is Dyscalculia?, Dr. B Adler, 2001, Kognitivt Centrum Sweden (An e-book).


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Value of Diagnosis: (The Child) Helps them to understand their own difficulties while dealing with

mathematics and offers remedial measures. Eliminates or lowers the risk of depression, traumatic

circumstances and suicidal tendencies. (The Parents) A great relief to the parents when they discover that

the disease is not incurable and a diagnosis is available. (The Teachers) It enables them to plan their

remedial work accordingly and in accurate directions avoiding un-required areas. (Psychologists and

Doctors) Design their diagnostic framework appropriate to the need and type of learning difficulty in a

child. (Society) It can help in improving societies all over health care system.

III.Thoughts, Emotions and Mathematics:

Thought: Def: An inner conversation with self. It is different from emotion. It may be origin of emotion.

Our thoughts play a major role in our well-being. They allow us to move beyond the present memories

both back into the past, through memories and forward into the future, through the power of imagination.

Thoughts express themselves in words and pictures. It is the essential ally of logic which enables us to

work towards a solution, step by step. We both think and feel (emote) with the brain. Even, these two

processes use the same path. Because, emotion moves at double the speed of thoughts we concludes that

emotions are stronger than thoughts, which in reality is not true. In simple words We are our Thoughts,

but we emotes through our Acts.

Mathematics is not merely an answer to the problem but rather a guanine process of arriving at the

answer. It is the journey itself and not only the destination. It is a network which links together our

different ambitions through which we try to reach to the Goal. So there are multitudes of paths which

lead to that goal and i.e. the right answer. Hence mathematics is a well-defined, exclusively structured

cognitive thought process. It is based on two fundamental parameters of Recognizing; demands reasoning

& ability to recognise things and Seeing Patterns.

In this framework, Thought is that central equilibrium which controls and guide us through mechanical

processes of learning this language of symbols; Mathematics. Here please remember that we are talking

about positive thoughts as there exist negative thoughts too, which get transformed into unconscious

references, which may show up later in different situation and are the main cause of learning difficulties

with mathematics. And it is our ability to recognize our strengths and weaknesses, and then overcome the

later, which will act as a foundation for positive thought development.


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Fear is a basic emotion and a very powerful one, which can be countered through another equivalent

emotion and i.e. Happiness; An impactful motivational force, and happiness create enthusiasm. This is a

best effective remedy to counteract fear. A common symptom amongst most people with learning

difficulties or Dyscalculia is the fear of failure (real or imaginary). There are two major reactionary sub-

systems which forms a basic degree of alertness in the biological structure of the defence mechanism

existing in our bodily system. These are

i) The Defence Reaction

Fig II: Origin of Thoughts and Emotions from the Brain

BRAIN

(Impulse)

Sensing/ Perception

Amygdala; (Brain Alarm present in rear part

of the brain which interprets sights/

im ressions

Thalamus

Senses

Travels toSends fast

message to

Transfer signal

to

Thoughts

Words/pictures

Action

Habit

Character

Joyful situation

(Real/Imaginary)

Traumatic situation

(Real/Imaginary)

+ve -ve

Traumatic situation

(Real/Imaginary)

Joyful situation

(Real/Imaginary)

Emotion

Expressing/

Acting/

Responding

Feelings+ve -ve


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Table IV: Assessment of Dyscalculia

Assessment

Tools

(Tests)

Neuropedagogical Neuropsychological Neuropediatric

It should

includes an

examination

of

Mathematical knowledge and

understanding

Reading ability and

comprehension

Writing ability and spelling

Communication and

interaction with his environment

Progress in lessons

Strategies for the own work

The students handling of

oral, written and visual

information The students strategies for

solving specific tasks

The students general learning

strategies

The students attitude to their

own learning ability

The students motivation

Mathematical Screening:

Understanding number

structure, number sequence,

Simple counting operations,

Complex counting operations

etc.

