A Case Study Of Teaching Addition And Subtraction To A Student With Dyscalculia

Psycho-Educational Research Reviews | Vol. 9, No. 3
London Academic Publishing, December 2020, pp 40– 55.
https://www.journals.lapub.co.uk/index.php/PERR
40
A CASE STUDY OF TEACHING ADDITION AND SUBTRACTION TO A STUDENT WITH
DYSCALCULIA
Abstract: In this study, it was aimed to teach the addition and
subtraction to a student with dyscalculia who is in third grade at
elementary school. Before preparing individualized program,
the student was given a pretest to measure about his level of the
subject. The instruction was carried out in a room in the school,
with a time of 40 minutes per day in the form of individual
instruction with the student. In addition, the study was supported
by a researcher-developed scenario booklet, concrete materials,
computer games, reinforcement award, and assignments. This
study was conducted as a case study, one of the qualitative
research methods. The data were analyzed by descriptive
analysis technique. Results of the study indicate that the student
achieved more than 90 % objectives on teaching basic addition
and subtraction skills at the third grade. Gains have been
actualized by the student with mathematic learning difficulties
with over 90 % success in 63 individualized lessons. On the
other hand, social validity data were collected through
observation and interviews to identify strengths or weaknesses
and changes occurring in the student work. As a result of the
studies, it has been determined that the student gained self-
confidence by enjoying his sense of accomplishment.
Keywords: Dyscalculia, mathematics learning disabilities,
teaching addition and subtraction
Beyza Koç PhD
Teacher
Ministry of National Education,
Konya
Turkey
Contact:
E-mail: koc_beyza@hotmail.com
ORCID: 0000-0002-5674-7037
İsa Korkmaz PhD
Full Professor
Necmettin Erbakan University, Konya
Turkey
Contact:
E-mail: ikorkmaz@erbakan.edu.tr
ORCID: 0000-0002-6647-1812

Psycho-Educational Research Reviews | Vol. 9, No. 3 (December 2020)
41
INTRODUCTION
It is impossible for all individuals to benefit from
general education in the same way, time and
efficiency. Different teaching methods and
applications need to be employed for different
individuals. Those are the individuals who require
special education. Special education is the part of
general education system that are provided to
students with disabilities in cognitive, behavioral,
social-emotional, physical and sensory areas and
they are individually planned and aim to maximize
the possibility of individual’s living independently
(Eripek, 1998). Individuals with special education
needs are classified by Turkey's Ministry of
National Education Special Education Services
Regulation (MONE, 2006). Classifications are
made according to the common characteristics and
educational needs of individuals, although each
individual's needs are unique. One of these
classifications is specific learning disability for
particular subject. Based on DSM-5; it is a
disorder that is validated with valid personalized
success measurement tests and comprehensive
clinical evaluation and is diagnosed when
individual's learning and school skills are
significantly and measurably less than expected
according to the age of the person (Köroğlu, 2013).
According to the Special Education Services
Regulation; an individual with specific learning
difficulties is defined as a person who is in need of
special education and supportive education
services due to difficulty in listening, speaking,
reading, writing, spelling, paying attention and
mathematical operations. In fact, this disorder
arises in one or more of the informational
processes which are necessary to understand and
use the language in written or verbal language
(MONE, 2006). DSM-5 criteria are used in the
diagnosis of learning disability in Turkey. In
DSM-5; Learning Difficulties in schools are
defined in three subgroups as reading disorder
(dyslexia), numerical (mathematical) disorder
(dyscalculia) and disorder of written expression
(dysgraphia) (Köroğlu, 2013).
Difficulties with counting, learning number facts,
doing mathematical calculations, telling time,
counting money, measurement, mental math and
problem solving strategies are called as
mathematical difficulties (dyscalculia) (Cortiella
& Horowitz, 2014). Students who have learning
disabilities (dyscalculia) in mathematics have
difficulty in daily life because they have difficulty
in using quantities such as money, time and
direction. They do not understand the prices and
their efforts to calculate products' total prices in
their daily shopping. Using hand and finger for
calculation of prices may embarrass them publicly.
The complexity of mathematical processes made it
difficult to define what it means to have a
mathematical learning disability (Geary, 2003).
Although there are many definitions about
dyscalculia, dyscalculia in the most general sense
is the defect and inability to recognize and use
mathematical relationships, and to recognize, use
and write numerical symbols (Butterworth, 2003).
Researchers (Chinn, 2004; Dowker, 2004, 2005;
Gifford, 2005; Hannell, 2005) emphasize that
mathematical difficulties are often associated with
problems in other areas, and that mathematical
skills should be considered together with the
difficulties associated with language, spatial
orientation and memory (cited in Dowker, 2009).
Geary (2004) explained that the difficulties
experienced by students with dyscalculia include:
dividing items into subgroups, estimating,
remembering the concepts of numbers, counting
down, understanding and applying the concept of
time, money, sorting, finding the direction
(left/right), recognizing number models and
understanding and applying the language of
mathematics. In addition, children with
mathematics learning difficulties have difficulty in
performing simple arithmetic operations (Shalev
& Gross-Tsur, 2001) and using recall based
procedures to solve verbal problems.
It is viewed that teaching mathematics is very
tough subject for students in all level in every
society. Besides that, some students really
experience mathematics learning difficulty for
some reason even though they do not have any
mental problems. Although 40 % of students have
difficulty in mathematics, dyscalculia is about 4 to
6 % of the population (Beachman, Trott, 2005).

