The Impact of Mathematics Interventions in High Schools: a Mixed Method Inquiry

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How to cite this thesis

Surname, Initial(s). (2012) Title of the thesis or dissertation. PhD. (Chemistry)/ M.Sc. (Physics)/ M.A. (Philosophy)/M.Com. (Finance) etc. [Unpublished]: University of Johannesburg. Retrieved from: https://ujdigispace.uj.ac.za (Accessed: Date). THE IMPACT OF MATHEMATICS INTERVENTIONS IN HIGH SCHOOLS: A MIXED METHOD INQUIRY

DUDUZILE ROSEMARY MKHIZE

THESIS

submitted in fulfillment of the requirements for the degree

PHILOSOPHAE DOCTOR

CURRICULUM STUDIES

in the

FACULTY OF EDUCATION AND NURSING

at the

. UNIVERSITY OF JOHANNESBURG

PROMOTER: DR B.V. NDUNA

May 2011 DECLARATION

Student Number: 920319425

I declare that

THE IMPACT OF MATHEMATICS INTERVENTIONS IN ~IIGH SCHOOLS: A MIXED METHOD INQUIRY

is my own work and that all the sources that I have used or quoted have been indicated and acknowledged by means of a complete bibliography.

~:-:.~.:--::.~{ er' -.~ . / ( Ms D. fu.-Mkhize) Date

ii SYNOPSIS

This study investigated the impact of mathematics interventions on learner participation and performance in mathematics within Gauteng 47 high schools in the Johannesburg area over a five year period. Motivating the study was the perpetual implementation of mathematics interventions against the backdrop of persistent mediocrity in learner matriculation achievement in this subject. The essence of the research problem was the scarcity of knowledge relating to the effectiveness and impact of mathematics interventions.

The strategy of inquiry employed was an explanatory research design which entailed a sequential collection and analysis of quantitative and qualitative data.

Quantitative findings revealed that only 10% of learners who participated in interventions were enabled to enroll in mathematics essential to pursue mathematics related professions at tertiary level. Thus, the intention to redress the prevalent limited access to professional careers requiring a strong basis in mathematics has not been dented. Regarding learner performance in mathematics, Friedman tests for nonparametric hypothesis testing revealed that there was no significant evidence that the interventions had an impact on learner performance over the five year observation period.

Qualitative data analysis explained the quantitative findings and further uncovered the positive impact of mathematics interventions. Furthermore, strengths and weaknesses of the mathematics interventions were identified as opposed to the quantitative findings which seemed to negate the existence of the impact of mathematics interventions. Through the findings of this study, factors that may be limiting the effectiveness of mathematics interventions were uncovered. These were interwoven into a base knowledge that can influence positive practices and future research related to optimizing the impact of mathematics interventions in high schools.

iii KEY TERMS

Impact

Mathematics

Mathematics interventions

High schools

Adolescent learners

Mathematics learner participation

Mathematics learner performance

iv ACRONYMS

ATDQT Ability to Do Quantitative Thinking CASE Cognitive Acceleration Through Science Education CDE Centre for Development Enterprise CMP Connected Mathematics Project CPMP Core-Plus Mathematics Project CSR Comprehensive School Reform CSRI Comprehensive School Reform Interventions EMIS Education Management Information Systems HG Higher Grade IE Feuerstein Instrumental Enrichment 1M Integrated Mathematics K-12 MCC K-12 Mathematics Curriculum Centre MEP Mathematics Education Project MiC Mathematics in Context NCS National Curriculum statements NAEP National Assessment of Educational Progress NCTM National Council of Teachers of Mathematics NGO Non Governmental Organisation OBE Outcomes Based Education PROTEC Programme for Technological Careers RADMASTE Research and Development in Mathematics, Science and Technology Education RME Realistic Mathematics Education SG Standard Grade SIMMS Initiative for Montana Mathematics and Science STATKON Statistical Consultation Services SUPEDI Supplementary Education Programme ,SYSTEM Students and Youth into Science, Technology Engineering and Mathematics v TIMSS Third International Mathematics and Science Study TOPS Teacher Opportunity Programme WWC What Works Clearinghouse

vi DEDICATION

This project is dedicated to the ever shining STARS in my life: my mother Ruth Mkhize (MaSthole) and my bother Sfiso Ignatius Mkhize.

Though you are gone, your memories are forever with me, God be with you till we meet again at Jesus' feet.

vii ACKNOWLEDGEMENTS

My heartfelt gratitude and highest praise goes to God my maker, Jesus my savior and the Holy Spirit my teacher and comforter. Let the glory be unto Him! I am also deeply indebted to:

~ Dr Nduna my supervisor, for his brilliant guidance, but above all, for having Job's patience and Solomon's wisdom in his dealings with me.

~ Richard Devey, the head of Statkon for his invaluable assistance in the statistical analysis for this project.

~ University of Johannesburg Interlibrary staff, especially Godfrey. You are my unsung heroes .

~ Canon Collins Educational Trust in Southern Africa, for their much appreciated financial support.

~ Nkosinomusa (Mfane) Mkhize, my dearest motivator, your prompting made it impossible for me to rest without finishing this project. You are more than a son to me and this achievement belongs to you.

~ Makha for your never failing faith in me. I could never have a better daughter than you.

~ Nkonzo and Rashida : Ukuzala ukuzelula. I am glad you are in my life.

~ Nokwanda, my little sister and friend; for supporting the unknown project. You are the best!

~ My father, Steven Mkhize who with my dearest late mother, planted the seed of love for educational pursuits in my formative years.

~ My brother Bongane and his wife Khanyi. Ngiyabonga MaKhabazela. viii ~ My sister in-law 'Mntakwethu' Thandiwe Mkhize; your ever ready support, warmth and love are highly valued.

~ Mbuyi, 'Tsala', my God given sister and friend. Thank you for being there for me and for sharing your beloved mother Ivy Kashe, my friend and counsellor. This project is her accomplished prediction.

~ All our children from the eldest Lindokuhle to the youngest, Minenhle . Keep the faith and reach for the stars, with God nothing is impossible.

ix TABLE OF CONTENTS

CHAPTER 1 1

1. INTRODUCTION 1 1.1 BACKGROUND OF THE STUDY 1 1.1.1 Interventions as Catalyst for Policy Implementation 1 1.1.2 National Interventions in Response to Policies of Change 2 1.1.2.1 SYSTEM 3 1.1.2.2 OBE: Curriculum Intervention 3

1.1.3 Mathematics Interventions in the 21st Century 5 1.1.3.1 National Strategy for Mathematics Education 5 1.1.3.2 Continued Mediocrity 6 1.1.3.3 Forthcoming Mathematics 6

1.2 STATEMENT OF THE RESEARCH PROBLEM 7 1.3 RESEARCH QUESTIONS 8 1.4 PURPOSE STA TEMENT 9 1.5 AIM AND OBJECTIVES OF THE STUDy 9 1.5.1 Aim of the Study 9 1.5.2 Objectives of the Study 9 1.6 SIGNIFICANCE OF THE STUDy 10 1.6.1 Practical Significance 10 1.6.2 Theoretical Significance 10

1.7 OPERA TIONAL DEFINITIONS OF TERMS 10

1.8 THEORETICAL FRAMEWORK AND THE OVERVIEW OF THE STUDy 11 1.8.1 Theoretical Framework 11 1.8.2 The Overview of the Study 12 1.8.2.1 Sampling 13 1.8.2.2 Ethical Issues 13 1.8.2.3 Data Collection and Analysis 14

1.9 DEL/MITA TlON OF THE STUDy 15 1.10 PHILOSOPHICAL ASSUMPTIONS 15 1.11 PLAN OF THE STUDy 16 1.12 SUMMARy 17

x CHAPTER 2 18

2. ADOLESCENT LEARNERS IN MATHEMATICS 18 2.1 INTRODUCTION 18 2.2 MATHEMA TICS PARTICIPA TlON AND PERFORMANCE IN HIGH SCHOOLS 18 2.3 PLACING LEARNERS FIRST 19 2.4 ADOLESCENCE: THE GOLDEN AGE FOR LEARNING 20 2.4.1 Cognitive Growth during Adolescence 21 2.4.2 Coping and Resilience for Adolescents 22 2.4.2.1 Coping Styles for South African Adolescents 23

2.5 IDENTITY FORMATION VERSUS IDENTITY CRISIS 25 2.5.1 Statuses for Identity Formation 26 2.5.2 Agents of Identity Formation 28 2.5.3 Learning Mathematics as Identity Formation 29

2.6 SELF THEORIES AND MATHEMATICS IDENTITIES 30 2.6.1 Entity and Malleable Intelligence Beliefs 30 2.6.2 Helpless and Mastery Responses to Failure 30 2.6.3 Pursuit of Goals in Learning 30 2.6.4 Self-Efficacy in Mathematics Learning 31 2.6.5 Self Theories and Self Efficacy as Constructs of Identity 32 2.7 INFUSING ADOLESCENCE IN MATHEMATICS LEARNING 32 2.8 SUMMARy 33

CHAPTER 3 34

3. GLOBAL MATHEMATICS INTERVENTIONS 34 3. 1 INTRODUCTION 34 3.1.1 The Role of Interventions in Education 34 3.1.2 Timeframe for Interventions' Effectiveness 34

3.2 COGNITIVE INTERVENTIONS 35 3.2.1 Link between Cognitive and Mathematics Interventions 36

3.3 COMPREHENSIVE SCHOOL REFORM INTERVENTIONS 37 3.3.1 Components that define CSRI 38 3.3.2 Research Evidence for CSR's Effectiveness 39 3.3.3 Publications on the Impact of CSR 41

xi 3.4 MATHEMATICS STANDARDS BASED INTERVENTIONS 42 3.4.1 Connected Mathematics Project (CMP) 44 3.4.1.1 Overview and Objectives 44 3.4.1.2 Impact of Attainment by CMP Students 45 3.4.1.3 Conclusion on the CMP Impact 46

3.4.2 Mathematics in Context (MiC) 46 3.4.2.1 Overview of MIC 46 3.4.2.2 Impact on MIC Students Attainment 47 3.4.2.3 Conclusion on the MIC Impact 48

3.4.3 The Core-Plus Mathematics Project (CPMP) 48 3.4.3.1 An Overview of CPMP 48 3.4.3.2 CPMP Curriculum 50 3.4.3.3 CPMP Lessons 51 3.4.3.4 Studies on the Impact of CPMP 51 3.4.3.5 Impact of CPMP on College Preparation 52 3.4.3.6 Conclusion on CPMP 52

3.4.4 SIMMS Integrated Mathematics 53 3.4.4.1 Overview of SIMMS 1M 53 3.4.4.2 Evidence of Effectiveness of SIMMS 1M 54 3.4.4.3 Classroom Practices and College Preparedness 3.4.4.4 Conclusion of SIMMS 1M

3.5 VALIDATION OF MATHEMATICS INTERVENTIONS 55 3.6 RESEARCH ON THE IMPACT OF INTERVENTIONS 56 3.7 RECENT EFFORTS TO IMPROVE LEARNER PERFORMANCE 56 3.8 SUMMARy 58

CHAPTER 4 59

4 SOUTH AFRICAN MATHEMATICS INTERVENTIONS 59 4.1 INTRODUCTION 59 4.2 CONTEXT FOR NATlONAL INTERVENTIONS 59 4.2.1 South African Education Systems prior to 1994 59 4.2.1.1 Missionary Education System 60 4.2.1.2 Colonial Education System 60 4.2.1.3 Bantu Education 61

4.2.2 The Goals and Outcomes of Bantu Education 62 4.2.3 Research on Bantu Mathematics Education 64

xii 4.3 MATHEMATICS INTERVENTIONS PRIOR TO 1994 65 4.3.1 PROTEC '" 66 4.3.2 Applications Oriented Mathematics Project.. 67 4.3.3 Mathematics Education Project (MEP) 67 4.3.4 Mathematics Centre for Primary Teachers 67 4.3.5 Star Schools '" 68

4.4 POST 1994 EDUCATIONAL ENViRONMENT 69 4.5 CLASSIFICATION OF POST 1994 INTERVENTIONS 71 4.5.1 RADMASTE 72 4.5.2 SySTEM 73 4.5.3 DINALEDI 74 4.5.4 Girl Learner Project. , '" '" 76 4.5.5 SUPEDI , 76 4.6 EMERGING RESEARCH ON INTERVENTIONS 77 4.7 EDUCATIONAL CHANGE SINCE 1994 77 4.8 SUMMARy 79

CHAPTER 5 80

5 RESEARCH DESIGN FOR THE STUDy 80 5.1 INTRODUCTION 80 5.2 RATIONALE FOR MIXED METHODS DESIGN 80 5.3 THE VALUE FOR THE CHOSEN RESEARCH DESIGN 81 5.4 JUSTIFYING PHILOSOPHICAL ASSUMPTIONS FOR THE STUDy 83 5.5 STRATEGY OF INQUIRy 84 5.6 SPECIFIC RESEARCH METHODS 85 5.6.1 The First Phase 85 5.6.1.1 Research Design for the First Phase 86 5.6.1.2 Sampling 87 5.6.1.3 Data Collection 88 5.6.1.4 Data Analysis 89 5.6.1.5 Eliminating Threats to internal Validity 90 5.6.1.6 Ensuring External Validity 90 5.6.1.7 Ethical Issue 91 5.6.1.8 Ensuring the Statistical Rigour 91

5.6.2 The Second Phase 92 5.6.2.1 Research Design for the Phase 92 5.6.2.2 Sampling 93 5.6.2.3 Data Collection 94

xiii 5.6.2.4 Empathetic Interviewing as an Ethical Stance 95 5.6.2.5 Data Analysis 96 5.6.2.6 Merging Quantitative and Qualitative Results 97 5.7 SUMMARy 97

CHAPTER 6 98

6 PRESENTATION AND ANALYSIS OF QUANTITATIVE DATA 98 6.1 INTRODUCTION , 98 6.2 SAMPLING AND SAMPLES 98 6.2.1 A Sample of Mathematics Interventions 99 6.2.2 A Sample of Schools 99 6.3 DATA ON PARTICIPATION IN MATHEMATICS 100 6.3.1 Statistics on Learner Participation in AS Schools 101 6.3.1.1 Discussion of Learner Participation in Mathematics for AS Schools 108

6.3.2 Descriptive Statistics on Enrolment in Mathematics for CD Schools 108 6.3.2.1 Discussion of Learner Enrolment in Mathematics in CD Schools 111 6.3.3 RESULTS ON ENROLMENT IN MATHEMATICS IN EF SCHOOLS 112 6.3.4 Summary of Participation in Mathematics 119 6.3.5 Conclusions on the Impact of Interventions on Participation 120

6.4 DATA ON PERFORMANCE IN MATHEMATiCS 121 6.4.1 Descriptive Statistical Analysis of Data 121 6.4.2 Testing the Normality of Data Distribution 123 6.4.3 Hypothesis Testing 125 6.4.4 The Impact of Interventions on Learner Performance 127 6.5 CONCLUSIONS ON QUANTITATIVE DATA ANALYSIS 127 6.6 IMPLICATIONS FOR THE QUALITATIVE PHASE. 128 6.7 SUMMARy 128

CHAPTER 7 130

7 PRESENTATION AND ANALYSIS OF QUALITATIVE DATA 130 7.1 INTRODUCTION 130 7.2 SAMPLE AND DATA COLLECTION 130 7.3 DATA ANALYSIS 131 7.4 EMERGING THEMES 132 xiv 7.4.1 Interventions are for Schools that Perform Well 132 7.4.2 The Impact on Teachers' Mathematical Content Knowledge 134 7.4.3 The Focus of Interventions on Content Knowledge 135 7.4.4 Preparation for the New Curriculum 136 7.4.5 The Impact on Resources 138 7.4.6 Extra Mathematics Lessons for Bright Learners 141 7.4.7 Problematic Learners 142 7.4.8 Poor Participation of Teachers in Interventions 145 7.4.9 Improvement Caused by Teachers 147 7.4.10 Discrepancy between Claimed Success and Reality 148 7.4.11 Learner Centred Approach Limitations 150 7.4.12 Learners' Lack of Ability for Higher Grade Mathematics 152 7.5 EXPLAINING THE QUANTITATIVE RESULTS 153 7.5.1 Perceived Aims and other Aims of Interventions 153 7.5.2 Content Based Versus Learner Based Programmes 155 7.5.3 Interventions Target Bright Students 157

7.6 EXPLANA nON FOR SPECIFIC INTERVENTIONS 157 7.6.1 Impact for Intervention AB 157 7.6.2 Impact for Intervention CD 158 7.6.3 Impact for Intervention EF 159 7.7 IMPACTDETECTED BY QUALITATlVE METHODS 159 7.8 CHALLENGES FACING INTERVENTIONS 160 7.9 SUMMARy 160

CHAPTER 8 161

8 SUMMARY, DISCUSSIONS, CONCLUSION AND RECOMMENDATIONS 161 8.1 INTRODUCTION 161 8.2 SUMMARY OF THE STUDy 161 8.2.1 Rationale for the Study 161

8.2.2 Summary on Literature Review 162 8.2.2.1 Summary on Adolescent Learners in Mathematics 162 8.2.2.2 Summary on Mathematics Interventions 163 8.2.2.3 International Perspective 163 8.2.2.4 National Perspective 164

8.2.3 Influence of Literature Review on the Study 164 8.2.4 Summary of Research Design and Data Collection 165 8.3 KEY FINDINGS RELATED TO THE OBJECTIVES OF THE STUDy 166 8.3.1 Findings Related to Objective 1: Investigation of the Impact.. 166

xv 8.3.1.1 Lack of Impact through Quantitative Methods 167 8.3.1.2 The Impact through Qualitative Methods 168

8.3.2 An explanation of Findings Related to Objective 2 169 8.3.2.1 The Aim and the Role of Mathematics Interventions 169 8.3.2.2 Focus on Increasing the Matric Pass Rate 169 8.3.2.3 Limited Implementation of Some Mathematics 170

8.3.3 Finding Related to Objective 3: Learner Centred Practices 170 8.3.4 Findings related to objective 4: Strengths and Weaknesses 170

8.3.4.1 Strengths for the Interventions 170 8.3.4.1.1 Improving Mathematical Content Knowledge for Teachers 170 8.3.4.1.2 Improving Resources for Mathematics Teaching 171

8.3.4.2 Weaknesses of the Interventions 171 8.3.4.2.1 Lack of Clarity on the Objectives for Interventions 171 8.3.4.2.2 Selecting Bright Learners: Pros and Cons 172

8.4 APPLICATlONS FOR FINDINGS 173 8.4.1 Achievement Based Mathematics Interventions 173 8.4.2 Independent Research of Interventions' Impact.. 174 8.4.3 Broadening Learner Centred Practices in High Schools 174 8.4.4 Extending Group Work to Cooperative Peer Learning 175 8.4.5 Building on the Strengths and Rectifying Weaknesses 175

8.5 RECOMMENDATIONS FOR FURTHER RESEARCH 176 8.5.1 Closing the Gap between Research and Interventions 176 8.5.2 Extension of the Study 176 8.5.3 Grounding Research on Mathematics Interventions on Dewey's Pragmatism 177 8.5.4 Longitudinal Studies 178 8.5.5 Exploring the Role of Implementing Agents of Interventions 178 8.6 FINAL REMARKS '" '" 178 8.7 CONCLUSION 179

