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EXAMINING THE LEVEL OF DYSCALCULIA AWARENESS AMONG PRIMARY AND SECONDARY SCHOOL MATHEMATICS TEACHERS IN URBAN MAINSTREAM SCHOOLS IN SOUTH KAZAKHSTAN

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Examining the Level of Dyscalculia Awareness among Primary and Secondary School Mathematics Teachers in Urban Mainstream Schools in South Kazakhstan

Azhar Satybaldy

Submitted in partial fulfillment of the requirements for the degree of Master of Science

in

Educational Leadership

Nazarbayev University Graduate School of Education

April 29, 2022

Word Count: 25102

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AUTHOR AGREEMENT

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IF THE SUBMISSION IS BASED UPON WORK THAT HAS BEEN SPONSORED OR SUPPORTED BY AN AGENCY OR ORGANIZATION OTHER THAN NU, I

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I hereby accept the terms of the above Author Agreement.

Author’s signature: Azhar Satybaldy Date: 21/04/2022

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Declaration

I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been submitted for the award of any other course or degree at NU or any other educational institution, except where due acknowledgement is made in the thesis. This thesis is the result of my own independent work, except where otherwise stated, and the views expressed here are my own.

Signed: Azhar Satybaldy Date: 21/04/2022

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Ethical Approval

53 Kabanbay Batyr Ave.

010000 Astana,

Republic of Kazakhstan 22th October 2021

Dear Azhar,

This letter now confirms that your research project entitled Examining the Level of Dyscalculia Awareness among Primary and Secondary School Mathematics Teachers in Urban Mainstream Schools in South Kazakhstan has been approved by the Graduate School of Education Ethics Committee of Nazarbayev University.

Yours sincerely,

Rita Kasa, Assistant Professor

On behalf of Zumrad Kataeva Chair of the GSE Ethics Committee Assistant Professor

Graduate School of Education Nazarbayev University

Block C3, Room 5006 Office: +7 (7172) 70 9371 Mobile: +7 777 1929961

email: zumrad.kataeva@nu.edu.kz

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CITI Training Certificate

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Acknowledgement

First and foremost, I would like to thank my family for their support throughout my thesis journey. I am grateful to my husband and daughter, whose patience, and ongoing encouragement gave me the strength not to stop and continue along this long process. I also thank my mother for her ongoing emotional support and motivation. Her support has been a source of great encouragement and strength for me.

I also express my sincere gratitude to my thesis supervisor Dr. Kasa for her professional guidance from the beginning of my study through the end of my thesis writing. Her professional expertise helped me grow as a researcher. I appreciate all the support Dr. Kasa provided me along this journey.

I would also like to thank the university librarians for their academic support and assistance in providing me with needed information, documents, and books.

Finally, I would like to thank my groupmates, Asem and Aizhan, for their emotional support, encouragement, and motivation. They are those who fully understood and went through the same hardships as me. It is a blessing to have friends like you.

Without the support of all those who were a part of my long journey, I would not have been able to finish this thesis. I am grateful to each of you.

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EXAMINING THE LEVEL OF DYSCALCULIA AWARENESS AMONG PRIMARY AND SECONDARY SCHOOL MATHEMATICS TEACHERS IN

URBAN MAINSTREAM SCHOOLS IN SOUTH KAZAKHSTAN Abstract

Dyscalculia is defined as a specific learning disability in mathematics with some challenges in arithmetic skills, math problem-solving skills, calculations, processing, and remembering mathematical facts (APA, 2018). Although this phenomenon is less studied than reading difficulties such as dyslexia, its prevalence rates are no less and range from 3% to 6% among the world's population (Kucian & Von Aster, 2015). Dyscalculia poses significant difficulties in school as students with dyscalculia have a greater degree of math anxiety and poorer achievement than other students (Kucian et al., 2018). Dyscalculia is a permanent disability; however, adequate support and early identification may reduce to the minimum the difficulties it causes to the child (Sousa et al., 2017). Accordingly, teachers’

sufficient knowledge regarding dyscalculia is essential in identifying at-risk students and providing the necessary support to them in the classroom.

The present study examined the level of dyscalculia awareness among primary and secondary school mathematics teachers in urban mainstream schools in South Kazakhstan.

This study utilized a quantitative survey research design. Overall, 751 teachers from 60 schools participated in an online anonymous survey. The present study examined teachers’

knowledge about dyscalculia across three dimensions i.e., definition and nature of

dyscalculia, its symptoms, and methods of intervention. The findings indicate that teachers have limited knowledge about the definition and nature of dyscalculia as well as its

symptoms. However, teachers are better informed about intervention methods than the nature and symptoms of dyscalculia. It was revealed that, on average, teachers at both levels of education hold very similar views about this disability. Furthermore, it was

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revealed that teachers’ exposure to the phenomenon of dyscalculia is associated with better knowledge about dyscalculia.

Keywords: inclusive education, dyscalculia, teachers’ awareness, teachers’

knowledge, primary school, secondary school, Kazakhstan.

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ОҢТҮСТІК ҚАЗАҚСТАНДАҒЫ ҚАЛАЛЫҚ ОРТА МЕКТЕПТЕРДЕГІ БАСТАУЫШ ЖƏНЕ ОРТА БУЫНДАРЫНЫҢ МАТЕМАТИКА ПƏНІ

МҰҒАЛІМДЕРІНІҢ ДИСКАЛЬКУЛИЯ ТУРАЛЫ ХАБАРДАРЛЫҚ ДЕҢГЕЙІН ЗЕРТТЕУ

Аңдатпа

Дискалькулия - арифметикалық дағдылар, математикалық есептерді шешу дағдылары, есептеулер, математикалық фактілерді өңдеу жəне есте сақтаудағы қиындықтары бар математикадағы оқу кемістігі ретінде анықталады (APA, 2018).

Бұл құбылыс дислексия сияқты оқу қиындықтарына қарағанда аз зерттелгенімен, оның таралу деңгейі кем емес жəне əлем халқы арасында 3% -дан 6% -ға дейін ауытқиды (Kucian & Von Aster, 2015). Дискалькулия мектепте айтарлықтай

қиындықтар туғызады, өйткені дискалькулиясы бар оқушылардың математикалық мазасыздық деңгейі жоғары жəне басқа оқушыларға қарағанда оқу үлгерімі төмен (Kucian et al., 2018). Дискалькулия тұрақты құбылыс; дегенмен, адекватты қолдау жəне ерте анықтау балаға əкелетін қиындықтарды барынша азайта алады (Sousa et al., 2017). Тиісінше, мұғалімдердің дискалькулия туралы жеткілікті білімі қауіп тобындағы оқушыларды анықтау жəне оларға сыныпта қажетті қолдау көрсету үшін өте маңызды.

Бұл зерттеу Оңтүстік Қазақстандағы қалалық орта мектептердің бастауыш жəне орта сыныптарында математика пəні мұғалімдерінің дискалькулия туралы хабардарлық деңгейін зерттеді. Бұл зерттеуде сандық зерттеу дизайны қолданылды.