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Butterworth (1999) stated that approximately 10
% of the population is dyslexic.
In DSM-5, it is reported that learning disability in
school-age children with different languages and
cultures are between 5 and 15%, and the reading
disorder is between 4 and 9% and mathematics
disorder is between 3 and 7% (Köroğlu, 2013). It
is stated that the students who have mathematics
learning difficulties are about two years behind
their peers and one year behind their peers in terms
of working memory capacity during learning
mathematic strategies used to solve simple (4+3)
and complex (16+8) addition operations (Geary,
Hoard, Byrd-Craven, & De Soto, 2004). Students
with learning difficulties in mathematics generally
use underdeveloped calculation strategies such as
finger counting when performing calculations.
One of the issues related to early mathematics
skills is that children can perform addition and
subtraction procedures quickly by the way of
recalling without calculation. This is the ability of
automaticity. In general, 50 % of children without
learning disabilities who are in the 3rd grade gain
automaticity rapidly. However, students with
learning disabilities can improve automaticity later
than other children (Bender, 2014).
Children with specific learning difficulties also
face emotional problems as well as academic
failures. Learning disabilities can lead to a
decrease in children's self-confidence and an
increase in anxiety and stress levels. As declared
in DSM-5, specific learning disorder can have
negative functional consequences through
lifetime, including lower academic success, higher
rates of high school dropout, lower rates of
postsecondary education, high levels of
psychological distress and poorer overall mental
health, higher rates of unemployment and lower
incomes (Köroğlu, 2013)
For all students with mathematics learning
difficulties or normal development, it is necessary
to determine the deficiencies in mathematical
skills, to investigate the causes of these problems
and to propose solutions for these reasons as
mathematics is one of the prerequisite skills for all
academic life. In fact, the main aim of this research
is to examine how a student with mathematics
learning difficulties acquires the addition and
subtraction skills and to demonstrate the
knowledge and skills of the student before and
after the study.
METHOD
In this study, an intrinsic case study from
qualitative research methods was used. In an
intrinsic case study, the researcher is primarily
interested in an understanding a specific individual
or situation. The particulars of the case in order to
shed some light on what is going on and study a
particular student to find out why that student is
having trouble learning to read and count
(Fraenkel, Wallen & Hyun, 2012).
This research was carried out in an elementary
school of the ministry of national education in one
of the central districts of Konya Province in the
second term of 2016-2017 academic year. The
school where the research was conducted was
chosen since the researcher was working as the
deputy director of that school. This study is a
single-case research consisted of a student with a
dyscalculia report. While selecting the student, the
researcher had previously interviewed the school
counselor and decided that the participant would
be a primary school student in the third grade to
teach the addition and subtraction. The researcher
first found the names of the students who had
mathematics learning difficulties in the third
grade. The reason why the student was selected
from third grade is that in the first and second
grade curriculum, addition and subtraction are
composed of basic knowledge and skills which are
not complicated. On the other hand, it was thought
that it would be too late to teach addition and
subtraction in the fourth grade.
It was also noticed that there were different
students with mathematics learning disabilities in
the same class. First, five third grade students with
mathematics learning disabilities were
interviewed. It was determined that two students
knew the addition and subtraction procedures
(addition without-regrouping and subtraction
without- regrouping tens). It was decided that the
study would not be able to work with these two
students as they should have no knowledge of
addition and subtraction for the study. Among the
other three students, two students who were in the

