Online Teaching and Learning of Primary Mathematics in Saudi Arabia: A Study on the Impact of COVID-19

This study examines the impact of COVID-19 on online teaching and learning of primary mathematics in Saudi Arabia. It explores the perceptions of teachers and students, and the effect of gender and years of teaching experience on using online tools. The study aims to contribute to the field of educational research and provide a comprehensive understanding of online learning tools and teaching.

1.1 Background....................................................................................................................1
1.1.1 Education in Saudi Vision 2030.............................................................................................1
1.1.2 The Educational Impact of COVID-19: The Case of Primary Mathematics Teaching
and Learning in Saudi Arabia........................................................................................................1
1.1.5 Online Teaching and Learning..............................................................................................5
1.3 Significance of The Study...................................................................................................6
1.4 Overview of The Study........................................................................................................7
3.1 Introduction........................................................................................................................3
3.2 Adopted research philosophy..............................................................................................3
3.2.1 Ontology..................................................................................................................................4
3.2.2 Epistemology...........................................................................................................................5
3.2.3 Pragmatism.............................................................................................................................6
3.3 Research design: Mixed methods.......................................................................................7
3.4 Sample sizes and sampling strategies...............................................................................10
3.4.1 Sample sizes...........................................................................................................................10
3.4.1.1 Quantitative stage..............................................................................................................................10
3.4.1.2 Qualitative stage................................................................................................................................12
3.4.2 Sampling strategies...............................................................................................................13
3.4.2.1 Quantitative stage..............................................................................................................................14
3.4.2.2 Qualitative stage................................................................................................................................15
3.5.1 Questionnaire .......................................................................................................................16
3.5.2 Semi-structure interview .....................................................................................................19
3.5.3 Non-participant observation................................................................................................21
3.6 Pilot study..........................................................................................................................23
3.7 Data analysis.....................................................................................................................23
3.7.1 Quantitative data analysis....................................................................................................23
3.7.2 Qualitative data analysis .....................................................................................................24
3.8 Validity and reliability.......................................................................................................26
3.8.1 Validity .................................................................................................................................26
3.8.2 Reliability..............................................................................................................................28
3.9 Ethical considerations......................................................................................................29
3.10 Summary.........................................................................................................................31
References...............................................................................................................................32
Introduction chapter: about 2000 words

Literature review chapter: 3000 – 5000 words
Methodology chapter: 8000- 10000 words
Introduction Chapter