Анонимді онлайн сауалнамаға қаланың 60 орта мектебінен барлығы 751 мұғалім қатысты. Бұл зерттеу мұғалімдердің дискалькулия туралы білімін үш өлшем

бойынша зерттеді, яғни дискалькулияның анықтамасы мен табиғаты, оның белгілері жəне қолдау əдістері. Нəтижелер мұғалімдердің дискалькулияның анықтамасы мен

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табиғаты, сондай-ақ оның белгілері туралы білімі шектеулі екенін көрсетеді.

Дегенмен, мұғалімдер дискалькулияның табиғаты мен белгілерінен гөрі қолдау əдістері туралы жақсырақ хабардар екені айқындалды. Орташа алғанда екі буындағы мұғалімдердің дискалькулияға көзқарастары өте ұқсас екені анықталды. Сонымен қатар, мұғалімдердің дискалькулия құбылысымен бұрынғы байланысы дискалькулия туралы жақсы біліммен байланысты екені анықталды.

Түйін сөздер: инклюзивті білім беру, дискалькулия, мұғалімдердің

хабардарлығы, мұғалімдердің білімі, бастауыш мектеп, орта мектеп, Қазақстан.

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ИССЛЕДОВАНИЕ УРОВНЯ ОСВЕДОМЛЕННОСТИ О ДИСКАЛЬКУЛИИ СРЕДИ УЧИТЕЛЕЙ МАТЕМАТИКИ НАЧАЛЬНЫХ И СРЕДНИХ КЛАССОВ В ГОРОДСКИХ ОБРАЗОВАТЕЛЬНЫХ ШКОЛАХ ЮЖНОГО КАЗАХСТАНА

Аннотация

Дискалькулия определяется как особая неспособность к обучению в

математике с некоторыми проблемами в арифметических навыках, навыках решения математических задач, вычислениях, обработке и запоминании математических фактов (APA, 2018). Хотя это явление менее изучено, чем трудности с чтением, такие как дислексия, показатели его распространенности не меньше и составляют от 3% до 6% населения мира (Kucian & Von Aster, 2015). Дискалькулия создает

значительные трудности в школе, поскольку учащиеся с дискалькулией имеют большую степень беспокойства по математике и более низкую успеваемость, чем другие учащиеся (Kucian et al., 2018). Дискалькулия имеет постоянный характер;

однако адекватная поддержка и раннее выявление могут свести к минимуму трудности, которые это вызывает у ребенка (Sousa et al., 2017). Соответственно, достаточные знания учителей о дискалькулии необходимы для выявления учащихся из группы риска и оказания им необходимой поддержки в классе.

В данном исследовании изучался уровень осведомленности о дискалькулии среди учителей математики начальных и средних классов городских

общеобразовательных школ Южного Казахстана. В этом исследовании

использовался количественный исследовательский дизайн. Всего в анонимном онлайн-опросе приняли участие 751 учитель из 60 городских общеобразовательных школ. В настоящем исследовании изучались знания учителей о дискалькулии по трем параметрам: определение и характер дискалькулии, ее симптомы и методы вмешательства. Результаты показывают, что учителя имеют ограниченные знания об

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определении и природе дискалькулии, а также о ее симптомах. Однако учителя лучше информированы о методах вмешательства, чем о природе и симптомах дискалькулии. Выявлено, что в среднем учителя обоих уровней образования

придерживаются очень близких взглядов о дискалькулии. Кроме того, выявлено, что предыдущий контакт учителей с феноменом дискалькулии в значительной степени связана с более высоким уровнем знаний о дискалькулии.

Ключевые слова: инклюзивное образование, дискалькулия, информированность учителей, знания учителей, начальная школа, средняя школа, Казахстан.

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Table of Contents

Introduction ... 1

Background of the Study ... 1

Inclusive Education and Dyscalculia in Kazakhstan ... 3

Problem Statement ... 4

Purpose of the Study ... 5

Significance of the Study ... 6

Definitions of Central Concepts ... 8

Thesis Outline ... 9

Literature Review ... 10

Specific Learning Disabilities and Dyscalculia ... 10

Definition, Nature, and Symptoms of Dyscalculia ... 14

Theories of Dyscalculia ... 16

Heterogeneity and Types of Dyscalculia ... 27

Diagnosis ... 30

Interventions to Support Students with Dyscalculia ... 33

Teachers’ Awareness of Dyscalculia ... 38

Research in Kazakhstan ... 50

Methodology ... 54

Research Design ... 54

Survey Questionnaire ... 56

Sample ... 59

Data Collection Procedures and Research Ethics ... 60

Data Analysis ... 62

Findings ... 65

Demographic Characteristics ... 65

Teachers’ Awareness of the Definition and Nature of Dyscalculia ... 68

Teachers’ Awareness of the Symptoms of Dyscalculia ... 71

Teachers’ Awareness of the Interventions ... 76

Relationship Between Teachers’ Exposure to the Phenomenon of Dyscalculia and their Level of Knowledge of this Disability ... 77

Discussion ... 80

Low Primary and Secondary School Mathematics Teachers’ Awareness of the Definition and Nature of Dyscalculia ... 80

Low Primary and Secondary School Mathematics Teachers’ Awareness of the Symptoms of Dyscalculia ... 82

Moderate Primary and Secondary School Mathematics Teachers’ Awareness of the Interventions to Support Students with Dyscalculia ... 85

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Similar Primary and Secondary Teachers’ Knowledge about Dyscalculia ... 88

Exposure to the Phenomenon of Dyscalculia is Associated with a Better Level of Knowledge about Dyscalculia ... 89

Conclusion ... 93

Teachers’ Level of Knowledge about Dyscalculia: Answers to the Research Questions and Hypotheses ... 93

Limitations and Future Research ... 95

References ... 97

Appendices ... 108

Appendix A ... 108

Appendix B ... 109

Appendix C ... 116

Appendix D ... 119

Appendix E ... 120

Appendix F ... 122

Appendix G ... 126

Appendix H ... 133

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List of Tables

Table 1 Review of the Literature: Teachers’ Knowledge of the Definition and Nature of

Dyscalculia ... 39

Table 2 Review of the Literature: Teachers’ Knowledge of the Causes of Dyscalculia ... 41

Table 3 Review of the Literature: Teachers’ Knowledge of the Symptoms of Dyscalculia (by types) ... 43

Table 4 Review of the Literature: Teachers’ Knowledge of the Interventions to Support Students with Dyscalculia ... 46

Table 5 Demographic Characteristics of Respondents ... 66

Table 6 Teachers’ Exposure to the Phenomenon of Dyscalculia and Dyslexia ... 67

Table 7 Teachers’ Knowledge of the Causes of Dyscalculia ... 69

Table 8 Statistically Significant Items on the “Definition and Nature of Dyscalculia” ... 70

Table 9 Statistically Significant Items on the “Symptoms” of Dyscalculia (items 1,3,5) ... 71

Table 9 a Statistically Significant Items on the “Symptoms” of Dyscalculia (items 6,8,12,14) ... 74

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List of Figures

Figure 1 Three-dimensional Representation of the Parietal Regions of the Brain ... 20

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Introduction Background of the Study

Mathematics is one of the primary subjects at school which is foundational in

acquiring knowledge and skills. Mathematics is not only an important school subject but is also used in everyday life which is heavily based on numeracy starting from time

management, shopping, calculating money, and other social and economic activities.