BIBLIOGRAPHY 181

xvi List of Tables

Table 2.1: Coping styles in adolescents from nine countries. (Adapted from

Seiffege-Krenke,2004:369) 23

Table 2.2: Criteria for the Identity Statuses (Marcia, 1980:162) 27

Table 3.1: CPMP Core Curriculum (Source: Schoen and Hirsh, 2003: 313) 50

Table 3.2: CPMP Course 4 Units (Source: Schoen and Hirsh, 2003: 314) 51

Table 4.1: Per capita expenditure for education by race (Department of

Education, 1997b:11) 62

Table 5.1: One group-interrupted Time series design (Adapted from Lunenburg &

Irby, 2008:52) 87

Table 6.1 a: 2002 Mathematics Enrolment in Schools Targeted for AS 102

Table 6.1: 2003 Mathematics Enrolment in AS Intervention Schools 103

Table 6.2: 2004 Mathematics Enrolment in AS Intervention Schools 104

Table 6.3: 2005 Mathematics Enrolment in AS Intervention Schools 105

Table 6.4: 2006 Mathematics Enrolment in AS Intervention Schools 107

Table 6.5: 2002 Enrolment in Mathematics for CD Schools 109

Table 6.6: 2003-2004 Enrolment in CD Schools 110

Table 6.7: 2005 -2006 Enrolment Statistics in CD Schools 111

Table 6.8: 2002 Enrolment in Mathematics for EF Schools 113

Table 6.9: 2003 Enrolment in Mathematics for EF Schools 114

Table 6.10: 2004 Enrolment in Mathematics for EF Schools 115

Table 6.11: 2005 Enrolment in Mathematics for EF 117

xvii Table 6.12: 2006 Enrolment in Mathematics for EF 118

Table 6.13: Enrolment Time Series for Interventions 119

Table 6.14: Descriptive Statistics for Learner Performance in Three Interventions 122

Table 6.15: Shapiro-Wilkinson Test of Normality 122

Table 6.16: Mean Ranks performance for Interventions 126

Table 6.17: Friedman Test Statistics 127

xviii List of Figures

Figure 6.1: AS Matric Enrollement in mathematics 108

Figure 6.2: CD Matric Enrollement in mathematics 112

Figure 6.3: EF Matric Enrolment in Mathematics 119

xix APPENDICES

Appendix A Request to conduct research in GDE schools

Appendix B Approval to conduct research in GDE Schools

AppendixC Enrolment and Performance in Mathematics SG & HG during 2002-2006 for three interventions

Appendix 0 Mean Ranks for SG & HG % pass of three interventions

Appendix E Mean Ranks for SG percent pass of three interventions

Appendix F Grade 12 Mathematics Results in 2006 for all high schools in Gauteng

Appendix G High Schools that participated in AS intervention

xx CHAPTER 1

1. INTRODUCTION

1.1 BACKGROUND OF THE STUDY

Mathematics interventions popularly known as projects have been the engines for improving mathematics teaching and learning since the 1980s in South Africa (Levy, 1992 & 1994). However, during apartheid their efforts were countered by the laws of the day, making any systematic study of their impact meaningless. The birth of the South African democracy in 1994 ushered an era of transforming poor participation and performance for all learners, particularly those previously disadvantaged by Bantu Education Act of 1954 (Verwoerd, 1954:7, 15 & 25). The latter explicitly denied the Bantu child mathematics learning, with a consequent continued legacy of their low participation and performance in mathematics (Lawless, 2005:79).

Mathematics interventions in this new era assumed the role of transforming mathematics teaching and learning in schools within the national agenda of reconstruction and development (Department of Education and Training, 1995:5). Studying mathematics interventions and their impact, as this study did, does not only make sense, but it is imperative for the creation of knowledge with which to advance the cause of transforming learner participation and performance in mathematics.

1.1.1 Interventions as Catalyst for Policy Implementation

The Ministry of Education regarded the White paper on Education as a policy for transforming the educational legacies of the past, such as; "Access to

1 technological and professional careers requiring a strong basis in mathematics and science is denied to all but a fraction of the age cohort, largely because of the chronic inadequacy of teaching in these subjects" (Department of Education and Training, 1995:17). This implied that high school graduates lack competency in mathematics or did not do mathematics at all and this was the cause of poor teaching in mathematics. Hence a mathematics intervention was promulgated; "An appropriate mathematics, science and technology education initiative is essential to stem the waste of talent, and make up the chronic national deficit, in these fields of learning, which are crucial to human understanding and to economic advancement". (Department of Education and Training, 1995: 22). A framework and the goal for interventionswere stated as follows; "Special criteria will be needed to prepare students for subjects in short supply, particularly mathematics... Such interventions would be part of a comprehensive programme of special measures which are needed to enable more students to follow science -based careers" (Department of Education and Training, "1995:30).

This placed mathematics interventions in a crucial position as catalysts for transformation of mathematics education. Volmink (1995:102) confirmed this in his argument that: "The challenge that South Africa faces at this point in time is to develop and implement system-wide sustainable interventions to address the problems in education in general and in particular in science education". It is noted that science education is inclusive of mathematics education.

1.1.2 National Interventions in Response to Policies of Change

Heeding the call for transforming performance in mathematics by both learners and teachers, numerous interventions were implemented post 1995 (Nkabinde, 2008). These include RADMASTE, PROTEC and Star schools (Duma, 2004).

. 2 However, one that stands out was the flagship intervention, Students and Youth into Science, Technology Engineering and Mathematics (SYSTEM).

1.1.2.1. SYSTEM: The National Mathematics Interventions

SYSTEM was the comprehensive solution to the cycle of mediocrity in South African mathematics and science education (Kahn, Volmink & Kibi, 1995). According to Kahn et al. (1995) the SYSTEM initiative was viewed by numerous members of the Science & Mathematics Education community across the country, as a credible solution to a long standing problem. Volmink (1995:111) elaborated on the future of SYSTEM as follows: "It (SYSTEM) is a unique approach to system-wide, sustainable innovation in science education and has the potential to be extremely informative for future attempts of this kind in and beyond the borders of South Africa."

Indeed all countries love sustainable innovation. It therefore makes sense that more than a decade ago; SYSTEM was primed as a model for future interventions globally!

1.1.2.2. OBE: Curriculum Intervention

Outcomes Based Education (OBE) was introduced in 1997 as the new national curriculum. OBE found its way to the South African shores after its dramatic fall out with the school districts in the United States of America (USA), which had enthusiastically adopted it. A myriad of OBE's criticism and rationale for discontinuing with this education system include poor learner achievement in mathematics. For example, Pliska & McQaide (1994) and Davis & Fleknor (1994:65) argue that less than 20% of students could pass a mathematics skills test in state schools that implemented aBE across USA.

3 In response to discontinued aBE and its related programmes, its founder, Spady (NO: 58) argued that this was tantamount to placing systematic educational reform and programmes exemplifying this in wasteland. However, one of the programmes cited, Success for All is regarded as what works in school's reform for the 21st century (Me Chesney, NO: 2 & 11 and Joyce, Calhoun & Hopkins, 1999).

In fact, ten years after OBE was kicked out in the USA, 'Success for All' continued showing national gains in learner achievement (Borman, Slavin, Cheung, Chamberlain, Madden& Chambers, 2005 and Chamberlain, Daniels, Madden & Slavin, 2007). Contrary to Spady's claims educational reform was alive!

The implementation of aBE ICurriculum 2005 in South Africa was heralded by Spady and Schlebusch (1999:20) as a visionary education system for the new millennium of learning. The aBE paradigm means WHAT and WHETHER students learn successfully is more important than WHEN and HaW they learn something (Spady, 1994:8).

However, based on ten reasons Jansen (1997: 65) argued that aBE will fail. "For aBE to be successful even in moderate terms, requires that a number of interdependent innovations (interventions) to strike the educational system simultaneously" (Jansen, 1997:73). Jansen (1997: 73) also argued that aBE trivialises content knowledge.

Invariably, the majority of interventions in the late 1990s through the 21 st century had to be undergirded by the national policy in education, namely, OBEI Curriculum 2005. The latter was streamlined into National Curriculum Statements in 2001. Sadly, Spady's visionary education systems have not yet delivered success for all students in mathematics as the following sections discuss this.

·4 1.1.3 Mathematics Interventions in the 21 st Century

The few years of mathematics interventions at the turn of the century, did not seem to impact on poor learner performance in mathematics in high schools.

Both SYSTEM and aBE were implemented in 1997. However, the promise of solving the cycle of mediocrity and success for all in mathematics was not forthcoming at the turn of the century. Hence, the then Minister of Education Kader Asmal lamented: "Despite an improvement in the overall matric passes rate, 48,9% in 1999 to 57, 9% in 2000, the number of candidates from state schools who wrote maths on a higher grade fell from 50%, to 38% across two years. The number of young people who study mathematics with any degree of understanding and proficiency has declined when it should be increasing rapidly. As a result, mathematical illiteracy is rife in our society; and the pool of recruits for further and higher education in the information technology and science professions is shrinking" (Asmal, 2000: 15). This gave rise to yet another flagship intervention, Dinaledi with the same aim as SYSTEM.

1.1.3.1. National Strategy for Mathematics Education

In response to the declined enrolment of learners in higher grade mathematics, the National Department of Education launched a national strategy for mathematics, science and technology education in General and Further Education and Training in 2001. The national strategy is also called Dinaledi. Its mission statement was "to strengthen the teaching and learning of mathematics ... in General and Further Education and Training, using appropriate curricula, teaching methodologies and learning support materials" (Department of Education, 2001:14).

5 1.1.3.3. Forthcoming Mathematics Interventions

The Department of Education admitted that there still exists a problem of poor participation and performance by learners in mathematics in high schools (Department of Education, 2004). Hence, the Dinaledi was consolidated. Also, Mlambo Ngcuka (2006) launched JIPSA (Joint Initiative for Prioritised Skills) which viewed mathematics teachers as scarce skills (http://www.info.gov.za.za/speeches/2006/). But, more importantly, scarce skills are based on the continued few high school mathematics graduates. This is disconcerting since mathematics competency, for example, is the requirement for high school graduates to purse a career in Chartered Accounting. 6 However, Bernstein (2005:231) proposed a new mathematics intervention as a solution to the problem. Needless to say, the new intervention was conceptualised and would be run by her organisation, the Centre for Development Enterprise (CDE). The research referred to by Bernstein was also conducted by CDE. Bernstein's call for a new national intervention in mathematics is not new. Volmink (1995) had enthusiastically hailed SYSTEM as an intervention which could be a panacea for all the ills in mathematics education in the country and abroad!

Clearly, the country is set for yet another series of mathematics interventions! It is about time for the development of the body of knowledge of mathematics interventions. It is this background that underpins this study.

1.2 STATEMENT OF THE RESEARCH PROBLEM Mathematics interventions are now entrenched in South African high schools since their promulgation as catalysts to redress the deficit in mathematics achievement for the majority of the South African youth (Department of Education and Training, 1995:17, 22 & 30).

After more than a decade of mathematics interventions, calls for new mathematics interventions have been made as a result of their ineffectiveness (Bernstein, 2007). But, these calls have no shred of research that will be used as a foundation for more effective mathematics interventions. According to Gall, Gall & Borg (2003: 3-6) there are four types of knowledge that research contributes to education: (1) description, (2) prediction, (3) improvement or interventions and (4) explanation. Gall et al. (2003:4) elaborate on intervention geared research; "The third type of research knowledge concerns the effectiveness of interventions". There is a deficit on the third type of research knowledge focusing on mathematics education in South Africa (see Vithal, Adler & Kietel, 2005). In general, there is much debate on improvement

7 or interventions, that is, interventions associated with effective schools and learner achievement (Kamper, 2008, Prew, 2007 & Coleman, 2003). Available research on mathematics interventions is limited to researchers' experiences of mathematics intervention they were involved with, for example, Graven's (2005:206) experiences of Programme for Leaders in senior Phase Mathematics Education. Such research tends to be highly subjective. But more importantly, these are case studies. Lunenberg & Irby's (2008:97) caution against generalizing on case studies; "generalizations to broader populations is typically not appropriate for this type of research". This leaves the country with very little to work with, in navigating the way forward for mathematics interventions in high schools.

Contemporary research in mathematics education is developing an inclination towards the impact of mathematics interventions on learner performance and participation (Harwell, Post, Maeda, Davis, Cutler, Andersen & Kahan, 2007; Heck, Banilower, Weiss & Rosenberg, 2008; Post, Smith & Star, 2007; Star, Smith & Jansen, 2008 and Tarr, Reys, Chavez, Shih & Osterlind, 2008). Going forward with new interventions without research on their impact is as good as embarking on a journey without a map or direction. This is unacceptable in a country that still desperately needs to transform its past. Hence, there is a need for studies such as this, which investigate mathematics interventions with a view to navigating a path towards more effective mathematics interventions.

1.3 RESEARCH QUESTIONS

• What is the impact of mathematics interventions on the high school learner performance in mathematics?

• What is the impact of mathematics interventions on the high school learner participation in mathematics?

8 • What is the trend of impact of mathematics interventions over a five year period?

• What learner centred practices are promoted by interventions?

• How are mathematics interventions perceived by mathematics teachers?

1.4 PURPOSE STATEMENT

The purpose of the study was to investigate mathematics interventions and their impact in high schools.

1.5 AIM AND OBJECTIVES OF THE STUDY

1.5.1 Aim of the Study

The aim of the study was to contribute towards the body of knowledge on the impact mathematics interventions in high schools.

1.5.2 Objectives of the Study

The research attempted to: a) Investigate the impact of mathematics interventions in high schools. b) Explore and explain the impact of mathematics interventions in high schools from teachers' point of view. c) Explore the factors for the impact of mathematics interventions. d) Identify strengths and weaknesses of mathematics interventions in high schools.

9 1.6 SIGNIFICANCE OF THE STUDY

1.6.1 Practical Significance

In contrast to evaluation research for particular mathematics interventions (Simkins & Perreira, 2005; Taylor, 2007 and Taylor & Mabogoane, 2007), this study investigated more than one mathematics interventions. Unlike the aforementioned studies, the intention was not to promote or build on one case study, but, to find the common threads that could be hampering progress in improving mathematics education in high schools despite several interventions.

1.6.2 Theoretical Significance

Huff (2009:28) cites an enduring topic as one criterion for theoretical contribution. More importantly, Goddard and Melville (2006:120) reiterate that the policy on science and technology states that South African research should be "more responsive to the needs of the majority of our people..." This study is responsive towards the enduring topic in our country, namely, policy implementation in education (section 1.1.1) and the worldwide reform in mathematics education. Also, scarce skills which are mainly based on high level mathematics are among the priority needs in our country. Hence, this study is poised to make a significant theoretical contribution.

1.7 OPERATIONAL DEFINITIONS OF TERMS

Four terms are encapsulated in the concept of the study. These are mathematics interventions, learner, learner participation, learner performance. To avoid any confusion, the four terms are given operational definitions for this study. Both learner participation and performance are defined in mathematics for matriculation examinations or senior certificate. Learner participation in mathematics will mean enrolment or registration in higher grade mathematics for the senior certificate or matriculation

10 fJ !

examinations. This is in accordance with the prevalent view of senior certificate as a benchmark for students' performance (Taylor, 2007: 3) and enrolment in higher grade mathematics demands more capable students than enrolment in standard grade mathematics (Maharaj, 2005:15).

It is noted that higher and standard grade mathematics have been phased out since the implementation of the streamlined aBE curriculum, namely, the National Curriculum Statements (NCS). This brought about enrolment in mathematics or mathematical literacy. The first matriculation examinations for NCS were written in 2008.

Learner performance in mathematics will mean a pass in higher or standard grade mathematics. In the South African context a pass in mathematics is given by 33.5% and above.

Mathematics intervention means mathematics programme or project or initiative with a purpose of increasing or improving learner participation and pass rate in mathematics.

Learners In this study learners meant adolescent learners in high schools.

1.8 THEORETICAL FRAMEWORK AND THE OVERVIEW OF THE STUDY

1.8.1 Theoretical Framework

Literature review provided a theoretical framework for the study and ensure that unnecessary duplication was avoided (Bordens & Abbot, 2007:60 and McMillan & Schumacher, 2006:75). Preliminary literature review identified mathematics learning in high schools, educational and mathematics interventions as focus areas for literature review. Reviewing literature on mathematics interventions was only logical. 11 The rationale for the inclusion of adolescents in this study was that the South African constructivism in mathematics education was mainly spearheaded for primary schools and popularized by Stellenbosch University in the 1990's (http://academic.sun.ac.za/education/facultvJremus/index.html).This gave rise to the widespread problem solving and learner centred approaches in mathematics learning and teaching. However, most research was done for primary mathematics learners (Murray, Olivier & de Beer, 1999:305 and Newstead & Olivier, 1999:329).

In pursuit of high school relevance, this study was based on learner centred learning, thus on adolescents and their learning. This was in view of the expanding literature on positive development of youth (Peterson, 2004), which recognizes that the high school educational environment can be developed to meet the core needs of the adolescents, hence enhancing their learning (Newell & Van Ryzin, 2007). Coupled with this were calls that adolescent development was a critical missing focus in school interventions (Comer, 2005). Intertwined with adolescent learner in high schools was the national and international literature on mathematics interventions.

1.8.2 The Overview of the Study

Addressing the research questions for the study requires a mixed method study. A mixed method design where qualitative methods are used as to explain quantitative findings espoused by (Creswell & Clark, 2007:72 and Ivankova, Creswell & Clark, 2007), boded well with the research problem. Therefore, the study had a sequential mixed method design, where the quantitative phase of the study was followed by the qualitative phase.

12 1.8.2.1. Sampling

The mixed method sampling design was in accordance with Onwubuzie & Collins's (2007) proposed typology for sampling in mixed methods where both random and non-random sampling is employed. Non-random sampling was used to select a sample of mathematics interventions which operated in Gauteng. Out of this sample, random sampling was employed to select schools which participated in interventions. In the qualitative phase, non-random sampling was employed to select a sample of intervention schools from the random sample of schools selected in the quantitative phase.

1.8.2.2. Ethical Issues

Ethical considerations were in accordance with Goddard and Melville (2006: 108-109 and 138-139). These two authors go beyond suggesting informed consent, no deception, privacy and confidentiality and accuracy. They also suggest avoiding dubious subjects and dubious ways of researching. Letters requesting participation in the study were written to active and non-active participants. Active participants were teachers from schools that participated in interventions. Non-active participants were those who provided documentation on mathematics interventions, these include the Gauteng Department of Education and service providers for interventions. They were regarded as non active because interventions were not mean to impact them, but they were involved in the implementation of interventions and this made them sources of information.

Reciprocity will also be incorporated as part of ethical issues in the study. (Glesine, 2006:102; Patton, 2002:408 and Seidman, 2006:109). In this case it will take the form of advocacy of the plight of schools participating in interventions. Findings with a bearing towards enhancing the quality of

13 interventions and their implementations will be highlighted to the Department of Education.

1.8.2.3. Data Collection and Analysis

Data will be collected and analysed sequentially in quantitative and qualitative phases respectively. Data from the quantitative phase will address the first four research questions. The number of learners registered for mathematics in grade 12, and learners' results at the end of each year (2002-2006), will be collected from sample intervention schools.

Descriptive statistical analysis will be utilized to measure the impact of interventions for each year. This will be followed by the employment of time series which will investigate the trend of the impact of interventions over a five year period.

Data from ,qualitative phase will address the last two research questions, will also explain the findings from quantitative findings. Data will be collected through qualitative group interviews. All transcription from qualitative interviews will be done by the researcher, since Patton (2002: 441) argues that doing your own transcription provides an opportunity to get immersed in data which in turn generates emerging insights. After transcription, analysis will be carried out.

Data analysis will be in accordance with recommendations by Rubin and Rubin (2005:201), hence transcribed material will be classified, compared, weighed and combined to extract the meaning and implications. Since explaining quantitative findings will be the purpose of qualitative phase, meaning extracted will be in the context of quantitative findings.