43
same class and having a learning disability report
were found to know single digit numbers and two
digit numbers, but they weren't able to write and
read three digit numbers and could not do addition
or subtraction. It was decided that one of the
students in the same class would be the student to
be selected for the subject of this study.
The student's class teacher was interviewed and his
approval was received. The teacher said that the
parent of the student had only visited the school
once or twice in three years. The teacher’s
communication with parent was only carry out by
phone in case of need. The parent’s permission for
this study was obtained by phone firstly and then
the permission form was signed by the student’s
father when he came to meet with the researcher
before studying.The student's personal and
academic status was determined by the way of
individual interviews with students, classroom
teachers, school counselors and parents by the
researcher. Information about the student which
was formed according to the interviews is given
below: The real name of the student was not used
and labeled as ALP.
ALP: He was a 10-year-old male student and was
born in Konya. He studies in the third grade. He
came to his present school and class at the
beginning of the second grade. He changed two
teachers before. He did not have any
developmental problem such as speaking or
walking. He attended the preschool and loved it.
He also learned how to read and write on time.
However, his writing was very complicated with
incomplete sentences and included many
mistakes. When he first came into the class, he was
frequently hiding himself under the desk. Despite
the persistence of the teacher, his family, and the
efforts of the school counselor, he did not sit on his
seat like his classmates during classes. However
this problem disappeared by the third year. He
liked watching cartoons, playing computer games,
and playing soccer very much. His father was a
truck driver, his mother was a housewife. The
family’s socio-economic level was mediocre. He
had a brother who was in the second grade in
elementary school and a two-year-old sister. Since
he still had a big trouble in mathematics class in
the second grade, the school counselor directed
him to a psychologist and thus he was diagnosed
as a student with learning disability. His mother
had never sent him to special education and
rehabilitation centers since she did not want him to
be labeled as a mentally disabled person by the
community. She took care of all his school
relations.
DATA COLLECTION PROCESS AND STEPS OF CASE
STUDY
Data triangulation was employed to ensure the
reliability of the research, and interview,
observation and document review techniques were
used at the data collection stage. Observation notes
were kept while the studies were carried out with
the student. In addition, the status of the student in
physical education and mathematics classes was
observed and recorded. The student was asked to
draw a picture of his family and himself in order
to have information about the value given to the
concepts of parents and siblings by him and their
psychological status in family relations. His
drawing was interpreted by a teacher who had a
certificate of Analysis of Children's Picture. In
addition, semi structure interviews were made
with the student's parents, teacher and classmates.
Those interviews were recorded, transcribed and
analyzed. After every day studying with the
student, notes were reported about the
developments into the research journals.
The course hours, goals and activities to be
performed during the study had been determined
beforehand and the study was performed within
the scope of that pre-prepared program. The
application part of the study was carried out
completely by the researcher. Individual studies
were conducted with the student. In the last three
courses, the student was tested with mixed
exercises. Firstly, the student was subjected to a
preliminary examination and his knowledge of
mathematics was tested. In this preliminary
examination, firstly, the student was asked the
basic information about the addition and
subtraction which were expected to be known
already. In this level, it is necessary for the student
to know the values of numbers, the concept of size
of numbers, the writing and reading of numbers
(up to three digits), which are the basic skills for
addition and subtraction. With the help of the