Furthermore, an inadequate level of mathematical skills may impact individuals’

educational perspectives, employability, and salaries even if they are highly literate (Parsons et al., 2005; Rivera-Batiz, 1992, as cited in Soares et al., 2018). The term used to describe students who have challenges in arithmetic skills, calculations, reasoning,

remembering math facts, and solving mathematical problems is called dyscalculia (American Psychiatric Association, 2018). The term itself stems from the Greek word

“dys” which means “badly”, and the Latin word “calculare” which means “to count”

(Kunwar & Sharma, 2020). So, the term dyscalculia means bad at counting. Students with dyscalculia manifest in the classroom with short-term and long-term memory problems, symptoms such as confusing mathematical symbols and signs, and having difficulties with measurement, direction, time, and speed. They are not able to subitize and do not have an intuitive grasp of numbers (Williams, 2013). They may often use their fingers when counting while their peers left this strategy a long time ago.

Mathematical disability is common among mathematics learners (Sousa et al., 2017).

It is estimated that 3 to 6% of people worldwide have dyscalculia (Haring, 2020; Kosc, 1974; Kucian & Von Aster, 2015; Shalev & Von Aster, 2008). Statistics aside, individuals with dyscalculia are likely to encounter serious hardships starting from their school years and persisting throughout their lives (Sousa et al., 2017). Dyscalculia has a significant influence on people’s lives affecting their career choices, psychological and emotional

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wellbeing, as well as social relationships (Wadlington et al., 2006). This can be seen in the case of a teacher with dyscalculia who was trying to avoid having lunch with his

colleagues and always used a credit card so as not to be in a situation to count money (Wadlington et al., 2006).

It is important to note that not every student with difficulties in mathematics will necessarily have dyscalculia. Mazzocco (2005) suggests distinguishing between mathematical difficulties and disabilities, the former being more overarching than the latter. Mathematical difficulties may be related to insufficient instruction, social environment, home, and school atmosphere. Whereas, mathematical disability has a biological set of causes (Mazzocco, 2005). Mathematical difficulties are affected by environmental causes and may disappear after an intervention. On the other hand, mathematical disability is long-lasting, and symptoms may not disappear with proper assistance. In any instance, children with this disability would definitely benefit from initiated support (Kosc, 1974).

Dyscalculia is a less researched phenomenon compared to reading disabilities such as dyslexia. The fact that dyscalculia is less often encountered than dyslexia and other learning disabilities, does not mean that the disorder is rare. Perhaps it is camouflaged under disorders (Dias et al., 2013) such as ADHD, dyslexia, depression, anxiety, as well as other factors such as crowded classes, social and family problems, inadequate teaching methods, or curriculum (Shalev & Von Aster, 2008). Dyscalculia may co-occur with dyslexia in 50% of cases, and with ADHD in 40% of cases (Williams, 2013). These statistics reasonably explain the possible reason for the underdiagnosis of the learning disability.

Another reason for the underdiagnosing of dyscalculia is an identification gap which leads to a late diagnosis of the disability. Altarac and Saroha (2007, as cited in Graves,

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2018) reported that in the USA many children remain undiagnosed with a learning disability (LD) until the ages of 10-14 and 15-17. The authors claim that the reason is not that LD starts at these ages, but that there exists a gap between when the child is suspected to have a learning disability and eventually diagnosed with having it. This gap can

continue for 3.5 years. There is a tendency that children with LD are diagnosed more often as they become older (Child Trends, 2016, as cited in Graves, 2018). Thus, there is a need to close the gap between the first suspicion of the condition and the diagnosis of it.

One more reason for the underdiagnosing of dyscalculia could be the social notion that a person is either good or bad at mathematics (Holaway, 2020). Mathematics is one of those subjects where many students perform poorly, and dyscalculia is one of the many reasons for low academic achievement in mathematics (Kunwar & Sharma, 2020). A common feature of students with dyscalculia is that they can be successful in other subjects but challenged in mathematics. The danger is that these students don't get the help they need; their condition should be regarded as more serious than simply being bad at mathematics (Hornigold, 2015, as cited in Kunwar & Sharma, 2020).

Research has shown that teachers play a crucial role in identifying learning disabilities among students (Dias et al., 2013). For example, dyslexia as a learning disability most often begins to manifest itself when students get to school (Chideridou- Mandari et al., 2016). This factor makes a teachers’ role significant in the identification of dyslexia and its further development (Chideridou-Mandari et al., 2016). It would be fair to presume that a teachers’ role in identifying dyscalculia is equally important.

Inclusive Education and Dyscalculia in Kazakhstan

Since 1991, Kazakhstan has prioritized inclusive education as one of the important strategic directions in the development of its education (Makoelle, 2018). Kazakhstan has ratified international documents including the UN Convention on the Rights of the Child in

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1994, the Convention on the Rights of Persons with Disabilities, legislated in 2015, and Convention against Discrimination in Education legislated in 2016 (Ramazanova, 2020).

Signing these documents that affirm equal access to education for people with special educational needs, Kazakhstan demonstrates a determination to maintain and support inclusive education and the international movement of Education for All (EFA). Since then, the government has established several documents at the legislative level. The latest legislation on inclusive education was signed by president Qasym-Zhomart Tokayev on the need to update the current standards that are used in inclusive and special education

(Sputnik, 2021). It is expected that the standards will be updated according to the

Convention on the Rights of Persons with Disabilities. Kazakhstan has made considerable effort and progress in the development of inclusive education; however, it is only at the start of a long way toward implementation in the classrooms (Makoelle, 2018). Despite the ratified reforms and steps taken to improve inclusive education, there remain inconclusive issues of recognizing and addressing learning disabilities like dyscalculia in the

classrooms. Currently, it is not recognized and there is no legislative basis for diagnosing, assessing, and assisting dyscalculia as a disability in Kazakhstan.

Problem Statement

A significant amount of research can be found in the literature on teachers’

knowledge of other learning disabilities like dyslexia, etc. However, a relatively scarce amount of research can be found on teachers' awareness of dyscalculia (Williams, 2013).

Research that exists indicates that the lack of teachers’ knowledge about dyscalculia has been revealed as one of the biggest barriers in assisting children with dyscalculia (Graves, 2018). Consequently, teachers’ insufficient knowledge regarding dyscalculia can lead to a failure to see the symptoms of students in the classroom and provide the

necessary assistance to them. Because the more teachers know about the nature of

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dyscalculia and are trained on educational methods, the more effective support they can provide for their students (Butterworth et al., 2011, as cited in Sousa et al., 2017). This, in turn, will positively affect the learning of students who have dyscalculia and other

difficulties in mathematics.