14 1.9 DELIMITATION OF THE STUDY

Limitations of the study will be discussed in hindsight of the study since these were encountered during the study. However, delimitations mark the boundaries of the scope and variables of the study (Goddard & Melville, 2006:14 and Lunenburg & Irby, 2008:134). The following delimitations were imposed:

• The population for the study was confined to government high schools in the Gauteng province;

• Mathematics interventions that have operated in at least ten high schools in Gauteng for at least three years were eligible for inclusion in the study;

• Quantitative methods regarded performance and participation in mathematics grade 12 as dependent variables that defined the impact of mathematics interventions. Hence, mathematics interventions became independent variables;

• This study was delimited to perspectives and experiences of interventions to teacher participants because grade 12 learners, who have experienced the interventions over the years, had since left the high school system.

1.10 PHILOSOPHICAL ASSUMPTIONS

Addressing research questions will require the employment of both quantitative and qualitative methods. According to Morgan (2007:48-76) this qualifies for a loss of paradigm and a regain for pragmatism. In particular, Dewey's pragmatism will be adopted as the philosophical foundation for the study. This will further be discussed in chapter 5.

15 1.11 PLAN OF THE STUDY

The report on the study will have eight chapters, contents of which are briefly given below.

Chapter One

This chapter gives the motivation for the study, research problem, research questions, its brief methodology, the value of the study and its limitations.

Chapter Two

This chapter reviews literature on adolescent learners in mathematics. This entails the discussion of adolescence traits that have the potential of enhancing mathematics learning for high school learners.

Chapter Three

The chapter will review international literature on educational interventions that specifically increase learner achievement in mathematics. The last part of the chapter will review mathematics interventions that are based on mathematics curriculum which aims to improve mathematics learning and learner achievement.

Chapter Four

This chapter reviews South African mathematics interventions within the context of the country's old educational systems prior to 1994 and a new educational system after 1994.

Chapter Five

This chapter will discuss in detail the research design for the study.

16 Chapter Six

This chapter will present the quantitative data, its analysis and the findings.

Chapter Seven

This chapter will present the qualitative data and its analysis within the context of quantitative findings. Therefore, this chapter merges findings from two phases into one.

Chapter Eight

This chapter makes conclusions about the findings on the study. Recommendations are then made based on the conclusion.

1.12 SUMMARY

Chapter one laid the foundation for the study by espousing the background of mathematics interventions and how these fit in within the policy of educational change in the country. Hence, the significance of the study was viewed from a practical and theoretical perspective. Research questions dictated the choice of the mixed methods design and the consequent placement of the study within pragmatism. The study will now be pursued in accordance to its stated plan in this chapter. Therefore, literature on adolescence and its relevance in mathematics learning and achievement will be reviewed in the following chapter.

17 CHAPTER 2

2. ADOLESCENT LEARNERS IN MATHEMATICS

2.1 INTRODUCTION

This chapter discusses the adolescent learners in mathematics, since they constitute learners in high schools. The discussion is placed within the context of the ongoing poor performance by adolescents in mathematics internationally and locally, as well as the call to understand these learners as part of the development of their learning programmes (interventions). Then adolescence is discussed with a focus on its associated opportunities for enhanced learning in mathematics.

2.2 MATHEMATICS PARTICIPATION AND PERFORMANCE IN HIGH SCHOOLS

Research in the past two decades shows that participation in mathematics, for a learner in high school is declining. Dosey, Mullis, Lindquist & Chamber (1988) found that children tend to enjoy mathematics in primary school but this level of enjoyment tends to fall dramatically when children progress into and through high school. Meece, Wigfield & Eccles (1990: 60) claim that American surveys reported that only half of high school learners enrol for mathematics courses beyond grade 10. This is a consequence of students' reports of uneasiness, worry, and anxiety related to mathematics during the early adolescent years (Meece, Wigfield & Eccles, 1990: 61).

This problem still persisted in the twenty first century. For example, Byrne (2003:316) found that there is low participation and performance in mathematics for high school learners. Also, Wang and Goldschmidt (2003:3) found that the

18 distribution of mathematics course taking among various subgroups not only differed in Grades 8 but also became increasingly inequitable by grade 11. The recent study by Chouinard and Roy (2008:31) of 1 130 participants from 18 secondary schools also supported the hypothesis of a regular decline of motivation in mathematics during high school. Highlighting the seriousness of low performance in mathematics by teens in the US, Kronholz (2004:1-2) called it an economic time bomb!

The same problem is also prevalent in South Africa. The Department of Education attests to this: "The number of learners who participate and successfully pass mathematics and science in grade 12 is very low" (Department of Education, 2001:8).

2.3 PLACING LEARNERS FIRST

The South African policy on education is clear on the position of all learners in educational programmes.Curriculum development, especially the development of learning programmes and materials, should put learners first, recognising and building on their knowledge and values and lifestyles experience, as well as responding to their needs. Different learning styles and rates of learning need to be acknowledged and accommodated both in the learning situation and in the attainment of qualifications (National Department of Education, 1997:2).

This call for prioritizing the exploration of ways of responding to the needs of high school mathematics learners and understanding their knowledge and values as part of theory of mathematics interventions in high schools (Marshal, 2006:356). The majority of high school learners are between 12 to 18 years of age making high schools a habitat for adolescents. Therefore, understanding high school learners means understanding of adolescence which is a well researched developmental stage for high school learners.

19 Hence, the following sections will give an overview of the developmental stage of high school learners and the opportunities of learning capabilities appropriated by the stage.

2.4 ADOLESCENCE: THE GOLDEN AGE FOR LEARNING

Traditionally, adolescence has been regarded as a storm and stress phase (Chandler, Lalonde, Sokol & Hallet, 2003:61; Flannery & Wester, 2004 and Kaufman, 2001). However; Coleman and Hendry (2004:208) argue that the stormy phase concept has been declared a myth by several researches in the 1950s. For example, Bandura (1964) argued that it is a fiction to regard adolescence as a stormy phase.

Contrary to the stormy phase concept, research has found that the large majority of adolescents appear to get on well with adults and are able to cope effectively with demands of school (Siddique and D'Acry, 1984 in Coleman and Hendry, 2004:209).

Subsequent to the study by Siddique and D'Acry, research on positive youth development (Peterson, 2004) and associated learning interventions in schools (Weissberg & O'Brien, 2004) continue to view adolescence with optimism (Park, 2004). In their monograph Silbereisen and Lerner (2007) view several approaches to positive youth development by a variety of researchers in this field. For example, Benson (2007:33) espouses a model of viewing and researching positive youth development as developing assets. One of these assets seems to be the cognitive growth accomplished by learners during adolescence.

20 2.4.1 Cognitive Growth during Adolescence

Literature on adolescence indicates that physical growth among adolescents is coupled with the unobserved drastic cognitive growth (Keating, 2004:45-84). The array of newly acquired cognitive abilities by adolescents or specifically, high school learners herald good news for mathematics learning!

Coleman and Hendry (2004: 36) assert that there is improvement in attention, both short and long term memory for adolescents. Harris and Butterworth (2002:306) argue that adolescence is marked by new forms of systematic thinking which includes capacity for abstract thinking. Adding to the above cognitive abilities that come with adolescence, Lefrancois (2001: 488) and Berk (2005:365) claim that adolescents have advanced meta cognitive skills and their cognitive self regulation improves.

Much of adolescents' cognitive growth has been explained in terms of Piaget's developmental theory. For example, Berks (2003:362) regards this cognitive growth as the attainment of formal operational stage which has two main features, namely, hypothetico-deductive reasoning and propositional thought. Berk (2003: 363) further elaborates on hypothetico-deductive reasoning as follows: "When faced with a problem adolescents start with a general theory of all possible factors that might affect the outcome and deduce from its specific hypothesis or prediction about what might happen. Then they test these hypotheses in an orderly fashion to see which ones work in the real world".

In mathematics learning, several cognitive engagements can be identified (Helmes and Clarke, 2001:133). These include, mathematical reasoning (Ellis, 2007:3, Rasmussen and Marrongelle, 2006:5) and problem solving which is regarded as both an objective and a process in mathematics learning (Dixon,

21 2004). Therefore cognitive growth presents an opportunity for mathematics learning in high schools.

Much as learning is a cognitive activity, a strong connection between affect and mathematical cognition has been cited (Ashcraft and Ridley, 2005:315). It is noted that emotional and affective problems are still viewed as the dark side of adolescence (Kail & Cavanaugh, 2007:363). However, much research on how adolescents cope with this problem has been conducted.

2.4.2 Coping and Resilience for Adolescents

Research acknowledges that learners face unique challenges during adolescence, which include socio emotional development (Kail and Cvanaugh, 2007:339) and academic and school performance (Seiffge-Krenke, 2004:367; Compass, Connor-Smith, Saltzman, Thomsen and Wadsworth, 2001:87-127).

Social support systems have been found to enhance students' emotional adjustment to their challenges (Newman, Newman, Griffin, O'Connor and Spas, 2007: 441). In adjusting prosocial behaviour academic achievement increases in turn. (Martin, Martin, Gibson and Wilkinson, 2007:689). Therefore research on adolescence has focused on finding pathways to adjustment of adolescence during this transitional phase or resilience.

Adjusting effectively or resilience is said to be a result of a positive coping style (Seiffe-Krenke, 2004: 367-382). Adolescents usually employ two positive coping strategies, these are, active coping and internal coping (Seiffe-Krenke, 2004: 369). However, some use maladaptive coping style, which results in negative outcomes, such as problem behaviour and depression (Beam, Gil-Rivas, Berger and Chen, 2002:343).

22 There has been research on interventions of preventing maladaptive copinq style (Chaplin, Gilham, Reivich, Elkon, Samuels, Freres, Winder and Seligman, 2006:110). This has shown positive results. Of interest has been international research on coping styles for adolescents which included South African adolescents.

2.4.2.1. Coping Styles for South African Adolescents

An international study of coping strategies by adolescents in 22 countries was conducted by Gelhaar, Seiffge-Kreneke, Bosma, Cunha, Gillespie, Lam, Loncaric, Macek, Steinhausen, Tam and Winkler-Metzge (2004). This research found the majority of South African adolescents use active and internal coping' in the face of challenges. The following table summarizes the findings in nine countries.

Table 2.1 Coping styles in adolescents from nine countries. (Adapted from Seiffege-Krenke,2004:369) Country Active Coping Internal Coping Withdrawal Germany 40,4 34,8 24,7 Switzerland 38,1 40 21,9 The 37,9 37,9 24,1 Netherlands Croatia 38 38 23,9 Portugal 35,5 39,2 25,3 Finland 36,1 47,2 16,7 Czech Republic 38,7 41,3 20 South Africa 36,9 35,4 27,7 Hong Kong. 35,4 37,5 27,1

23 The above table indicates that more than 72,3% of adolescents in South Africa are capable of surmounting challenges which may negatively impact their academic achievement. Only 27,7% are at risk. Research has shown that hopelessness and risk behaviour are particularly prevalent in high poverty neighbourhoods (Bolland, 2003).

South Africa has a significant number of these neighbourhoods. For example, Hoogeveen and Ozier (2006:59) found that many communities in the former homelands have little economic activity, such that the mean employment rates in these communities approach 75%. There is overwhelming evidence that in the post apartheid period poverty and inequality have increased (Bhorat and Kanbur ,2006:13, May,2006:321 and Leibbrandt, Poswell, Naidoo and Welch(2006: 95). Some researchers have argued that increased poverty is more prevalent among black communities (Armstrong, Lekezwa and Siebrits (2009).

In presenting a case for rural areas in South Africa as being impoverished communities lacking in the basic needs, Rakgokong (1994:80) further argues that resea-rch on mathematics education has an urban bias. Hence, according to Rakgokong's (1994:81) thesis, research on mathematics education excludes South African impoverished communities. In view of findings by Seiffege-Krenke (2004), coping styles of the country' impoverished youth may be an unexplored avenue of research in mathematics education with potential gains in mathematics achievement in high schools.

This research places South African adolescents' coping styles on par with those of adolescents from the Czech Republic and Hong Kong (http://timssandpirls.bc.edu).

24 These two countries are the front runners in the series of international research on learner achievement in mathematics and science, namely, The Third International Mathematics and Science Study (TIMSS) of 1995 which has subsequently become the Trends in International Mathematics and Science Study in 2003 and 2007 (http://www.iea-dpc.de/timssinternationaI12.html).

Since the coping styles are associated to academic achievement (Martin, Martin, Gibson and Wilkinson, 2007:689), the placement of South African adolescents on par with adolescents who are known to be achievers in mathematics does raise questions about whether the capability of the South African adolescents are being fully tapped. This is of particular importance in view of the cognitive development inherent during adolescence.

Thus far it has been established that adolescents have cognitive capability and coping strategies to deal with challenges that may be presented by learning mathematics. One more important aspect for adolescents that may have an effect in their learning is the identity formation that takes prominence during this stage.

2.5 IDENTITY FORMATION VERSUS IDENTITY CRISIS

Ericson (1968) popularised identity crisis as prevalent among the adolescence developmental phase. However, Marcia (1980) modified the 'identity crisis' by to 'identity formation by adolescents' which has a positive connotation. Subsequent to Marcia's modification of identity crisis, contemporary research on adolescents is more on identity formation as part of positive youth development (Graf, Mullis & Mullis, 2008:57; Kroger, 2007; Silbereisen & Lerner, 2007; Sartor & Youniss, 2002).

25 Hence, formation of identity as opposed to identity crisis has ushered in a platform for positive youth development. Statuses of identity formation as promulgated by Marcia (1980) are briefly discussed in the following section.

2.5.1 Statuses for Identity Formation

It is noted that recent research suggests a modification of the identity development model (Schwartz & Montgomery, 2002 and Kroger, 2007). More importantly, African researchers, for example, (Nsameng, 2002:61) assert that adolescent psychology is a Eurocentric enterprise. Hence, he views adolescence identity as having to fit in with the Western mould which is dominated by America.

Nevertheless, according to Marcia (1980:161) identity formation is a process during adolescence that has four statuses, namely, identity achievement, foreclosure, identity diffusion and moratoriums. These are defined in terms of decision making period, which are the personal investment (commitment) to an ideology and an occupation.

Hence scales have been developed to measure statuses of the youth. For example, Crocetti, Rubini, Meeus (2008: 207) used the Utrecht-Management of Identity Commitment Scale to investigate identity statuses for the youth from various ethnic groups. Eryigit and Kerpelman (2009:1137) used the Turkish version of the Identity Processing Style a-Sort (IPsa) to examine the identity styles for the youth in Turkey. Finally Graf, Mullis & Mullis ( 2008:61) employed the Extended Version of the Objective Measure of Ego Identity -II to examine adolescent identity formation in tow cultures.The following table summarizes the criteria for these four statuses.

26 Table 2.2: Criteria for the Identity Statuses (Marcia, 1980: 162)

Occupation and Identity Foreclosur Identity Moratoriums Ideology Achievement e Diffusion

Crisis present absent Present or absent In crisis

Commitment present present absent Present but vague

Identity achievements are adolescents who have experienced a decision making period and are pursuing self-chosen occupation and ideological goals. Foreclosures are young people who are also committed to occupation and ideological positions, but these have been chosen by their parents or (other adults ofinfluence), rather than themselves.

Identity diffusions are those adolescents who have no occupational or ideological directions. Even though some diffusion went through moratoriums, others have not.

Moratoriums are youngsters who are struggling with occupational and lor ideological issues as they experience a decision making period. Graf, Mullis and Mullis (2008:57-69) found that adolescents in India had higher moratoriums than those in the USA.

It is noted that there are several contextual identities, for example, ethnic and national identity (Wissink, Dekovoc, Yagmur, Stams & de Haan and Sabatier,2008:185-205 ), sexual identity (Parker, Blaise Adams, and Phillips, .2007:205) as well as political, religious and occupational identities (Solomontos Kountouri and Hurry, 2008: 241-258). Hence, some researchers have cited categories of identities (Hendry, Leo, Mayer and Kloep, 2007:181).

27 However, in this study the focus is on the general academic identity and in particular identity in mathematics learning for high school students.Marcia described the formation of identity in terms of the commitment by the youth (Berzonsky, 2004:304). For this study the context within which the identity formation occurs is mathematics learning. The main agents for such an identity formation are peers, parents, school and teachers context (Adams and Paliian, 2004:238). However, the discussion will be confined to schools and teachers as agents of this identity formation.

2.5.2 Agents of Identity Formation

Adams and Palijan (2004:237) contend that the major institutions of socialization for identity development are the culture, school and the family. The school plays the most significant role in the identity formation of adolescents as a socializing agency.

Literature reveals that school connectedness in adolescents results in the positive outcomes (Whitlock, 2006). Attesting to this Ma (2003:340) found that "Students' self esteem was the single most important predictor of their sense of belonging". School connectedness and a sense of belonging is a package that comes with perceptions and support that adolescents get from the communities they belong to. But Bouchey and Harter (2005:673) found that perception of teachers concerning perceptions of students' competence in mathematics as well as their support, predicted students' own self perceived importance, competence, scholastic behaviour. and performance in mathematics. In general, teacher support to adolescents enhances achievement (Klem & Connell. 2004).

There is research which regards the process of learning mathematics as an identity formation.

28 2.5.3 Learning Mathematics as Identity Formation

According to Lerman (1998:85) a far more useful notion than understanding is that of the forming of identities in the mathematics classroom. Identity is constituted in discursive practices, which carries what constitute knowledge in that practice.

Lerman's (1998) proposition of 'forming identities in the mathematics classroom' is based on the situated learning theory by Lave and Wanger (1991). In situated learning, teachers are viewed as masters of practice and learners as apprentices. Therefore, apprentices or learners are in the process of forming identities in a community of mathematics practice.

There has been research on turning mathematics classrooms into communities of practice where learners are viewed as apprentices who are in the process of becoming expert mathematicians (Winbourne and Watson, 1998: 177-184). In other words they are in the process of forming specific identities in mathematics, namely mathematics experts.

The discussion above elaborated more on the schooling environment that encourages identities in mathematics learning. Not much was said on the part played by the learner in the formation of the identity. To explore the part played by the learner in identity formation, Brodsky's (2004:303) concept of meaning is adopted. He conceptualizes identity as, "a self theory, a conceptual structure composed of self-representational and self-regulatory constructs": To understand the process of identity formation, self theories are discussed in the following section.

29 2.6 SELF THEORIES AND MATHEMATICS IDENTITIES

Dweck (2000) defines self theories in terms of beliefs about intelligence type an individual has, as well as helpless and mastery responses to failure and goals pursued during the process of learning.

2.6.1 Entity and Malleable Intelligence Beliefs

Dweck (2000:2) argues that learners either believe they have malleable intelligence or fixed intelligence also called 'entity' theory. Learners who believe they have fixed intelligence are for ever preoccupied with illustrating that they have enough intelligence. On the contrary learners who believe intelligence to be something that they can cultivate through learning, will always apply more effort to succeed.

2.6.2 Helpless and Mastery Responses to Failure

On the one hand Dweck (2000:7) found that learners with a helpless response to failure withdraw effort when faced with challenges, even though they have had more successes in problem solving than failures. On the other hand learners with mastery responses to failure applied more effort when confronted with challenges and hence ended up succeeding. Believers in entity intelligence tend to adopt a helpless response to failure, since to them they have enough intelligence to overcome the challenge or they do not have. On the other hand, malleable intelligence believers will expend more effort until they succeed.