CHAPTER 1: INTRODUCTION
1.1 Background
1.1.1 Education in Saudi Vision 2030
The "Saudi Arabia Vision 2030" aims to develop education in several aspects (Saudi Vision,
2030, 2016). One of the main objectives of this national transformation program is to improve the
educational system in the country, such as improving the basis of learning, updating assessments and
curricula, and ensuring that education is not affected by any emergency, such as what happened with
COVID-19 (OCED, 2020). Although education was greatly affected by the global pandemic, the
speed of response by the Ministry of Education and the support of Vision(Education in Saudi Vision,
2030) alleviated the suffering of students and parents by providing an educational platform that
contributed to this crisis significantly (Saudi Ministry of Education, 2021). According to the Ministry
of Education of Saudi Arabia (2017), one of the goals of the Vision is to build the current curriculum
around the stringent requirements of character development, skills, numeracy, and literacy. To ensure
that educational achievements align with market demands, educational institutions need to work
closely with the corporate sector.Saudi Arabia has achieved universal access to education for a large
and geographically dispersed school-age population. With its impressive gains in enrolment, however,
Saudi Arabia has stretched the capacity of educators and administrators to deliver and assure high-
quality learning. The advances in participation will now need to be matched with equivalent progress
in student learning and skills if the Kingdom is to achieve the ambitious development goals outlined
in Vision 2030.
1.1.2 The Educational Impact of COVID-19: The Case of Primary Mathematics Teaching and
Learning in Saudi Arabia
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The effect of COVID-19 on the educational sector resulted in the closure of schools
worldwide (Oraif&Elyas, 2021). According to Rahman et al. (2019), more than one billion students in
schools and universities were affected by school closures. Moreover, the structure of learning and
schooling has been changed by the closing of schools. (Tarkar, 2020). Hence, education has changed
significantly with an increasing shift in technology usage and online teaching and learning methods
(Oraif&Elyas, 2021).
In Saudi Arabia, although online learning was implemented in the country before the
pandemic, it was simple and in its infancy. The educational system had to be changed significantly to
allow students to learn and attend schools remotely (Oraif&Elyas, 2021). For example, before the start
of the 2020 academic year, Saudi Arabia's Ministry of Education launched a new digital platform
called Madrasati (translated as "My School"). This new platform was built to tackle the impact of the
pandemic on education for both staff and students in the country (Alshehri et al., 2020). The digital
platform enables students and teachers to engage in visual communication, conduct classes online,
and conduct assessments and examinations. Alongside this digital platform, the Ministry also
introduced more than twenty TV channels for each educational level, ranging from primary to high
schools (Oraif&Elyas, 2021).
1.1.4 Saudi Arabia's Primary Mathematics Curriculum and Achievement
Saudi Vision 2030 emphasizes mathematics in elementary schools, where students' identities
are formed, and their minds are exposed to a wealth of previously unknown material. This paves the
way for knowledge and community engagement. This is due to the government's emphasis on
strengthening Science, Technology, Engineering, and Mathematics (STEM) education and putting
these topics at the forefront of educational advancement (Alhareth& Al Dighrir, 2014). According to
(Alhareth& Al Dighrir ,2014), the Saudi primary mathematics curriculum is built on real-life
applications that integrate science and mathematics. This might help students do better in math classes
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and give them a better connection and knowledge of the curriculum's basic concepts (Alghamdi,
2017).
These best curricula are designed to promote balanced understanding and vertical integration
across disciplines at all levels of education (Alafaleq& Fan, 2014). This promotes the development of
higher cognitive and comprehensive mathematics abilities at all levels of education (Alshehri& Ali,
2016). The design of these mathematical subjects in schools is based on a variety of learning
objectives, including 1) examining concepts and developing cognitive skills, 2) developing
comprehensive mathematical skills and techniques, and 3) enabling students to use logical reasoning
to overcome challenges and difficulties in life (Alshehri& Ali, 2016).
According to Alabdulaziz and Higgins (2021), the elementary mathematics curriculum
includes the six main themes shown in table 1.1. It should be taught to students with practical
application in daily life. Regarding Saudi Arabian students' mathematical performance, the country's
position in the Trends in International Mathematics and Science Study (TIMSS) in 2019 might be
used. The framework for the 2019 TIMSS evaluation offers the foundation for four international tests,
including math and science, for fourth and eighth-grade pupils (Mullis & Martin, 2017). According to
the Education and Training Evaluation Commission (ETEC) in Saudi Arabia (2019), based on the
TIMSS report (2019) about the mathematics assessment, Saudi Arabia placed 53rd out of 58
participating nations (with a score of 398 out of 1000) for fourth graders. In comparison to their
counterparts in other countries, a substantial proportion of fourth-grade Saudi Arabian pupils lacked
the fundamental foundations of mathematics (ETEC, 2019).
Table 1.1
Domain Content
Number  Whole numbers and comparisons of whole numbers
Place value up to1million
 Fractions
 Equivalent fractions (comparing, ordering, and placing them on a
number line)
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 Categorizing fractions (rational, irrational, and decimal)
Algebra  Defining and explaining patterns of multiplication and division
 Properties of addition and multiplication
 Basics of subtraction and division
 Algebraic representations of number sentences
Measurement  Units of length, area, volume, and mass
 Time intervals.
 Perimeter and area of squares
Geometry  Categorizing and describing solids
 Geometric concepts of lines (e.g., parallelism and perpendicularity)
 Angles and types of angles polygons (e.g., triangles and congruence)
 Locating numbers and fractions on a number line and a coordinate
plane
Statistics and
Probabilities
 Data collection, organization, and representation (points, columns).
 Creating bar graphs
 Reading and explaining data.
 Finding median and mode
 Histograms, pie charts
 Measures of central tendency
 Range
 Data analysis—interpretation and presentation § Measures of
dispersion
1.1.5 Online Teaching and Learning
With the focus of Saudi Vision 2030 on teaching and learning mathematics in primary schools, the
urgent need for online education has emerged dramatically after the global pandemic (Dhawan, 2020).
There was no agreement among scholars on a specific name for this type of education, as some used
to call it "open education." Fee (2009) referred to e-learning, while Salmon (2013) referred to it as
online education. Online education is defined as a way of transferring knowledge between the teacher
or the source and the learner through the Internet and using various devices, such as computers
(Dhawan, 2020; Nguyen, 2015).
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Online education is divided into two types, namely, synchronous and non-
synchronous education. Synchronous education refers to teaching and learning techniques in
which the learner(s) and instructor(s) are in the exact location at the same time to facilitate
learning (Oztok et al., 2013). Non-synchronous education's core idea is that learning may
occur multiple times and places depending on the learner (Yamagata-Lynch, 2014). When
there is a time constraint or a desire for flexibility in learning, this method is used (Yamagata-
Lynch, 2014). Learners have the option of downloading or attending their online session
whenever they wish. This form of learning allows for social interaction using a message
board, which is an example of an asynchronous tool, and the learner can learn mathematics at
their leisure. (Yamagata-Lynch, 2014).
1.2 Aims of The Study
The purpose of this study is to query the perceptions of Saudi primary school teachers and
students about online mathematics teaching and learning during the global pandemic. The goal of this
study is to find out what teachers and students in primary schools in the Kingdom of Saudi Arabia
have to deal with when they use online tools to teach and learn math.In addition, to see if there is an
effect of gender and years of teaching experience on using online tools in elementary school
mathematics teaching, It focuses on analysing the impact of teacher characteristics such as gender and
years of teaching experience. Albalaw (2017) It is believed that male teachers are more comfortable
with computer-enabled online media sources because it has been determined that male teachers with
at least ten years of teaching experience in the education environment in Saudi Arabia are more
comfortable using online educational tools and platforms than females in general (Bluegrass, 2017).
Furthermore, Wiseman et al. This results in educational benefits for teachers in a gender-segregated
society (Weizmann et al., 2018). Furthermore, Prendergast et al. (2018) argued that with the support
of the theory of planned behavior, parameters such as attitude and behaviour to adopt an entity, social
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factors, and behavioural control of processes influence a specific segment of users in support of a
particular educational reform (Prendergast et al., 2018). The purpose of this question is to find out if
there is an effect of gender and years of teaching experience on the use of online tools in elementary
school mathematics teaching.
1.3 Significance of The Study
The results of this research will enable policymakers in Saudi Arabia, and more specifically, the Saudi
Minister of Education, to revise their policies on primary mathematics curriculum design to enhance
students' mathematics learning and knowledge. Since the spread of the COVID-19 pandemic, it has
led to the emergence of significant challenges in the education sector, and according to the Saudi
Minister of Education (2021),
And he added:
He is proud of the development of the education system in the Kingdom of Saudi
Arabia under the supervision of the Ministry of Education, expecting that distance
education will be a project for the future and will continue to benefit from it and
invest in it in all circumstances during the pandemic and after the pandemic, and this
is a quantum leap for the digitization of education at the level of the Kingdom
(Ministry of Education, 2021, para 8).
Hence, this study is vital and timely because it will provide a comprehensive understanding
of online learning tools and teaching, particularly about vital curricular subjects such as
mathematics.
Furthermore, this research aims to contribute to the field of educational research that focuses
on online learning and teaching. Using a mixed-method approach and collecting quantitative and
qualitative data via questionnaires, interviews, and observations leads to a more in-depth
understanding of the results as well as an increase in the validity of the study's results by using two or
more approaches to ensure their accuracy and reliability about the study under investigation. Finally,
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the findings will contribute to previous research on the role of teachers' self-efficacy in using online
teaching tools and techniques to teach primary mathematics.
1.4 Overview of The Study
This Confirmation of Registration (CoR) report is broken down into three sections. This chapter,
Chapter 1 (Introduction), has provided an overview of the topic under investigation. More
specifically, the chapter has discussed the effect of the current pandemic on the educational sector in
general with a special reference to on-line mathematics learning in Saudi Arabia. Moreover, the
chapter has explained the Saudi 2030 vision regarding education in the country and has discussed
Saudi Arabia’s mathematical curriculum design and student evaluation as well as Saudi students’
students’ performance in TIMSS 2019. In addition. Finally, the chapter has explained the aims and the
significance of this research study.
Chapter 2 (Literature Review) will begin with a discussion on the definition of synchronous and
non-synchronous education and then will move on to the next section which is concerned with
teaching and learning primary mathematics. Moreover, it will present some of the theories used in
mathematics teaching and learning. It also will cover the underpinning theories of this study, which
are Technological Pedagogical Content Knowledge (TPACK), Moore's theory, and self-efficacy
theory. Then, it will present some barriers and enabling factors that have been presented in previous
studies related to on-line mathematics teaching and learning. Finally, the impact of the characteristics
of teachers, such as genders and years of teaching experience impact of teachers’ characteristics on
their self-efficacy is discussed.
The third chapter (Methodology) will explain the chosen research methodology for this
research. The chapter will start by explaining the chosen research philosophy and research design with
justification. The sample size and sampling strategy will also be explained, and the intended data
collection methods will be discussed. Finally, the chapter will discuss the analysis of the collected
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data, and the reliability and validity of this research. Ethical considerations have also been brought
forward.
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Literature Review
Chapter
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CHAPTER 2: LITERATURE REVIEW
2.1 Introduction
This chapter aims to present a review of literature on perceptions of school teachers and
children in Saudi Arabia regarding online mathematics teaching and learning during the global
pandemic (2020–present). Specifically, the concept of online teaching and learning that includes
synchronous and asynchronous learning will be discussed. The study’s underpinning theories, namely
the Technological Pedagogical and Content Knowledge (TPACK) framework and the Self-efficacy
theory will be discussed. Finally, potential barriers and enablers concerning online mathematics
teaching and learning will be discussed.
2.2 online teaching and learning
2.2.1 Definitions
As denoted by Singh and Thurman, (2019), Online learning is defined as the education which takes
place over the internet. It is also defined as e – learning which is described in other forms.
As per Fitton, Finnegan and Proulx (2020), online learning is the learning where the students and are
learning through virtual environment. Online learning helps the student to learn and enhance their
knowledge and understanding in the form as to how effectively they are undertaking various measures
of learning.
According to Coman et.al. (2020), Online learning is that form of learning which is done through
different devices in the manner such as using an electronic media which is internet and some other
aspects of acquiring the knowledge and education from.
There are some key differences of online learning definitions which are being addressed as
that there are different definitions which the scholars have addressed to and this helps in analysing the
major concerns of how the online learning is being done (Singh and Thurman, 2019). Online learning
is also defined as internet ways through which learning is made easy and possible for students.
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Interestingly, there is no consensus among scholars as to what defines online teaching and
learning.
Salmon (2013) and Al‐Qahtani and Higgins (2013) have defined online learning as the mode
of providing learning in which knowledge or information is shared online or provided to the students.
This definition, like many others provided by the researchers, emphasises the importance of
eliminating physical interaction and the promotion of online learning methods. Dhawan
(2020),Kauffman (2015), and Al‐Qahtani& Higgins (2013) offered similar definitions which also
emphasises the elimination of face-to-face physical interaction of teachers and students.
According to Dhawan (2020) and Kauffman (2015), online learning makes the teaching and
learning process more flexible, innovative and student-centred. Wang et al. (2014) confirmed that
teachers do not have to be physically present in classrooms for online teaching to be effective as
teachers can still access modern tools to convey their message in innovative ways.
Based on the above mentioned studies on online teaching, this study will adopt the following
definition for online learning: online teaching and learning is a way of delivering educational lessons
using the internet via audio or video calling tools which facilitate easy communication between
students and teachers (Online Learning Definition and Meaning, 2022).
2.2.2 Benefits and limitations of online teaching and learning
When it comes to time and location, online learning is quite adaptive. Every student has the
choice of selecting the most convenient location and time for them (Arkorful&Abaidoo, 2015).
According to Tareen and Haand (2020), the adoption of online learning gives students a great deal of
freedom in terms of when and where learning information is delivered or received. Through the use of
discussion boards, online learning can facilitate the formation of relationships between students. It
facilitates engagement by removing barriers such as the fear of speaking with other students. Students
are encouraged to communicate with others, as well as exchange and respect diverse points of view.
Overall, it provides more opportunities for students and teachers to interact (Lim, 2017).
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On the flip side, online learning causes learners to experience isolation, detachment, and a
lack of engagement (Hameed et al, 2008). To minimise such impacts, participants need to be self
motivated and have time management abilities (Akkoyuklu&Soylu, 2006). Further, clarifications,
explanations, and interpretations are less efficient online (Arkorful&Abaidoo, 2015). It is also
important to note that e-learning is more suited to social science and humanities than to fields like
medicine and engineering, where practical skills are required (Arkorful&Abaidoo, 2015).
2.2.3 Types of (online) teaching and learning: Synchronous and asynchronous
Broadly speaking, there are two key types of online teaching and learning, namely
synchronous and asynchronous. Synchronous teaching and learning corresponds to when the teacher,
student, and message are present at the same time allowing for continuous exchange of information
(Oztok et al., 2013). There are many tools for synchronous learning, such as web conferencing apps
like zoom, hashtags on twitter, video and instant messaging apps, YouTube Live, etc.
Synchronous learning tools which are not specific to mathematics now are signified as –
audio conferencing, web conferencing, video conferencing, instant messaging and chat messaging
(Lim, 2017). These are the examples of Synchronous learning tools which helps in addressing the
concern of how effectively and in appropriate manner there are these tools which are not only used in
mathematics but other subjects also (Kohnke and Moorhouse, 2020) There are certain advantages and
disadvantages which are explained and are mentioned as –
Advantages of Synchronous learning tools are – They effectively collaborate, engage the students
and e – learners about the major concerns as to how effectively they can be interactively learning new
things and gain knowledge, improvement in the learner outcomes are also identified (Zydney et.al.,
2019). There is also reduced cost to this process of learning.
Disadvantages of Synchronous learning tools - It is the learning tool which is strictly technology
based. There are local time barriers which is the major disadvantage of this tool (Dung, 2020). This
tool requires careful planning. It also demands higher speed internet connection which becomes the
major disadvantage while learning through this process.
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These offer some unique advantages in that students can ask real-time questions, be more
engaged, provide a greater sense of community by supporting peers, and even facilitate student-
teacher collaboration by sharing links and online resources in real time (Lim, 2017).
These unique advantages are being addressed by acknowledging the aspect of how effectively
and in appropriate manner the real time questions are asked and this is keeping the students engaged
due to the online learning process (Bahasoan et.al., 2020). The students and teachers are facilitated as
this process helps in understanding and keeping the perspective of online learning major for the
concern of gaining knowledge and online learning at large scale (Khan et.al., 2017). The collaboration
of students and teachers helps in understanding that with the help of this process there are major
concerns which are being addressed and are taken into application that online learning is facilitating
the major concepts of online learning and applying the key concepts of framing effectiveness and
efficiency through easy and effective learning process. Therefore, online learning has provided this
unique advantage of learning and analysing that the teachers and students are engaged in the online
process of gaining knowledge through effective and efficient manner.
Asynchronous learning has major advantages which help in denoting that they are important
aspects of learning too Lemke, (2022). These advantages are – more time to review the concepts and
provide material for learning and taking education and gaining knowledge, it helps in expanding the
network by providing the content to more of the students in an appropriate manner, it also helps in
starting the in course conversations. This form of learning does not allow for social interaction, and
the learner can read and learn at his or her leisure (Yamagata-Lynch, 2014). As such, asynchronous
learning is best suited for situations when there is a time constraint or a desire for flexibility in
learning (Yamagata-Lynch, 2014). The biggest disadvantages of asynchronous communication tools
are that it does not facilitate immediate feedback which can raise confusion (Almanthari et al., 2020).
2.3 Primary mathematics teaching and learning
2.3.1 Theoretical perspectives
A seminal mathematics education scholar, Skemp (1976), argued that there are two key types
of mathematics learning (i.e., habit learning vs intelligent learning) which lead to two different types
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of mathematics understanding (i.e., instrumental understanding vs relational understanding). Skemp
defined habit learning as learning through rote memorization primarily through practising without
grasping the true meaning of what is learnt. Intelligent learning on the other hand involves learning
through schemas, which is defined as are concepts that help organise and recognise information.
When facing new problems, the learner draws knowledge from schemas prepared via intelligent
learning instead of relying solely on memory.
The concept of instrumental understanding resonates with Kilpatrick et al. 's (2001) concept
of procedural fluency which is the knowledge of mathematical processes, and when and how to apply
them effectively, flexibly, accurately, and efficiently. Procedural fluency and instrumental
understanding are similar in that they rely on memorising and remembering. Relational understanding
pertains to knowing how to use a mathematical rule and why it works. The concept of relational
understanding which is defined as investigating the concepts along with continuum and integration
related concepts. The two concepts are similar in that this allows students to learn new concepts by
connecting them to what they already know.
From the above discussion, it is clear that both types of learning are important (Kilpatrick et
al., 2001). However, in the author’s opinion, relational understanding is very important for children as
it gives them the freedom to imagine and generate an infinite number of ideas. It is analysed that how
effectively and in appropriate manner the infinite number of ideas are generated and are creating value
for the freedom to imagine infinite ideas which are generated and this is related to rational
understanding at large scale (Bahasoan et.al., 2020). Rational understanding has helped in
understanding and initializing the aspects of how effectively mathematics is being understood to
students appropriately. Nevertheless, going by personal experience, accomplishing milestones and
getting recognition for the same is likely to how the students are encouraged to establish results and
learn for the findings. In the context of the current study, these concepts of mathematics learning and
understanding will be useful in determining the purposes of different online mathematics learning
tools.
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2.3.2 Online mathematics teaching and learning tools
2.3.2.1 Synchronous online mathematics teaching, learning and supporting tools
According to Divakaran (2015), synchronous online mathematics teaching and learning is
teacher-led education in which students interact with the teacher or peers simultaneously via web and
instructional video conferencing. As noted in Section 2.2.2, synchronous online teaching and learning
pertains to when students are ‘located in remote locations, and connected by videoconferencing, audio
conferencing, or both (Bernard et al., 2004; Murphy et al., 2011).
2.3.2.2 Asynchronous online mathematics teaching and learning and supporting tools
In asynchronous mathematics learning, students learn certain subjects of mathematics that are
determined by the teacher using educational platforms at different times and according to the student's
time and inclination (O'Sullivan et al., 2021). According to Moore et al. (2011), online mathematics
learning tools are any programs, software, or technology that can be accessed over an internet
connection and improve a teacher's capacity to communicate knowledge and a student's ability to
absorb the same. From the reviewed literature, there are several online tools fit for this purpose, such
as: MyMathLab, ALEKS, Enhanced WebAssign, and GeoGebra. Each of these tools will be briefly
discussed next.
There are some basic online tools which are analysed and are identified as how effectively
and in appropriate manner there are some major different types of asynchronous on-line mathematics
teaching and learning tools. These online tools are – Google docs, Drop box, Skype, Zoom Meeting
and platforms of brainstorming such as – Padlet and Mindmeister.
For primary mathematics to be taught to students there are specific examples which are
determined and are analysed for making the students study the basic concepts of how effectively the
mathematics is to be taught to the children and this helps in addressing the major concerns as to how
the mathematics is taught to the students at large scale and in proper manner (Zydney et.al., (2019).
The type of online mathematics tools which are helping to gain the maximum are helping to analyse
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and identify that the students are learning from the tools such as zoom meetings and brainstorming
platforms which are being created and framed for them.
The type which is being focused here is Zoom meetings and Google docs through which the
students are able to learn many things and are able to gain knowledge by understanding how the
problems of mathematics are solved in an appropriate and specific manner (Khan et.al., (2017). These
tools are used for the students who are studying in primary and through this there are aspects of how
effectively and in appropriate manner the online learning is made easy for them at large scale. Google
docs is the basic tool which helps in storing and providing the data and information through which the
students are able to gain the maximum and are providing the aspects and are providing the aspects of
how effectively there are major concerns in an appropriate manner of how effectively the knowledge
is gained and which helps in understanding mathematics and other subjects to students.
As it incorporates elements of algebra, geometry, and calculus, it is a dynamic geometry
application that allows students to create points, vectors, lines, conical parts, and conjunctions, as well
as effectively change them.
These are the elements which help in incorporating and understanding the maths at large scale
and this also helps in working with how the calculus, geometry and algebra are used and are creating
effective value of understanding and solving teh problems which are related to mathematics (Khan
et.al., (2017).
While most of these features of GeoGebra are beyond the needs of a Primary school student,
judicious use of the application can help teachers lay a strong foundation for students as they begin
their journey in mathematics, even when classroom teaching is not an option.
2.4 Potential barriers and enablers concerning online mathematics teaching and learning
In the world of online teaching, factors that aid the conducting of instruction are referred to as
enablers while those that impose challenges and difficulties in conveying instruction to the students
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are known as barriers. For efficient teaching, it is vital to overcome all barriers as they can negatively
impact the teaching as well as the learning process.
2.4.1 Potential barriers
A review of literature reveals that adopting information communication technology in
the delivery of online education has met four barriers. First, learning via online digital
platforms for the first time resulted in limited time frames and incompetency on the part of
instructors; this was highlighted in a survey of 100 secondary school students (Ghavifekr et
al., 2016).
Second, there is a distinct lack of appropriate online learning resources such as
computers and appropriate online teaching and learning tools. According to (Perrotta 2013;
Bringula et al., 2021; Perrotta, 2013), if teachers are given the opportunity and resources to
explore with computers, they can enhance their technological skills.
Third, there is a lack of technical support for students and teachers when it comes to
using online tools in teaching mathematics. This leads to ineffective communication between
students and instructors (Ghavifekr et al., 2016).The lack of technical support does not allow
for receiving good online education in comparison with face-to-face classroom environment
(Carver, 2016; Ghavifekr et al., 2016; Perrotta, 2013).
Fourth, Infrastructure and noise barriers are found to prevent teachers from
implementing technology in the teaching and learning process Coman et al. (2020). These are
lack of Internet connection, electricity, and other distractions such as noise and unavailability
of appropriate learning environments (Bringula et al., 2021; Doyumgaç et al., 2021; Perrotta,
2013).
2.4.2 Potential enablers
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Online content, online assignments, online assessment, instructor behaviour and
methods are all highlighted in the literature as enablers of online learning. Online content such
as videos, presentations and web links offer diversity of media and activities to help keep
students’ attention (Hew et al., 2020). In addition, Van Wart et al. (2020) believes that
synchronous onlinevideo conference platforms linked to online asynchronous platforms have
the potential to improve engagement and effectiveness.
Second, online assignments enable students to choose their learning path, the optimal
time, and the method for completing online assignments (Horn &Staker, 2014). The feedback
on submissions has many benefits; it improves students' engagement and learning
(Espasa&Meneses, 2010), precise feedback provides students with recommendation to
improve their work according to Alvarez et al. (2012), other studies (Tila& Levy, 2019)
showed that multiple submissions are seen as a good aid for online learning and provide the
ability to grade submissions quickly and accurately.
Third, according to Kara (2021), different types of examination and assessment
options such as (quizzes, timed tests, weekly assignments, and projects) can help to increase
the effectiveness of the online assessment. Moreover, Sahin and Yurdugül's (2020) noted that
allowing students to see their grades right after the online examinations were completed was
extremely popular (Khan & Khan, 2019).
The instructor's flexible procedures and ability to adjust quickly to situations assist
students to improve their online learning efficacy (Van Wart et al., 2020).Furthermore, the use
of constructivepersonalised feedback tailored to the needs of students helps as
well(Hatziapostolou&Paraskakis, 2010). In addition, quick responses to students' inquiries
help them become more motivated to learn online (Hew et al., 2020; Jaggars& Xu, 2016).
Fifth, psychological issues: During the COVID-19 epidemic, students' psychological
problems were critical in evaluating the efficiency of online learning. The comfort of home, taking
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online courses at home and enrolling in online classes from home, according to most students,
improved their attitude throughout the lockdown (Kara, 2021), and the ease of unfettered access to
online course information, according to Dhawan (2020), who noted how users can flexibly use tools
for online learning without time limits during this difficult era.
2.4.3 The Theory of Planned Behaviour
According to Kruglanski, et al. (2011), it is important to study the theories of behaviour to
analyse the ways in which barriers could be dealt with and enablers could be strengthened. As big a
role that enablers and potential barriers play in online learning, how individuals respond to the shift
from traditional classroom learning to one online depends significantly on social behaviour. The
Theory of Planned Behaviour (TPB) by Ajzen (1991) links the beliefs of an individual to his
behaviour. (see Figure 2.1). The theory states that the behaviour of humans integrates a logical
planning and reasoning process. In simple terms, the intention to perform or not to perform does not
take place in humans randomly; rather it is influenced by three key factors, namely perceived
behaviour control, attitude, and subjective norms (Tornikoski&Maalaoui, 2019). Perceived
behavioural control refers to the perception of a person regarding the level of difficulties in enticing a
behaviour (Ajzen, 1991).
Figure 1. Theory of Planned Behaviour (Ajzen, 1991)
10