There is insufficient research on dyscalculia in Kazakhstan, contributing to a low level of teachers’ knowledge about dyscalculia. Because dyscalculia is not officially diagnosed as a disability in Kazakhstan, there is no information on its prevalence across the country. According to the National Scientific and Practical Center for the Development of Special and Inclusive Education (NSPC DSIE) (2020), dyscalculia is referred to as a specific learning disability (SLD) in Kazakhstan and there is no exact definition of it.

Children in Kazakhstan are not officially diagnosed, assessed, or assisted by professionals and educators likely because of insufficient knowledge about SLD and dyscalculia.

Another problem is that inclusive education is conflated with special education in Kazakhstan (Makoelle, 2018). This is another likely reason that educators don’t have resources to support their students with learning disabilities such as dyscalculia. In

addition, as teachers report, they are neither trained on dyscalculia at the university level as students nor at the school level as educators (Zhanatbekova, 2018). This leads to a

situation where teachers miss the symptoms of students who need help and leave them without any assistance in learning. Since the role of teachers in the identification of dyscalculia is central, their knowledge about it remains crucial.

Purpose of the Study

The purpose of the study is to examine the level of dyscalculia awareness among primary and secondary school mathematics teachers in urban mainstream schools in one of the large cities in South Kazakhstan with respect to understanding the definition and nature of the phenomenon, recognizing its symptoms, and methods of intervention.

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The study seeks to answer the following research question:

To what extent are primary and secondary mathematics school teachers in urban mainstream schools in South Kazakhstan aware of dyscalculia in respect to understanding the definition and nature of the phenomenon, recognizing its symptoms, and intervention methods?

It also tests the following hypotheses:

H1: Primary and secondary school mathematics teachers’ awareness of the definition and nature of dyscalculia is low.

H2: Primary and secondary school mathematics teachers’ awareness of the symptoms of dyscalculia is low.

H3: Primary and secondary school mathematics teachers’ awareness of the interventions to support students with dyscalculia is low.

H4: The level of awareness about the definition, nature, symptoms of dyscalculia, and interventions among primary and secondary school mathematics teachers is at the same level.

H5: Exposure to the phenomenon of dyscalculia is associated with a better level of knowledge about dyscalculia. The exposure is measured via two criteria:

1. Theory: have respondents heard about the phenomenon of dyscalculia in any of the pre-service, in-service teacher training courses, from

colleagues/friends, or as a self-study.

2. Experiential: have they encountered students with math difficulties in class as suspected cases of dyscalculia.

Significance of the Study

There is relatively scarce research on teachers’ knowledge about dyscalculia even though the number of students diagnosed with dyscalculia is increasing (Chideridou-

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Mandari et al., 2016). The scarcity of literature and research makes it harder to identify the level of knowledge teachers have about dyscalculia and how they support their students in educational settings. Mathematical learning disability (MLD) poses significant difficulties in school as students with dyscalculia have a greater degree of math anxiety and poorer achievement than other students (Kucian et al., 2018). One of the reasons for students’

reluctance or negative reactions to learning mathematics may be teachers’ poor knowledge of MLD (Kunwar et al., 2021). Furthermore, dyscalculia may negatively affect the career choices of students with this learning disability. This is evident in the case of a student with dyscalculia who initially wanted to be a computer scientist, but after failing high school mathematics classes for two years in a row, his teachers set him on a course for a language degree as opposed to computer science (Wadlington et al., 2006). This advice opposite to the student’s career aspirations can be explained by the lack of teachers’

knowledge of dyscalculia. Teachers’ lack of knowledge is likely to result in inadequate assistance, low expectations, and little effort in supporting those students. Teachers’ little effort and low expectations for students are exemplified in the work by Zhanatbekova (2018), where teachers reported that they assigned simpler tasks to their students with mathematical difficulties in the classroom. Therefore, it is important for teachers to have adequate knowledge about dyscalculia, its manifestations in the classroom, and strategies of appropriate interventions and guidance in school for students with MLD. Otherwise, low levels of knowledge among teachers can lead to a failure to detect on time the symptoms of students with MLD who need help. However, existing national and

international findings indicate that the majority of teachers do not have enough knowledge about dyscalculia (Chideridou-Mandari et al., 2016; Dias et.al, 2013; Graves, 2018;

Karasakal, 2018; Zhanatbekova, 2018). Considering all of the above, the results of this study will be useful to inform the actions of the government, school administrations, and

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teachers themselves in Kazakhstan. It is also expected that this study will contribute to the academic field examining teachers’ knowledge of dyscalculia on primary and secondary education levels.

Definitions of Central Concepts

Different concepts are used in research related to difficulties in learning

mathematics. These terms include “mathematical learning difficulties”, “mathematical learning disabilities”, “dysnomia”, “arithmetical difficulties”, “developmental

dyscalculia”, etc. They all describe the notion of dyscalculia. As this thesis focuses on dyscalculia, these terms will be used in this study interchangeably.

The key terms of the study:

Dyscalculia is a term used for difficulties learning mathematics. These difficulties include poor memorization of math facts, poor calculation skills, as well as poor math problem solving and math reasoning skills (APA, 2018).

Numeracy - “ability to understand and work with numbers: the quality or state of being numerate” (Merriam-Webster, n.d.).

Knowledge - “the fact or condition of knowing something with familiarity gained through experience or association” (Merriam-Webster, n.d.).

Awareness - “knowledge and understanding that something is happening or exists” (Merriam-Webster, n.d.). In this study, teachers’ awareness of dyscalculia and their knowledge regarding its definition, nature, symptoms, as well as intervention methods are examined. Since these terms are used interchangeably in the literature, they are also used interchangeably in this study.

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Specific learning disability is defined as a condition affecting children in at least one of these learning areas: reading, writing, and mathematics, and is not the result of reduced intelligence or poor quality of education (APA, 2018). It is important to note that even though the terms “learning

disability” and “learning disorder” are not exact synonyms of one another (APA, 2018), they are used interchangeably in research and are used in this study as well.

Thesis Outline

This thesis introduces the phenomenon of dyscalculia and teachers' awareness of this disability in the world and in the context of Kazakhstan, which is presented and discussed in each chapter of this thesis. The first introductory chapter presents the problem

statement, significance of the research as well as clearly states the main aims and hypotheses of the study.

Chapter two reviews the existing literature on the phenomenon of dyscalculia and provides information about its definition, nature, symptoms, diagnosis, as well as intervention methods. The second chapter also highlights different theories that exist around dyscalculia. Eventually, teachers’ awareness of dyscalculia across the world and in Kazakhstan is also reviewed in this chapter.

The third chapter is concerned with the methodology used for this study. Chapter four analyses the results of the survey questionnaire regarding teachers’ knowledge of dyscalculia, which is then discussed with reference to the literature in chapter five. Finally, chapter six concludes with the overall findings and suggestions for further research.