2.6.3 Pursuit of Goals in Learning

Research on goal theory has found that goals pursued by learners during the learning process impact on their academic achievement. For example Elliot, Shell, Henry and Maier (2005:630-640) found performance avoidance goals

30 undermined mastery goals or mastery response to failure, whereas, performance approach had a more positive effect on performance.

Harackiewicz, Durik, Barron, Linnernbrink-Garcia and Tauer (2008: 105-122) found that achievement goals play an important role in developing interest in school work. This sets a positive environment for academic achievement. More importantly, research has shown that interventions that assist adolescents to set constructive goals have positive outcomes (Forneris, Danish and Scott, 2007:103-114).

2.6.4 Self-Efficacy in Mathematics Learning

In view of the fact that self theories are mainly about self beliefs regarding the learning tasks at hand, it is closely connected to self efficacy. The later has been found to correlate positively with academic achievement. This is substantiated by Pintrich (2003:671) that" students who believe they are able and that they can, are more likely to be motivated in terms of effort, persistence, and behaviour than students who believe they are less able."

In secondary school and compared to performance in other subjects, self efficacy beliefs have been shown to be the most highly related with performance in mathematics (Pietsch, Walker and Chapman, 2003). This was also confirmed by Stevens, Olivarez, Lan & Tallent-Runnels (2004) who found that self efficacy predicts motivational orientation and mathematics performance. According to Bong (2001 :23) self efficacy and goal theory are motivation constructs. Much research has linked achievement in mathematics with motivation and attitude, for example, DelFava (2005) and Hendricks (2005).

31 2.6.5 Self Theories and Self Efficacy as Constructs of Identity.

The discussion of self theories has espoused what learners believe about their intelligence, and how this impact in the way they respond to failure. The goal theory which is also part of self theories, established that given a learninq situation, learners will pursue performance avoidance goals or performance approach goals. Dweck (2000) found that learners are consistent in their beliefs and responses adopted towards failure. Hence, self theories and self efficacy in learning are constructs of learning identities.

Research points out that in the early adolescence, learners resort to avoidance strategies in mathematics classroom (Turner, Meyer, Anderman, Midgley, Gheen, Kang and Patrick (2002). The cause for this corresponds to self theories of learners: "Young adolescents may forego effort to succeed to protect their public image of competence." (Turner et aI., 2002:89).

While this behaviour corresponds with the adolescents' eagerness to look good to their peers, this also seems like these learners are foreclosures. Therefore, they have not committed themselves to making effort in mathematics learning.

2.7 INFUSING ADOLESCENCE IN MATHEMATICS LEARNING

From the above discussion, there is potential to enhance mathematics learning in high school. Optimal utilization of the cognitive growth of high school learners should underpin interventions that aim to increase performance in mathematics. Also the whole process of mathematics teaching and learning can be turned into positive identity formation for learners who are naturally at the height of identity formation. Positive aspect of self theories can be used as frameworks for forming positive identities in mathematics which will enhance self efficacy in mathematics.

32 Finally, South Africans have an opportunity tap into the positive copings styles of their adolescents (See Table 2.1). In keeping with the 'learner first policy', all the positive aspects of adolescence should be infused in interventions and schools. According to Cossa (2006) even rebellion by adolescents has a cause. Such rebellion may be a reaction against being treated as subjects and not as respectable citizens (Cushman, 2005).

Therefore the question for mathematics interventions in high schools should be how adolescents are incorporated in the intervention equation. This would mean infusing those adolescence aspects with a capability of enhancing mathematics learning into interventions in high schools, as a learner centred strategy in high schools.

2.8 SUMMARY

This chapter has discussed and highlighted positive aspects of adolescence in relation to learner centred approaches in mathematics learning in high schools. These characteristics which are naturally prevalent among high school learners as a result of their developmental stage could be infused in the learning process to enhance learner achievement in mathematics. The following chapter reviews global/international mathematics interventions..

33 CHAPTER 3

3. GLOBAL MATHEMATICS INTERVENTIONS

3.1 INTRODUCTION

In the previous chapter the foundation on which to base mathematics interventions was laid by discussing how adolescents learned. This chapter takes this foundation further, by reviewing international literature on mathematics interventions. As part of the introduction, a brief discussion of the general role of interventions and the time it takes for interventions to have effects. This will be followed by a review of three categories of educational interventions that have the potential to enhance learner achievement in mathematics.

3.1.1 The Role of Interventions in Education

There are mainly two roles for interventions in education. One is the route towards the improvement of education systems (Adey and Shayer, 1994: 2) and the other is the correction of a specific problematic area in education. For example Stoll (1995: 12) regards mathematics interventions in Southern Africa as efforts to break the vicious cycle, at some point or at least slow down the negative spiral of quality erosion of mathematics education in this region.

3.1.2 Timeframe for Interventions' Effectiveness

What works must be supported by the evidence of improvement in mathematics achievement. The effectiveness of the interventions can no longer be glossed over by unsubstantiated reports. Most researchers agree that the evidence of effectiveness must emerge within a specific period. For example, Adey and Shayer (1994) set two years as the necessary duration for the effectiveness of the intervention to have evidence.

34 CHAPTER 3

3. GLOBAL MATHEMATICS INTERVENTIONS

3.1 INTRODUCTION

3.1.1 The Role of Interventions in Education

3.1.2 Timeframe for Interventions' Effectiveness

What works must be supported by the evidence of improvement in mathematics achievement. The effectiveness of the interventions can no longer be glossed over by unsubstantiated reports. Most researchers agree that the evidence of effectiveness must .emerge within a specific period. For example, Adey and Shayer (1994) set two years as the necessary duration for the effectiveness of the intervention to have evidence.

34 Joyce, Calhoun and Hopkins (1999:19) have a shorter duration to show the effectiveness of an intervention. They assert:

• Even extensive renovations of the curricularlinstructional complex can. be made within the first year ofan initiative

• Student learning effects will occur during the first year.

Joyce et al. (1999) assert to have found no examples where a substantial change was not accompanied by student learning gains during the first year. "If they do not happen then, they are unlikely to occur later" ( Joyce et ai,1999:21). Setting a specific duration to judge the effectiveness of an intervention makes sense. If an intervention does not work for a specific duration of time, some adjustments have to be made as opposed to waiting for a miracle to happen.

3.2 COGNITIVE INTERVENTIONS

Feuerstein Instrumental Enrichment (IE) intervention will be discussed as representing cognitive interventions, since the majority of the latter seem to be based on IE. For example Cognitive Acceleration through Science Education (CASE) is a two-year cognitive intervention developed and implemented in 9 UK schools by Adey and Shayer (1994:78-89).

Though, its origins are in Israel, IE has also been adopted in other countries such as Canada, France and North America and has a track record of enhancing logico-mathematical intelligence for children, adolescents and adults (Campbell, Campbell & Dickinson, 2004:41). Using the IE theory, Mehl (1985:231) managed to bring down the failure rate from 50% to 0% for first year Physics disadvantaged students at the University of Western Cape.

35 Feuerstein Instrumental Enrichment was initiated by Feuerstein (1980). to enhance learning and achievement of immigrant adolescents in Israel. Feuerstein (1980:74) based his programme on the tenet that adolescents have experienced cognitive growth, but affective-motivational factors affecting the cognitive processes can combine negatively and influence the attitudes of learning among adolescents in a way that derails the effective cognitive functioning. He asserted that the derailed cognitive functions do not reflect a deficit in cognitive ability (Feuerstein, 1980: 403).

In elaborating on what IE does, Feuerstein (1980:403) states, "...the train of a person's thoughts are like a heap of stones, when a person removes one from the pile they all go tumbling over each other". Hence, the Feuerstein Instrumental Enrichment ensures that 'the stones are put together again', but more importantly; factors that resulted into their tumbling are removed.

It would seem that IE acknowledges adolescence as the golden age for learning and assumes theory of cognitive growth for adolescents (section 2.4.1). In the absence of expected academic achievement by adolescents, IE intervenes to correct the undesirable coping styles by learners (section 2.4), hence enabling adolescents to reach the desired academic achievement (section 2.5.1).

3.2.1 Link between Cognitive and Mathematics Interventions

In view of the capability of cognitive interventions to enhance logico mathematical intelligence, they could be used as mathematics interventions to enhance learning, hence improve achievement in mathematics. The latter is the product of enhanced logico-mathematical intelligence. Also, research shows that cognitive functioning is the pillar of mathematics learning. Examples include description or defining, understanding, analysis and justification of mathematical concepts (Reys and Lappan, 2007:678).

36 Problem solving is almost sine quo non to mathematics learning (Fuchs, Fuchs, Stuebing, Fletcher, Hamlett and Lambert, 2008:30). Algebraic reasoning (Jacobs, Franke, Carpenter, Levi & Battey, 2007:258), geometric reasoning (Barrett, Clements, Klanderman, Pennisi and Polaki (2006:187) as well as proportional reasoning Seeley (2004:22) are viewed as essential in effective learning of mathematics.

Also, Hiebert, Stigler, Jacobs, Giwin, Garnier, Smith, Hollingsworth, Manaster, Wearne and Gallimore (2005: 118) concluded that the absence of mathematical reasoning in American mathematics lessons is one of the main reasons behind the low performance of American high school learners in the TIMSS (Third International Mathematics and Science Study). According to Hiebert et al. (2005: 118) in high performing countries such as Japan and Hong Kong, more than 25% of the lesson is spent on mathematical reasoning.

Since mathematics learning is a cognitive activity, enhancing cognitive functioning through cognitive interventions, may have the potential of achieving what has eluded mathematics interventions in the country.

3.3 COMPREHENSIVE SCHOOL REFORM INTERVENTIONS

The second category of interventions with potential to enhance mathematics achievement is Comprehensive School Reform (CSR). This category is similar to research on school effectiveness (Kyriakides & Luyten, 2009 and Stringfiled, Reynolds & Schaffer, 2008). The latter focus on researching the variables that make schools effective, whereas CSR are interventions implemented to correct what is wrong in an educational system.

37 3.3.1 Components that define CSRI

According to Borman, Hewes, Overamn & Brown (2002:2) Comprehensive School Reform Interventions (CSRI) are defined by 11 components that, when coherently implemented, represent a comprehensive and 'scientific based' approach to school reform.

The following five of these components revolve around learning and achievement:

• Employs proven methods for student learning, teaching, and school management that are based on scientifically based research and effective practices, and have been replicated successfully in schools;

• Integration of instruction, assessment, professional development, parental involvement, classroom and school management;

• Includes measurable goals for student academic achievement and establishes benchmarks for meeting those goals;

• Includes a plan for the annual evaluation of the implementation of the schools' reforms and the students' results achievement;

• Meets one for the following requirements: the programme has been found through scientifically based research, to significantly improve the academic achievement of participating students.

From the above three of the defining components for the CSRI focus on teachers and parents. The latter must support the intervention, otherwise the intervention can not continue. Regarding the former, CSRI has to:

• provide high quality and continuous teacher and staff professional development and training;

• ensure that it is supported by teachers, principals, administrators, and other staff throughout the school; 38 • provide for the meaningful involvement of parents and the local community in planning, implementing, and evaluating school improvement activities.

3.3.2 Research Evidence for CSR's Effectiveness

Comprehensive School Reform (CSR) was founded on the basis of proven evidence that the intervention does improve schools (Slavin, 1998). Its premise continues to be based on educational research (Slavin, 2007:1). The impact of CSR interventions is annually researched scientifically in keeping with the fifth component. For example Borman, Hewes, Overamn & Brown, (2002) reviewed 800 studies, abstracts and summaries of models for Comprehensive School reform before a sample of 29 studies was selected for meta-analysis research (Borman et aI., 2002:11).

Findings were described in terms of four categories of effectiveness or impact on learner academic achievement (Borman et aI., 2002:28). These were the categories:

• Strongest Evidence of Effectiveness

• Highly Promising Evidence of Effectiveness;

• Promising Evidence of Effectiveness

• Greatest Need for Additional Research

The four categories were established based on a combination of the following criteria:

1) Quality of the evidence: This meant the CSR model must have had research evidence from the highest quality studies such as control -group studies.

39 2) Quantity of the evidence: This meant the CSR model must have had a relatively large number of studies from which to generalize the findings to the population of schools in the US.

3) Statistically significant and positive results: This meant the effects of the reform on student achievement were positive and statistically greater than O.

Therefore in terms of the criteria above the four categories were described as follows:

Strongest Evidence of Effectiveness: CSR model in this category have a large number of studies and observations from schools and students across the United States, such that their outcomes have been replicated in a number of contexts and are reasonable generalizable to the population of US schools. Also these models have statistically significant and positive achievement effects based on evidence from studies using comparison groups or from third party comparison designs (Borman et ai, 2002:29).

Highly Promising Evidence of Effectiveness. Models in this category are those that had positive and statistically significant results from comparison or third-party comparison studies, but did not have research bases that were as broad and generalizable as those of the models that met the highest standard. Three reform models met the criteria for the category.

Promising Evidence of Effectiveness. Models meeting this standard of evidence were reforms that had more than one study, but still too few to generalize from their results with confidence. All of these CSR models. had statistically significant positive effects from comparison or third-party comparison studies.

40 Greatest Need for Additional Research. The Greatest Need for additional Research category included reforms with only one study or those that did not have evidence of statistically significant positive achievement effects from comparison or third-party comparison studies. Seventeen of the 29 CSR models fell into this category. Nearly all of the reforms in this category were there because too few studies have been done to establish statistically reliable and generalizable results. Four of the 17 models had no evidence from either comparison or third-party comparison studies, and four models lacked evidence from third-party comparison studies.

Finally, four CSR models had only a single effect estimate from both comparison and third-party comparison studies.

3.3.3 Publications on the Impact of CSR

As evidence based intervention, CSR actively conducted a variety of studies on its effectiveness or evidence of its achievement in enhancing learner performance. Some of these studies are longitudinal studies (Aladjem & Borman, 2006), trial studies (Borman, Slavin, Cheung, Chamberlain, Madden & Chambers, 2005) and others are summative evaluations (Slavin & Madden, 2006).

Of interest is a study on one of the CSR model, Success for All (SFA) by Kozol (2005a). This was included in a book, titled The Shame of the Nation (Kozel, 2005b). Kozol (2005a:266) criticises the methodology of SFA schools he observed as having the motto; "If you do what I tell you to do, how I tell you to do it, when I tell you to do it, you'll get it right. If you don't, you'll get it wrong".

41 However, Kozol's (2005a) argument seems to be based on the segregation of black schools in the USA (Kozol, 2007:2). He thus link this situation to Apartheid and therefore all school reform and interventions aimed at Black schools can not be trusted as they are based on the rigid classroom management style (Kozol, 2005a:267).

Slavin (2006:621) responded to this criticism with the statistics showing improved academic achievements in national tests for students in SFA. Slavin further argued that Kozol has a right to his opinion, namely, disliking the CSR model in pursuit of his mission to speak for the schools in poverty.

What came up of Kozol's (2005a) argument is the fact that CSR model is mainly employed in predominantly black schools. It would have been enlightening if Slavin (2006) had given white schools that use the same model to enhance learner achievement.

The racial dimension of the CSR model is opposite to cognitive interventions which are used for all races. Also, there is no evidence that CSR has been implemented beyond the North American borders.

3.4 MATHEMATICS STANDARDS BASED INTERVENTIONS

The revision of the Curriculum and Evaluation Standards for Mathematics (National Council of Teachers of Mathematics (NCTM), 1989), the Professional Standards for Teaching Mathematics (NCTM, 1991) and the Assessment Standards for School Mathematics (NCTM, 1995) culminated into the Principles and Standards for School Mathematics document (NCTM, 2000). According to NCTM (nd) the three original documents provided focus, coherence and new ideas to efforts to improve mathematics education.

42 There are six principles for school mathematics address the following overarching themes (NCTM, 2000:1):

• Equity. Excellence in mathematics requires high expectations and strong support for all students

• Curriculum. A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics.

• Teaching. Effective mathematics teaching requires understanding what students know and need to learn. They must be challenged and supported throughout the learning process.

• Learning. Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.

• Assessment. Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.

• Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught.

The Standards for school mathematics describe the mathematical understanding, knowledge, and skills that students should acquire from prekindergarten through grade 12 (NCTM, 2000:3).

Principles and standards for school mathematics have motivated mathematics interventions that seek to enhance learner achievement in mathematics in American schools (Reys, Reys, Lappan, Holliday & Wasman, 2003:75). These interventions range from elementary through high schools and were implemented throughout the USA.

Examples of interventions in elementary schools include:

• Math Trailblazers (Carter, Beissinger, Cirul, Gartzman, Kelso & Wagreich, 2003)

43 • MATH Thematics (Billstein and Williamson, 2003) , and

• Mathematics in Context (Romberg and Shafrer, 2003).

In high schools examples are:

• MATH Connections (Cichon and Ellis, 2003) and • Interactive Mathematics programmes (Webb, 2003).

Two curriculum based interventions aimed at middle school learners, that is, Connected Mathematics Project (CMP) and Mathematics in Context (MiC) will be discussed. This will be followed by a review of two high school interventions. Middle schools include one year (grade 8) of what used to be regarded as junior secondary school in South Africa.

3.4.1 Connected Mathematics Project (CMP)

3.4.1.1. Overview and Objectives

Connected Mathematics Project is a middle school (grade 6-8) curriculum based intervention (Senk & Thompson, 2003: 190). CMP strives to develop student and teacher knowledge of mathematics that is rich in connections and deep in understanding and skill. It is underpinned by "all students should be able to reason and communicate proficiently in mathematics" (K-12 Mathematics Curriculum Centre (K-12 MCC), 2000:12). Professional development of CMP teachers is through summer workshops (Ridgway, Zawojeski, Hoover & Lambdin, 2003: 195). During these workshops, teachers experience the curriculum as students, and have an opportunity to share ideas and experiences with other colleagues. CMP has support materials consisting of 8 units for both the students and teachers for each grade. Other CMP resources are available and continuously updated at the CMP web site.

44 3.4.1.2. Impact of Attainment by CMP Students

Several studies on the impact of CMP on students learning and achievement have been conducted. Ridgway, Zawojeski, Hoover and Lambdin (2003) report on the study where two tests, one a measure of mathematical technique and the other intended to assess a range of mathematical competencies, were administered as pre-tests and post tests (Ridgway et aI., 2003:198). The study found: "the Connected Mathematics curriculum was effective in raising the attainment of students on challenging open response items that emphasized reasoning, communication, connections, and problem solving compared to the attainment of students in curricular less aligned with the Standards" (Ridgway et aI., 2003:207).

Also, a quasi-experimental study that used matched comparison groups to investigate the impact of CMP was conducted by Riordan and Noyce (2001). They concluded that CMP students performed significantly better on the state wide mathematics test than did students in traditional programmes attending matched comparison schools.

However, What Works Clearinghouse (WWC) evaluated the study by Riordan and Noyce (2001) above. \NWC (2004:3) concluded, "The study does not use a strong causal design: this study, which used a quasi-experimental design, did not use equating measures to ensure that the comparison group was equivalent to the treatment group."

Later on, another evaluation of studies on the impact of CMP showed mixed effects or evidence of inconsistent effects (What Works Clearinghouse, 2007).What Works Clearinghouse was established by the US Department of Education's Institute of Sciences. WWC has an aim "to assess the strength of the evidence that the evaluation study provides for the effectiveness of the intervention" (What Works Clearinghouse, 2006:1). 45 However, CMP was identified by the U.S Department of Education in 1999 as exemplary; that is, a programme which provides convincing evidence of effectiveness in multiple sites with multiple populations (Riordan and Noyce, 2001: 370).