As discussed in sections 2.4.1 and 2.4.2, the barriers associated with online teaching and
learning are a lack of training material, incompetence resulting from online training of staff, lack of
technical support, and an absence of infrastructure and noise barriers. Similarly, widely agreed
enablers for online teaching are a variety of online content to grab student’s attention, choice of
assignments, variety of assessment options, and flexibility of the instructor. While on the surface it
appears that all of the barriers listed are beyond an individual’s control, it can be argued that they
belong to the ‘perceived behavioural control’ component of the TPB. As such, the individual’s
perception can very well turn an enabler into a barrier and negatively impact their behaviour.
2.5 Teachers' key characteristics
2.5.1 Self-efficacy
Self- efficacy is defined as the confidence possessed by an individual regading their ability to
accomplish a task. The concept of self-efficacy is acquired from Bandura’s social-cognitive theory of
behavioural change that reflects the belief and ability of teachers to successfully cope with the
obligations and challenges related to professional life (Pfitzner-Eden, 2016). The self-efficacy theory
was introduced by Bandura (1977) and pertains to an individual’s belief in their inherent ability to
behave in a way necessary to produce specific performance attainments. In other words, self-efficacy
is a person's belief in their ability to achieve objectives in a given situation (Bandura, 1977). People
who exhibit a high level of self-efficacy, show a high motivation and a low level of stress (Bandura,
1977).
There is a direct relationship between self-efficacy and behavioural change. This is important
to be studied in order to analyse the relationship between self-efficacy and teaching practice. Using a
survey of 120 EFL (English as a foreign language) pre-service teachers which was conducted in
Turkish university, Kavanoz et al. (2015) found that teachers’ self-efficacy is positively related to
their attitudes toward using web-based instructions. In addition, previous research suggests that
teachers with a high level of self-efficacy in using technology, web pedagogical, content knowledge,
and STEM integration considered themselves capable of implementing information and
communication technologies (ICTs) successfully in science, mathematics, engineering, and
11

technology courses (Smith et al., 2015). Thus, it seems reasonable to assume there is a direct link
between the attitude towards adopting web-based instructions and the ability to implement ICTs.
However, the number of teachers with a high level of self-efficacy in online teaching was very low.
This was found after conducting a descriptive of 1049 teachers in the three states, one state
representing each of the American Association for Agricultural Education regions (Smith et al.,
2015).
According to Nikolopoulou and Gialamas (2015), different sets of barriers, such as poor
technical knowledge and skills can impact teachers’ perception of their capabilities in a negative way.
Moreover, it has been implied that most teachers are not given sufficient time to prepare for their
online sessions which affect their confidence in delivering these sessions, especially in mathematical
subjects, hence impacting their confidence (Nikolopoulou & Gialamas (2015). Other barriers, such as
class conditions, lack of equipment, and lack of support were found to impact the use of technology
and teachers’ self-efficacy (Nikolopoulou&Gialamas, 2015).
It should be noted that when teachers exhibit low technical know-how, their self-efficacy will
be low, causing them to resist utilising technology for their teaching, thereby negatively impacting
students’ learning (Nordlöf, Hallström and Höst, 2019). Therefore, it is important that the problems
faced by teachers during online teaching are considered and effective strategies are provided to them
to deal with these problems. Based on the definition of self-efficacy, the four sources that help
teachers effectively deal with the problems in online learning are mastery experiences, vicarious
experiences, verbal persuasion, and physiological and affective states. Nurlu (2015) notes that
mathematics teaching self-efficacy is the belief of the teachers in their skills to teach mathematics
successfully. A high sense of teaching self-efficacy contributes to positive behaviour. Further, Zuya et
al. (2016) confirmed that self-efficacious teachers are open to new ideas and methods and exhibit a
willingness to accept innovation to motivate and promote learning.
2.5.2 Self-efficacy in relation to Technological Pedagogical and Content Knowledge (TPACK)
Many virtual classrooms promote digital spaces (Merchant, 2012; Rowsell et al., 2013), and
some teachers employ these and online technologies to alter the learning environment in various ways
12

(Hill, 2011). Online technologies, according to Allen (2011) and Ferriter (2010), offer novel
pedagogical delivery of educational content. There are elements, that influence the ways these digital
spaces are employed in virtual classroom teaching Vannatta& Fordham, 2004). Teachers' self-efficacy
in connection to technological capabilities had a major influence on their attitudes toward adopting
technology in their teaching practices (Rohaan et al., 2012). Rohaan et al. (2012) go son to say that
boosting teachers' TPACK knowledge will affect their self-efficacy beliefs, which could lead to more
technology use in the classroom.The concept of TPACK has evolved over time with the most
extensive descriptions of the framework appearing in Mishra and Koehler (2006, 2008) (see Figure
2.2). It states that teachers' knowledge is separated into three categories: content, pedagogy, and
technology.
Technological Knowledge (TK)
Any definition of technology knowledge is at risk of becoming obsolete due to the ever-
changing educational technology. However, there are certain ways to think about and use technology
that can be used with any technological tool or resource.In existing studies on TPACK (e.g., Schmidt
et al. (2009) &Zelkowski et al. (2013)), TK has been operationalised using survey items, such as "I
know how to solve my own technical problems.", "I can learn technology easily" and 'I keep up with
important new technologies."
Technological Content Knowledge (TCK)
TCK refers to knowledge of how technology and content interact and influence one another
(Mishra & Koehler (2006). Teachers must have a full awareness of how the subject matter (or the
types of representations that can be generated) can be affected by the use of various technologies in
addition to the subject matter they teach (Schmidt et al., 2009). In existing studies on TPACK (e.g.,
Schmidt et al (2009) &Zelkowski et al. (2013) ), TCK has been operationalised using survey items,
such as "I know about technologies that I can use for understanding and doing mathematics", "I know
about technologies that I can use for understanding and doing literacy" and "I know about
technologies that I can use for understanding and doing science."
Technological Pedagogical Knowledge (TPK)
13

TPK is the understanding of how certain technologies might alter teaching and learning in
certain ways. To develop TPK, a better understanding of the constraints and affordances of
technologies, as well as the disciplinary environments in which they work, is required. In existing
studies on TPACK (e.g., Schmidt et al (2009) &Zelkowski et al. (2013) ), TPK has been
operationalised using survey items, such as "I can choose technologies that enhance the teaching
approaches for a lesson.", "I can choose technologies that enhance students' learning for a lesson" and
"I am thinking critically about how to use technology in my classroom."
Technological Pedagogical Content Knowledge (TPACK)
TPACK is a sort of emergent knowledge that includes all three "core" components (content,
pedagogy, and technology); it is an understanding that emerges from interactions between content,
pedagogy, and technological knowledge. Figure 2 shows the TPACK framework. TPACK is the
foundation of effective technology-assisted teaching. In existing studies on TPACK (e.g., Schmidt et
al (2009) &Zelkowski et al. (2013)), TPACK has been operationalised using survey items, such as "I
can teach lessons that appropriately combine mathematics, technologies and teaching approaches", "I
can teach lessons that appropriately combine literacy, technologies and teaching approaches" and "I
can teach lessons that appropriately combine science, technologies and teaching approaches.
2.5.3 Roles of teachers’ key characteristics on their self-efficacy
().
14