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Literature Review Specific Learning Disabilities and Dyscalculia

This chapter presents a review of the literature on the phenomenon of dyscalculia. To better understand this disability, sections of this chapter are organized firstly to define dyscalculia in relation to other learning disabilities. Secondly, to present information on how the term emerged, as well as to discuss the nature, and symptoms of dyscalculia. To address the possible causes of dyscalculia, views that exist around this phenomenon are also discussed. Sections in this chapter review the types of dyscalculia, diagnosis, interventions, and why we need to understand teachers’ awareness of this disability.

Research on learning disabilities conducted in Kazakhstan is also reviewed.

Specific Learning Disabilities

Dyscalculia is a type of specific learning disability (SLD). SLD is defined as a neurological disability that starts at school time and hinders the ability of children to learn, which manifests itself in foundational skills such as reading, writing, or mathematics (American Psychiatric Association, 2018). The prevalence rates of SLD vary between 5- 14% of the school-age student population in the world (Geary, 2013, as cited in Kunwar et al., 2021). SLD is an overarching term that encompasses learning disabilities such as dyslexia (difficulties in reading), dysgraphia (difficulties in writing), and dyscalculia (difficulties in mathematics). These types of learning disabilities are often comorbid with each other, i.e., people who have dyscalculia will often also have dyslexia or dysgraphia (Willcutt et al., 2019). This comorbidity makes the process of identification of SLD more difficult. Thus, to better understand each of these learning disabilities they are briefly explained in the following paragraphs.

Dyslexia is a language-related neurobiological disability manifested by inaccurate word recognition, poor spelling, and decoding competencies (International Dyslexia

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Association [IDA], 2002). Typically, people with dyslexia have reading difficulties, poor vocabulary, and poor understanding of what they have just read (IDA, 2002). Moreover, between 30-60% of children diagnosed with dyslexia also have comorbid math difficulties (Soares et al., 2018; Willcutt et al., 2019). One explanation for this common comorbidity is that it is more difficult for dyslexic students with reading difficulties (RD) to learn

mathematics involving word problems and symbols (Willcutt et al., 2019). Approximately 5% (Kaufmann & Von Aster, 2012) of primary school students and 6% (Robert & Sarah, 2014, as cited in Kunwar et al., 2021) of people around the world have dyslexia.

Dysgraphia is a “specific learning disorder in written expression” (Chung et al., 2020, p.46). People with dysgraphia have difficulties with writing and spelling skills, are often slower in writing than others, skip some letters in the words when writing, and may produce grammatical errors in the sentences (Chung et al., 2020). The literature reports varying prevalence estimates of the disability as between 10-34% among primary school students (Rosenblum & Dror, 2016) and 7-15% amongst school-age children around the world (Sharma, 2020, as cited in Kunwar et al., 2021).

The term “dyscalculia” literally means bad at counting (Kunwar & Sharma, 2020).

Sometimes it is referred to as “math dyslexia” or “number blindness”. However, it is a

“heterogeneous learning impairment affecting numerical and/or arithmetic functioning at behavioral, psychological and neuronal levels” (Kucian & Von Aster, 2015, p.3). People with dyscalculia have some challenges in arithmetic, calculations, reasoning, remembering math facts, and solving mathematical problems (APA, 2018). Children with dyscalculia often lag behind their peers in academic performance, and perform tasks inaccurately and slower than typically developing children (Monei & Pedro, 2017). Yet these difficulties are not caused by low intelligence levels (Monei & Pedro, 2017). It is important to note that dyscalculia should not be confused with acalculia, which is acquired later in life and is a

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consequence of brain injuries (Ardilla & Roselli, 2002). By contrast, dyscalculia is innate and has neurological origins.

Prevalence of Dyscalculia

It is difficult to evaluate the predominance of dyscalculia in the world mainly

because its identification directly depends on the definition of the disability. As there is no universally accepted definition of dyscalculia, different definitions applied in different countries lead to different diagnostic criteria. Thus, its prevalence rates cannot be

compared across countries. However, there are numerous studies with the same patterns of findings on the proportion of dyscalculic people in the population which makes a global estimate of between 3 to 6% reasonably reliable (Kosc, 1974; Kucian & Von Aster, 2015;

Shalev & Von Aster, 2008). Specifically, it is estimated that 6 to 8% of students in the world have dyscalculia (Sharma, 2020, as cited in Kunwar et al., 2021), and around 5% are in primary schools (Kaufmann & Von Aster, 2012). This is underpinned by the results of the two independent studies in India, in which prevalence rates reached 5.98% and 5.54%

in all primary school children (Ramaa & Gowramma, 2002). Kucian and Von Aster (2015), as well as Jovanović et al. (2013), have found that dyscalculia is more prevalent among boys than girls. However, there are studies that contradict this finding. Statistics from Austria (Landerl & Moll, 2010) and Pakistan (Ashraf & Najam, 2020), indicate that more girls have arithmetic difficulties than boys. There are even discrepancies in gender ratios among students with dyscalculia within the same study, depending on the

methodology. In the study of Ramaa and Gowramma (2002), the prevalence of dyscalculia among male and female students was based on the criteria used for the diagnosis. More boys were identified with dyscalculia when the researchers used diagnostic tests. Yet, more girls were identified based on the teachers’ observations of students’ strategies when solving problems which were then reported to the researchers. The prevalence was equal

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for both boys and girls if exclusionary criteria were applied. This means that if students met all the criteria that exclude all the external factors such as school absenteeism and include factors such as having an adequate motivation for learning, lagging behind for two years in arithmetic, and not having serious emotional and/or behavioral issues.

Comorbidity

One of the reasons affecting the prevalence rates of dyscalculia could be comorbid disorders under which dyscalculia could have been masked. The highest rates of

comorbidity with mathematical learning disabilities belong to reading disabilities (RD) and attention deficit hyperactivity disorder (ADHD). For a person with dyscalculia, the

possibility of also having dyslexia is 50%, and ADHD 40% (Williams, 2013). If a student with dyscalculia is also dyslexic, it will be even harder for them to solve word problems as previously discussed. Indeed, research reveals that students with dyscalculia who also have RD show worse results in solving word problems than those without RD (Andersson, 2008; Fuchs & Fuchs, 2002, as cited in Chideridou-Mandari et al., 2016). Given these statistics of comorbidity, the process of identifying one specific learning disability becomes more difficult, since one disorder may be masked by the second one.

Mathematical Anxiety

As math difficulties often coexist with the other disorders mentioned above, math anxiety can be an effect of these comorbid difficulties (Kucian & Von Aster, 2015).

Children with dyscalculia typically have a greater degree of math anxiety. For instance, Kucian et al. (2018) reported that students with dyscalculia had higher math anxiety and poorer performance in comparison with other children. Interestingly, Mammarella et al.

(2015) discovered that deficits in verbal working memory were specific to children with math anxiety, and deficits in visuospatial working memory were specific to children with dyscalculia (as cited in Kucian et al., 2018). However, currently, it is unknown whether

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math anxiety is a cause of dyscalculia, but it surely poses some problems for students with dyscalculia and affects their learning process by exacerbating the existing condition (Butterworth, 2005b).