Understanding arithmetic

signs and symbols

Numerical comprehension

Understanding geometrical

figures

Understanding spatial

relations

Spatial memory

Planning ability

Time planning Temporal orientation

Dyslexia

Dyspraxia and dysgrafia

Attention Deficit Disorder

(ADD)

Asperger syndrome

Tourette syndrome

Schizophrenia

Autism

Epilepsy

Skull trauma, brain tumors,

stroke

Personality ( Interaction,Communication, Behaviour,

Temperament, Character )

Cognitive development

(Processing information,

Flexibility in working out

solutions, Strategies)

Specific neuropsychological

processes

(Attention, control and

concentration, Motor

coordination and sensory

integration, Basic perception,

Spatial ability, Imagination,

Language ability, including

comprehension, Memory and

learning strategies)

Fine motor skills

General motor skills

Coordination

Perception

Balance

Lateral thinking

Muscle tone

Concentration and mental

stamina

Automatization of

movement

Motor planning andconscious movement

Excessive movement

Choice of movement

Refining the choice of

movement

Automatizing the choices

through practice


The assessment is necessary for parents & teachers to answer many of their immediate and secondary

questions like what are the reasons for the learning difficulties? Are we facilitating, helping and

teaching properly? Or are we only responsible for this situation? how we can overcome this situation?


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is there any possible solution available to the problem? Etc. While assessing Dyscalculia, it is necessary

to assess reading and writing ability in order to make one sure that out of the two none is causing the

other.

Neuropedagogical Assessment

A wider framework of broader prospective & observations is admirable to offer not only initial help but a

remedy with proper direction. The test is structured for the cognitive process lying at the core or which is

the main cause of learning difficulties.

Neuropsychological Assessment:

Designed by Neuropsychologist, the test examines link in between working of brain and our behavioural

responses. But it excludes examination of mathematical skills & knowledge. Cognitive and Psychological

assessment is the main objective to identify some very specific problems like uneven growth or

development, lack of concentration, restlessness, hyperactivity, lack of perceiving ability, poor motor

coordination etc.

Neuropediatric Assessment:

Its a medical health examination based on overall medical background (past or history) of the student

under assessment. It includes physical check-ups, eliminates neurological disturbances and serious

progressive diseases which may be the cause of learning difficulties in mathematics. Part of this medical

test also covers students motor skills (movement ability) like choice, speed, refining, and automatizing

choices. The early age (baby age) symptoms related with coordination are problems with focusing for

long time, problems with crawling and walking, repetitive actions, difficulty with learning new things,

stress and anxiety in new situations, delayed speech development, excessive motor activity etc. etc.

V. Diagnosis Dyscalculia:The staircase from Assessment to Diagnosis consists of two major steps. First is to understand individual

difficulties and second one is to make a suitable & specific diagnosis. A Diagnosis is the abstract of

explainable wide range of observed symptoms. It is not medical in nature, but rather it is a development

of special remedial environmental framework within the domain of medical care but treated outside i.e. at

the home or/and at school.

Let us first make ourselves clear about the fact that Dyscalculia is neither a disease nor a chronic

condition, but it is an inability of our mind and bodys dynamic equilibrium (which is continuously


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E-BOOK SUMMARY

changing & trying to adapt to new circumstances), to get adjusted with over demanding & vast filed of

mathematics. If we are able to understand this, it is possible to create that remedial environment which

will not only diagnose the Dyscalculia but in some cases will show enormous improvement which will be

beyond our prediction.

Developing Diagnosis is a medical concept constructed over centuries through a biological model of

progressive understanding (i.e. treatment should be different for different disorders. This model further

enables to standardise a worldwide classification and uniform system for the diseases. Such two major

systems are ICD-10 (International Statistical Classification of Diseases, injuries & causes of death),

developed by World Health Organisation (WHO) and DSM (Diagnostic and Statistical Manual)

developed by APAC (American Psychiatrists Association) which are compared below.

Table V: Comparing ICD-10 and DSM

ICD-10 DSM

DYSCALCULIA:

DefinitionIn the ICD-10, dyscalculia is named as a

specific mathematical difficulty and is

defined as follows:

315.1 Specific arithmetical

retardation

Disorders in which the main feature is a

serious impairment in the development of

arithmetical skills which is not explicable

in terms of general intellectual retardation

or of inadequate schooling.

Dyscalculia3

The DSM IV states that in the case of

dyscalculia:

As measured by a standardized test that is

given individually, the person's mathematical

ability is substantially less than you would

expect considering age, intelligence and

education.

This deficiency materially impedes academic

achievement or daily living.

If there is also a sensory defect, the

mathematics deficiency is worse than you

would expect with it.4

Source: Compiled by the Author from What is Dyscalculia?, Dr. B Adler, 2001, Kognitivt Centrum Sweden (An e-book).

It is imperative to check for psychiatric or neurological disease, before making a diagnosis e.g. an

individual with obsessive compulsive disorder might find counting and general learning difficult because

of their uncontrollable tendency towards compulsive thoughts and actions5.