Figure 2 TPACK framework (Harris, & Hofer, 2011)
Despite sweeping reforms, Saudi Arabia is still at its core a country built on values of social
conservatism (Adham et al., 2016). The knock-on effect of this is that the Saudi kingdom is still a
place where female identity can be a sensitive topic. According to Buabeng-Andoh, (2012) As the
pandemic changed the landscape of education, online learning became a global norm, and with this
came an ad hoc set of problems for Saudi Arabia. Female teaching staff and students are required to
partake in virtual learning; however, the use of video technologyis not straightforward to adopt in a
society where photography of females is still a cause for concern (Al Qahtani, 2011). This is because
video-recording a lesson(s) involves a teacher or instructor being on camera. Saudi women often
cover their hair and face. Whilst this trend is changing, the state of education in Saudi Arabia is still
largely government-controlled and as a result values tradition and conservativism over more
progressive and liberal ideas (Al Arfaj, 2001). This means that female instructors are less inclined to
turn on their webcams during online instruction.In fact,institutions, such as King Saud University
made it a policy to forbid female students and female instructors from turning on their webcams
during course instruction.
Garland and Martin (2005) noted workplaces which harboured greater concern for conformity
to behavioural standards were less likely to perform well in the delivery of online courses as opposed
to males. Nevertheless, it is important to research which aspects of online teaching invoke hesitancy
among female teachers in Saudi Arabia and how specifically those concerns can be addressed.
2.6 Roles of teachers' perceptions of instructional practices on their own teaching
According to a mixed-method study based on 102 prospective secondary school mathematics
teachers conducted by Mulenga and Marbán (2020), teachers' perceptions of digital learning play a
central role in online teaching of mathematics. Ulum (2021) suggests that to improve the efficacy of
15

online education, teachers' perceptions of online learning require appropriate instructional design and
the use of a wide variety of digital media. These can range from websites and programmes appropriate
to the subject, as well as various other online tools (Lin & Zheng, 2015). Their perceptionschanged
after using the online technological tools and platforms for education purposes and getting expertise
over it (Rahayu et al., 2020).
2.7 Roles of students’ voice
Students are one of the major stakeholders of education processes, so their voice is important
in the development of online teaching and learning experiences (Nthontho, 2017). Ever since the
pandemic forced long term shutdown of schools, and online learning became the new normal, the role
of students’ voice has become more important than ever. Giving students some sense of control in this
seemingly uncontrollable time, and keeping them meaningfully engaged in online classrooms could
make all the difference.
Online teaching and learning are found to be preferred more than face-to-face by students as it
enhances their learning experience by allowing them to interact with their teachers in any of the
asynchronous or synchronous environments with the help of using devices like laptops or mobile
phones with access to the internet (Nthontho, 2017). Online environment provides the opportunity for
students to interact with instructors in real-time, attend live as well as recorded lectures, ask queries
and get instant feedback from their supervisors on assignments which in turn increases their
motivation to learn, develop communication skills, and acquire good academic grades (Nthontho,
2017). Most of the Greek students in this study pursuing primary school education perceive online
teaching and learning to be more interesting than traditional learning because it allows them to ask
their queries anytime and access practice exercises, instructional videos, and lecture notes that
consequently improve their learning ability (Gialamas et al., 2013).
2.8 Research questions
On the basis of the above discussions, the current study sets out to address the following
three research questions:
16

● What online mathematics teaching and learning tools have been used during the global
pandemic by primary teachers and students in Saudi Arabia, and what are their
perceptions of these tools?
● What are the barriers and enablers that primary school teachers in Saudi Arabia
perceive as significant to their online mathematics teaching during the global
pandemic?
● Do Saudi primary school teachers’ self-efficacy concerning online mathematics
teaching differ according to their gender and years of teaching experience, and to
what extent their self-efficacy is influenced by these characteristics?
2.9 The study’s conceptual framework
Drawing from the relevant literature presented earlier in this chapter, Figure 2.3 sums up the
study’s underpinning theories and their relationship to each other, as well as the research focus on the
online learning tools and their use in online mathematics teaching and learning. Specifically, in
relation to the first research question (as stated in the previous section), It is framed by the work of
Skemp (1976) and Kilpatrick (2001), discussing the types of teaching and learning of mathematics
that lead to the different types of mathematical understanding. The focus of the second research
question is informed by Ajzen's (1985) Theory of Planned Behaviour (TPB) while the focus of the
third and final research question is framed by Bandura’s (1977) theory of self-efficacy and Mishra
and Koehler’s (2006) Technological, Pedagogical, and Content Knowledge (TPACK) framework as
well as the relationship between the
17

1

Methodology
Chapter
2

CHAPTER 3: METHODOLOGY
3.1 Introduction
The purpose of this chapter is to explain the research methodology that will be applied in this
study. It will start with a justification of the chosen research paradigm that underpins the design of
this study. The chapter will then discuss data collection methods that will be employed in this study.
Moreover, the chapter will explain the mechanism for determining the sample size, and how the data
will be analysed. Finally, validity, reliability, and ethical considerations will be considered. This study
will aim to answer the following research questions:
 What on-line tools were used by primary teachers for teaching mathematics during the
global pandemic in Saudi Arabia and their perceptions of these tools?
 What are the barriers and enablers that primary school teachers in Saudi Arabia
perceive as significant to their on-line mathematics teaching during the global
pandemic?
 Do Saudi primary school teachers’ self-efficacy concerning on-line mathematics
teaching differ according to their gender and years of teaching experience, and to
what extent their self-efficacy is influenced by these characteristics?
3.2 Adopted research philosophy
Research philosophy can be defined as “a system of beliefs and assumptions about the
development of knowledge (Saunders et al., 2019, p. 130). Creswell and Clark (2017) argue that all
types of research start with a philosophical basis, and researchers should be aware of the assumptions
that they make in order to gain knowledge during their studies. The underpinning research
philosophies will enable researchers to understand their research position and it will determine the
3

research process (Creswell & Clark, 2017). According to Saunders et al. (2019), the researcher will
make a number of assumptions about reality and knowledge at each stage of the study process. These
assumptions then will lead to the chosen research philosophy which will lead the research process.
The assumptions of the research philosophy, such as ontology and epistemology will now be
discussed.
3.2.1 Ontology
Ontology should be a part of any research project. A set of beliefs about the "nature of
reality" is referred to as "ontological assumptions" (Saunders et al., 2019, p. 127). The important
factor in oncology for scientific investigation is the way in which it influences people’s assumptions
concerning reality, for instance the nature of mind and scientific findings, and the way in which a
phenomenon under investigation is thought about and examined (Blaikie& Priest, 2019; Scotland,
2012).
A wide range of ontological perspectives exits, but this study focuses on two prominent ones:
positivism and interpretivism, which are also known as: objective which means quantitative research
and subjective which means qualitative research (Maarouf, 2019). The former is concerned with the
existence of facts (Bryman, 2016; Zyphur&Pierides, 2019) and is linked to realism (Zyphur&Pierides,
2019).
The latter assumes the existence of only one true truth that is represented in reality and
producing an empirical evidence when investigating reality is restricted to the use of certain reliable
and valid tools (David & Sutton, 2011). Salvador (2016) defines realism as a component of
positivism's ontological philosophy, which is based on comprehending the nature of scientific
practise; Blaikie and Priest (2019) give a similar description. Some academics, such as Donnelly
(2019), argue that realism is multifaceted, dependent on claims, acts, explanations, and results, and
4

hence lacks a core definition. Interpretivism, which is linked to relativism, emphasises how one's
personal perspective shapes reality as a result of interaction (Scotland, 2012).
As a result, there will be no one truth since the participants will construct it for themselves
and reality will be seen through the eyes of every participant (Coe, 2017). The ontological perspective
of the current study contains both interpretivism and posivtism as the research topics are consistent
with various philosophical viewpoints. For instance, the aim of research questions one and two will be
to investigate a realistic situation by looking for online tools used in teaching elementary mathematics
and learning about the challenges that teachers and students face in using these tools, as well as the
enabling factors that contribute to their use. The third research question was developed to look into
teachers' perceptions of online tools used in mathematics instruction, as well as the extent to which
years of teaching experience, gender, and self-efficacy influence those perceptions, and to adopt the
viewpoint that individual experiences and knowledge are explanatory, and a single fact will be
unable to present them.
3.2.2 Epistemology
The research's philosophical foundations, or epistemology (McGannon et al., 2019), are
concerned with how and where knowledge is generated (Biddle &Schafft, 2015; Cohen et al., 2017).
Understanding the way knowledge is acquired is Epistemology's main purpose (Scotland, 2012;
Bryman, 2016). Bacci (2019) states that Epistemology is linked with the way knowledge can be
formed by what people can see rather than just on statistical fact. It is worth noting at this point that
the current investigation is divided between two primary epistemological positions: subjectivism and
objectivism. Scotland (2012) considers that
Objectivist epistemology attracts objectivity, which asserts that "the researcher and the researched are
independent entities" (p.10), and that the truth is independent and is obviously determinative (Shaw
5

&Selvarajah, 2019). Second is, according to (Scotland, 2012; Seth, 2014) Subjectivist epistemology,
which is founded on relativism. This idea claims that knowledge originates through our interpretations
and interactions, rather than existing independently of what we already know (Scotland, 2012).
Furthermore, this epistemological perspective facilitates the development of individual understanding
of the research problem (Matney, 2019).
The epistemological perspective of the current study incorporates both objectivity and
subjectivity. Objectivity is employed to analyse the effects of instructors' self-efficacy, years of
teaching experience, and gender on their capacity to effectively use these tools in order to answer the
third study question. The investigation will be conducted using quantitative approaches
(questionnaires). The current study assumes that each participating teacher and student will have
different applications and opinions about the use of online tools for teaching mathematics at the
primary level, as well as their perceptions of the obstacles and enabling factors they will face, in
response to the first and second research questions. As a result, explanations can be used to acquire a
better understanding of the current study (Scotland, 2012), revealing that reality can be formed by
various people from various perspectives.
Despite the advantages listed above, there are drawbacks to interpretivism. One of these
limitations is that interpretivists prefer to gain a deeper understanding and knowledge of phenomena
within the context’s complexity rather than generalise their findings to other people and contexts
(Cohen et al., 2011), which leaves a gap in verifying the validity and utility of research findings using
scientific procedures. The second criticism of interpretivism is that it has a subjective rather than an
objective ontological viewpoint (Mack, 2010). As a result, research findings are unquestionably
influenced by the researcher’s personal interpretations, belief systems, methods of thinking, or
cultural preferences, potentially resulting in several biases.
3.2.3 Pragmatism
6

Kankam (2019) claims that pragmatism entails "joined behaviours and shared meanings"
(p.86). Robson and McCartan (2016) defined the pragmatic paradigm as a practical rather than a
theoretical method to deciding the best way to address a research challenge. This study benefits from
the use of pragmatism as a paradigm because it helps to circumvent the contradiction between
interpretivism and positivism by including a variety of research methods (i.e. qualitative and
quantitative). These many points of view can help to improve the possibilities of gaining a thorough
answer to the study's questions. Furthermore, pragmatism improves the design by emphasising the
positive aspects of each technique while minimising the negative aspects. This is accomplished by
combining two forms of research (quantitative and qualitative; Feilzer, 2010; Creswell, 2014),
resulting in a triangulation aspect in the current study.
The goal of this study is to find out what online resources are utilised in Saudi primary
schools to teach and learn mathematics, as well as what variables impede or facilitate their usage, as
well as the extent to which self-efficacy and gender play a role. As a result, the pragmatic viewpoint is
appropriate for the study since it allows for a greater comprehension of truth and acceptance of
dualism (e.g., blending idealism with realism; see Brock & Mares, 2014; Creswell, 2014). The
validity of the results gained from the questionnaires is supported in the current study by data
acquired via classroom observation and the semi-structured interviews with teachers and students,
resulting in rich and thorough results.
3.3 Research design: Mixed methods
As pragmatism is a popular basis for mixed methods research, a number of academics and
thinkers (Tashakkori&Teddlie, 2003; Cohen et al., 2017) have endorsed the link between pragmatism
and mixed methods research.According to Mackey and Gass (2016), mixed-methods design is defined
as the association of qualitative and quantitative research (Bryman, 2016). It explores and answers
questions using both qualitative and quantitative approaches and beliefs (Cohen et al., 2017). Mixed
7

methods research, according to Bryman (2016), entails not only integrating two research
methodologies—qualitative and quantitative—but also offering a comprehensive grasp of the study
challenges.
There exist four types of mixed methods, and they are triangulation design, embedded design,
exploratory design, and explanatory design.
Firstly, the triangulation design is also known as simultaneous triangulation (Doyle et al.,
2009). According to Denzin (1987, p. 291) triangulation is “the combination of methodologies in the
study of the same phenomenon”. Methodological triangulation involves applying both quantitative
and qualitative techniques at the same time in order to collect the data (Bishop & Holmes, 2013;
Creswell & Clark, 2017; Doyle et al., 2009). In triangulation research design, both methods are given
equal weight. According to Dzurec and Abraham (1993), qualitative and quantitative studies are both
used in order to understand the research under study. For example, the qualitative data will add more
depth to the collected quantitative data and will provide more in-depth explanation of the findings of
the quantitative data (Dzurec& Abraham, 1993).
Secondly, the embedded design is a mixed method design in which one data set supports a
study that is predominantly based on the other data type (Creswell et al., 2003). This design is
employed when researchers need to include qualitative or quantitative data in a predominantly
quantitative or qualitative study to address a research topic. At the design level, the embedded design
combines different data sets, with one form of data embedded within a technique structured by the
other data type (Kanga et al., 2015). The embedded design that includes qualitative data in a
quantitative design helps to explain the results of a correlation model and it can be done either
concurrently or sequentially.
Thirdly, the exploratory design is a sequential type of design where the qualitative stage is the
first in the development of the quantitative stage (Bishop & Holmes, 2013). It is used to develop and
test tools and classification (Creswell & Clark, 2017).
8