This section has given an overview of several common learning disabilities. The next sections of the literature review specifically focus on dyscalculia. They discuss its

definition, nature, symptoms, types, and potential causes of the disability. Also, they discuss different views and theories that exist around dyscalculia in the research field.

Definition, Nature, and Symptoms of Dyscalculia

The term “dyscalculia” was first used in 1940, yet it was only acknowledged in 1974 when Ladislav Kosc defined it as:

...a structural disorder of mathematical abilities which has its origin in a genetic or congenital disorder of those parts of the brain that are the direct anatomico- physiological substrate of the maturation of the mathematical abilities adequate to age, without a simultaneous disorder of general mental functions (p.47).

Kosc’s (1974) study has established that the notion has nothing in common with mental disabilities which affect people’s intellect and thinking. He further stated that people differ from each other by their abilities and if developmental dyscalculia (DD) is present in children, does not mean that abilities are evenly afflicted by the disorder (Kosc, 1974). This means that children with dyscalculia may excel in one area but underachieve in another. Their intellect may be either low or at an average level regardless of having

dyscalculia.

Kosc (1974) has classified dyscalculia into (1) verbal dyscalculia, (2) practognostic dyscalculia, (3) lexical dyscalculia, (4) graphical dyscalculia, (5) ideognostical dyscalculia, and (6) operational dyscalculia. Verbal dyscalculia is when a person is constrained to recognize the spoken numerical quantities, or vice versa, cannot speak out numerals that have been shown to them although they can read or write the same numbers. Practognostic dyscalculia is manifested by the problems with comparing real or illustrated things,

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sequencing them, and understanding concepts such as bigger/smaller, more/less, and other comparisons. Lexical dyscalculia is present when a child is not able to read math symbols, operational signs, and multi-digit numbers, cannot distinguish pairs of numbers (6 and 9, 2 and 5, 3 and 8), and may read numbers reversed (17 as 71). Graphical dyscalculia is demonstrated when a child cannot write numbers or symbols whether it is orally dictated or if the child should replicate a written number. They may write them inverted or rotated.

Interestingly, a child may be able to write the word for a dictated number, but not the numerical value. In the literature, the lexical type is also called “numerical dyslexia” and the graphical type is called “numerical dysgraphia” (Kosc, 1974). It is important to note that these reading and writing difficulties are specific to the mathematics domain.

Ideognostical dyscalculia is displayed when problems arise in the conceptual

understanding of mathematics. Children cannot solve simple mental calculations and do not understand the concept of conservation (e.g., “6”, “4+2”, and “2*3” are equivalent to each other). Finally, operational dyscalculia can be found in children who confuse and cannot use math symbols correctly, cannot select appropriate math symbols (or strategies) to solve problems, and continue to use their fingers to count when their peers have

progressed to use other strategies. Despite this classification, the symptoms of different types of dyscalculia can be combined and found in one child.

Generally, children with dyscalculia have problems with the conceptual

understanding of counting principles: one-to-one correspondence, in which one word corresponds to one number; stable order, in which the order of the numbers should not be changed when counting; cardinality, in which the last component of a set also indicates the quantity of the whole set; abstraction, in which any assortment of objects can form a set and be counted; order irrelevance, in which the order of the numbers/objects can be changed, and it does not affect the counting; and counting features which involve standard

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direction and adjacency (an inaccurate belief that objects should be counted consecutively) (Geary, 2004, p.6). Moreover, children with dyscalculia often have problems with

managing money, time (i.e., telling time from an analog clock, managing time in daily life) (Williams, 2013), and measurement (i.e., weight, temperature, and speed) (Sousa et al., 2017). They may struggle with applying the correct methods, formulas, and rules to solve math tasks; in severe cases, they cannot even solve simple calculations (Sousa et al., 2017).

Besides, it is difficult for them to understand the actual representation of mathematical formulas (Soares et al., 2018). It is challenging for them to further move to theoretical interpretations of math concepts (Sousa et al., 2017). Additionally, they have short-term and long-term memory problems manifested by difficulties in memorizing multiplication tables, facts, and rules (Williams, 2013). Moreover, they have sequencing and directional confusion i.e., difficulties in distinguishing between Left and Right, as well as East and West (Williams, 2013). Furthermore, children with dyscalculia have difficulties in visual- spatial orientation and lateralization (Michaelson, 2007). They are not able to give explanations of and grasp information from maps and graphs (Sousa et al., 2017).

Dyscalculia is not itself an effect of poor instruction, reduced intelligence, lack of motivation, emotional or social problems. Yet, undiagnosed it could exacerbate any existing difficulties with motivation and emotional issues.

Theories of Dyscalculia

Numerous theories exist around the notion of dyscalculia. They can be grouped into three main paradigms: neurobiological, cognitive, and educational. While the

neurobiological perspective treats dyscalculia as a neurological disorder, the cognitive perspective treats it as a working memory deficit. What they both have in common is an

“internalist” view of dyscalculia which views the causes as an innate deficit of neurological or cognitive mechanisms. In contrast to these first two theories, the

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educational perspective remains externalist, which means that the behavioral features of dyscalculia are caused by environmental factors (Williams, 2013). These three

perspectives are discussed in more detail below.

Neurobiological Perspective

The theories that fall under the neurological perspective are concentrated around systems such as the approximate number system (ANS) and object tracking system (OTS) whose efficiency determines mathematical competency. Neuropsychologists have mainly focused on investigating the two broad fields as the human brain and the genome. They define dyscalculia as an innate neurological disability that involves impairments in the structure and function of relevant areas of the brain and has a genetic predisposition.

Hypotheses that support the idea of the biological causes of dyscalculia are termed domain- specific core deficit hypotheses. They imply that there are specific brain areas that are responsible for numerical cognition.

Researchers in the field of dyscalculia who adopted the neurobiological perspective searched for a core deficit in dyscalculia and argued that there should be a core

characteristic for numerical awareness. These researchers have considered that the competency to recognize, manipulate, and compare magnitudes is a core characteristic of numerical skills (Chinn, 2015). These numerical skills are supposed to have neural correlates in particular regions of the brain. The deficiencies in those brain areas that constrain this ability were then thought to be a potential cause of dyscalculia. The

hypothesis that supports this view is predominantly known as a deficit in the approximate number system (ANS) (Mazzocco et al., 2011). It implies that people with dyscalculia have difficulties in comparing and distinguishing between magnitudes in an approximate manner with the use of a mental number line. These approximate non-symbolic number representations or, in other words, number senses are considered to be innate in newborns

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and also in many animal species (Fias, 2016). For the reason that animals and newborns cannot state the exact number of magnitudes, the term “approximate” is included. This hypothesis is also known as the number sense theory. ANS acuity is usually tested with a non-symbolic number comparison task where a child should decide whether one of the two presented strings of dots contains a greater number of dots (Traff et al., 2017). Research indicates that children with dyscalculia have less accuracy in ANS than other children (Mazzocco et al., 2011). Moreover, the results of the study by Mazzocco et al. (2011) demonstrated that ANS deficiency is a feature characteristic of children with dyscalculia.