3.4.1.3. Conclusion on the CMP Impact

There are contrasting findings of the evidence of effectiveness of CMP. An interesting case is a mixed method study by Covington and Clarke (2001 :4710A). The qualitative methods for this study found; "CMP classroom provided more opportunities to learn mathematics than traditional classes", but in the same study, quantitative methods found no significance Improvement in the achievement for CMP students.

It would seem that if qualitative methods are used to evaluate the effectiveness of CMP, positive results are found, but quantitative methods tend to refute these. Therefore it is not very clear whether CMP does improve mathematics achievement or not, as this depends on the research design for the study.

3.4.2 Mathematics in Context (MiC)

3.4.2.1. Overview ofMiC

The programme was developed from 1991 until 1998 by the Wisconsin Center for Education Research at the University of Wisconsin-Madison and the Freudenthal Institute at the University of Utrecht in the Netherlands (Romberg and Shafer, 2003: 225).

Connections are a key feature of the programme - connections among the topics, connections to other disciplines, and connections between mathematics and meaningful problems in the real world.

46 MiC emphasizes the dynamic, active nature of mathematics and the way mathematics enables students to make sense of their world (K-12 MCC, 2000: 14).

According to Romberg and Shafer (2003:233) the Realistic Mathematics Education (RME) approach was selected as the development model for MiC for the following reasons:

• RME is epistemologically similar to that envisioned by the NCTM.

• Freudenthal Institute conducted an impressive experiment in a US school which gave a conclusion that, "All students had the opportunity to succeed and, in doing so, exceeded expectations by demonstrating higher order thinking and a high level of maturity about mathematical reasoning in algebra" (De Lange, Burril & Hamberg, 1993:158).

The core MiC materials has 40 units, 10 at each grade level, 5-8. These provide learners with opportunities to progress from informal notions towards using mathematical reasoning and representations to model and solve non-routine problems (Romberg and Shafer, 2003:226).

3.4.2.2. Impact on MiC Students Attainment

Romberg and Shafer (2003: 234) emphasize that the evidence of improved achievement of MiC on students' mathematics is still preliminary. Evidence of effectiveness was gathered from field testing, case studies and limited external assessment. Romberg and Shafer (2003: 248) claim "We believe the pattern of variations in achievement can be associated with variations in opportunity to learn with understanding, instruction, and preceding achievement".

47 These researchers caution: "Although our preliminary evidence is encouraging and supports broader implementation of MiC, we also note the need for more complex research and analysis of classroom culture and its impact on student achievement and curriculum implementation" ( Romberg and Shafer, 2003: 249). Again, What Works Clearinghouse assessed MiC's evaluation differently. "The study does not use a strong causal design: This study which used a quasi experimental design did not use equating measures to ensure that comparison group was equivalent to the treatment group" (WWC, 2006:6).

3.4.2.3. Conclusion on the MiC Impact

Considering the duration of its development and the fact that MiC is in partnership with Realistic Mathematics of Freudenthal Institute which has been in existence for more than twenty years, more impact studies could have been conducted. The published impact study cited above has been developed by MiC's developers; as expected they claim improved learner achievement.

3.4.3 The Core-Plus Mathematics Project (CPMP)

3.4.3.1. An Overview ofCPMP

Core-Plus mathematics programme was rated among the top exemplary programmes by the US Department of education in 999 (http://www.mwich.edu/cpmp. nd) . Also four of the top 25 high schools on the 2003 Newsweek list of "America's best high schools used Core-Plus Mathematics curriculum (http://www.newsweek.com/2003/the-best-high-schools in America.html, nd).

48 Publications of studies on CPMP surpass other standard mathematics interventions discussed in this chapter. These include articles, papers presented at conferences, book chapters and dissertations based on CPMP. Articles in journals include the investigation of teacher variables that related to student achievement when using a standard-based curriculum Schoen, Finn, Cebulla & Fi (2003:228-259). Schoen et ai's findings support the importance of professional development aimed at preparing to teach the curriculum, in this case the CPMP curriculum. Such preparation included changing teachers' behaviours towards learners' ability to perform high in mathematics. Harris, Marcus, McLaren & Fey (2001: 310-318) describe ways in which a curriculum can support the teaching of mathematics through problem problems solving using examples drawn from the CPMP.

Papers presented at conferences include"A report on advances in secondary mathematics curriculum development in the United States and imminent directions: Core plus Mathematics as a case study" by Zierbath (2003). Zierbarth uses CPMP as an example of how new high school mathematics curriculum have developed in the USA over the past decade resulting from the publishing of the NCTM (1989, 1991) Standard documents. The report is concluded by the growth of the CPMP related professional development activities that are an integral part of successful implementation of a reform curriculum in mathematics.

Dissertations included; "The relationships among teachers' understanding of mathematical functions, a reform curriculum, and teaching" (Wyberg, 2002).The study indicated a positive relationship between mathematical content knowledge and teaching approaches that are consistent with the intended CPMP Curriculum. Breyfogle (2001) the study investigated the notion of change that occurred in both teaching and reflection practices of one teacher as he taught Course 1 of the Core -Plus Mathematics curriculum.

49 3.4.3.2 CPMP Curriculum

Schoen and Hirsh (2003: 311) state that CPMP is designed to make mathematics accessible to the college bound and the employment bound students. It has three core year courses and the fourth year designed for college bound students as illustrated in the following tables.

Table 3.1: CPMP Core Curriculum (Source: Schoen and Hirsh, 2003: 313).

Unit No Course 1 Course 2 Course 3 1 Patterns inData Matrix models Multiple-Variable Models 2 Patterns of Patterns oflocation, Modelling Public opinion change Shape and size 3 linear models Patterns ofassociation Symbols Sense and Algebraic reasoning 4 Graph Models Power Models Shapes and Geometric reasoning 5 Patterns inspace Network Optimization Patterns in Variation and visualisation 6 Exponential Geometric Form and its Families ofFunctions models function 7 Simulation Patterns inChance Discrete Models ofChange Models Capstone Planning a The Environment and Making the best of IT: Optimal benefit Carnival Mathematics forms and Strategies

50 Table 3.2: CPMP Course 4 Units (Source: Schoen and Hirsh, 2003: 314).

Mathematical, Physical and Social, Management, and Core Units Biological Sciences or Health Sciences or Humanities Engineering 1.Rates ofChange 6.Polynomials and Rational 5.Binomial Distributions and Functions Statistical Inference 2. Modelling Motions 7.Functions and Symbolic 9.lnformatics reasoning 3.Logarithmic Functions and a.Space Geometry 10. Problems solving, Data Models Algorithms, and Spreadsheets 4. Counting models

3.4.3.3 CPMP Lessons

K-12 Mathematics Curriculum Centre (2000:22) describes CPMP lessons. as being organised in a four-phase cycle:

• Launch whole-class discussion establishing a context for the lesson;

• Explore small group investigation of more focused real world problems;

• Share and summarise - a whole class discussion enabling groups to summarise results of investigations and construct a shared understanding of important concepts, methods and approaches and;

• Apply - task to be completed individually to assess understanding gained in the lesson.

3.4.3.4 Studies on the Impact of CPMP

Post tests of CPMP and matched group of traditionally educated students were conducted on Course 1 &2 (Schoen and Hirsch, 2003:321-330). Results revealed that CPMP students had an advantage on the contextual problems.

51 Similar findings were obtained with the National Assessment of Educational Progress (NAEP) tests.

Also in a field test Schoen, Fey, Hirsch and Coxford (1999:449) found: "CPMP students significantly outperformed students in the nationally representative Ability to Do Quantitative Thinking (ATDQT) norm group. Huntley (2000:337) concluded that CPMP students generally solved equations more successfully than control students, but they explained their reasoning poorly.

3.4.3.5 Impact of CPMP on College Preparation for its Graduates.

In view of its component for college bound students, CPMP's impact has to include preparedness of its graduates to succeed beyond school. Schoen and Hirsch (2003:339) acknowledge that more studies are required in this area, that is, the performance of CPMP graduates in tertiary mathematics courses. However, in comparing two high schools, CPMP and non-CPMP, they found: "This preliminary evidence suggests that students who experienced the pilot CPMP were at least as well prepared for calculus as students in a more traditional curriculum" (Schoen and Hirsch, 2003:340). The bottom line for these findings is that CPMP graduates are no better than graduates from the traditional curriculum!

3.4.3.6 Conclusion on CPMP

CPMP seems to have more studies claiming impact on learner achievement in mathematics, albeit What Works Clearinghouse's allegation that studies submitted for its evaluation did not meet WWC's criteria of what is considered evidence of effectiveness (What Works Clearinghouse, 2007). CPMP's publications and national accolades seem to suggest that this is a high impact intervention.

52 3.4.4 SIMMS Integrated Mathematics

3.4.4.1 Overview of SIMMS 1M

The Systemic Initiative for Montana Mathematics and Science (SIMMS Project) incorporated Integrated Mathematics (1M) in 1996. Both the SIMMS and the SIMMS 1M are state projects which were initiated by the Montana Council of Teachers of Mathematics with the financial assistance from the National Science Fund.

Not only is SIMMS 1M state owned, but it is also teacher owned. For example unlike other reform curricula, teachers played a significant role in its development, that is, the team of its developers consisted of 75 teachers and only 8 university personnel (Lott, Burke, Allinger, Souhrada, Walen & Peble, 2003:400). The key features for SIMMS 1M according to K-12 MCC (2000:30) are:

• Its use of world contexts in an integrated approach for all students, and

• It is designed to replace all secondary mathematics courses.

Lott et al. (2003: 400) adds to the above the following features:

• Problem centred and application based,

• Technology based and

• Sensitive to multiple perspective and negative effects of bias and stereotyping, and multimodal to accommodate multiple learning styles.

The curriculum is divided into six levels of Arithmetic, Algebra, Geometry, Trigonometry, Statistics-Data Analysis and Probability-Combinatorics. According to Lott et al. (2003:401) the following core attitudes are expected from students:

• mathematics is useful;

• mathematics is more than following rules;

• mathematics is communicating and discussing and 53 • making informed mathematical decisions.

3.4.4.2 Evidence of Effectiveness of SIMMS 1M

Improvement in students' achievement in mathematics was evaluated through pre-pilot and pilot studies. According to Lott et al. (2003:414-416), both these did not yield a significant difference in performance between SIMMS and comparison groups when standardised mathematics achievement tests were taken.

Lott, Burke, Allinger, Souhrada, Walen & Peble (2003:414) attribute this to the fact that;"Approximately 75% of the secondary mathematics teachers had some type of in service using the SIMMS Project curriculum and philosophy. As a result, teaching methods for the SIMMS and Non-SIMMS students had become similar".

3.4.4.3 Classroom Practices and College Preparedness

Albeit lack of evidence on improvement in mathematics achievement of the SIMMS students, classroom observations indicated that SIMMS teachers improved their pedagogical habits such as their understanding of content and questioning technique. They also practiced multiple assessment techniques and applied more advanced time management techniques. Also the study on the college preparedness showed that students with at least three years of SIMMS 1M who proceed to mathematical related courses at tertiary, do so with success (Lott et al., 2003).

3.4.4.4 Conclusion of SIMMS 1M

. Lack of scientific achievement evidence is well explained by the evaluators (Lott et aI., 2003). Without this explanation, it has been easy for critiques to 54 generalise; "Integrated math no matter what you call it, is water down math, fuzzy and substandard math" (Nancy Inchinaga in Jacob (2001: 269). However, the use of integrated science and mathematics curriculum where the treatment is unique for the experimental group had different findings. Hill (2002) found that students in the integrated mathematics/science programme scored significantly higher than students in the traditional programme in mean achievement scores. Coupled with Hill's study, the success of SIMMS graduates in tertiary and the reported classroom practices; the intervention seems to be effective.

3.5 VALIDATION OF MATHEMATICS INTERVENTIONS

to validate their effectiveness through research evidence (Kilpatric, 2001:42 Mathematics standards based interventions have not been fully supported by all in the US (Kilpatric, 2003:1). The opposition groups called for back to basics mathematics (O'Brien, 2007:666). Calls were made to schools not to implement the interventions until they were validated by research (Kilpatric, 2003:2). Consequently, politicians passed legislation that called for mathematics interventions 2).

Consequently, a movement to validate standards for school mathematics by research was born which culminated in the development of a conceptual framework for linking research and practice (Battista, Fey, King, Larson, Reed, Smith, Struchens & Sutton, & 2007: 108), which was made to the NCTM Board of directors. However, some researchers (Heid, Middleton & Larson, and 2006:76) admitted that linking standards with research was a challenge.

55 The issues discussed in the publication by Kilpatric, Martin & Shifter (2003) are in line with sections 2.4.1 and 3.4.1. These are the implications of cognitive complexity of school algebra (Chazan & Yerushalmy, 2003:123-135) and research on cognitive science on mathematics education. This is further recognition of the role that is played by cognitive interventions to enhance mathematics learning and achievement.

3.6 RESEARCH ON THE IMPACT OF INTERVENTIONS

Recently, there has been an increase of research on the impact of mathematics interventions. For example Star, Smith III & Jansen (2008) studied how students experience learning·through the standards based interventions. Harwell, Post, Maeda, Davis, Cutler, Andersen & Kahan (2007) investigated the impact on learner achievement in mathematics standardized tests. Also, Smith and Star (2007) have argued for a broader conception of impact based research that targets new dimensions of programme linterventions effect, other than achievement in mathematics. This would include areas which have received less focus, such as students' attitudes in mathematics (Smith & Star, 2007:3).

3.7 RECENT EFFORTS TO IMPROVE LEARNER PERFORMANCE IN MATHEMATICS After more than a decade of standards based mathematics interventions in the US, a National Mathematics Advisory Panel (the Panel) was established by President Bush in 2006 to advice on the corrective actions for the continued poor learner performance in mathematics. The consequence of this problem is as follows: "During most of the 20th century, the United States possessed peerless mathematical prowess, not just as measured by the depth and number of the mathematical specialists who practiced here but also by the scale and quality of its engineering, science, and financial leadership, and

56 even by the extent of mathematical education in its broad population. But without substantial and sustained changes to its educational system, the United states will relinquish its leadership in the 21 st century" (National Mathematics Advisory Panel, 2008: xi).

The Panel conducted. its task taking note of the President's emphasis on "the best available scientific evidence". Hence, the Panel's report took a strong position on the primacy of quantitative methods in education research (Kelly, 2008:561). However, this position received heavy criticism from the majority of the mathematics education research community, for example Cobb & Jackson (2008:573) and Sloane (2008:624).

According to Boaler (2008:588) the emphasis on scientific inquiry by the panel rendered the field of mathematics education virtually invisible! Lobato (2008:595) argued for alternative recommendations as "the report by the panel neglected research grounded in a process view of causality research". Such criticism from the mathematics education research community is a clear indication that there has been a shift from quantitative to qualitative research in this field. Otherwise they would not have a problem with the recommendation to put emphasis on scientific research.

In her lamentation about the loss of the developed research on effective teaching in mathematics Boaler (2008: 589) quotes Adler among these developers. Interestingly the claimed research on effective mathematics teaching did not result into effective learning which would have enhanced performance.

57 In conclusion, despite mathematics interventions (section 3.4) emanating from the implementation of the Principles and Standards for School Mathematics (NCTM, 2000), the aim for the establishment of the National Mathematics Advisory Panel was to advise on the corrective actions for the continued poor performance in mathematics (National Mathematics Advisory Panel, 2008:xi).

Therefore, mathematics interventions prior the establishment of the NMAP seem to have not been successful in turning around poor learner performance in mathematics for American students.

3.8 SUMMARY

This chapter discussed three types of interventions with the potential of enhancing learner performance in mathematics. The discussions have alluded to the importance of the research based evidence of effectiveness of mathematics interventions. The chapter discussed global mathematics interventions. Studies on their effectiveness were discussed. However, recent developments discussed seem to indicate that these interventions have not been effective in enhancing achievement in mathematics.

The following chapter will review the context and the status quo of mathematics interventions in South Africa.

58 CHAPTER 4

4 SOUTH AFRICAN MATHEMATICS INTERVENTIONS

4~ 1 INTRODUCTION

In the previous chapter, mathematics interventions in other countries were discussed. This chapter reviews literature on mathematics interventions in South Africa. Mathematics interventions are shaped by the country's mathematics education. The latter is embedded in the country's education system. South African mathematics interventions will be discussed in the context of two education systems that underpinned the former Bantu Education system and the current democratic education system. To make accurate reference to literature of the education system in the first part of the century, Bantu referred to Black Africans in South Africa.

4.2 CONTEXT FOR NATIONAL INTERVENTIONS

Like all educational interventions in the South African school system, mathematics interventions have been driven by the politics of the country. The latter can be divided into the period before 1994 and after 1994, which demarcated Bantu education system from democratic education system.

4.2.1 South African Education Systems prior to 1994

Three education systems existed for Africans in South Africa up to 1994. These were missionary, colonial and Bantu Education systems.

59 4.2.1.1 Missionary Education System

According Lekhela (1972:12) the genesis birth of Bantu education was due to missionaries. These were inspired by the eighteenth century evangelical revival in England and the subsequent advent of Dr van der Kemp of the London Missionary Society at the Cape in 1799. The nature of education that the missionaries offered was predominantly religious, calculated to win the Bantu for God and rid them of their heathen beliefs and customs (Lekhela, 1972:14). Albeit this noble objective of the missionaries, Verwoed (1954:5) argued that South African Natives remained to a great extent a heathen community.

4.2.1.2 Colonial/National Education System for the Bantu

The predominant missionary education for the Bantu changed to secular when the fell under the control of the colonial government whose objective and concern was to civilize and train the Bantu. According Lekhela (1972:15) Governor Sir George Grey promulgated the objective of Bantu Education during the colonial epoch; "Train Bantu youth in industrial occupations and fit them to act s interpreters, evangelistsand school masters among their own people".

The nationalization of Bantu Education in 1910 eventually led to the development of its national objective. This was developed to compromise between the European 'Equalists' and the 'Segregationists' among the Europeans, the former regarded the Bantu as equals and the latter regarded the Bantu as inferior (Lekhela, 1972: 18). Hence, the objective of the Bantu Education was to facilitate the effective organization of the African's experiences so that his tendencies and powers may develop in a manner satisfactory to himself and the community in which he lives, by the growth of socially desirable knowledgeattitudes and skills (Lekhela, 1972:18).

Seemingly the above objective for Bantu Education resulted into a model undesirable to some. Verwoed (1954:7) lamented on what he regarded as the 60 defect of Bantu Education; "In the past system for Bantu Education the curriculum and education practice ignored the segregation or apartheid policy and blindly produced pupils trained on a European model." This defect was corrected by the introduction of the Bantu Education which was in line with the Apartheid Policy.

4.2.1.3 Bantu Education as Part of Apartheid Policy

The narrow election victory of the National Party in 1948 gave Afrikaans new authority and change on the Bantu Education system. According to Horrell (1968:39) the government of the day adopted a plan which had been recommended by the Eiselen Commission (1949-1951). This culminated into the promulgation of the Bantu Education Act, Act 47 of 1953 which ushered in the Bantu Education system. Verwoed (1954) motivated the corrective intentions'of this Act.; "The Native education system under the old system was unsympathetic to the country's policy (Verwoed ,1954: 7).