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questions asked to the student, it was realized that
the student had no knowledge about the value of
the digits.
The student ranked the single-digit numbers in
terms of their value. However, he did not succeed
in the ranking of the double digit numbers. In
addition to not being able to read and write three
digit numbers, he also made mistakes in reading
and writing two digit numbers. He was unable to
add up the numbers when his fingers were not
enough to count (the numbers whose results were
higher than 10 in total) and he was unsuccessful in
subtraction when his fingers were not enough.
According to the results of this preliminary test, it
was determined that the basic skills required for
the student to carry out the addition and
subtraction calculations from first to third grade
level such as values of numbers including three-
digit numbers (hundreds, tens, and units digits),
how to read and write numbers including three-
digit numbers and how to order numbers including
three-digit numbers from smaller ones to the
bigger ones or vice versa.
Therefore, these basic skills were primarily
included in the study program, which were
necessary for addition and subtraction. Then,
addition without-regrouping, addition with
regrouping, subtraction without-regrouping and
subtraction with regrouping tens and hundreds
operations were taught respectively. Studies were
also supported with concrete materials, computer
games, reinforcement awards and assignments.
The mistakes made by the student were
determined after each lesson and those mistakes
were taken into consideration while planning the
next lesson. After the learning level of each skill
had reached to at least 90 % success, the next skill
was started to be taught.
At first, the study started with natural numbers.
The student who learned the concept of digit
values easily read two-digit and three-digit
numbers and managed to establish relationship
between numbers in terms of their values. Since it
complied with the Ministry of National
Education's 3rd grade mathematics curriculum of
the elementary school, operations with numbers up
to 3-digit were included in the program. While the
students who had normal development were
expected to learn these goals at 93 % in lessons,
the students with mathematics learning difficulties
learned them with success by over 90% in 63
lessons at individualized curriculum.
The student with mathematics learning difficulties
who learned numbers up to 3-digit was then
introduced to addition without-regrouping
operations. In order to better understand the
concept of addition, the teaching process was
supported with abacus and concrete materials.
Carpenter and Moser (1984), examined the
different strategies used by children with normal
development to solve mathematical problems
about addition and they mentioned about 3
strategies which were counting all, counting-on
from larger and recall (retrieving the added
numbers from long-term memory by regrouping).
While using the counting-all strategy, the union of
the two sets is counted by using physical objects
or fingers until counting up to total result.
Although it is the most commonly used strategy, it
does not work for additions with numbers larger
than 10 because that strategy requires using the
fingers of a hand. At this point the counting-on
from larger strategy is more favorable than the
previous one; it requires saying the larger number
in the problem first and counting the smaller one
on it. With this strategy, students learn to start
counting with the largest number, so they gain
time. The last strategy in the addition requires the
use of long-term memory and allows the results to
be achieved by keeping the numbers in mind. In
this strategy, with repeated practice and
empowerment, the student memorizes the basic
facts and uses them when necessary. For example,
the student memorizes the 4+5=9 problem over
time.
The researcher thought that teaching ‘’counting-on
from larger strategy’’ to the student who was
incompetent with addition would be the most
useful thing and he created a scenario including
that strategy. The student would gain the ability of
carrying out operations more easily by this way
and with the help of the scenario developed by the
researcher. In fact, using this strategy help the
student be able to do addition operations without
using any concrete material. The researcher

45
created a small scenario book by drawing and
painting pictures. With the strategy of ''counting-
on from larger'' addition without-regrouping,
addition with regrouping, subtraction without-
regrouping and subtraction with regrouping tens
and hundreds skills were easily acquired by the
participant student. The scenario book consisted of
5 pages. During the adaptation period, the scenario
firstly encouraged the student to use his fingers
while performing a mathematical operation. In this
scenario, the steps of the required addition
operation were:
For Example;
6 (larger number is in our pocket)
+ 3 (smaller number is on our hand)
9
While carrying out the addition, we say that we
should put the larger number into our pocket since
it is heavy and we cannot hold it anymore. We hold
the smaller number, i.e. show the other number
(smaller one) with our fingers. We add the number
on our hand to the number that we have in our
pocket. We start counting on from the larger added
in the problem. For example, we hit our pocket and
say ''6''. We count on by showing our fingers
''7,8,9''. The answer is 9. If the numbers are equal,
we hold one of the numbers by hand and put the
other one into our pocket. While we count-on from
the number in our pocket in an addition operation,
we count down the number in our pocket in a
subtraction operation. This method made it more
enjoyable to acquire mathematics operation skills
and it provided convenience to the researcher and
the participant student as it might be used for the
further applications.
The scenario booklet created by the researcher is
as follows:
Figure 1. The scenario booklet created by the researcher
One day, Ali flies a kite and his kite
stays on top of the tree. Ali starts crying
and tries to find ways of how to get his
kite back.
Suddenly, a bird comes in. It shows the
balloons that are held by the other birds
on the tree. Each balloon has numbers
to be added to each other. If he can add
the numbers in the balloons correctly,
the balloons will be his. By this way, Ali
will reach his kite.