Butterworth (2005a) has proposed a second core deficit called numerosity coding. It states that deficit in an innate number sense that allows recognizing the numerosities causes dyscalculia. To illustrate this, every day people encounter many numbers in different forms such as Arabic numerals (2), Roman numerals (II), number words (two), quantities (e.g., two dots, two books), time (2 o’clock), size, and height (Kucian & Von Aster, 2015). The common characteristic of these number expressions is that they display the number of elements (cardinality) in a set, which is the “numerosity” of a set according to Butterworth (2005a). The ability of subitizing and estimating quantities are the core elements of this hypothesis (Gillum, 2014). Subitizing is the skill of exactly naming the number of elements up to three or four, whereas estimating is approximately stating the number of elements above these numbers (i.e., above four). Another important element of this hypothesis is that it is not important for the things to be visible, they may be physical, audible, or abstract; the most important thing is to be able to recognize the numerosities.

Furthermore, Butterworth (2005a) argues that all other difficulties of children with

dyscalculia emerge from a deficit in numerosity, which implies a “lack of intuitive grasp of numbers” (p.12). For instance, addition and subtraction are usually taught to children through applying them and manipulating the sets. This means that development of

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arithmetic skills is based on the understanding of numerosities. What Butterworth (2005a) argues is that if children struggle with subsequent arithmetic concepts, it is due to their lack of intuitive grasp of numbers.

The neural correlates of the aforementioned domain-specific core deficit hypotheses suggest that numerical awareness is affected by impairment in the brain area called the intraparietal sulcus (IPS) (Butterworth, 2005b). Neuroimaging studies have shown that different functional and structural abnormalities in the brain areas that are responsible for number processing are mainly located in the intraparietal sulcus (IPS) (Kucian & Von Aster, 2015), specifically, the horizontal intraparietal sulcus (HIPS) (Dehaene et al., 2003;

Wilson & Dehaene, 2007). Research indicates the functional differences in the brains of children with dyscalculia as compared to those without dyscalculia. For instance, the study conducted by Price et al. (2007) revealed decreased IPS activation in DD children in numerical comparison tasks as compared to their peers with typical IPS functions. Other studies have found structural differences, reporting less volume of grey and white matter in IPS in children with dyscalculia compared to typically developing children (Rotzer et al., 2008; Rykhlevskaia et al., 2009, as cited in Kucian & Von Aster, 2015).

Other researchers have explored multiple brain areas that are involved in numerical processing. Dehaene et al. (2003) have proposed a triple-code model for number

processing and explained to what extent particular brain areas are involved in numerical skills. This model hypothesized three mechanisms of representation: a “quantity system”

which is responsible for the non-verbal representation of magnitudes, a “verbal system”

which is responsible for the lexical representation of numbers, and a “visual system” in which numbers are presented in an array of Arabic numerals (Dehaene et al., 2003). The model’s neural correlates state that the “quantity system” is affected by the horizontal segment of the IPS region (HIPS), the “verbal system” is affected by the left angular gyrus

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(AG) and perisylvian areas, and the “visual system” is affected by posterior superior parietal lobes (PSPL) (Dehaene et al., 2003; Soares et al., 2018). Dehaene et al. (2003) proposed that these three parietal regions together exist in the process of numerical cognition and are utilized depending on the nature of the task (Figure 1). The quantity system located in the HIPS forms the “phylogenetic precursor” of mathematical

proficiency (Fias, 2016, p.3). For example, the study by Thioux et al. (2005) reported that the HIPS region is specific to the number domain and activates more in response to number words than other categories of words such as animal names. In the study by Thioux et al. (2005), participants were given number words and names of animals. The Figure 1 Three-dimensional Representation of the Parietal Regions of the Brain

Source: From “Three Parietal Circuits for Number Processing”, by S. Dehaene, M. Piazza, P. Pinel, and L. Cohen, 2003, Cognitive Neuropsychology, 20(3), 487-506

(http://doi.org/10.1080/02643290244000239 ). [In the Public Domain].

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tasks included the comparison of number words (i.e., whether “seven” is bigger/smaller than “five”) or animal names (i.e., whether a “bear” is fiercer than a “dog”), and a categorization task (i.e., whether a number is even/odd or an animal is a mammal/bird).

The HIPS activated bilaterally more to numbers than to animal names independent of the tasks. This is indicative of the specificity of the HIPS region to the number domain and is convincing evidence for the core deficit hypotheses. Except for the HIPS region, the left AG and PSPL are not specific to the number domain. The left AG activates more when verbal representation is required (Dehaene et al., 2003). It is proposed that the left AG is

“part of the language system” and is involved in language-related tasks such as

multiplication, which requires a lexical representation of numbers (Dehaene et al., 2003, p.494). For instance, research found deficits in both numerical and verbal areas, in which children with dyscalculia presented with decreased brain activations in response to multiplication tasks (Berteletti et al., 2014). The PSPLs are involved and active while contrasting, estimating, and counting the quantities (Dehaene et al., 2003). However, PSPL is not only related to number processing but also is involved in other functions such as visuospatial processes, attention, and spatial working memory. For instance, a study has reported that PSPLs were activated when children subitized or moved their eyes (Simon et al., 2002, as cited in Dehaene et al., 2003). This means that numerical cognition is a complex process that involves additional brain areas apart from IPS that affect number processing. The implication of multiple brain areas signifies that dyscalculia has more complex causes than was initially proposed by ANS theory (Fias, 2016). It is important to understand how the brains of children with dyscalculia are different from others. However, it should also be considered that brain imaging studies are mostly criticized for their

“restricted applicability to education and classroom interventions” (Kaufmann, 2008, p.167).

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It is accepted among researchers that people have a second system associated with number processing known as an object tracking system (OTS) (Henik et al., 2011; Traff et al., 2011; Wilson & Dehaene, 2007). This system involves visuospatial skills which allow the child to track up to 3 to 4 objects while observing them (Wilson & Dehaene, 2007).

OTS is tested in children by the subitizing task in which participants should exactly name the number of presented dots. Children with dyscalculia can subitize a maximum of 3 dots, whereas their peers do this up to 4 dots (Traff et al., 2017). It is accepted that infants sometimes use their visuospatial skills rather than their innate capacities to recognize numerosities (Wilson & Dehaene, 2007). However, research remains inconclusive that deficits in the OTS may cause dyscalculia (Wilson & Dehaene, 2007).

Rousselle and Noel (2007) have presented another view called the access deficit hypothesis. According to this hypothesis, dyscalculia is caused by the inability to link symbols to their underlying magnitudes. Access deficit is also characterized as a disconnection syndrome (Wilson & Dehaene, 2007). This means that the disconnection between “symbolic numbers and innate magnitude representations” may cause dyscalculia in children (Skagerlund & Traff, 2014b, p.2). According to this view, people with

dyscalculia may have intact non-symbolic number processing (ANS), but impaired symbolic number processing which prevents them from connecting the symbols to their underlying quantities (Wilson & Dehaene, 2007). The neural evidence for this hypothesis states that the brain of people with dyscalculia fails to link its frontal lobes to the parietal areas while the child develops (Traff et al., 2017). One study found that white matter in the brains of children with dyscalculia grew neither in the frontal nor in the parietal regions as compared to their typically developing peers (Ranpura et al., 2013, as cited in Traff et al., 2017). These results, as the authors further argue, may provide evidence that dyscalculia is partially a disconnection syndrome (Rouselle & Noel, 2007).