Finally, the explanatory design consists of two stages. The first stage starts with collecting the
quantitative data, and thereafter the qualitative stage will begin. The goal in here is to explain or
improve the quantitative results (Creswell & Clark, 2017; Bishop & Holmes, 2013).
There are advantages and limitations of using mixed methods approach to research.
According to Bryman (2006), triangulation, completeness, balancing weaknesses and providing
stronger conclusions are among these advantages. For instance, triangulation enables the research to
have a high level of credibility by supporting the results of quantitative methods with qualitative
methods or vice versa Carvalho & White, 1997). Moreover, it will enable the study to show more
comprehensive analysis of the phenomenon under investigation (Bryman, 2006), because it presents a
variety of data sets in different ways to explain different aspects of a phenomenon of interest. Using
the mixed method approach will allow the researcher to balance the weakness and the limitations of
each approach and build a stronger and more accurate conclusions (Creswell, et al., 2013). According
to Creswell and Clark (2017), by employing a mixed method approach, the research will be able to
answer a variety of research topics. This strategy will help in providing solutions to the research
problems which cannot be addressed by using either qualitative or quantitative methods alone. Since
both the qualitative and quantitative research will be used, each will enable a better clarification of the
results by drawing better conclusions for the problem under investigation.
Although the mixed methods approach has significant number of advantages, there are some
limitations to its use. Doyle et al. (2009), for example, argue that using mixed approaches might lead
to inconsistencies between two types of outcomes. This is due to the fact that quantitative and
qualitative approaches rely on different sets of ontological and epistemological assumptions.
Furthermore, it has been suggested by Johnson and Onwuegbuzie (2004) that conducting mixed
methods research by a single researcher may be problematic. This is especially true if quantitative and
qualitative phases must be conducted simultaneously. In addition, sequential studies require more
time and consume large resources in order to carry out each distinctive stage (Doyle et al., 2009).
9

The triangulation approach was chosen for this study because of the nature of the research
questions, which are directed at two groups of people: teachers and students. Adopting both
quantitative and qualitative approaches to generate more accurate results and a better understanding
(Creswell, 2014). Furthermore, by achieving findings in two different ways (quantitative and
qualitative), the two methodologies' flaws are overcome (Creswell, 2014; Scott et al., 2015).
3.4 Sample sizes and sampling strategies
3.4.1 Sample sizes
A sample is a group of people picked at random or in any way that is appropriate to select
sample size from the general population for the purpose of a research study (Salant&
Dillman,1994). However, more often researchers face significant challenges in determining
their sample size(Cohen et al.,2017). Hence, there are a set of factors that help determine the
sample size. The goal of the study, the research questions, and the research design, for
example, all play a role in establishing the size of the sample required for the study (Cohen
et al.,2017; Salant& Dillman,1994).
3.4.1.1 Quantitative stage
It has been argued that for quantitative research, a larger sample size is preferable
since this will provide a higher level of reliability and credibility (Cohen et al., 2017). In
educational research, Choen et al. (2011, p. 144) argued that a “sample size of 30 is held by
many to be the minimum number of cases if researchers plan to use some form of statistical
analysis on their data”. However, there is a need for a careful consideration when deciding on
the sample size. For example, the accuracy of the estimation of the size of the population, and
10

the variance between them (The population's heterogeneity) are important factors to be taken
in consideration (Denscombe, 2014).
For the purpose of this research, the target population is mathematical teachers and all
students in grades 4th, 5th and 6th in Jeddah in Saudi Arabia, for more detail see table 3.1.
According to Al-Ghamdi (2021), currently there are 1,772 mathematical teachers in primary
schools, of which 978 are male and 794 are female teachers. As for the student population
which group aged 8-10 years, according to Al-Ghamdi (2021), they are 125,540 students.
This age group is the main level in Saudi primary school, and they are more cognitively
advanced than the early grades, so this study focuses on them.
To calculate sample size from these populations, there are many websites indicated by
cohen et al. (2017) that can calculate sample size which of them (e.g.,
www.macorr.com/ss_calculator.htm). this website was used by this study to determine the
sample size of the qualitative method. Denscombe (2014) stated that researchers need to be
confident in the degree of accuracy, as the sample must be representative. The level of
confidence is usually 95% or 99% (Cohen et al., 2011). Moreover, confidence intervals are
also needed. A confidence interval is the accurate and adequate margin of errors (Black,
1999). Confidence intervals of five were chosen in this study. This study has less variation
within the population because its sample is bigger. Based on this information from the
formula adopted, the required sample size for the quantitative phase for 383 student and 316
teachers. It has been noted by Cohen et al. (2017) that researchers should overestimate their
sample due to non-responses factor from prospective participants. Hence, for the purpose of
this study, the researcher aims to invite 400 potential participants for each (i.e., teachers and
children in primary schools) to complete the questionnaire.
11

Table 3.1
Sample Size of teachers
Table 3.2
Sample Size of studentsl
3.4.1.2 Qualitative stage
According to Baden and Major (2013), for qualitative research, it is recommended to apply a
smaller sample size so that informational redundancy could be avoided. This is determined by a
number of factors, including the research topic, as well as time and cost constraints. Although in
qualitative studies the sample size depends on "saturation” (this mean, the researcher cannot get more
12
TotalFemaleMaleGender
1772794978Total
100%44.81%55.19%Percentage (%)
316.00142.00174.00Sample Size
TotalFemaleMaleGender
1255406252963011Total
100%49.80%50.19%Percentage (%)
383.00191.00192.00Sample Size

or new information from population (Saunders et al., 2018)), which is necessary to investigate the effect
of a certain amount of information power (the more information the sample has that is relevant to the
study, the fewer the participants needed), it has been suggested that there are no similar criteria for
evaluating the sample size in qualitative studies (Malterud et al., 2016; Mertens, 2014). As it has been
indicated abovethat this study will be using a mixed methods approach, where both qualitative and
quantitative techniques will be carried out at the same time. The qualitative technique will collect data
through semi-structured interviews with teachers and targeted students as well as non-participant
observations in order to obtain more in-depth insights into on-line teaching and learning tools in
primary school.
The semi-structured interviews will be conducted with eight teachers (four male and four
female teachers) who have different interval years of teaching experience, for example from less than
9 years, 9-18, 19-28, and more than 28 years so that each interval has two teachers of a different
gender. This will ensure equal representation from each gender. These four age intervals were
determined according to the statistical life span of education of Saudi teachers. For instance, in Saudi
Arabia, students graduate at the age of 23 years old and retire when they reach 60 years old (General
Organization for Social Insurance, n. d.), totalling a maximum of 37 years of teaching experience.To
determine the sample size for the observation, there are four categories of years of teaching
experience and two teachers’ genders (4*2 = 8 teachers) and 16 students (eight boys with two boys
from each of the four male teachers’ classes, and eight girls with two girls from each of the four
female teachers’ classes).
3.4.2 Sampling strategies
According to Oppong (2013), sampling is considered as a process for selecting appropriate
participants in order to be part of the study under investigation. Moreover, it has been suggested by
Cohen et al. (2017) and Oppong (2013) that it might not be possible to collect all the information out
there to reach the objectives of the research. Hence, the concept of sampling refers to selecting a small
13

subset of the target population Cohen et al., 2017). There exist two different key types of sampling
methods that researchers can follow i.e., probability and non-probability sampling (Cohen et al.,
2017). This means that with probability sampling, every member of the population has a fair chance
of being selected, whereas with non-probability sampling, this is not the case as (Cohen et al., 2017;
Creswell & Clark, 2017). The sampling strategy for the quantitative and qualitative studies will be
discussed in the following sections.
3.4.2.1 Quantitative stage
It has been suggested that when the purpose of the research is to make generalisations, then
probability sampling should be chosen (Cohen et al., 2011). The strategy is the plan that is set forth to
be sure that the sample is used in the research study represents the population from which is drawn the
sample (Cohen et al., 2017). Probability sampling is most commonly employed in survey research,
where the researcher will be able to deduce information about a target population from the sample in
order to answer the research question (Saunders et al., 2019).
The probability sampling technique will be employed in this study. In order to choose a
suitable sample for this research, simple random sampling procedures – a sub-type of the probability
sampling technique - will be used. According to Cohen et al. (2011, p. 153), when using simple
random sampling, “each member of the population under study has an equal chance of being selected
and the probability of a member of the population being selected is unaffected by the selection of
other members of the population”.
Simple random sampling has a number of advantages, including the fact that all members of
the population have an equal and independent probability of being chosen. While this method is
employed alongside all other probability sampling schemes, it is the foundation for all random
sampling methods. Furthermore, it is the most straightforward and straightforward method of putting
all possible plans into action. As a result, it is thought to be the least biassed sampling approach. This
sampling strategy, on the other hand, has significant disadvantages, such as the need to know and
14

define the complete population. Furthermore, assigning a unique label to each member of the
population is inconvenient.
3.4.2.2 Qualitative stage
Sampling in most qualitative research uses non-probability sampling methods (Cohen et al.,
2017). In this type of sampling, selecting the participants depends on the researcher targeting a
specific small group from the wider population (Cohen et al., 2011). Cohen et al. (2017) explained
that in most qualitative research the focus is on the uniqueness as well as the exclusive and subjective
distinction of the phenomenon or individuals selected to participate. This indicates that these
participants will represent themselves only and their findings cannot be generalised. In the context of
this study, the purposive sampling technique – a sub-type of the non-probability sampling technique -
will be applied to select participants for the qualitative stage. Here, the researcher will “hand-pick the
cases to be included in the sample on the basis of their judgement of their typically or possession of
the particular characteristics being sought” (Cohen et al., 2011, p. 156). The aim is to provide more
detailed and in-depth information regarding the problem under investigation (Gall et al., 2007).
According to Oppong (2013), applying purposive sampling requires the classification of the subjects
(i.e., participants) according to a pre-determined set of criteria (such as mathematical teachers). This
implies that individuals in this sample will be selected by the researcher based on what they possess
that is richer and more accurate than others. so, will include dividing the whole target population into
groups that are homogenous with similar characteristics, such as gender (Cohen et al., 2011). In the
context of this study, teachers will be divided into two groups, one for male teachers and the other for
female teachers. According to Cohen et al., (2017), in order to group the target population into groups,
there are two stages that should be followed. First, the researcher should outline and determine the
characteristics of the wider targeted population that should be included in the sample. Second, the size
of each group of the sample should be determined either based on the researcher’s logical judgement
15

or other statistical techniques. In this research, these characteristics will be based on gender and the
number of years of teaching experience.
According to AUTHORS, purposive sampling is cost effective method and also helps in
saving time. This sampling also helps in avoiding repetition query for each and every individual.
However, AUTHORS found that purposive sampling increases the vulnerability to errors when
judgement is being made by the researcher. AUTHORS state that one of the limitations of purposive
sampling is that it provides low levels of reliability. The authors also argued that there is high level of
bias in it. But according to AUTHORS purposive sampling assists the researchers to obtain maximum
amount of information out of the collected data.
3.5 Data collection methods
3.5.1 Questionnaire
A questionnaire is a research tool that contains a variety of questions or other types of stimuli
intended to collect information from the respondent. A research questionnaire is usually a mixture of
closed-ended questions and open-ended questions. (Cohen et al., 2017). Open-ended questions allow
participants to provide answers with their own words and from their own perspective. Closed
questions, on the other hand, provide participants with “a number of alternative answers from which
the respondent is instructed to choose” (Saunders et al., 2019, p. 452).
One of the advantages of using questionnaires is that it provides wide coverage of members of
the population compared to other areas such as observation and interview. Moreover, this method of
collecting data is considered to be cost effective, trustworthy, valid, and simple to complete (Cohen et
al., 2017). This is done through the use of qualitative questionnaires such as open-ended questions and
quantitative such as closed-ended questions questionnaires to collect explanatory information to
answer the research questions that were created earlier. In addition to the freedom of the respondent to
16