46
Ali decides to add the numbers to each
other. First, he gets the numbers in the
balloon below. But the larger number is too
heavy. That's why he puts it in his pocket
first. He holds the smaller number on his
hand. That means he shows it with his
fingers.
He tells the larger number (5) and hits his
pocket in order to make sure that the larger
number is in his pocket. Then, he counts on
from the larger number in his pocket by using
the numbers on his hand. He counts ''6,7,8''.
The answer is 8. Let's add the numbers in the
other balloons with the help of the same
method. Let's help Ali reach his kite.
Ali reaches his kite with the help
of the balloons.

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FINDINGS
FINDINGS RELATED TO COUNTING SKILLS
The operations and skills in mathematics are
consecutive. That means learning an operation or
skill requires learning the concepts or skills that
precede it. In the process of editing the content of
mathematics, it should be taken into consideration
that concepts, skills or processes are prerequisites
of each other (Yıkmış, 1999). In this study, the
student's knowledge of numbers was measured
first in order to have the student with learning
difficulties gain the desired math skills.
Figure 2. The student's preliminary knowledge of numbers
Figure 3. The student's knowledge of numbers after the practice

48
FINDINGS RELATED TO ADDITION
After the student with mathematics learning
difficulty had acquired the necessary skills to carry
out addition without-regrouping and addition with
regrouping operations appropriate to the level of
3rd grade, addition operation skills began to be
taught. Firstly, it was aimed to have the student
understand the meaning of addition exactly. For
this purpose, it was aimed that the student
understood that addition is an incrementation
operations and the student carried out addition
calculations by using an abacus. After the student
had understood the logic of addition, a method for
addition operations (put the larger number into
your pocket and hold the smaller number on your
hand) was taught to the student with the help of a
scenario developed by the researcher. As a result
of this process, it was determined that the student
achieved a success of 90 % in addition without-
regrouping and addition with regrouping
operations.
difficulty had acquired the necessary skills to carry
out addition operations appropriate to the level of
3rd grade, problems related to addition process
were studied. Although the student had sufficient
automaticity on addition operations, he was
insufficient for understanding the problems and
determining the order of the operations, so some
of the problems were explained to the student by
the researcher by drawing the visuals. After
understanding the problems, the student solved
them himself by using his skills. As the main
purpose of the study was to teach the skills of
addition and subtraction to the participant student,
the researcher did not carry out any additional
activity to have the student with learning
disabilities understand the problems. Figure 3
shows the student's ability of addition before the
practices, and Figure 4 shows the student's ability
of addition after what had been worked on.
Figure 4. The student's addition performance after the practices
Figure 5. The student’s level of addition skill after the activities