A comparison of Diagnosis Dyscalculia with other learning difficulties can be well understood from the

following table

3 What is Dyscalculia?, Dr. B Adler, 2001, Kognitivt Centrum Sweden (An e-book).4 Ibid5 Ibid


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Table VI: overlapping Diagnosis

Type of

Disorder

Definition &

Characteristics

Cognitive &

Psychological

Causes

Diagnosis Remedial (Help)

Work

Acalculia

(Pop:

Learning difficulties

arise from emotional

blockings. Despite

-Loss of self belief

and confidence

-feeling of

-Individual care,

-separate

teaching etc.

-private talks with

the teacher, or

-in tougher cases


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Boys) having cognitive

ability face problems.

Despite average

intelligence, possess

severe difficulties with

mathematics

uselessness, failure -Motivation

Boosting

activities

-emotional

support

with the school

psychologist, where

emotional blockings

can be cured.

Attention

Deficit

Disorder

(ADD) &

Fundamental Problems

with attention and

working memory.

-affect mathematical

ability indirectly

- concentration

difficulties, being

easily disturbed, and

problems learning to

draw, read and write

letters and numbers,

as well as

difficulties with

planning, keeping to

a strategy, and

generalizing learned

knowledge.

-diagnosis of

behaviour

Can use some of the

remedies discussed

in the above listed

disorders

Attention

Deficit

Hyperactivity

Disorder

(ADHD)

High incidence of

other learning

difficulties.

Problems with

counting, reading

and

Writing

- Behavioural

Diagnosis

Can use some of the

remedies discussed

in the above listed

disorders


VI.Help Work:As an appropriate diagnosis cannot be done before the age of 10 years, it is not the only way. Another

way is to provide help and use of other remedial measures. The complete help is rather a long process.

Help starts very much earlier than diagnosis and has to be provided long after the diagnosis is over. Hence

it is advisable to provide remedial support throughout the span of 20 years from the beginning of Childs

learning process to tackle this disorder effectively. A general model of help is elaborated below


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Action Plan:The action plan should be developed by teachers, parents and the student themselves, working in alliance,

and it should be understood and agreed on by the student themselves. A successful action plan will

include the following features6:

Professional presentation

Clearly assigned responsibility

Realistic goals

Clearly defined structure Collaboration and allocation of roles

There should be some one mainly responsible for the implementation and evaluation of the program. It is

important that every school finds a simple but effective way to systematically document each students

6 What is Dyscalculia?, Dr. B Adler, 2001, Kognitivt Centrum Sweden (An e-book).

Role of Parents

-Relieving,

-reducing,

-compensating the problem.- Working with Motivation and

Blockings

Role of Society (Others)- Working with Motivation and

Blockings

-change in mindset from traditional to

modern is necessary

Role of

Counsellors, and

Psychologists

- Working with

Concentration and

Attention

- Working with

Perception and

Spatial skill

-Working with the

Temporal

Awareness

-Working with theMemory

Role of Teachers

-Motivating

relearning

- Working with

Numerical

Comprehension

- Working with

Automatization,

- Working with

Language

Comprehension

- Working with

Problem Solving- Working with

Logical Thinking

Fig III: A General Model of Help

Child /Student with

Dyscalculia


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progress, relevant assessments, and the development of the program itself7. Everyone involved in the

program should receive regularly up-dated copies of the action plan.8 There also needed open meetings of

experience sharing, transforming negative feelings of student into positive one. Individualistic help as

compared to group help should be more appropriate for clear and comprehensive action plan & for the

action plan to work. Identification of exact order to implement different strategies of action plan is

necessary. Moreover, it is also essential to repeat a remedial exercise in case it does not work in first

attempt. Also identifying exact difficulty to effectively counterattack it, which can be termed as

Mathematical reasoning is required. Further student should be provided with mathematical tests designed

exclusively for this purpose.

Time has come that we should addresses important issues concerning dyscalculia, and it has been our

main aim to present what we in the field now know about the subject in a clear, understandable way

which we have fulfilled. The discussion above was helpful look at reasons for dyscalculia, diagnosis, and

above all, how to provide the right kind of help.

Disclaimer: The Article is a Summary by Gaurav R. Wankhade of an e-book by Dr. B. Adler 2001,

Kognitivt Centrum Sweden titled What is Dyscalculia?

7 Ibid.8 What is Dyscalculia?, Dr. B Adler, 2001, Kognitivt Centrum Sweden (An e-book).

Dyscalculia From Detection to Diagn

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