withdraw at any time he wants, and to hide personal data, which gives him the confidence to answer
honestly.
On the contrary, there are some disadvantages of using questionnaire to collect data.
According to Wright (2017) when collecting data through questionnaire, there some issues with the
sample. For instance, if the data will be collected through a self-reported questionnaire, then
participants may not provide accurate information regarding their characteristics and demographics.
Moreover, it has been argued that researchers will be facing the self-selection bias issue when
collecting data through questionnaire (Thompson et al., 2003). Self-selection bias appear when
participants are given the freedom to participate in the survey (Lavraks, 2008). Self-selection is the
average response probability, and is the covariance between the values of the target variable and the
response probabilities in the Internet-population. There are two types of bias: one created by
interviewing only the Internet population rather than the entire target audience (under-coverage bias)
and the other induced by respondents in the Internet population self-selecting (self-selection bias)
(Bethlehem, 2010).
According to Cohen et al. (2017), one way that degrees of response, intensity of response, and
the shift away from dichotomous questions and rankings have been managed is through the use of
rating scales. Likert scales are useful scales for researchers because it incorporates a degree of
sensitivity and differentiation of response. A Likert scale (named after its creator, Rensis Likert, 1932)
allows for a variety of responses to a question or statement. The categories must be distinct in order to
cover the entire range of possible responses that respondents may choose to provide (Cohen et al.,
2017).To provide alternatives for responses to the questions, the current questionnaire will use a five-
point Likert scale (strongly agree to strongly disagree). The following were the scores for each
statement’s responses: 1 = strongly disagree; 2 = disagree; 3 = undecided; 4 = agree, 5 = strongly
agree.
There has been a lot of research done on Likert scale items or categories, and there have been a
lot of seemingly contradicting results. Guilford (1954), for example, claimed that determining the
17

ideal number of categories is a matter of empirical decision based on the context. The number of scale
points utilised for the items has no effect on the instrument’s reliability and validity, according to
Mattel and Jacoby (1971, as cited in Croasmun&Ostrom, 2011).
3.5.1.1 Questionnaire for teachers
The current teachers' questionnaire will be divided into four sections. The first section
will include questions concerning participants’ demographic data (i.e., their years of teaching
experience and gender). The second section will consist of eleven open-ended questions all
related to the first research question, which is about on-line mathematics learning and
teaching tools. The third section consists of two open-ended questions related to the second
research question, which is about enabling factors and obstacles that help or limit on-line
mathematics teaching and learning in primary schools. The fourth section contains 24 closed-
ended questions, and four open-ended questions, they are related to the third research
question about measuring the influence of the teacher's gender and years of teaching
experience on their self-efficacy to use technology in their on-line teaching. the closed-ended
questions are divided into four parts (e.g., the first part related to Technological Knowledge
(TK), the second part related to Technological Pedagogical Knowledge (TPK), the third part
related to Technological Content Knowledge (TCK) and the final part concerned the
Technological Pedagogical Content Knowledge (TPACK). these questions have been taken
from Schmidt, (2009) and Zelkowski, (2013) and modified the questions to be appropriate for
this study. For example, the question "I know how to solve my own technical problems" has
been modified to be "I am confident in solving my own technical problems during my on-line
mathematics lessons"(see Appendix A).
3.5.1.2 Questionnaire for children
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For children's questionnaire, because children’s cognitive capacities differ from adults, adult
studies cannot simply be applied to children (Van Laerhoven et al., 2004). Children from the age of
eight years are seen to be capable of providing credible reports on their well-being (Landgraf, 1996;
Rebok et al., 2001). Therefore, a questionnaire will be designed for children using words that can be
easily understood and related to the first and second research questions.
Building on the previous discussion about the teacher questionnaire, this study will adapt the
teacher questionnaire to suit students, changing the words of teaching to learning and discourse from
teachers to students.
Likert scales have been used in a lot of research projects with kids (Mellor & Moore, 2014).
Response scales usually include three to five response points. The Strengths and Difficulties
Questionnaire (Wolfe, 1996), for example, is based on a 3-point response scale, as is the Children's
Impact of Traumatic Events Scale-Revised (Wolfe, 1996). (Goodman, 1997). This research will
employ a fifth Likert scale on a children's questionnaire as used in the teacher's questionnaire, so the
findings from both teachers and children are easily comparable.
As for the questionnaire for children, it was built on the basis of the teachers' questionnaire,
taking into account the simplification of the language in line with their understanding. The
questionnaire consists of three sections. The first section contains questions about their demographic
data e.g., The grade class of study in which they are studying and their gender. The second part
consists of four open-ended questions all related to the first research question about on-line
mathematics learning tools. The third section consists of four as well open-ended questions, and they
are related to [the second research question which is about barriers and enabling factors of on-line
learning.
3.5.2 Semi-structure interview
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.. There exist different types of interviews. According to Mathers and Hunn (1998), questions
for structured interviews are planned and written ahead of time. In a structured interview, all
candidates are asked the same questions in the same order, whereas in an unstructured interview, the
interviewer asks questions that have not been prepared in advance. Instead, in a free-flowing dialogue,
questions develop spontaneously, which implies that various candidates are asked different questions.
In a semi-structured interview, the interviewer just asks a few predefined questions while the rest of
the questions are unplanned (Mathers& Hunn,1998).
The current study will be using the semi-structured method with eight teachers and four
students.This is because the order of the questions can be semi-fixed depending on the participants’
answers. Hence, there exists some kind of flexibility, unlike with close-ended questions. Moreover,
depending on the received answers, the interviewer will have the ability to ask additional questions
which are not determined before the conduct of the interview (Cohen et al., 2017; Privitera&Ahlgrim-
Delzell, 2018).
Semi-structured interviews are not without some limitations. For example, the interviewees
may only divulge what they are willing to reveal regarding their impressions of events and ideas
(Walford, 2007). As a result, such reactions could be a long way from "reality". “Interviews alone are
an insufficient source of data to research social life,” Walford (2007, p. 147, as cited in Alshenqeeti,
2014) claims. That is, both the interviewer and the interviewee may have insufficient information or a
mistaken recall. Furthermore, huge volumes of information are expected to be divulged through
interviews. As a result, we should take the advice of Scheurich (1995, p. 249 as cited in Alshenqeeti,
2014), who emphasises the need of interviewers to concentrate on the main points in the research
questions that must be obtained from the interview. Furthermore, interviews have been criticised
(Robson, 2002) as time intensive in terms of data collection and analysis because they must be
transcribed, categorised, and perhaps translated.
In the context of this study, the interview questions are grouped under three sections to clearly
mirror the focus on the study’s three research questions (see Appendix _). The
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The interview questions will be based on instruments from previous research (e.g., Kamble et
el., 2021; Thomson, 2010). These instruments will be modified in order to be consistent with the
variables that will be used in this study which are on-line tools, barriers and enablers of on-line
education, role of gender and years of teaching experience to use these on-line tools. In this tool,
nine questions were divided into three groups equally, as each group consists of three questions and
relates to the three research questions. The interview questions contained in Thomson (2010) and
Kamble et al. (2021) are relied on, and the vocabularies of mathematics and on-line tools were added
to the questions in order to be suitable for this study (see appendix D).
The current study’s semi-structured interview que is based on the interview questions
contained in my study by Kamble et al., (2021) and Thomson, (2010). The semi-structured interview
questions were derived for this study, and these questions were divided into three sections, each
section related to the three research questions. The details are as follows:
The first section relates to the first research question, which consists of three questions. For
example, the second question is adapted from Thomson (2010): "How has online learning changed in
the past several years, with the availability of new technologies such as virtual classrooms,
whiteboards, blogs, video podcasts, etc.? Are these technologies covered in your course?What are the
benefits and challenges of the various technologies (for you and/or for your students)? What tools for
teaching and learning mathematics are currently available for teachers in on-line mathematics
teaching?
The second section also consists of three questions related to the second research question.
For example, is adapted from the Kamble et al., (2021) study question "Did the present social
situation and characteristics in the country discourage learners from participating in the online
sessions?" to become, "Does the current social situation in Saudi Arabia help or hinder teachers and
students from participating in teaching mathematics online?" Why?
21

The third and final section also consists of three questions related to the third research
question. For example, is adapted from the study of Kamble et al., (2021), "What were your
experiences transitioning from a face-to-face learning environment to an OLE?" to become, "What
experience did you gain from years of experience in teaching mathematics in the traditional learning
environment that helped you move to teaching mathematics online?"
3.5.3 Non-participant observation
Another way to collect qualitative data is through the use of observations. This observation
will be used to address all three research questions. Observations allow the researcher to assess
interactions in a social setting and make systematic records of them in a variety of forms and
situations, which can be used to supplement other types of data (Cohen et al., 2017).
.
However, this study may face some limitation by using observations. Due to cultural barriers in
the Middle East and specifically in Saudi Arabia, it will not be feasible to observe live on-line
sessions of female participants. Hence, to ensure equality between the samples, the researcher is
restricted to access the recorded sessions of on-line lessons. To overcome this problem, the researcher
will ask to record the lessons held by the females, and male then they will be observed later.
The advantages of this method are to save time, in addition to providing a list of online tools
used in teaching mathematics at primary schools and some enabling factors and barriers based on
what is mentioned in the literature (Zhang, 2003).
The current study will be using synchronous On-line Mathematics Teaching Observation
Checklist developed by Hunter the City University of New York (2020) for primary schools in Saudi
Arabia. The observation will consist of four main sections, and each section will consist of a set of
22

criteria according to The City University of New York. (2020). For instance, the first section will be
about an instructional design and contains seven criteria. The second section will be related to the
learning environment and time management, and it will include four criteria. The third section will be
related to students’ engagement, and it will include eight criteria. The final section will be related to
assessment and feedback, and it will contain three criteria. The three sections relate to the three
research questions (see Appendix C).
Observations will be conducted after collecting the on-line questionnaires and conducting the
interviews. More specifically, by observing the recoded on-line sessions of the lesson, the researcher
will have the ability to determine which on-line mathematics tools teachers and student are using
these, and also to determine the challenges and the obstacles that face teachers will be identified and
the methods that are being applied to overcome these obstacles will be observed.
.
Due to cultural barriers in the Middle East and specifically in Saudi Arabia, it will not be feasible
to observe live on-line sessions of female participants. Hence, to ensure equality between the samples,
the researcher is restricted to access the recorded sessions of on-line lessons. To overcome this
problem, the researcher will ask to record the lessons held by the females, and male then they will be
observed later.
3.6 Pilot study
During the pilot study, the questionnaire will be distributed to a small group of participants
(i.e., teachers and children), around 40 participants of the actual participants sample as 10 children
and 30 teachers (15 male teachers and 15 females’ teachers), In order to ensure that the questions are
formulated in a clear way and are free from any errors.The minimal number of participants for pilot
research, according to Saunders et al., (2009), is ten.
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Moreover, a pilot study will be carried out in the format of semi-structure interviews with two
teachers one of the male teachers and the second will be female teachers in order to ensure that the
interview instrumentand questions are clear, and valid. In addition, during the pilot phase, the
researcher is intending to observe two on-line lessons one of them male teachers and the second will
be female teachers and follow the checklist mentioned above in order to avoid any complications
during the actual observation phase.
3.7 Data analysis
3.7.1 Quantitative data analysis
There exist two types of statistics, and they are descriptive and inferential statistics.
According to Cohen et al. (2017) descriptive statistics only describe the state of the population and
the sample in terms of range, median, mean, and standard deviations. However, this type of statistics
cannot provide any predictions or explanations for the study under investigation. On the other hand,
inferential statistics (such as aONE-WAY NOVA test) enable researchers to make broader inferences
about a population
The quantitative data which will be collected through questionnaires will be analysed using
quantitative analysis. More specifically, for the first research question, (which is concerned with
identifying what on-line teaching and learning tools have been used during the global pandemic by
primary school teachers and children in Saudi Arabia)will be analysed by using descriptive statistics.
As for the second research question which is concerned with identifying barriers and enablers
that primary school teachers in Saudi Arabia face in their on-line teaching and learning during the
global pandemic, it will be analysed by descriptive the arithmetic averages .
Finally, the third research question ("Do Saudi primary school teachers’ self-efficacy
concerning on-line mathematics teaching differ according to their gender and years of teaching
experience, and to what extent their self-efficacy is influenced by these characteristics?”) sets out to
24

test the association between gender and years of teaching experience (the independent variables) and
self-efficacy (the dependent variable). Since the sample is large, all the statistical tests will follow the
parametric tests and there is no need to use the normal distribution tests (Field, 2018). According to
Ross (2017), the central limit theorem (CLT) states that as the sample size grows higher, the
distribution of sample means approaches a normal distribution, independent of the population's
distribution. Therefore Field (2018), explained that for the CLT to hold, sample sizes of 30 or more
are frequently considered sufficient. Finally, a multiple linear regression will be used in order to
estimate the effect of the independent variables on the dependent variable. This study will be using
SPSS software in order to perform all the above mentioned statistical tests.
3.7.2 Qualitative data analysis
There exist different types of analysis techniques that can be used when analysing qualitative
data, so that this study will be using one of them which is thematic analysis in order to analyse the
qualitative data to be collected through responses to open-ended questionnaire questions, semi-
structured interview responses, and observation notes.
Thematic analysis, on the other hand, is defined as “a method for identifying, analysing and
reporting patterns within data” (Braun & Clarke, 2006, p. 79). It is a thorough examination that
includes coding and the identification of primary themes and sub-themes.
This study will first start with transcribing the interviews data into a written text, and
thereafter translate the collected data from Arabic into English. This is study will rely on when
translating the texts of the semi-structured interview from Arabic into English With the help of
bilingual experts, as Yu et al. (2004) emphasized that the use of bilingual experts helps to ensure the
translation of texts from one language to another. Thereafter, the transcripts will be transferred into a
software which is called Nvivo in order to analyse the qualitative data.
25