49
FINDINGS RELATED TO SUBTRACTION
difficulty had acquired the neccessary skills
required for the addition operations sufficiently,
concrete materials (abacus, floor blocks, etc.) and
visual images were used in order for the student to
comprehend the logic of the subtraction
operations.The visual picture drawn by the
researcher was used to explain the difference
between addition and subtraction. According to
this picture, the addition is represented by a girl
who collects flowers into her basket and increases
the number of her flowers; the subtraction is
represented by the girl who puts her flowers from
the basket back to their place and decreases the
number of her flowers. In order to perform a
subtraction operation, the minuend must be bigger
than the subtrahend. The researcher explained this
situation with the help of a picture showing that as
a big man can't get out of a small size door, a larger
number cannot be subracted from a smaller
number. This picture was also drawn by the
researcher. It was determined that the student with
learning difficulties understood the subject more
easily thanks to these pictures.
In order for the student with a learning difficulty
to understand that subtraction is a decreasing
operations, the student peformed subtraction
operations with an abacus. Afterwards, it was tried
to be taught the student subtraction by counting
backwards and using the regrouping techniques
which had been learned by the student for addition
During this lesson, it was seen that the student was
insufficient in counting backward, and so counting
backwards exercises were performed.
After the student had acquired the ability to count
backwards, it was seen that the student achieved
over 90 % of the objectives in the subtraction
without-regrouping and subtraction with
regrouping operations which were appropriate for
the levels up to 3rd grade by using the ''in my
pocket-on my hand'' technique. Mixed exercises
were carried out in order for the student to
differentiate between subtraction with regrouping
and subtraction without-regrouping operations.
The problems including both addition and
subtraction operations were studied with the
student after he had learned how to carry out
addition and subtraction operations. The student
had difficulty in understanding some problems and
determining the order of the operations and those
problems were explained by the researcher to the
student. After understanding the problems, the
student solved them himself. As the main purpose
of the study was not to improve the student's
comprehension of the problems, the researcher did
not carry out any additional activity to have the
student understand them.
During the last three study hours, the student was
tested with mixed (addition-subtraction)
operations and it was found that the student
achieved over 90 % of subject. Figure 6 shows that
the student had no knowledge of the subtraction
operation while Figure 7 shows the student's
ability of subraction after the practices.
Figure 6. Preliminary knowledge of the student about his subtraction skill
Figure 7. The student’s level of subtraction skill after the practice

50
Figure 8. Mixed problems from the latest session of the practice
FINDINGS RELATED TO SOCIAL VALIDITY DATA

51
Social validity data were collected by having
interviews with the student's parents, classmates
and class teacher about strengths and weaknesses
of the research and the changes that occurred in the
student and by observing the student's math and
physical education lessons.
After the interviews with the student, his parents
and the teacher, it was found that the student had
difficulty in learning or weren't able to learn at all
due to his learning difficulties. This situation
caused the student to be excluded by his friends
and labeled as a lazy boy. At the first meeting with
the student's parents, it was stated that ALP wasn't
able to understand the subjects since he had mental
problems and his performance related to subjects
was very bad. At the end of the study, the student's
parents expressed that their son learned how to do
addition and subtraction operations although they
hadn't expected it to happen.
At the first meeting with the student's teacher, the
teacher thought that ALP was not able to learn
since he had some mental problems. Then, the
mathematics operations and work sheets done by
ALP were shown to the teacher and ask about
them. He was amazed at the level of ALP, and said
that ALP was no longer passive in the mathematics
class. Moreover, the teacher stated that ALP was
more engaged in mathematics lessons and he could
perform addition and subtraction at the level of his
friends.
At the first meeting with the student's friends, one
of his friends R.A. described him as socially
incompatible and a lazy boy. He said that ALP,
who had learning difficulties, could not succeed in
lessons because of not studying. In the meeting
after the practices, the samples of the activities
which ALP could do were shown to student R.A.
and he was asked about ALP’s performance in
mathematic skills. At first, R.A. was surprised and
said that ALP could learn, and sometimes he saw
him doing his assigments during breaks.
In order to understand the mental state in his home
environment, ALP was asked to draw a picture
about his family and home environment.
Children's drawings are an effective tool for
reflecting children's observations, experiences,
problems or ideas (Chang, 2005). The child's
drawings are not only a criteria for identifying
children psycho-pedagogically, but also reflecting
the mental capacity, personalities and inner world
of children (Doğru and et al., 2006). In 1970,
Burns and Kaufman developed the Kinetic Family
Drawing Technique. In this technique, children are
asked to draw a picture of their family including
themselves. This picture aims to reveal the child's
attitudes towards family and general family
dynamics. Having children draw pictures of their
family members can help experts who work with
children understand children's social values and
world views (Malchiodi,1998). For example, the
father figure is often drawn as reading newspapers
or doing some gardening, and the mother is always
placed in the kitchen as preparing food for the
family (Lee, Lim & Chia, 2017).
In his family-themed picture, the student ALP
drew himself while he was reading a book in his
room. His father and two siblings play games in
the children's room, while his mother works in the
kitchen. According to him, his father is generally
busy with a mobile phone and takes care of his
siblings. The figure of ALP is in the lower part of
the paper and is quite small.
DISCUSSION, CONCLUSION AND SUGGESTIONS
It is possible to find lots of studies in which
various methods were used to teach counting skills
to the students with learning difficulties in
mathematics. For example, Zerafa (2015) states
that with appropriate interventions, students with
mathematics learning difficulties can make
progress in understanding the basic numbers. In
Kaufman, Handl and Thony's (2003) research with
six students with low mathematics performance,
the students learned counting skills, symbols,
addition, subtraction and digit values by means of
the explicit teaching method in which
manipulative tools (bead, counting bar, base ten
blocks, etc.) were used. Browder, Jimenez,
Spooner, Saunders, Hudson, and Bethune, (2012)
developed a conceptual model in order to provide
mathematical skills to the students with moderate
and severe developmental disabilities.The
student's performance in mathematical skills
(counting groups of 5 objects, counting up to 10 by
heart etc.) increased with the help of systematic
clues and feedback-based instruction. Mononen,
Aunio, Koponen and Aro (2014) investigated the
studies on teaching early numeracy to the children