Therefore, according to Verwoed (1954: 15 &18) the Bantu Education Act had to ensure that the school system equips the Bantu to serve Europeans and his community. Any other curriculum was viewed as disruptive to the community life of the Bantu and a danger to the community of the European (Vewoed, 1954: 24). Also the financial policy will be such that,"the Bantu themselves will contribute in an increasing measure towards the cost of expanding their education services" (Verwoed 11954:8). This legacy continued through 1994 where the per capita expenditure for different races was as follows:

61 Table 4.1:Per capita expenditure for education by race (Department of Education, 1997b :11)

RACE PerCapita Expenditure White R4772 Indians R4423 Coloureds R3601 African [Department of Education and Training R2110 (DET)] African (Homelands) R1524

Bantu Education in sync with the country's policy thrived during the 1954-1975 period. The government expressed its contentment with Bantu Education (Van Dyk, 1965:1). However, this system ushered in South Africa's crisis in education, which culminated in 1976 Soweto students' boycotts (Murphy, 1986:1).

The government responded to this crisis by initiating investigations on reforming Bantu Education, albeit lack of readiness to change. For example, a recommendation for a single educational system for all groups by de Lange Commission (1981) was rejected (Bot and Schlemmer, 1986: 11). Regardless of the resistance from the government of the day, Bantu education was set on a transformation course in the 1980s.

The last decade of the second half of the 20th century marked the birth of a national democratic education system for all South Africans and the demise of Bantu Education. However, the latter can be viewed as the bedrock for mathematics interventions to this day.

4.2.2 The Goals and Outcomes of Bantu Education

The goal of Bantu Education Act of 1954 was articulated by Verwoerd (1954: 15) , that "The school must equip the Bantu pupil to meet the demands which the economic life of South Africa will impose upon him". Elaborating on this 62 imposition, Verwoerd (1954:25) continued: "There is no place for the Bantu in the European community above the level certain forms of labour".

Certain forms of labour were regulated by the Job Reservation Act of 1954 which prevented the Bantu from mathematical related professions such as engineering which were reserved for Whites (Matyu, 2010). Speaking at the graduation ceremony of University College of Zululand, Van Dyk (1965:6) testified to this: "It is not the sale concern of the Bantu university colleges to produce the graduates and the increasing numbers of doctors, agriculturalists, engineers and scientists".

Marginal participation in mathematics for the Bantu was thus expected. Malherbe (1969:10) pointed out: "Of the 2 093 Bantu students who wrote matric examinations in November 1967, only 125 attained university entrance standard with a pass in mathematics". A similar sentiment had been articulated by Ackerman (1966) in Horrell (1968:72): "During the period 1958 to 1965, a total of 431 matriculants have passed mathematics... From this limited number of possible candidates the medical faculty of the University of Natal and the science faculties of the three university colleges have to draw their students." This led to a very. few number of candidates who chose to be trained as mathematics teachers. This resulted in many pupils being taught mathematics by teachers not qualified to do so (Harrel, 1968:72). However, some researchers were not happy with this situation. For example, Mentz (1968) in Malherbe (1969:10) complained that lack of training in mathematics and science had retarding effects on the Bantu.

63 According to Malherbe (1969: 10) the University of Natal wanted to correct this by offering mathematics and science courses to Bantu teachers. A letter seeking permission for this intervention was written to the Minister of Education, but permission was declined. The University of Natal requested reasons for the decline. The response according to Malherbe (1969:10) was that "the Minister does not give reasons for his decisions". However, in the 1970s interest in research on Bantu mathematics education trickled. This could have been incited by the 1976 Soweto students' boycotts.

4.2.3 Research on Bantu Mathematics Education

Research by Van Den Berg (1978) investigated the mathematical ability of the Black man. He found that Black men definitely had mathematical ability. However, their meagre material environment contributed to the fact that their mathematical potential was not developed to the full. The non-conducive environment for mathematics learning included shortage of teachers in mathematics, shortage of or poor facilities and inflexibility of syllabi which stifles creativity (Bot and Schlemmer, 1986:28).

After ascertaining that Black men had the mathematical ability Van Den Berg (1980) conducted research on teaching and learning strategies that promotes black pupil's insight into mathematics. Recommendation on this study was that the Black man's traditionalgroup-directedness must be utilised as group oriented strategy in learning and teaching mathematics (Van Den Berg, 1980: 77). He further recommended training and in-service training of Black teachers in the implementation of group oriented educational strategy (Van Den Berg, 1980: 79).

Contemporary research indicates the benefits of group work. For example, some researchers regard collaborative learning as having the potential to inculcate creativity among learners (Nevin, Thousand, Villa, 2002:267).

64 Mkhize (1999) found that students in high schools prefer to work in collaborative groups because they understand one another better than their teachers. Collaborative group work has been also named the movement for the 21 st century (Perterson, 2002:1) because of its connection with democratic education and inclusion (Kesson, Koliba & Paxton, 2002:3 and Spon-Shevin, Ayers and Duncan, 2002:209).

More importantly, group work is regarded as the integral part of Outcomes Based Education (Wikens, 2002:68). Hence, one of the proposed seven critical cross field outcomes by the (South African Qualifications Authority (SAQA), 1997) is that Learners will work effectively with others as members of a team, group, organisation and community. It is interesting three decades ago Van de Berg found group work to be in sync with the Black man's way of life!

Even though research by Van den Berg was pointing in the direction of enhancing mathematics learning for Blacks, it is noted that some research focused on enhancing the Black man's compliance in carrying out his responsibility in the Western cultural context (Nel, 1977).

Nevertheless, full blown mathematics interventions were initiated towards the end of 1970s up throughout the 1980s. In view of the policies of the day in education, these were implemented as Non-Governmental initiatives.

4.3 MATHEMATICS INTERVENTIONS PRIOR TO 1994

Sisulu (1986:96) captures the scenario during the 1979-1989 period. "Ten years after the 1976 uprising we remain united in our demand for the ending of apartheid education and the establishment of a democratic, people's education". This period was still under the laws of Bantu education, thus Non Governmental Organisations (NGO's) were running interventions.

65 Other interventions were a response to the 1983 Department of the provision of education in the Republic of South Africa. According to Kahn (1993:37), this required all teachers to have a senior certificate. Examples of interventions in response to this include Teacher Opportunity Programme (TOPS) which was implemented in 1984 (Murphy, 1985). In the following paragraphs, a handful' of mathematics interventions during this period are briefly discussed.

4.3.1 PROTEC

This intervention was started by the professional institute of engineers in order to improve the number of black matric graduates entering the economy as scientists, engineers and technologists. Hence, PROTEC stands for Programme for Technological Careers. According to Levy (1992:337) PROTEC's objectives were achieved through selecting high school mathematics and science students who are above average in relation to their peers in their own class.

Then the selected students participate in a programme with the following activities: • Saturday school: This entailed supplementary tuition in mathematics, science and English. • Vacation school whose focus was providing learners with communication skills. • Vacation camps that aimed at assisting learners in their personal development and exposure to the world of work. Mathematics and science supplementary tuition was a vehicle for the core aim of the intervention, which according to Levy (1992:337) was, "to develop leadership skills needed for successful entry into industry and world of work". PROTEC developed 'model lessons' in mathematics and science. At the conference for political dimensions of mathematics education, PROTEC was cited as a strategy for improving the South African school mathematics status quo (Marsh, 1993:301).

66 4.3.2 Applications Oriented Mathematics Project

This intervention was based at the University of Western Cape. According to Julie (1993:210) it was initiated in 1983 because of the need for an application based mathematics curriculum. Hence, it allowed participants to develop mathematics from real life situation (Julie, 1993:211). These were then used to develop support materials for teachers in mathematics classrooms.

The intervention also initiated a publication called 'people's mathematics' which drew together on what people said about mathematics. In view of the date of inception, the intervention had an objective to contribute towards the policy debate about mathematics education in South Africa (Julie, 1993:212).

4.3.3 Mathematics Education Project (MEP)

MEP was initiated in 1985 at the University of Cape Town. The intervention was mainly run and coordinated by the academic staff of the Faculty of Education. According to Breen, Colyn and Coombe (1993:228) the goal was to provide primary and secondary school teachers with in-service training through workshops. Support materials addressed the following prevalent problems among mathematics teachers:

• Lack of confidence in mathematics content;

• Underexposure to alternative methodologies and resources, and

• Denied development by the education system.

4.3.4 Mathematics Centre for Primary Teachers

Mathematics centre for primary teachers was initiated in 1985 in Johannesburg. According to Patchitt (1993:236), the intervention's aims were the following:

67 • To increase the mathematical competence of lower primary teachers from Soweto.

• To assist teachers in utilising the knowledge to develop and improve teaching techniques.

• To modify existing mathematical aids so that they can be produced by teachers with limited financial resources, and

• To improve the mathematical achievement of pupils.

These objectives were achieved through development of home grown methods and testing these in Soweto classrooms. Intervention at the classroom level set this initiative apart from others. According to Patchitt (1993:236) this approach led to the development of structures within the community to continue the process of change, even after the withdrawal of the intervention.

4.3.5 Star Schools

Star Schools were initiated in 1965. According to its founder, this intervention caters for the bright learners. Star schools were initiated in 1965 by William Smith. He elaborates on what motivated the founding of Star schools as follows: "Star schools started in association with the newspapers as supplementary education. The need was that education was going down the drain: simply put, pupils were increasing and teachers were decreasing" (Smith in Levy, 1992:506).

The strategy employed to achieve their aim was the provision of extra evening classes and weekend courses in mathematics and science. Smith in Levy (1992: 507) claims that the methodology of teaching in Star schools is based on the fact that, "the secret of any teaching is to entertain with your subject". Even though the methodology being employed by Star Schools is not elaborated on, it is mentioned. This was not the case with the two previous interventions.

68 Star schools' interventions cut across the 1960s to date. Unlike other interventions, this had no intention on correcting mathematics education, but was run as a business. In 2009, Star schools had over 240 classrooms and 15 000 learners countrywide (http://www.starschools.co.za. 21/04/2009). Students pay a tuition fee to attend these classes.

Excluding Star Schools, all the above-mentioned mathematics interventions sought to correct marginal mathematics education which had resulted from the Bantu Education Act of 1954. The difficulty with these interventions was the absence of policy supporting their efforts, that is, at the time mathematics education was still under the policies of Apartheid, in particular the Bantu Act Education Act of 1953.

This changed in the 1990s when the first White Paper of Education by the Department of Education was promulgated in 1995. This was followed by the 1996 Constitution of the Republic of South Africa, Act 108 of 1996 whose preamble included: "to heal the divisions of the past ... free the potential of each person ..." This is 'very appropriate for the mathematics education system in South African which had been fraught with division that ensured that the majority of Blacks are excluded from the then European economy (see section 4.2.2).

4.4 POST 1994 EDUCATIONAL ENVIRONMENT

The following explains the new environment under which interventions operated after 1994. "During the years of apartheid in South Africa, funders gave money directly to NGO's who were running programmes to address the shortcomings of the education system. After 1994, attention shifted and many NGOs started working directly with the state, helping it to implement the new policy of Outcomes Based Education" (School Development Conference Report, 2008:5).

69 Implementing the policy on Outcomes Based Education also meant redressing the results of apartheid education. For example, Hindle (1997) elaborated on old professionalism which had to be eradicated in accordance with the OBE. "I am not talking about the so-called professionalism which tried for many years to turn teachers into factory workers. Not the professionalism which was used as a device, calling for absolute and uncritical compliance" (Hindle, 1997:24).

Verwoerd (1954:18) had highlighted that the success of Bantu Education was dependent on teachers' faithful fulfilment of their duties. Teachers had to be abide by the Act despite the teachers' associations who had by means of resolutions, "had expressed themselves strongly against the findings of the Education Commission and the Bantu education Act, and that they have declared themselves in favour of equal education" (Verwoed , 1954:19). Despite such resolute from the government ,the opposition to Bantu Education was universal among Africans and the ANC called for its total rejection (Department of Education, 2004:7).

To ensure compliance of teachers; "The Department of Native Affairs , which has often been characterised as not being equipped to administer Native education, has therefore been equipped to provide effective control and leadership as no official body before" (Verwoed, 1954:8).

Such control led to some teachers being banned, prosecuted or deported (Karis and Carter,1977:29-35 and Pampalis, 1991:199-200) The audit on teacher education found that methodologies employed in mathematics classrooms were generally teacher centred and emphasize the recall of content with little attention paid to developing critical and analytical skills (Hofmeyer & Hall, 1996: 74). These researchers further recommended that

70 "urgent attention should be given to the quality and quantity of teachers in mathematics" (Hofmeyer & Hall, 1996:82).

In contrast to the era before 1994, the environment was very fertile for mathematics interventions to correct the legacy of the past education system.

4.5 CLASSIFICATION OF POST 1994 INTERVENTIONS

Mathematics interventions after 1994 were categorized into four major areas by Stoll (1995: 12). The classification indicates the focus and intended outcome of the intervention. These are:

• Intervention projects aimed at the improvement of school curricula and related materials;

• Interventions aimed at strengthening the existing teaching force through in service training;

• Interventions aimed at improving pre-service science teachers training curricula;

• Interventions aimed at increasing enrolments at tertiary level - science based study programmes.

Stoll's four areas of interventions are interrelated, for example, curricula interventions aim to enhance mathematics achievement so as to increase the number of students entering science related programmes at the tertiary level. In view of the education systems within which interventions operated, their discussion will be chronological.

The 1995 White Paper on Education and Training promulgated a new era in mathematics education for all South Africans. In his message, the then Minister of education Bhengu pronounced that "South Africa has never had a truly . national system of education and training, and it does not have one yet.

71 Our message is that education and training must change" (Department of Education, 1995:1). Elaborating on the expected changes he stated that "The ideal, namely, excellence in education for all" and the cultivation 'and liberation of the talents of every young South African, is still a long way off, but we are on our way! "(Department of Education,1995:2).

Cultivation and liberation of talent in mathematics was one of the priorities in the new era; "An appropriate mathematics, science and technology education initiative is essential to stem the waste of talent, and make up the chronic national deficit, in these fields of learning, which are crucial to human understanding and to economic advancement." (Department of Education and Training, 1995).

Therefore, mathematics interventions after 1994 did not only enjoy the support of the government, but had an obligation to cultivate and liberate talent in mathematics. It is for this reason that the next paragraphs will unpack and discuss interventions after the new education system came into being after 1994.

4.5.1 RADMASTE

RADMASTE is an acronym for Research and Development in Mathematics, Science and Technology Education. According to Bradley in Levy (1992:366) the intervention was initiated in response to the increasing number of requests by mathematics and science teachers and educators to participate in informal teacher development activities.

This was a non-profit organisation under the School of Science Education of the University of the Witwatersrand. Unlike the previous interventions whose focus was on learners, RADMASTE intervention focuses on mathematics and science teacher development. Bradley in Levy (1992: 370) claims that RADMASTE uses knowledge from research for their teacher development activities. This is to be

72 expected because the intervention is based at a university and all its directors and founders are tenured academics at the same university.

The teacher development or adult education in mathematics and science is based on the principle of multiplier effect which means one competent teacher will affect positively a number of learners. Activities for teacher development entail workshops as well as developing support materials that educators can use in their classrooms over and above textbooks. RAOMASTE's activities cue privately funded.

4.5.2 Student and Youth in Science, Technology, Engineering and Mathematics (SYSTEM)

SYSTEM was initiated and operated in the era of the 1995 policy of Education and Training. A number of concept papers were presented at conferences of mathematics and science education during the period 1995 through 1997. For example, Volmink (1995:108) presented a paper on SYSTEM as the model of effective interventions at the conference held in Botswana. This was a conference on Improving Science and Mathematics Teaching in Southern Africa: Effectiveness of Interventions.

According to Volmink (1995: 108-115), SYSTEM was a two-pronged strategy. The first prong sought to address the immediate problem of wasted potential of mathematics and science students who failed to pass these subjects at matric level due to inadequate teaching in schools. The strategy to address this problem was through a one-year second-chance programme. During this period, students were provided with intensive tuition in mathematics and science which prepared them to re-write and pass these subjects at matric level.

73 Volmink (1995: 110) elaborated on the second prong as seeking to initiate a high standard initial teacher education in mathematics and science. Consequently, this part would address the chronic shortage of competent teachers in mathematics and science. The White Paper on Education provided an enabling environment for SYSTEM. In view of the holistic nature of the SYSTEM intervention, Volmink (1995) asserted that it would be an effeCtive intervention for mathematics and science education's systemic change.

4.5.3 DINALEDI

Dinaledi can be regarded as the flagship intervention for the twenty first century. It is the implementation model of the National Strategy for Mathematics, Science and Technology Education. The Strategy and Dinaledi were launched in 2001 by the National Department of Education. One hundred and one schools were selected in nine provinces to participate in the project. Each province was allocated a number of schools, in Gauteng eleven schools participated in the Dinaledi project.

Its thrust was ; "To raise participation and performance by historically disadvantaged learners in Senior Certificate mathematics and physical science" (Department of Education, 2001:14). The expected outcomes for Dinaledi were stated as follows:

• The number of learners, especially girls, studying Mathematics and Physical Science in Grades 10-12 will increase;

• The number of learners taking these subjects on Higher Grade will increase;

• The pass rate in Mathematics and Physical Science, especially on Higher Grade will rise;

• The capacity of teachers to deliver quality Mathematics and Physical Science education will improve;

74 • Learners will be encouraged to choose science as a field of study at the tertiary level;

• Well-resourced schools with computer-aided learning will be created.

Dinaledi intervention is based on three pillars of effective learning in mathematics, namely learners, curriculum delivery by teachers and necessary resources in schools (Department of Education, 2001:20). One of the strategic objectives for Dina/edi is to identify and nurture talent and potential. Hence, the vacation camps are provided for top students in Dina/edi schools in June/July. To address quality teaching, workshops by Cuban teachers are run for teachers in Dina/edi schools. The provincial departments provide necessary resources such as computers in these schools.

Despite the claims made by Bernstein (2005:230) that the Strategy is not effective, the Department of Education (2004:11) cites its achievements as follows: "Participation in mathematics and science has increased by over 10% in Ditmted! schools. System-wide performance has increased in three years (2001, 2002 and 2003), that is, in 2003, 58% of learners who wrote Mathematics passed, 11% of these learners passing at the higher grade level.Participation and performance of African learners have recorded encouraging improvements. The 102 Dina/edi schools contribute about 11% of the total African learners who pass mathematics".

Dina/edi intervention is a holistic intervention in that it seeks to address both the learner and teacher variables that lead to poor participation and performance in mathematics.

The following interventions are much smaller in scale and tend to have special foci.

75 4.5.4 Girl Learner Project

This intervention is known to have been initiated by the National Department of Education. However, the little that is known about it has been taken from the intervention in GAUTENG schools. Its aim is to improve learner performance and attainment level in the FET band with a particular focus on African female girl learners (Duma, 2004).

The operations for the intervention entail identifying girls with potential to succeed in Science, Mathematics and Technology from disadvantaged schools. An enrichment programme then provided for them during Saturday and vacation schools. This entails extra tuition in mathematics and science. It also entails the career guidance component which seeks to encourage girl learners to pursue Science, Engineering and Technology careers.

4.5.5 SUPEDI

SUPEDI is an acronym for Supplementary Education Programme. Duma (2004:2) says the programme targets both primary schools and high schools. The focus of the intervention is on mathematics materials that have been imported from the United States of America. SUPEDI has a teacher development component which is centred on these materials. Teacher development entails workshops and classroom support. The content of these workshops according to Duma (2004:2) included topics on how to develop mathematical concepts using mathematics materials. Another topic included in these workshops is how to involve the learners in lessons which is mainly the demonstration of how to use mathematics materials. This intervention has materials development as its focus.

76 4.6 EMERGING RESEARCH ON INTERVENTIONS

In recent years, research on educational interventions in the country has emerged. This was based on the evaluation of educational projects which by and large was overseen by the Joint Education Trust. Examples include an overview of 12 schools reform projects (Roberts, 2002) and the baseline study of Khanyisa Education support (Taylor & Mabogoane, 2007).