The analysis process of the qualitative data will start with coding which can be defined as the
process of collecting evidence and classifying ideas which will expand on the researcher’s perspective
(Cohen et al., 2017; Creswell & Clark, 2017). According to Bogdan and Biklen (2003) qualitative
analysis can be seen as a process of systematic review in bringing together research evidence to assist
us better understand what works and inform our practise. A qualitative study reinforces and gives
strength to the results of a quantitative study. Classifying the data into themes and patterns will
provide more in-depth knowledge and understanding of the research problem. Braun and Clarke
(2006) identify six practical steps that should be followed before, during, and after the thematic
analysis stage which are: identifying the data, generating meta-codes, researching, reviewing,
identifying and naming topics, and producing a report. Thereafter, the coding process which consists
of dividing the texts into small unites and assign a code for each unit will be applied. Then, these the
generated codes will be grouped into different themes.
.
According to Privitera and Ahlgrim-Delzell (2018) as technology grows and becomes easier,
other types of visual data appear in qualitative work such graphics, images, and films. Visual data can
be useful because it can record individual’s behaviour in a natural setting while at the same time retain
it for examination by others. Since one of the limitations of collecting the qualitative data is observing
the live on-line sessions with female teachers, the use of video recordings will help the researcher to
replay these sessions as needed when coding and analysing the data (Privitera&Ahlgrim-Delzell,
2018).
This study will use NVivo software in this stage because, it has proven to be a wonderful
resource (Hilal&Alabri, 2013). NVivo can manage vast amounts of data, including more than 20
hours of transcripts, according to Hilaland labri (2013). Data can be coded more liberally than with
“paper and pen” approaches, and while this most likely results in over-coding (a problem identified by
Blismas& Dainty, 2003), it allows thoughts and issues to arise more freely without the need to force
data into pre-determined categories. Another nice benefit of the software is that categories and nodes
26

may be altered or reshuffled at any time, allowing old data to be easily moulded to fit into the
evolving framework when new data re-focused the study. The ability to reproduce and distribute
discoveries is a final point to consider when considering the value of software; it is critical to keep all
stakeholders informed of all advances. The software enables for easy copying and dissemination by
CD-ROM or e-mail. With a typical “paper and pen” system, this capability would be incredibly
difficult to achieve.
3.8 Validity and reliability
The validity and reliability of the study should be considered by the researchers, as Cohen et
al. (2017) have demonstrated that threats to validity and reliability cannot be completely eliminated;
however, the effects of these threats can be mitigated by paying attention to validity and reliability
throughout the research.In this following sub-sections, validity and reliability will be discussed, and
the steps which this study will adopt to ensure reliability and validity will be explained.
3.8.1 Validity
Through the use of positivist paradigms and concepts in quantitative research, Cohen et al.
(2017) defined validity as having real, factual data (Cohen et al., 2017).According to Cohen et al.
(2017), there are certain assumptions, instruments, statistics, and content that are called "faithful
premises" by positivists.When it comes to quantitative research, there are three categories of
validity.Firstly, according to Creswell and Clark (2017), the capacity to generalise and secure the
results utilising a random sampling size technique for the relevant population is referred to as external
validity. Secondly, Edmonds and Kennedy (2017) emphasise that the ability to measure the created
promises through the study is referred to as construct validity. Thirdly, according to Develllis, (2016)
and Hair et al., (2010) Internal validity refers to the ability to determine whether or not the research
was conducted appropriately.
27

According to Creswell and Clark (2017) and Thomas (2013), construct validity can provide a
clear picture of the outcomes by highlighting the interaction between different variables and providing
insights into the constructed knowledge as well as the elements that impede or promote on-line
learning. This type of validity will be employed in this study since it can help determine how using
online mathematics teaching and learning materials affects instructors' self-efficacy in the classroom.
To make sure that the research instruments are good and safe to use, a pilot study will be done to
check for construct validity for the current study.
Validity in qualitative research refers to the truthfulness that can emerge from data acquired
using an interpretive technique (Creswell & Clark, 2017). According to Cohen et al. (2017) and
Edmonds and Kennedy (2017), having a quality assessment for the research is crucial, especially for
interpretive data, which is dependent on participants' viewpoints or opinions, which can vary over
time. As a result, the validity of the qualitative methods used in this study is based on how honest
students and teachers think they are. Although measuring validity is difficult, there are certain tactics
that may be used to improve qualitative research methodologies' validity (Cohen et al., 2017;
Edmonds &Kennedy (2017).In the context of qualitative research, three ways of demonstrating
validity have been identified, according to Creswell (2013) and Creswell and Clark (2017): the
dependability and credibility, well-known approach and triangulation. The findings will be
summarised using a well-known method, and participants will be asked whether the results are true
(Creswell, 2013; Creswell & Clark, 2017). According to Cohen et al., (2017) the triangulation method
collects data from a large number of people, making it easier to validate data than other methods. In
the context of the current study, triangulation can also occur in the form of data collection methods,
such as the use of questionnaires, observations, and semi-structured interviews. This will aid the
current investigation in finding a balance between the approaches' flaws and strengths.
3.8.2 Reliability
28

According to Oppenheim (2009) and Thomas (2013), reliability in quantitative study
generally defined as having to repeat a same scale or test on the same sample over a short period of
time and receiving the same result each time; some researchers refer to reliability as stability (for
example, Cohen et al., 2017). In the context of this research, a large number would imply that the
initial experiment and a later replication had extremely similar results. Equivalent measures of
reliability assess the capacity to achieve the same findings with the same identical tests or procedures
(Cohen et al., 2017). When it comes to the study's reliability, The question is whether the results
would be the same if the experiment were done using the same sample. Because different realities (for
example, participants' perspectives) are totally feasible in interpretative research and might potentially
alter over time, reliability is a concern in qualitative research (Thomas, 2013). According to Thomas
(2013), reliability is "in my opinion, unimportant in interpretive research" (p.139), because
perceptions might be changed if they are repeated in qualitative (interpretative) research. By
following the criterion of credibility stated above, the current research aims to verify that the
researcher's interpretation of the data is accurate and that the findings will be in line with the
information gathered from the participants. Furthermore, the quality of the collected data can be used
to measure the interview's credibility (Creswell, 2009). As a result, a voice recorder will be used to
record all interview transcripts. The transcripts of the interviews will also be written in Arabic, which
is the first language of the participants. The researcher will translate the transcripts from Arabic to
English, and another translator will double-check the accuracy of the translation. The data and
findings will be more reliable as a result of this approach. Qualitative research makes it difficult to
achieve the same results. This is the case because qualitative data is narrative and subjective. For this
purpose, Lincoln and Guba (1985) believe that it is more crucial to consider the data's dependability
and consistency in order to achieve the same results. The goal is to agree that the findings and results
are consistent and dependable based on the data gathering methodologies, not just to have the same
outcomes. Merriam (1998) claims that the human instrument can improve its trustworthiness through
training and experience. According to Lincoln and Guba (1985) and Merriam (1998), three ways can
ensure the results' dependability: triangulation, investigator's position, and audit trial. The researcher
29

should use a range of approaches to collect data, such as surveys, interviews, and classroom
observations. Learners, students, past students, language instructors, topic instructors, and programme
workers must all contribute data. As a result, acquiring a variety of data from a variety of sources can
help to improve the data and outcomes' trustworthiness. The replication of the study will be
straightforward in this approach. This approach was used in this investigation.
The investigator's role: In order to increase the research's reliability, the investigator must
clearly explain the various procedures and phases of the inquiry. As a result, the investigator should
go through every aspect of the study in considerable depth. He or she should thoroughly examine the
study's rationale, design, and subjects. Trial by audit: To finish this technique, the researcher must
explain how data is collected, analysed, and different themes are generated, as well as how the results
are obtained. As a result, this precise information can help with replication and provide credibility to
the study. This research has gone into great detail.
3.9 Ethical considerations
Ethical considerations according to Coe et al. (2017) indicate determining how people are
employed in research and whether or not they are at risk of being harmed. While conducting any
study, it's important to keep in mind ethical considerations (Cohen et al, 2017). Research participants
must be protected from injury by adhering to ethical standards at all times. As a researcher, you must
treat participants with respect, be honest with instructors, students, and their parents about your
study's aim, and avoid harming yourself or your subjects (Cohen et al, 2017; Robson & McCartan,
2016). Furthermore, ethics are essential to the quality of research by removing biases, reporting
accurate data, and adhering to accepted methods (Cohen et al, 2017). Ethics may be more difficult to
manage when utilising qualitative methods than quantitative ones, due to the qualitative approach's
reliance on human interactions and interpretation (Mertens, 2014). As a consequence, how the
participants' opinions are recorded is critical.
30

Codes of professional practice, such as the UKRIO Code of Good Practice in Research in
University of Reading, and the British Educational Research Association's Code of Conduct must be
adhered to ensure that the research is performed lawfully and ethically (Cohen et al., 2017). (Bera,
2011). The ethical implications of this study will be extensively investigated. All participants'
identities and privacy will be protected at all times.
The Saudi Arabian Ministry of Education and the Ethics Board of the University of Reading's
Institute of Education will both endorse the initiative. Because this study will include children,
parents and school principals will get information sheets and permission forms (Cohen et al, 2017).
As a result, the use of a permission form is crucial to research ethics since the study participants will
be instructors and students in schools. As a consequence, four permission forms were established,
each with a documented assurance of secrecy and privacy (for participation by school heads,
instructors, parents, and students) (see Appendix G-K). The data gathered from the interviews and
observations may only be accessed by the researcher and the research supervisors. Which will be
held in a secure location until the study is completed. To guarantee each participant's safety and
comfort, they will be able to leave at any time throughout the study process, which will be performed
entirely online.
3.10 Summary
The purpose of this chapter was to explain the research methodology which will be applied in
this study. This study will be based on the pragmatic paradigm in which a mixed-method approach to
research has been chosen as research design for this study. More specifically, the study will apply the
triangulation research design and collect quantitative and qualitative data at the same time. For the
quantitative stage, an on-line questionnaire with closed-ended and open-ended questions will be
distributed to 400 primary mathematics teachers and 400 students in primary schools in Saudi Arabia.
As for the qualitative stage, observation and a semi-structured interview will be carried out with eight
mathematics teachers (four male teachers and four female teachers, one teacher for each Grade 3, 4, 5,
31