52
between 4 and 7 years with low mathematics
performance. They emphasized that studies on
early numeracy teaching focused more on explicit
teaching, computer aided education, game-based
instruction and teaching with concrete visual
representations and these applications were
effective. According to our research findings and
other related research on this subject, it can be said
that the student with learning difficulties in
mathematics can acquire numeracy skills through
appropriate interventions and appropriate teaching
methods. For this student, firstly the appropriate
plan and program should be prepared, physical
conditions should be arranged and the teaching
process should be planned by using feedback. It
can be said that students who have learning
difficulties should be given more attention and
time in the teaching of numeracy.
In this study through a scenario developed by the
researcher, addition skill was taught to the student
with mathematics learning difficulty with the
method of putting the larger number into a pocket
and adding the smaller number on it by using
fingers. The counting up from given strategy has
also shown consistency with other studies:
Baroody (1995) conducted a study on teaching
addition to mentally handicapped and normal
children. The teaching was designed as six
separate steps. In the sixth step; the larger number
was kept in mind, as many fingers as the smaller
number were opened, and then the answer was
found by counting on from the larger number. It
was found that the application conducted in the last
step was more effective for all the children to learn
addition operations. Tournaki (2003) examined
the effectiveness of test-based (memorization) and
strategy-based (counting on from given) methods
in teaching addition of single digit numbers to the
normal students and the students with learning
difficulty. While the normal student accelerated in
addition with both of the methods, the children
with learning disabilities gained faster results with
the strategy-based method.
Although the student was able to perform the
addition operations, he was insufficient to
understand the problems and determine the order
of operations. According to Olkun (2015), it was
stated that students with learning disabilities
needed more concrete examples since they could
not have the necessary cognitive and memory
skills to solve multi-stage problems. Students with
mathematics learning difficulties have difficulty in
learning, understanding and remembering
arithmetic operations (Shalev et al., 2001) and
using recall procedures to solve verbal problems
(Geary, 2004). Vassaf (2011) stated that these
operations could be done correctly by the students
with learning difficulties when the numbers that
should be added or subtracted are told by someone
else. However, those students cannot decide which
operations ( multiplication, addition etc.) to do
when they hear or read the problems on their own.
As a result, it can be said that the addition consists
of three stages. In the first stage of the addition,
with the help of the 3D objects, visuals, figures and
concrete materials, it must be taught to the students
conceptually that addition is an increasing and
adding operation. After the student understands
the essence of addition, the addition can be taught
with the strategy of counting smaller numbers on
from the larger numbers by using fingers. For the
student with learning difficulties, these first two
stages are important and need to be focused on. At
the third stage, the student can now perform
addition operations by using mental abilities. It
might take a long time for the students with
dyscalculia to reach the third stage. The student
who is capable of addition is now ready to deal
with mathematics problems. Students who have
learning difficulties may have a trouble in
organizing maths problems in their memory since
they have cognitive problems. In this case,
problem solving skills of the students with
dyscalculia can be improved with the help of the
strategies such as narration, storytelling, giving
examples from daily life and drawing by using
number bars, visuals, 3D objects etc.
In the teaching of subtraction operations, as in the
operation of addition, with the help of the 3D
objects, visuals, figures and concrete materials,it
must be taught to the students conceptually that
subtraction is decreasing operation. After the
student understands the essence of subtraction, in
order to subtract a number from another one, the
strategy of counting backwards from the larger
number to the smaller one by using fingers is