At the 2008 conference on 'What works in school development in South Africa', deliberations were around the outcomes of evaluation research of educational interventions, for example, Taylor (2008) and Schollar (2008) reported on recent mathematics intervention (Hofmeyer, 2008).

It is noted that this research, as indicated by the title of the conference, focused on whole school development, rather than on mathematics education. Hofmeyer's (2008) mathematics intervention had a strong inclination on the gifted children's theory whilst Schollar's (2008) research was based on primary mathematics research.

4.7 EDUCATIONAL CHANGE SINCE 1994

Sections 1.1.3.1 and 1.1.3.3 of chapter 1 have already pointed out that the 21 st century mathematics interventions were not successful in ameliorating the deficit in mathematics learner performance in South Africa. Varied reasons have been given. For example, Du Preez and Roux (2008:77) argue that teachers have a negative view towards the methodology that has been used in these interventions.

In general, most literature on the impact of policy on South African education has a preoccupation on the intended impact and the development of the policy on .education and never the actual change. For example Motala and Pampalis' (2001) study on impact of policy on the South African education has theoretical 77 chapters such as 'the transformation of education and training in the post Apartheid period' (Mahomed, 2001:105) and a critical examination of the development of School Governance policy and its implications (Karlsson, McPherson & Pampallis, 2001:139).

A South African experience on the implementation of education policy (Sayed & Jansen, 2001) also gives an impression about the possible impact of the implementation process, even to a small extent. However, implementing policy for this thesis is still very much tied to policy origins and evolution (Mathieson, 2001:43, Nzimande, 2001 :38 & Donaldson, 2001:62). Policy concepts, contests and criticism (Lungu, 2001 :92 and Soudien, Jacklin & Hoadley, 2001 :78) seem to be part of policy implementation, never its impact.

Elaborating on the main reason for little progress for the educational change and success since 1994, Taylor and Jansen (2003:4) assert that: "A lack of systemic thinking and implementation capacity has been major barriers to reaching goals of educational reform in post apartheid South Africa. There is every indication that basic education in South Africa remains one of the most inefficient and ineffective in Africa, despite the disproportionate per-capita amounts spent on South African pupils. "

The American mathematics education community claim progress in research even if reality indicates otherwise. For example, on one hand the National Mathematics Advisory Panel was established by President Bush to redress the threat of the United States losing its mathematical prowess (National Mathematics Advisory Panel,2008:xi). On the other hand mathematics education experts claim they have made progress in research on mathematics learning (Roschelle, Singleton, Sabelli, Pea, and Bransford, 2008:610-617). More importantly, they are vehemently opposed to the proposed scientific .research by the National Mathematics Advisory Panel in establishing what works (Boaler, Cobb, and Greeno & Collins, 2008: 618).

78 In South African there is acknowledgement of the lack of satisfactory progress in mathematics achievement by learners (section 1.1.3.2) which is a good starting point towards solving this problem.

4.8 SUMMARY

This chapter discussed South African mathematics interventions in the context of education systems that prevailed prior 1994 and after 1994. The emerging evaluation research for specific educational projects was also briefly discussed, but this had a focus on school effectiveness and primary schools. The lack of educational change since 1994 in South Africa was indicated. However, this is viewed as an acknowledgement of the problem with mathematics interventions. Having laid the theoretical framework for the study, the following chapter will then discuss research design of the study.

79 CHAPTER 5

5 RESEARCH DESIGN FOR THE STUDY

5.1 INTRODUCTION

In the previous chapter South African mathematics interventions were discussed. In this chapter, the research design for studying their impact is unpacked in detail. Research designs are plans and procedures for research that include the decisions from broad assumptions to detailed methods of data collection and analysis (Creswell, 2009:3). This chapter discusses the mixed method research design chosen for the study. The discussion starts with the factors that have influenced the choice of the research design and its perceived value for the study. This is followed by the two broad components of the design, namely, the philosophical foundations and the overarching strategy of inquiry. Finally, specific methods for quantitative and qualitative data collection and analysis are discussed.

5.2 RATIONALE FOR MIXED METHODS DESIGN

There is a notion that the researcher's world view and or paradigms impact the choice of the research design. For example, Creswell (2009:20) asserts that the research design chosen for the study is based on bringing together a worldview or assumptions about research. Guba and Lincoln (2005:183) assert that paradigms define the world view of the researchers and they are a set of beliefs that guide action. Hence, this view implies that world views by researchers guide how they design and conduct research! This study upholds the view that the research problem and the research . questions are the bases from which research design decisions are made (Gorard & Taylor, 2004:4, Morse, 2003:189, and Rideneour & Newman, 2008:1). 80 The research problem (section 1.2) points out the gap in research on the impact of mathematics interventions despite their entrenchment in high schools. Available research is limited to case studies or once off pre and post test designs. Neither of these gives a holistic view of the impact of the interventions.

Also, the first three research questions revolve around the quantitative impact of mathematics interventions (section 1.3). The impact of interventions is assessed by the measurable performance of learners in mathematics. In our South African context, such measurement is done through senior certificate mathematics examinations (Maharaj, 2005:14) and these are by and large quantitative methods.

However, the last two questions seek to investigate the experiences and perceptions of participants in the interventions (section 1.3). McMillan and Schumacher (2006:315) assert: "Qualitative research is first concerned with understanding social phenomena from participants' perspectives". Denzin and Lincoln (2008:4) share the same sentiment regarding the personal experiences as being part of qualitative data.

Hence, to address the research problem and the research questions for this study, the mixed methods design was viewed to be the most appropriate. A decision also endorsed by Onwuegbuzie & Leech (2007:475) in their statement, "In mixed method studies, research questions drive the methods used".

5.3 THE VALUE FOR THE CHOSEN RESEARCH DESIGN

Mixed methods designs are regarded as emerging methods (McMillan & Schumacher, 2006:399). So much that some, for example, Hammon and Gromis (2006:216) still regard mixed methods as a "Chaos of discipline". . Recommendations have been made to explain preference of mixed methods design above either quantitative or qualitative modes of inquiry, so as to avoid

81 using mixed design as a fashion fad (McMillan & Schumacher, 2006:405). Hence, this section briefly discusses the value and further justification for the study's research design.

Gorard & Taylor (2004:1) assert that both quantitative and qualitative approaches have their unique strengths. Hence, greater strength can come from their combination. For example, processes are only fully understood and thus can only be enunciated by those who went through them through qualitative interviews (Patton, 2002:84). According to Willis (2007:6) qualitative methods are better ways of getting at how humans interpret the world around them. Translating this to the current study means, how participating teachers in mathematics interventions experience and perceive these.

But, many qualitative researchers have acknowledged the limitations of generalizability, validity and reliability in qualitative inquiry (Bogdan & Biklen, 2003:33).Yet, generalizability, internal and external are the pillars of inferential statistics which is a pillar of quantitative research methods (Keller, 2005 and Singh, 2006:136).

Also, qualitative methods according to Janesick (2000:385) "look at the larger picture, the whole picture, and begin with research for understanding of the whole". On the other hand "quantitative research takes apart a phenomena to examine the components" (Merriam , 1998:6). Indeed, the performance of learners in mathematics is one component of the impact, generally expected from mathematics interventions (section 3.6) and the whole picture of the impact includes an array of factors that lead to achievement in mathematics by learners.

82 These factors would include, for example, teacher factors; that is, teaching, teachers' knowledge and teachers' development (Mewborn, 2003:45-52), as well as learner factors such as cognitive development of high school learners (Kyriakidas & Luyten, 2009: 167), enhancing their cognitive functioning (section 3.4.2) and assisting them to form identities in mathematics communities (section 2.5.3).

Further investigation of some of these factors can be through qualitative methods. Thus any mono method for studying the impact of mathematics interventions would be very limited!

5.4 JUSTIFYING PHILOSOPHICAL ASSUMPTIONS FOR THE STUDY

According to Creswell (2009:9) the design has three components, namely the philosophical assumption, the strategy of inquiry and the specific research method. Aligning a study to a paradigm is regarded as the bedrock of good research (Hallebone, 2009:45).

According to Gray, Karp and Dalphin (2007:22) if we follow a paradigm, "we put on a pair of glasses which colours our behaviour with a particular interpretation". However, for this study the dictate of the mixed method design is the research problem and questions as has been elaborated in section 5.2. Even though this removes an alignment of the study to a particular worldview (Greene & Caracelli, 2003: 91), situating the study in a philosophical foundation is still relevant (Ivankova, Crewell & Plano Vicki, 2007:262).

Two philosophical foundations for the mixed methods designs are espoused by Plano, Clark & Creswell (2008:27-65, 66-104); these are pragmatism by Morgan (2007:48) and transformative-emancipatory perspective by Mertens (2003:135).

83 Pragmatism is an appropriate philosophical foundation for this study. According to Morgan (2007:48-76) a loss of paradigms and a regain of pragmatisms occurs when qualitative and quantitative methods are combined.

In view of more than one perspective for pragmatism (Siesta & Surbules, 2003:9), Dewey's pragmatism has been chosen for the study. According to Siesta & Burbules (2003:9), Dewey's pragmatism deals with questions of knowledge and acquisition of knowledge within a philosophy that takes action as its most basic category. This view is relevant to the study of the impact of mathematics interventions which is supposed to be the outcome of putting into action the policy on education (see section 1.1.1).

Regarding the research design; "Dewey's pragmatism proposes neither a specific research 'program' for the conduct of research, nor any specific research methods. What it does offer, however, is a distinct perspective on educational research, a specific way to understand the possibilities and limitations of research in, on, and for education" (Siesta & Burbules, 2003:107). Dewey's pragmatism is in line with the proposed view by Rideneour and Newman (2008:27) of a qualitative-quantitative interactive continuum, rather than the view of diametrically opposed qualitative and quantitative paradigms held by, for example, Guba and Lincoln (2004:17). Dewey's pragmatism implies and recognises the limitations of either quantitative or qualitative research methods for this study. Hence, both methods will interact in a continuum.

5.5 STRATEGY OF INQUIRY

An explanatory design is the strategy of inquiry for the study. A strategy of .inquiry provides a specific direction for procedures in a research design (Creswell, 2009:11). According to Sryman (2006:254) selecting and explaining

84 the strategy of inquiry is of particular importance as it contributes to the build up of typologies of mixed research methods out of examples, rather than the current prevalent theoretical and logical typologies of mixed methods research. McMillan & Schumacher (2006:402) elaborate on the strategy for the research design by saying that: "Quantitative and qualitative are gathered sequentially often in two phases, with the primary emphasis on quantitative methods. Initially, quantitative data are collected and analysed. The qualitative data are needed to explain quantitative results or further elaborate on quantitative findings". The assumption in the explanatory design is that quantitative results provide a general picture of the research problem while the qualitative results refine, explain or extend the picture (Ivankova, Crewell and Plano Clark, 2007:264).

5.6 SPECIFIC RESEARCH METHODS

According to Creswell (2009:15) the third element in the research design framework is the 'specific methods' being utilised. For this study, this means specific methods for two phases, namely, the first phase and the second phase.

5.6.1 The First Phase

In line with the explanatory design for the study, quantitative research methods are employed in the first phase. According to Maree and Piertersen (2007: 145) the quantitative research process is systematic and objective in its ways of using numerical data from only selected subgroups of a universe or population to generalize the findings to the universe. The numerical data for the impact of interventions is in terms of learner performance and enrolment in senior certificate examinations mathematics. The .population from which these will be selected are learners from high schools who participated in mathematics interventions.

85 5.6.1.1 The Research Design for the First Phase

The research problem in this study revolves around the impact of mathematics interventions over a time period in the past. There is no way control or random assignment can be effected at this stage as part of the quantitative inquiry strategy. Hence, the quasi experimental design is adopted. It is the norm to adopt quasi experimental designs where control and random assignment of subject is difficult (Babbie, 2004:349 and Leary, 2004:297).

While quasi experimental designs are not true experiments, they provide reasonable control over most sources of invalidity, these are usually stronger than pre-experimental designs (McMillan & Schumacher, 2006:252). Also, according to Muijs (2004:27), quasi experimental research is especially suited to looking at the effects of an educational intervention. These designs have one advantage over the experimental designs, that is, they are studied in natural educational settings (Muijs, 2004:29).

Among several types of quasi experimental research, the interrupted time series is most suitable for the study. A time series is the measurement of one or two variables measured over time in sequential order (Keller, 2005:255). Justification for this choice comes from Shadish, Cook, & Campbell (2002:172) who assert that interrupted time series is a special kind of time series that can be used to assess treatment impact. Measurement or observations can be on different but similar units.

A time series, whose measurement/observation is on one group, is called a one group interrupted time series (Lunenburg & Irby, 2008:52). More importantly the interrupted time series design is a particular strong quasi experimental alternate to randomized designs when a time series can be found (Shadish, Cook, & Campbell, 2002:172 and Rossi, Lipsey & Freeman, 2004:291). One group interrupted time series design for this phase is illustrated in the following table.

86 Table 5.1: One group-interrupted Time series design (Adapted from Lunenburg & Irby, 2008:52)

Intervention

Pre -Intervention - Post - Intervention

00000 x 00000

For this study, observations were the learners' performance in mathematics over eight to ten years. Observations were made over the pre-intervention period and the post-intervention periods. These two periods were interrupted by a mathematics intervention.

5.6.1.2 Sampling

In view of the expected impact of mathematics interventions on high school learners, three nested samples were selected for this phase, namely, the umbrella sample of three mathematics interventions which included a sample of 47 high schools. The former had a sample of 24 509 grade 12 mathematics learners who participated in at least one of the three mathematics interventions. The criterion sampling (Onwuegbuzie and Leech, 2007:114) was used to select a sample with the sample size (n1) of 3 mathematics interventions.

The criterion for the selection was mathematics interventions must have operated in Gauteng high schools for a period longer than three years. At least ten high schools must have participated in these interventions.

87 After a sample of mathematics interventions were selected, stratified random/proportionate sampling (Leary, 2004:122) was employed to select the sample of high schools with the sample size (n2) of 50.

This sampling was conducted according to the definition of the stratified random sample by Scheaffer, Mendenhall III & Ott (2006:119) who state: "A stratified random sample is obtained by separating the population elements into non overlapping groups called strata, and then selecting a simple random sample from each stratum".

All grade 12 learners enrolled for mathematics within the sample of high schools were automatically the sample of learners that participated in mathematics interventions. The third sample of grade 12 had no fixed sample size as enrolment in mathematics differed each year through the period of observation, that is, 2002-2006. Appendix C shows that a total of 24 509 from 47 high schools participated in 3 sample interventions over this period.

5.6.1.3 Data Collection

Quantitative data can be collected through instrumentation or through archival data sources (Gaur & Gaur, 2006:29). Archival data was used for this phase. This entailed getting senior certificate results in mathematics for Gauteng high schools from the examinations' results archives of Gauteng Department of Education (GDE).

Archival data is a typical time series design data (Bordens & Abbot, 2005:306). Such data collection results into secondary data analysis which is viewed to be among the emerging research methods (McMillan & Schumacher,2006: 406). Four cited benefits for secondary data analysis are time efficiency, cost .effectiveness, data quality and increased sample size (McMillan & Schumacher, 2006: 407). All consideration that needed to be made before the secondary data

88 analysis method was chosen was met for this study. These solicit the following questions according to McMillan &Schumacher (2006: 407):

• Was the data collected from the population of interest?

• Does the data set contain variables that will allow the research questions to be answered?

• Are the data easily accessible?

• More importantly, is secondary data analysis as rigorous as primary data analysis?

A letter was written to the curriculum unit requesting documents on all mathematics interventions that operated in high schools since 2000 (see appendix A). The letter also requested permission to use applicable data from these documents.

Another letter was written to the examinations unit of the Gauteng Department of Education (see Appendix B). The request in this letter was for senior certificate mathematics results from 1995 through 2007 for Gauteng high schools. The information provided secured the secondary data for the sample of high schools and learners.

5.6.1.4 Data Analysis

Descriptive and inferential statistical analysis of data was conducted using Excel Toolpack (Keller, 2005:13) and SPSS (Muijs, 2005:83). Descriptive data analysis organised and summarized data in a convenient and informative way (Keller, 2005:2). This gave central and variability of performance in mathematics for all three interventions over a period of five years.

89 Inferential data analysis was used to draw conclusions about the performance in mathematics of learners that participated in mathematics interventions during the period of their implementation.

5.6.1.5 Eliminating Threats to Internal Validity

Leary (2004:305) argues that quasi experimental designs can also successfully eliminate threats to internal validity. These threats to internal validity are:

• Biased assignment of participants to conditions;

• Differential attrition which refers to loss of participants during the study;

• Pretest sensitization;

• History, and

• Maturation.

The time series design automatically counters all the above threats. Archived data is naturally occurring, posing no threat to either bias or attrition to loss of participants to original participants. Pre-test sensitization is irrelevant for the design of this study. History and maturation were the only threats, but the trend analysis before the intervention provided the level of growth and maturation in mathematics performance and participation regardless of interventions. Qualitative interviewing also contributed to the elimination of the history and maturation threats.

5.6.1.6 Ensuring External Validity

External validity is the degree to which the results of the study can be applied to subjects or settings other than the one in which the research took place (Leary, 2004: 422).

90 The whole design of this study, particularly its sampling, is replicable. This emanates from the ongoing implementation of mathematics interventions as a result of poor performance in the subject, particularly, in high schools. Therefore, the impact of interventions can be investigated in the same manner as the study.

5.6.1.7 Ethical Issues

Secondary data analysis removes much of the concerns around ethical issues (McMillan & Schumacher, 2006: 410) as there is no participation in the study required. However, pseudo names for three interventions and numbers for schools were used to ensure confidentiality.

Three interventions were named AB, CD and EF. Each school in the sample had a number from 1 to 47 (see appendix for a full listing of sample schools). Forms requesting permission to conduct the study were submitted to Gauteng Department of Education (see Appendix A). In response permission to conduct the study was granted (see appendix B). Meetings to seek buy in of the study were held with the appropriate officials at the Head office and district offices. The following section will elaborate on the quantitative phase of the study which endeavours to shed more light on the quantitative impact of interventions.

5.6.1.8 Ensuring the Statistical Rigour

Supplementation of the researcher's statistical expertise with a recognized expert in statistics in strengthening of both the design and analysis of quantitative research is recommended by Gall, Gall and Borg (2007:126). Therefore, Statistical Consultation Services (STATKON) of the University of Johannesburg was employed in quality assurance of the statistical design and its analysis.

91 STATKON provides a professional, goal oriented statistical consultation services to post graduates students and researchers at the University of Johannesburg in respect of among other things, statistical analysis of quantitative data (http://www.uj.ac.za/researcherinnovation/Statkon).

5.6.2 The Second Phase

In line with the mixed method design of the study, the primary purpose of the second phase was to explain and further elaborate on the quantitative findings (section 5.5). The secondary purpose for this phase was to complement the quantitative findings in view of the growing consensus among researchers that qualitative and quantitative complement each other (Gall, Gall and Borg, 2007:32).While the purpose to explain is clear enough, complementing quantitative phase needs some clarification.

It has been indicated that teachers are among an array of factors that influence learner performance in mathematics (section 5.3). However, quantitative phase only focused on the impact of interventions in terms of learners' performance and participation in mathematics. Hence, the impact of mathematics interventions on teachers was not captured. This phase complemented this lack of information by bringing on board teachers' perspectives and experiences on mathematics interventions.

5.6.2.1 Research Design for the Phase

Qualitative interviewing was the research design employed for the qualitative phase as this facilitates talking and listening to the teachers' perspectives and experiences of mathematics interventions (Rubin and Rubin, 2005: 3).

