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Similarities between Singapore and South Africa
The analysis of the data shows that there are no similarities between the way teachers in Singapore and South Africa reported on their feelings with regards to feeling comfortable using of computers in their teaching (0.86). There is sufficient evidence from the analysis which suggests that no significant similarities were found between the two countries with regards to this item. It is, therefore, clear that teachers in South Africa cannot compare themselves to their Singaporean counterparts in terms of how comfortable they feel about the use of computers in their teaching.
However, the analysis of the data generated congruent coefficients that were above 0.95 in 87.5% of the items. There is empirical evidence to deduce that South Africa can benefit from exploring the way in which Singapore addresses these issues. It is clear from the results that it is possible to compare the teachers‟ ready access computer staff in their schools (1.00) and the support they had for integrating computers into their teaching activities (0.98) between South Africa and their Singaporean counterparts.
There are further items where the congruent coefficient between Singapore and South Africa makes it possible to explore the similarities, such as how teachers have allowed their learners do the following computer activities during mathematics lessons to
explore mathematical principles and concepts (1.00),
practise skills and procedures (1.00),
look up ideas and information (0.99) and
process and analyse data (1.00).
Therefore, it can be concluded that significant similarities were found between learners in both countries with regards to how teachers have asked their learners to use computer activities during mathematics lessons. Furthermore, the overall congruent coefficient regarding teachers‟ self-reporting on their use of computers in the classroom was 0.97, which is above the required threshold. Since these congruent coefficients compare favourably with the recommendation of 0.95 they can therefore be regarded as acceptable for equivalence for teachers in the two countries, South Africa and Singapore. Therefore, the overall congruent coefficient suggests that significant similarities were found between learners in both countries with regards to how their teachers have used different teaching strategies. Furthermore, a lower value of the RMSD, after rotation, also indicates that teachers‟ views between the two countries were closer to each other than before rotation.
Since Singaporean learners (611 out of 1 000) outperformed their South African (352 out of 1 000) counterparts, it may be of value to investigate how the Singaporean teachers use computer activities in their mathematics classrooms with regards to those items that showed a congruent coefficient of more than 0.95.
Similarities between the United Arab Emirates and South Africa
In this study, it is imperative to investigate how the United Arab Emirates teachers use computer activities in their mathematics classrooms. Since United Arab Emirates learners (456 out of 1 000) outperformed their South African (352 out of 1 000) counterparts.
The analysis of the data shows that there is little similarity between the way United Arab Emirates and South African teachers reported on their feelings with regards to feeling comfortable in using computers in their teaching (0.59). The congruent coefficient is lower than the required threshold. It is, therefore, clear that South Africa cannot compare itself to the United Arab Emirates in terms of how comfortable they feel about the use of computers in their teaching.
However, the analysis of the data generated congruent coefficients that were above 0.95 for the two countries in 87.5% of the items, and as such it is fair to deduce that South Africa can benefit from exploring the way in which the United Arab Emirates addresses these issues. It is clear from the results that it is possible to compare the ready access computer staff in their schools (0.99) and the adequate support they had for integrating computers into their teaching activities (0.99) between South Africa and their United Arab Emirates counterparts.
There are further items where the congruent coefficients between the United Arab Emirates and South Africa where above 0.95 which included how often teachers have asked their learners do the following computer activities during mathematics lessons to
explore mathematical principles and concepts (0.98),
practise skills and procedures (0.99),
look up ideas and information (1.00) and
process and analyse data (0.99).
Therefore, it can be concluded that significant similarities were found between learners in both countries with regards to how often teachers have asked their learners use different computer activities during mathematics lessons.
Similarities regarding teaching strategies
This section provides the results based on the teachers‟ views on the research question 2, namely “How do South African learners compare with their selected international counterparts with regards to how their teachers have used different teaching strategies?” That said, Annexure K indicates the component loadings and the rotated component loadings between South Africa and each of the countries analysed in the study based on their teaching strategies.
It should be noted that the conclusions are drawn based on the following statements:
a) If Ø < 0.95, then the results show that there were no significant similarities between South African learners and their selected international counterparts with regards to teaching strategies.
b) If Ø ≥ 0.95 then, the results show that there were significant similarities between South African learners and their selected international counterparts with regards to teaching strategies.
1. CHAPTER ONE: BACKGROUND OF THE STUDY
1.1 Introduction
1.2 Background of the study
1.3 Rationale of the study
1.4 Problem statement
1.5 Framework used in this study
1.6 Purpose of the research
1.7 Research questions under investigation
1.8 Statistical techniques used in this study
1.9 Significance of the study
1.10 Assumptions of the study
1.11 Advantages and disadvantages of using secondary data
1.12 Delimitation of the study
1.13 Reliability and validity
1.14 Structure of the thesis
2. CHAPTER 2: LITERATURE REVIEW
2.1 Introduction
2.2 Importance of international studies
2.3 Overview of international comparative studies
2.4 South Africa participation in the international studies
2.5 Annual National Assessment (ANA) conducted in South Africa
2.6 Mathematics strategy in South Africa
2.7 Integration of technology into the classroom
2.8 Teachers‟ beliefs
2.9 Diffusion of Innovation Theory
2.10 Challenges with technology integration
2.11 Mechanism of technology adoption
2.12 Theoretical Framework
2.13 Development of mathematics TPACK
2.14 Review of TPACK studies in education
2.15 TPACK framework for pre-service mathematics teachers
2.16 Studies that have used factor analysis
2.17 Gaps identified in the literature
2.18 Conceptual framework used in this study
2.19 Conclusion
3. CHAPTER 3: RESEARCH METHODOLOGY
3.1 Introduction
3.2 Trends in Mathematics and Science Study (TIMSS)
3.3 Research design
3.4 Sampling used in the TIMSS 2011 study
3.5 Data collection and instruments
3.6 Current study
3.7 Research approach
3.8 Research methods
3.9 Sampling technique used in the present study
3.10 Data collection
3.11 Research questions used in this study
3.12 Data analysis
3.13 Procedure for analysis data
3.14 Ethical considerations
3.15 Closure
4. CHAPTER 4: FACTOR ANALYSIS AND DESCRIPTIVE STATISTICS FINDINGS
4.1 Introduction
4.2 Descriptive statistics
4.3 Descriptive statistics used in the study
4.4 Population and sampled schools
4.5 Biographical information
4.6 Major areas of study in relation to mathematics
4.7 Use of computers by mathematics teachers
4.8 Use of computer activities by learners
4.9 Mathematics resources used by teachers
4.10 Conclusion
5. CHAPTER 5: ANALYSIS OF THE INFERENTIAL STATISTICS
5.1 Introduction
5.2 CATPCA technique
5.3 Orthogonal procrustean rotation
5.4 Tucker congruent coefficient
5.5 Research questions
5.6 Similarities regarding computer activities
5.7 Similarities regarding teaching strategies
5.8 Similarities regarding content coverage
5.9 Conclusion
6. CHAPTER 6: CONCLUSION AND RECOMMENDATIONS
6.1 Introduction
6.2 The importance of comparative studies
6.3 Rationale of the study
6.4 Literature review
6.5 Research questions used in the study
6.6 Discussion of the research findings
6.7 Methodological reflection
6.8 Scientific reflection
6.9 Recommendations for policy and further research
6.10 Limitations
6.11 Conclusion
7. LIST OF REFERENCES