53
taught. After that, the students can now perform
subtraction operations by using mental abilities on
their own. It is possible to say that the students
who have learning difficulties stay longer in this
stage. As stated for the addition problems,
students with dyscalculia have difficulty in
understanding the problems, so it can be said that
various strategies can be used to perceptually
improve their problem solving abilities.
As a result of the interviews conducted with the
student himself, his family and the teacher, it was
seen that the student could not learn or had hardly
learned because of his learning difficulties.This
situation caused the student to be excluded by his
friends and seen as a lazy boy. Many studies have
shown consistency with these findings. Similar
findings had been stated in some studies
(Kabasakal, Girli, Okun, Çelik & Vardarlı, 2008),
it was determined that students with special needs
were not preferred to carry out a joint study by
their friends and they were perceived as persons
with compliance and communication problems.
The studies examining the relationship between
emotional situation and cognitive success indicate
that there is a positive relationship between
depression and anxiety levels of children with
learning disabilities. Children and adolescents
with mathematics disorder have symptoms such as
not going to school, skipping the school, and
depression (Karabekiroğlu, 2012). Therefore, the
development of positive problem solving skills in
social areas also helps to cope with the lack of
mathematical ability.
As a result of this study, it was found that the
students with dyscalculia had difficulties in their
social environment and daily life, those students
acquired the gains of the middle school
mathematics curriculum at a very low level and the
teachers had insufficient knowledge about
''Dyscalculia'' (Hacısalihoğlu Karadeniz, 2013).
The lack of guidance from parents at home and
their exclusion from the society at school because
of their low academic achievement may have led
those students to experience depression. It can be
said that if a student feels unhappy and alone in the
family, this situation affects his social skills,
academic achievement and communication with
peers negatively.
During the research, ALP was asked to draw a
picture about his family and home environment in
order to understand his mental state in the home
environment. When ALP described the picture he
had drawn, he expressed that he loved his father
very much, but his father didn't love him and he
cared about only his siblings. The researchers state
that the students show their mental state in their
paintings when their family-themed pictures are
taken into consideration. It can be said that the
student is unhappy and alone in the family and this
situation affects his social skills, academic
achievement and communication with peers
negatively.
To summurize the result of this study reveals that
although there is a negative bias about
mathematics by the students with mathematics
learning difficulties, mathematics must be made
attractive for those students by using games,
rewards, concrete materials and fun activities.
Besides, computer games specific to a subject can
be used. Different types of activities that appeal to
five senses can be carried out. If the lessons are
based on the common grounds of students with
learning disabilities and associated with everyday
life, they can help them develop positive attitudes
about mathematics. Teachers should not have
negative thoughts for those students.
Individualized Learning Plans should be prepared
for the students with mathematics learning
difficulties before teaching the aims of the
curriculum and the teaching process should be
carried out in line with those plans. When teaching
counting skills, the next goal should not be taught
before achieving the objectives that must be
learned first. The basic mathematical skills, which
must be gained in order to carry out addition
operations, should be taught as a priority. The
basic mathematical skills, which must be gained in
order to carry out subtraction operations, should be
taught as a priority, too. The families of students
with mathematics learning difficulties should take
this situation seriously and cooperate with the
student and the teacher in order to ensure an
effective education for their children. Guidance
should be provided to support those families.
Since the participation of the students with

54
learning difficulties in an active social-cultural
activity influences their self-concept positively, it
will be beneficial to provide guidance services that
direct these students to social-cultural activities
appropriate for their interests and abilities.
Aknowlegment: This study was derived from first
author’s doctoral dissertation.
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