and 6, with two lessons for each teacher for observation), in order to answer the research questions
and provide more insights into the tools that are used during on-line sessions in primary schools.
The quantitative data will be analysed using statistical tests (i.e., descriptive statistics, two-
ways ANOVA and multiple regressions will be applied by using SPSS) in order to test the association
between the variables in this study. On the other hand, the qualitative data will be analysed by using
thematic analysis where themes and patterns will be identified from the primary collected data. This
chapter also explained the adopted measures to ensure validity, and reliability for each stage of the
research such as and the use of triangulation.There have also been ethical considerations highlighted.
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RESEARCH
INSTRUMENTS
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QUESTIONNAIRE FOR TEACHERS
Dear Teacher,
I would like to invite you to complete this on-line questionnaire as part of my doctoral research
project at the University of Reading (UK). The study and its questionnaire set out to examine on-line
tools used as part of on-line primary mathematics teaching and learning, and to investigate key
barriers and enablers concerning primary school teachers face when teaching mathematics on-line in
Saudi Arabia. In addition, the effect of teachers’ gender and the years of their teaching experience on
their self-efficacy concerning on-line mathematics teachers will also be examined.
You have been invited to complete this questionnaire because you teach primary
mathematics.
The questionnaire will take approximately 15 minutes to complete and will be conducted via a secure
platform. You will be completing this questionnaire anonymously, and data collected will be held
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securely and in strict confidence for the purposes of the research only. The results of the study will not
be presented in a way that will identify you.
This project has been reviewed following the procedures of the University Research Ethics
Committee and has been given a favourable ethical opinion for conduct. The University has the
appropriate insurances in place. Full details are available on request.
By completing this survey, you are consenting to your participation in this research study.
If you would like more information about this research project, please contact me at
If you have any queries regarding protection of your personal data, please contact
Thank you in anticipation for your assistance.
Yours sincerely,
SECTION 1
1. Your gender: Male ( ) Female ( )
2. The age group of primary children you teach: Grade3 ( ) Grade 4( ) Grade 5( ) Grade6 ( )
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3. Your school’s name: ( )
4. Which region do you work in?: ( )
5. Your years of teaching experiences:
Teaching experience is divided into four groups as shown in the following table, please tick the appropriate
group for your teaching experience.
Less than 9 years, 9-18
years
19-28 years more than 28
years
SECTION 2
1. Which are some of the on-line tools you normally use when teaching mathematics on-line? (Examples of
mathematics-specific on-line tools are Algebra, Equation Edito, etc. Examples of generic on-line tools are
Microsoft teams, Wimba, etc.)
2. What do you like about some of these on-line tools? Please explain your answer.
3. What do not you like about some of these on-line tools? Please explain your answer.
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4. What are the on-line tools that you do not have and wish to have to support your on-line mathematics
teaching? Please explain your answer.
5. What are the educational platforms you use to teach mathematics on-line at your school? (Such as Madrasati
platform)
6. Which mathematical topics are easier to teach on-line? Please explain your answer.
7. Which mathematical topics are more difficult to teach on-line? Please explain your answer.
8. What are some of the on-line tools that you have used in your on-line mathematics lessons that can help
your pupils to develop their mathematical procedural skills?
9. What are some of the on-line tools that you have used in your on-line mathematics lessons that can help
your pupils to develop their mathematical conceptual understanding?
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10. From your experience of teaching mathematics on-line during the global pandemic, what went
well in your view? Please explain your answer.
11. From your experience of teaching mathematics on-line during the global pandemic, what did not
go well in your view? Please explain your answer.
SECTION 3
1. From your experience, what are some of the key barriers that prevent you from teaching mathematics on-
line effectively? Please explain your answer.
2. From your experience, what are some of the key enablers that help you to teach mathematics on-line
effectively? Please explain your answer.
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SECTION 4
Strongly
Disagree
Mostly
Disagree
Not Sure
Mostly
Agree
Strongly
Agree
4.1 Technological Knowledge (TK)
1. I am confident in solving my own
technical problems during my on-line
mathematics lessons.
2. I am confident that I can learn
technology easily to help support my on-
line mathematics teaching.
3. I am confident that I can keep up with
important new technologies to help
support my on-line mathematics
teaching.
4. I am confident in playing around with
technology to help support my on-line
mathematics teaching.
5. I am confident in my knowledge about a
lot of different technologies that can be
used to support my on-line mathematics
teaching.
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6. I am confident in my technical skills I
need to use technology effectively to
support my on-line mathematics
teaching.
4.2 Technological Pedagogical Knowledge (TPK)
1. I am confident in choosing technologies
that enhance my on-line teaching
approaches.
2. I am confident in choosing technologies
that enhance my students' learning during
my on-line lessons.
3. I am confident in my ability to think fully
about how technology could influence
the teaching approaches I use in my on-
line lessons.
4. I am confident in my ability to think fully
about how to use technology in my on-
line teaching.
5. I am confident in adapting the use of the
technologies that I am learning about to
different on-line teaching activities.
6. I am confident in my knowledge on how
technology can be used to assess
students’ learning.
4.3 Technological Content Knowledge (TCK)
1. I am confident in my knowledge about
technologies that I can use to help my
students understand numbers and
arithmetic operations.
2. I am confident in my knowledge about
technologies that I can use to help my
students understand algebra.
3. I am confident in my knowledge about
technologies that I can use to help my
students understand geometry.
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4. I am confident in my knowledge about
technologies that I can use to help my
students understand measurement.
5. I am confident in my knowledge about
technologies that I can use to help my
students understand data analysis.
6. I am confident in my knowledge about
technologies that I can use to help my
students understand probability.
4.4 Technological Pedagogical Content Knowledge (TPACK)
1. I am confident in using technology to
encourage my students to discuss
mathematical concepts and processes
with me and their peers during my on-
line mathematics lessons.
2. I am confident in using technology to
encourage my students to show me their
mathematical reasoning.
3. I am confident in using technology to
encourage my students to test a solution
to try to solve mathematical problems
during my on-line mathematics lessons.
4. I am confident in using technology to
encourage my students to practise using
mathematical problem-solving strategies
during my on-line mathematics lessons.
5. I am confident in using technology to
encourage my students to represent
mathematical concepts that they are
learning in different ways during my on-
line mathematics lessons.
6. I am confident in using technology to
encourage my students to apply their
mathematical knowledge to solve real-
life problems during my on-line
mathematics lessons.
OPEN-ENDED QUESTIONS
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1. Which aspect(s) of teaching mathematics on-line, do you feel most confident doing? Please explain your
answer.
2. Which aspect(s) of teaching mathematics on-line, do you feel least confident doing? Please explain your
answer.
3. Do you think Saudi primary school teachers’ gender affect their confidence level in teaching mathematics
on-line? Please explain your answer.
4. Do you think Saudi primary school teachers’ teaching experience level affect their confidence level in
teaching mathematics on-line? Please explain your answer.
Thank you very much for completing this questionnaire.
77

QUESTIONNAIRE FOR STUDENTS
Dear Student,
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I would like to invite you to complete this on-line questionnaire as part of my study which aims to
learn more about on-line mathematics teaching and learning in your classroom.
You have been invited to complete this questionnaire because you are a primary school
student, and your mathematics teacher sometimes deliver on-line mathematics lessons.
The questionnaire will take approximately 15 minutes to complete.
Only the people working on the project will know about your answers. I will not tell your school and
your parents how you answered.
This project has been reviewed following the procedures of the University Research Ethics
Committee and has been given a favourable ethical opinion for conduct. The University has the
appropriate insurances in place. Full details are available on request.
By completing this questionnaire, you are giving your permission to participate in my study.
If you would like more information about this research project, please let your teacher know.
Thank you in anticipation for your assistance.
Yours sincerely,
79

SECTION 1
Dear Student,
To complete this part, all you have to do is choose your answer in the drop-down list.
1. Your gender: Male ( ) Female ( )
2. Which class are you studying in? Grade 3 ( ) Grade 4 ( ) Grade 5 ( ) Grade 6 ( )
3. Your school’s name: ( )
4. Which city do you live in? ( )
SECTION 2
Use simple words to answer the following questions.
1. Can you tell me what are some of the tools you have been using in your on-line mathematics lessons, and
which mathematical topics are they for? (Examples of mathematics-specific on-line tools are A lgebra, Equation
Edito, etc. Examples of generic on-line tools are Microsoft teams, Wimba, etc.)
2. What do you like about some of these on-line tools? Please explain your answer.
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3. What don’t you like about some of these on-line tools? Please explain your answer.
4. What are the educational platforms you have been using to learn mathematics on-line at your school?
SECTION 3
1. Which mathematical topics are easier to learn on-line? Please explain your answer.
2. Which mathematical topics are more difficult to learn on-line? Please explain your answer.
3. What do you like about learning mathematics on-line during the global pandemic? Please explain
your answer.
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4. What don’t you like about learning mathematics on-line during the global pandemic? Please
explain your answer.
INTERVIEW QUESTIONS FOR TEACHERS
Before we start this interview questions, can you let me know how many years of teaching
experience do you have?
1. On-line tools
1.1. Generally speaking, what are some of the on-line tools you typically use when
teaching mathematics on-line during the pandemic? (Examples of mathematics-
specific on-line tools are Algebra, Equation Edito, etc. Examples of generic on-line
tools are Microsoft teams, Wimba, etc.)
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1.2. In your on-line mathematics lesson that I observed, can you remind me which tools
were used during the lesson?
1.3. Are there any tools that you used in your on-line mathematics lesson that I observed
that you liked or found most useful? If so, which ones? Please explain your answer
1.4. Are there any tools that you used in your on-line mathematics lesson that I observed
that you disliked or did not find useful? If so, which ones? Please explain your
answer.
1.5. What on-line tools do you lack and would like to have to support your on-line
mathematics teaching? Please explain your answer.
1.6. I observed that you used an educational platform to teach mathematics on-line in
your class; do you use any other platformsin mathematics lessons? Please explain
your answer.
1.7. In your on-line mathematics lesson that I observed, you taught [xxx]. Did you find it
easy or difficult to teach [xxx] on-line? Please explain your answer.
1.8. In general, which mathematical topics are more difficult to teach on-line? Please
explain your answer.
1.9. In general, which mathematical topics are easier to teach online? Please explain your
answer.
1.10. What are some of the on-line tools that you have used that can help your
pupils to develop their mathematical procedural skills?
1.11. What are some of the on-line tools you have used that can help your pupils in
developing their mathematical conceptual understanding?
1.12. In your on-line mathematics lesson that I observed, which aspect(s) of that
lesson went well and which aspect(s) did not go well in your view? Please explain
your answer.
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1.13. Generally speaking, from your experience of teaching mathematics on-line
during the global pandemic, what went well in your view? Please explain your
answer.
1.14. Generally speaking, from your experience of teaching mathematics on-line
during the global pandemic, what did not go well in your view? Please explain your
answer.
2. Barriers and enablers
2.1. From your experience, what are some of the key barriers that prevent you from
teaching mathematics on-line effectively? Please explain your answer.
2.2. From your experience, what are some of the key enablers that help you to
teach mathematics on-line effectively? Please explain your answer.
3. Self-efficacy
3.1. In thinking about your on-line mathematics lesson that I observed, which
aspect(s) of teaching mathematics on-line, do you feel most confident doing? Please
explain your answer.
3.2. In thinking about your on-line mathematics lesson that I observed, which
aspect(s) of teaching mathematics on-line, do you feel least confident doing? Please
explain your answer.
3.3. Generally speaking, do you think the gender of Saudi primary school teachers
affect their confidence level in teaching mathematics on-line? Please explain your
answer.
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3.4. Generally speaking, do you think the years of teaching experience of Saudi
primary school teachers affect their confidence level in teaching mathematics on-line?
Please explain your answer.
INTERVIEW QUESTIONS FOR CHILDREN
1. Generally speaking, what are some of the on-line tools you typically use when learning
mathematics on-line during the pandemic? And which mathematical topics are they for?
(Examples of mathematics-specific on-line tools are Algebra, Equation Edito, etc.
Examples of generic on-line tools are Microsoft teams, Wimba, etc.)
2. In the on-line mathematics lesson that I observed, can you remind me which tools were
used during the lesson?
3. What do you like about some of the on-line tools that were used in the on-line
mathematics lesson that I observed? Please explain your answer.
4. What don’t you like about some of the on-line tools that were used in the on-line
mathematics lesson that I observed? Please explain your answer.
5. Generally speaking, which mathematical topics are easier to learn on-line? Please explain
your answer.
6. Generally speaking, which mathematical topics are more difficult to learn on-line? Please
explain your answer.
7. Which aspects of the on-line mathematics lesson that I observed do you like the most?
Please explain your answer.
85

8. Generally speaking, what do you like about learning mathematics on-line during the
global pandemic? Please explain your answer.
9. Which aspects of the on-line mathematics lesson that I observed do you dislike the most?
Please explain your answer.
10. Generally speaking, what do not you like about learning mathematics on-line during the
global pandemic? Please explain your answer.
OBSERVATION FORM
Date Time School’s name
Teacher’s name Numbers of students
Lesson objective(s):
Detailed summary of the lesson
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Feature Notes
On-line mathematics teaching and
learning tools that are used in this
lesson; what they are used for; and
how they are used.
What about this on-line lesson that
went well?
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What about this on-line lesson that did
not go as well?
88