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Recent research shows that there are deficits not only in number processing but also in magnitude processing skills (Traff et al., 2017). The deficit in magnitude processing implies difficulties with other magnitudes apart from numbers such as time and space. This view is supported by the study of Skagerlund and Traff (2014a), who have found that children with dyscalculia had deficits not only in the ANS but also difficulties with the perception of time and processing the spatial information.

Within the neurobiological frame, genetic studies show that dyscalculia runs in families. For instance, Landerl and Moll (2010) conducted a “family transmission analysis” of arithmetic difficulties and found that the prevalence rate was higher among family members of children with mathematical difficulties. The first twin study of mathematics disability has provided essential evidence for the heredity of dyscalculia. In that study, 40 identical and 23 same-sex fraternal twins were tested, and it was revealed that 58% of monozygotic (identical) and 39% of dizygotic (same-sex) twins also had dyscalculia (Alarcón et al., 1997). In addition, Shalev et al. (2001) discovered that families and relatives of children with math learning disabilities are ten times more prone to be identified with dyscalculia than other people (as cited in Geary, 2004).

Research in the neurobiological area emphasizes the brain and genome as potential causal factors of dyscalculia. Nevertheless, researchers from the cognitive area highlight the involvement of other cognitive mechanisms apart from biological factors that may cause dyscalculia.

Cognitive Perspective

The cognitive view of the phenomenon of dyscalculia put forward the existence of additional deficits which could be affected by non-numerical factors such as deficits in executive functioning and different components of the working memory (Traff et al.,

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2017). The hypothesis that supports this view can be found in the literature as a domain- general cognitive hypothesis (Henik et al., 2011; Traff et al., 2017).

Cognitive psychologists one of which is David Geary, suggest that dyscalculia is a cognitive disorder of working memory. Geary (2004) proposed three main subtypes of dyscalculia: procedural, semantic memory, and visuospatial. The procedural subtype implies difficulties in learning and applying basic mathematical procedures which are proposed to be caused by deficits in verbal working memory, conceptual knowledge, and attentional control. The semantic subtype implies difficulties in retrieving math facts which may be due to deficits in long-term memory. Finally, the visuospatial subtype implies difficulties in the understanding of spatially represented quantities, which involves problems in geometry, understanding graphs, tables, and using a mental number line (Geary, 2004). There is a debate among researchers on whether working memory

constitutes a cause of dyscalculia. Some of these researchers have highlighted the absence of conclusive evidence for a cognitive basis for dyscalculia (Butterworth, 2005a).

However, it is widely accepted that many children with dyscalculia have difficulties remembering and retrieving mathematical facts (Traff et al., 2017).

The cognitive theory also proposes defective executive functioning as a possible cause of dyscalculia in children. Executive functions are responsible for broad processes such as attention shifting, processing speed, updating the information, switching from one method to another, organization, and planning skills (Karagiannakis & Cooreman, 2017).

This can be seen in a study conducted by Van der Sluis et al. (2003) in which children with arithmetic difficulties were slower in naming the numbers and quantities than the control group. Additionally, these children showed deficits in the tasks that tested their processing speed and cognitive shifting abilities. Similarly, a study by Traff et al. (2017) has found deficits in the executive function of shifting ability and visuospatial working memory in

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children with dyscalculia. However, the processing speed for the children in this study was not affected; they named colors and numbers at a normal range of speed. Currently,

literature is inconclusive about the causality of executive function deficits to dyscalculia.

Yet, it is evident that children with dyscalculia present with difficulties in executive functioning such as attention shifting and processing speed (Traff et al., 2017).

Notwithstanding, there exists another view from the educational researchers on the causes of dyscalculia, which is discussed further.

Educational Perspective

Some researchers from the field of mathematics education say that dyscalculia does not exist and instead has emotional and experiential causes which means that the causes come from external factors (Gifford, 2006). Their view originates from a disagreement with the whole ideology of the models of disability, specifically with the medical model (Lindsay, 2003, as cited in Gifford, 2006). They argue that paradigms such as those proposed in the neurobiological view that stand for the innate nature of the disability use unfavorable words such as “deficits”, which do not coincide with some teachers' beliefs about setting an inclusive environment in the classroom with positive anticipation about all their students (Gifford, 2005; 2006). Educational researchers criticize the cognitive

theories of disability saying that it fits the “medical model” of disability (Lindsay, 2003, as cited in Gifford, 2006). These researchers explain that it is more concentrated on medical factors that are “within-child”, whereas environmental factors, socio-cultural diversity, students’ emotions, and feelings are under-considered. In addition to this, they argue that concentrating on children’s memory problems may actually produce children with dyscalculia. Dowker (2004) adds that such “labeling could turn a child’s learning delay into a deficit” (as cited in Gifford, 2006, p.45). In response to the genetic predisposition of

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dyscalculia, Gifford (2006) emphasizes the “home learning environment” as a possible bridge that conveys poor math personalities in families.

Researchers have found a link between a child’s family characteristics and academic performance. The factors such as low socioeconomic status (SES), “home learning

environment” regardless of SES, and parental perspective on math such as mothers’ low self-confidence in math can cause dyscalculia in children, according to Gifford (2006).

Studies that are based on the view of educational researchers report that mothers’ poor numeracy skills and low self-esteem in math affect children’s numerical experience and hence, academic achievement (Young-Loveridge, 1989, as cited in Gifford, 2006).

Evidence suggests that children who belong to low SES families have poorer achievement scales, and children who were not exposed to the early experience of number learning at home regardless of SES have lower arithmetic progress than children who were exposed (Sammons et al., 2002).

Other factors that should be considered according to educational researchers are the attitudes and feelings of the students themselves. This is evident from the case of some students who ended the usage of compensating strategies for other disciplines after losing their math confidence (Bfuzka et al., 2000, as cited in Gifford, 2006). Gifford (2006) claims that “failure to learn or to demonstrate learning may be due to a child's attitudes towards the learning or assessment situation” (p.42). Additionally, Gifford and Rockliffe (2012) state that insufficient “educational experiences” and difficulties in mathematics can lead to math anxiety and hence hinder the learning of students. Gifford (2006) argues that there is a need for a more multi-dimensional model of MD, which would consider all the factors and circumvent the “medical model”. However, a significant part of the scientific community thinks that these external factors should be considered not as a cause but as

Сурет

Table 1 Review of the Literature: Teachers’ Knowledge of the Definition and Nature of Dyscalculia
Table 4 Review of the Literature: Teachers’ Knowledge of the Interventions to Support Students with Dyscalculia
Table 5 Demographic Characteristics of Respondents
Table 6 Teachers’ Exposure to the Phenomenon of Dyscalculia and Dyslexia
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