92 Qualitative interviews are also regarded to be the key in understanding the individuals' lived experiences (Seidman, 2007:9; Glesine, 2006:37; Gubrium & Holstein, 2001:4 and Johnson, 2001:104). In interpreting their experiences, participants become meaning makers (Warren, 2001:83) and not the researcher. Focus group interviews in particular, were chosen as a method of interviewing. Hence, these were semi-structured interviews that involved guiding questions but allowed participants to express their opinions (Willis, 2007: 3).

Focus group interviews brought about a range of advantages such as the production of amounts of qualitative data that would be less accessible without the interaction found in a group (Morgan, 2001:141) and multiple perspectives on experiences of the implementation of interventions (Glesine, 2006:102).

Also, the suitability of focus group interviews for impact studies on interventions is endorsed by Patton (2002: 388) who stated that "focus groups are used to identify a program's strengths, weaknesses, and needed improvements as this method of interviewing gathers perceptions about outcomes and impacts".

5.6.2.2 Sampling

Intensity sampling strategy was employed to select the nested sample of two focus groups of teachers within the selected sample of two schools for this phase. In intensity sampling groups or individuals that experience the phenomenon intensely are studied (Onwuegbuzie and Leech, 2007:113). Hence sample schools that participated in more than one intervention were viewed as having experienced interventions intensely. Intensity sampling was also in line with the principle of selecting a sample with a realistic chance of reaching data saturation in qualitative inquiry (Onwuegbuzie and Leech, 2007:105).

93 Other researchers regard this as selecting a sample that is able to generate a thorough database on the type of phenomenon under study (Kemper, Springfield and Teddlie, 2003:275).

Literature on focus groups does not have consensus on the size of groups and the number of members in a group. For example, Krueger (2000:73) says the size of noncommercial focus groups is 6-8 and Glesine (2006:110) says 6-10. However, Morgan (1997:43) argues that three members in a group may be adequate for data saturation. He supports this by citing focus groups of three members, who were highly involved that hav!ng six of such individuals can render the group unmanageable. Therefore, the target number of teachers in a focus group was three in this research, making a total of six teachers in two schools.

5.6.2.3 Data Collection

The instruments for qualitative data collection were based on the last two research questions (section 1.3) which are as follows:

• What learner centred practices are promoted by interventions? • How are mathematics interventions perceived by mathematics teachers? This is in keeping with Shank (2006: 45) who strongly recommends a few questions, as too many questions gets across to the interviewee as a sense of rush to get answers and thus gives quick superficial answers. Two aforementioned questions were reworked to avoid double barrel questions (UNISA, 2007:23) into the following four questions:

• What learner centred practices are promoted by interventions?

• In accordance to ethical considerations (see 5.6.1.7), pseudo names for three interventions were used in the following questions.

• What are your experiences from EF intervention?

94 • What are your experiences from AB intervention?

• What are your experiences from CD intervention?

Questions were asked in accordance with Seidman's (2006:78) techniques in asking questions and these are that the interviewer should:

• Listen more and talk less.

• Follow up and explore on what participants say, but don't interrupt.

'. Ask participants to reconstruct, not to remember.

• Keep participants focused.

The researcher had to adopt attributes of being a learner who is non-directive (Glesine, 2006:89), caring and respectful towards the participants (Kruger, 2000:98). A tape recorder was used with the permission of participants to capture the interviews. But field notes were made throughout the interviews to complement the tape recorder.

5.6.2.4 Empathetic Interviewing as an Ethical Stance

Unlike the quantitative phase, ethical consideration in this phase went beyond permission seeking (section 5.6.1.7) and basic ethical guidelines of informed consent, no deception, privacy and confidentiality and accuracy (Christians, 2000:138-139; Denscombe, 2007:141-147 and Ryen, 2004: 230). Non-monetary reciprocity was included in accordance with contemporary literature on ethical considerations (Fontana & Frey, 2008:117, Glesine, 2006:102 and Seidman, 2006:106).

According to Seidman (2006:109), the best reciprocity is having an interest in participants and honouring their words when the research report is presented in "public.

95 Glesine (2006:102) argues that the researcher's reciprocity should be an involvement in advocating participants' plight. Failure to do this is similar to exploiting the participants for the researcher's gain only.

Fontana and Frey (2008:117) also assert that the researcher's involvement in advocating the participants' plight is an ethical stance which could be implemented through empathetic interviewing. The latter is in line with the growing view that the interviewer /researcher is not neutral (Fontana & Frey, 2008:116). Also, Chase (2008: 74-77) argues that a researcher adopts an authoritative or supportive or interactive voice in an interview.

Therefore, in this research, empathetic interviewing with a view of later advocating the plight of participants was employed. The researcher opted to adopt a supportive voice through the interviews and through reporting the research project as part of ethical considerations. This was in accordance with the discussion above.

5.6.2.5 Data Analysis

Literature on focus group interviews does not reveal distinct data analysis of transcripts from focus groups, for example Morgan (1997) and Krueger (2000). Therefore, the normal qualitative data analysis was employed.

According to Babbie (2004:370) qualitative data analysis is the non-numerical examination and interpretation of data for the purpose of discovering underlying meanings. Extracting meaning and implications entails comparisons, weighing and combining materials from the interviews implications (Rubin and Rubin, 2005:201).This will be further discussed in chapter 7.

96 5.6.2.6 Merging Quantitative and Qualitative Results

It was noted in section 5 .5 that the explanatory strategy of inquiry for the study means the qualitative methods are used to explain quantitative data. Therefore, qualitative data was analyzed with a view of searching explanations for the quantitative results. Thus, in presenting qualitative data and its analysis, the results from both phases become merged.

5.7 SUMMARY

This chapter discussed the research design for the study. The first part of the discussion entailed elaboration on the overarching concepts aligned to the chosen mixed methods design, such as the rationale, value and the philosophical assumptions for the study. The second part of the chapter illuminated on the chosen strategy of inquiry of the study, thereby discussing specific research methods for the study. The following chapter presents results from the first phase of the study's research design.

97 CHAPTER 6

6 PRESENTATION AND ANALYSIS OF QUANTITATIVE DATA

6.1 INTRODUCTION

This chapter is a presentation and analysis of quantitative data and its analysis which according to the research design discussed in the previous chapter is the outcome of data collection in the first phase of the study. The first part of the chapter presents data on participation of learners in each of the three sample interventions. This is done within the framework of statistical data analysis of the impact of interventions on the participation of learners in mathematics. A very low participation in higher grade mathematics restricted the analysis to descriptive statistics only.

The second part of the chapter analyses the impact of interventions on learner performance and this was mainly through hypothesis testing. Hence both descriptive and inferential statistical analyses were employed. Then, conclusions are made about quantitative impact of mathematics interventions. Implications for the next chapter wrap up the chapter.

6.2 SAMPLING AND SAMPLES

The nested sampling (section 5.6.1.2) meant that a sample whose variables were of interest, was within the chosen peripheral samples. The latter were mathematics interventions and the high schools respectively. Non-random sampling selected three interventions and random sampling was used to select high schools. Criterion sampling (Onwuegbuzie & Collins, 2007:286) was used to select a sample of three interventions. The criteria for section were:

• Must have operated for more than three years; 98 • Must have operated in Gauteng high schools;

• Must have been implemented in at least ten Gauteng high schools.

• Within the three selected mathematics interventions, stratified random sampling was employed to choose a sample of high schools (section 5.6.1.2).

6.2.1 A Sample of Mathematics Interventions

AS is a provincial flagship intervention targeted at low performing schools, but had a specific aim to improve participation and performance in mathematics of learners. All AS schools were previously disadvantaged. This intervention was initiated in 2002 and is still ongoing.

CD was a multimillion project lnltiated and implemented in 2000 in nine provinces including Gauteng and funded by big businesses in South Africa. It was well publicized as being the panacea of all the education ills, in particular mathematics teaching and learning. CD was completed in 2004. CD was published on TV and other media. However, such publication was market based rather than research based.

EF is a national flagship project for transforming the quality of mathematics education and hence performance of learners in mathematics. It was initiated in 2001 by the Department of Education and was implemented in one hundred and one high schools in nine provinces. It can be viewed as having been implemented in 2002.

6.2.2 A Sample of Schools

There are six hundred and seven public high schools in Gauteng (EMIS, 2006). A total of two hundred and two high schools participated in all three selected interventions for at least three years. Fifty was the target sample size in

99 accordance with Denscombe (2007:24) who asserts that the sample should be a little more than twenty per cent of the population. Excel random sampling technique espoused by Keller (2005:148) was employed to select a sample of thirty eight schools from two strata, that is, schools that participated in AS and CD.

The sample of thirty eight schools was randomly selected from a population of schools that participated in AB and CD. In keeping with the recommendation from De Vos, Strydom, Fouche and Delport (2007:199) for sampling with small populations, all twelve high schools in EF were to be included in the sample for the study.

One school in EF and two in AB were extreme outliers. In qualitative investigation, an outlier can uncover issues which may throw a new light in the study. However, in quantitative analysis an outlier can sway statistics in a total different direction from the rest of the population being represented (Keller, 2005:617). Hence, the outliers were removed from the sample. Consequently, the sample of 50 ended up being 47 schools that participated in AB, CD and EF.

6.3 DATA ON PARTICIPATION IN MATHEMATICS

Enrolment in Higher Grade (HG) and Standard Grade (SG) mathematics represented participation in mathematics. Data on enrolment in mathematics HG and SG for 47 sample high schools was collected from the archives of Gauteng Department of Education. Percentage ratios of learner enrolment in HG and SG were calculated for each school. Subsequent to this descriptive statistics, that is mean and standard deviation for enrolment in HG and SG mathematics were determined using Excel's Toolpack.

100 6.3.1 Statistics on Learner Participation in AS Schools

Tables 6.1a through Table 6.4 provide statistics of learners who were enrolled in SG and HG mathematics in twenty two schools that participated in AB. Data is for the period from 2002 through 2006. Even though AB was implemented in 2003, data in the year 2002 is given as a baseline or status quo before AB.

101 Table 6.1a: 2002 Mathematics Enrolment in Schools Targeted for AS

O/OSG %HG Schools Learners Learners 26 100 0 SG Statistics Summary 27 100 0 Mean 97.61957 28 100 0 Median 100 29 95.24 4.76 Mode 100 30 98.36 1.64 Std Deviation 3.933861 31 100 0 Sample Variance 15.47526 32 100 0 33 97.22 2.78 Skewness -2.54563 34 100 0 Range 16.92 35 97.33 2.67 Minimum 83.08 36 96.34 3.66 Maximum 100 37 94.85 5.15 Sum 2245.25 38 100 Count 23 39 94.87 5.13 HG Statistics Summary 40 83.08 16.92 41 100 0 Mean 42 100 0 Median 43 100 0 Mode 0.82 44 100 0 Std Deviation 0 45 92.31 7.69 Sample Variance 4.286949 46 100 0 Skewness 18.37793 47 100 0 Range 2.296084 48 95.65 4.35 Minimum 16.92 Maximum 0 Sum 16.92 Count 51.1 .Enrolment in 2002 represents the status quo of enrolment in mathematics in schools targeted for AS intervention before its implementation.

102 Appendix E shows that out of a total of twenty two schools, only 30 learners enrolled for HG mathematics. According to Table 6.1a, the percentage of learners enrolling in HG mathematics was only above 10% in one school, that is, school number 40. It must have been this situation that necessitated an intervention!

Table 6.1: 2003 Mathematics Enrolment in AS Intervention Schools

Learner Enrolment in SG & HG Mathematics Statistics Summary SG HG Schools Learners %SG Learners %HG SG % Enrolment 26 19 95 1 5 Mean 96 27 10 100 0 0 Median 98 28 81 87 12 13 Mode 100 29 31 100 0 0 Std dey 5.0615 30 62 98 1 2 Sample Var 25.6190 31 40 88 5 12 Kurtosis 2.6834 32 52 98 1 2 Skewness 1.71840 33 42 97 1 3 Range 19 34 116 91 11 9 Count 21 36 100 98 2 2 HG % Enrolment 37 59 98 1 2 Mean 5.86666 38 83 81 19 19 Median 4 39 64 95 3 5 Mode 2 40 32 96 1 4 Std dey 5.16674 41 99 100 0 0 Skewness 1.5007 42 68 98 1 2 Range 19 43 28 100 0 0 Minimum 0 44 35 94 2 6 Maximum 19 45 41 100 0 0 Count 14 46 34 100 0 0 47 90 100 0 0 TOTALS 1250 62

103 In 2003, a total of 1312 learners enrolled for SG and HG mathematics in 21 AS schools. Seven schools did not register any students in HG and a total of 62 learners (5%) enrolled in HG mathematic in 14 schools. It is noted that much as enrolment in HG, is low, there was an increase from 30 in 2002 to 62 learners in 2003 the year of AS implementation.

Table 6.2 : 2004 Mathematics Enrolment in AS Intervention Schools

Learner Enrolment in SG &HG Mathematics Statistics Summary SG HG Schools Learners %SG learners %HG Mean 94.4090 26 32 94 2 6 Standard Error 1.2752 27 17 100 0 0 Median 97 28 74 96 3 4 Mode 100 29 38 92 3 8 Std dev 5.9813 30 89 98 2 2 Sample Var. 35.777 31 52 98 1 2 32 49 100 0 0 Skewness -1.309 33 52 98 1 2 Range 19 34 129 98 2 2 Count 22 35 97 95 5 5 36 80 82 17 18 37 67 100 0 0 %HG Enrolment 38 114 99 1 1 Mean 6.277 39 76 97 2 3 Standard Error 1.2388 40 23 92 2 8 Median 4.5 41 91 91 9 9 Mode 2 42 126 97 3 3 Std dev 5.2558 43 36 100 0 0 Sample Var 27.624 44 18 82 4 8 Kurtosis 1.6429 45 29 81 7 19 Skewness 1.448 46 35 97 1 3 Count 18 47 86 90 9 10 TOTALS 1410 74

104 Table 6.2 above presents enrolment in 2004. The total enrolment in SG mathematics increased from 1250 to 1410. However, there was only a slight percentage increase in the learner enrolment in HG mathematics. In 2003, a mean of 5.87% learners were enrolled in HG and in 2004 the mean increased to 6.28% .Three more schools enrolled learners in HG.

Table 6.3: 2005 Mathematics Enrolment in AS Intervention Schools

Learner Enrolment in SG & HG Mathematics SG HG Schools Learners %SG Learners %HG Statistics Summary 26 25 92 2 8 %SG Enrolment 27 41 100 0 0 Mean 96.4090 28 118 98 2 2 Median 98 29 59 93 4 7 Mode 100 30 94 94 6 6 Std dey 3.5544 31 39 95 2 5 Sample Var 12.6341 32 36 100 0 0 Kurtosis -1.2719 33 87 98 1 2 Skewness -0.5250 34 123 91 11 9 Range 10 35 132 91 13 9 Minimum 90 36 188 96 7 4 Maximum 100 37 106 92 9 8 38 129 99 1 1 39 163 100 0 0 % HG Enrolment 40 28 96 1 4 Mean 5.2667 41 97 100 0 0 Median 5 42 150 98 2 2 Mode 2 43 37 100 0 0 Std dey 3.08 44 66 100 0 0 Sample Var 9.4952 45 36 90 4 10 Kurtosis 46 47 100 0 0 Skewness 0.099628 47 110 98 2 2 Count 15 TOTALS 1911 67

105 In 2005 (Table 6.3) a total of 1978 learners were enrolled in SG and HG mathematics in twenty two schools. However, only 67 of these were enrolled for HG mathematics. As expected, the mean percentage of learners enrolled in HG decreased from 6.27% in 2004 to 5.267% in 2005. The standard deviations in SG and HG enrolment were still very low at 3,5% and 3,08% respectively, thus still indicating very low variability in mathematics enrolment tendency by learners.

106 Table 6.4: 2006 Mathematics Enrolment in AS Intervention Schools

Learner Enrolment in SG & HG Mathematics SG HG Schools Learners %SG Learners %HG Statistics Summary 26 12 85 2 15 Mean 93.8181 27 31 100 0 0 Mode 100 Standard 28 136 96 6 4 Deviation 6.7020 29 62 89 7 11 Skewness -0.8465 30 93 94 6 6 Range 21 31 83 97 2 3 Minimum 79 32 61 100 0 0 Maximum 100 33 61 100 0 0 34 104 88 14 12 35 79 91 8 9 36 213 98 5 2 %HG Enrolment 37 122 98 2 2 Mean 8.5 38 98 100 0 0 Median 7.5 39 147 98 2 2 Mode 2 Standard 40 34 100 0 0 Deviation 6.47044 Sample 41 54 87 8 13 Variance 41.8667 42 241 99 2 1 Kurtosis -1.05671 43 39 79 10 21 Skewness 0.48263 44 53 82 11 18 Range 20 45 37 86 6 14 Minimum 1 46 39 100 0 0 Maximum 21 47 114 97 3 3 Count 16 TOTALS 1913 94

2006 was the only year with an increase of 29 learners enrolling in SG and HG mathematics. But it had the highest number of learners (94) enrolling in HG

107 mathematics over a period of observation. But the number of schools that had enrolled learners regressed to 16, almost equal to the original 15 schools at the beginning of the intervention.

6.3.1.1 Discussion of Learner Participation in Mathematics for AS Schools

Participation in mathematics increased from the period of the first implementation of AB in 2002 from 1312 learners to 2007 learners. However, enrolment in HG mathematics remained firmly below 10% throughout the period between 2002 and 2006. Figure 6.1 encapsulates the picture of enrolm ent for the given period.

Figure 6:1 AS Matric Enrolmen t in Mathematics

120 i 100 ~ Iii 80 SG 60 - I . HG 40 - 20 - - -- f 0 2002 2003 2004 2005 2006 Time (2002-2006)

Figure 6.1: AS Matric Enrollement in mathematics

6.3.2 Descriptive Statistics on Enrolment in Mathematics for CD Schools

Short versions of tables are presented for enrolment of learners in CD schools. However, Appe ndix E will be referred to, for the actual numbers of learne rs who enrolled in SG and HG mathematics. The statistics in tables 6.5 through 6.7 were only for percentage enrolment in fourteen schools that participated in CD from 2000 through 2004. It was expected that by 2002, the intervention would have been so entrenched that its impact in enrolment would be quite significant. 108 However, Table 6.5 shows that in 2002 a similar trend to AS enrolment seemed to exist in the ratio of SG enrolment to the HG enrolment. The mean HG enrolment was 90.9% in all schools compared to 9.26% for SG enrolment. Similarly, there is not much variability in the enrolment trends of all sample schools since the standard deviation was 7.8%. The mode of 100% enrolment in SG was also a trend in AS schools. In view of a similar trend, years of CD interventions is now paired. Table 6.6 pairs the statistics for 2003 and 2004 and Table 6.7 pairs 2005 and 2006.

Table 6.5: 2002 Enrolment in Mathematics for CD Schools

Schools %SG %HG 12 95.6 4.4 SG Statistics Summary 13 75 25 Mean = 90,9 Mode = 100 14 77.3 22.7 Standard Deviation = 9.523 15 100 0 Sample Variance = 90.687 I 16 100 0 Minimum = 71.8 Max = 100 17 97.9 2.1 Count = 14

I 18 100 0 i i 19 88.6 11.4 HG Statistics Summary i 20 91.8 8.2 Mean = 9.264, Mode = 0 ! i 21 97.3 2.7 Standard Deviation 7.778 ) 22 93.1 6.9 Sample Variance 60.50 23 91.2 8.8 Minimum =0 Max=25 24 71.8 2.8 Count = 11 25 93.1 6.9

A peek into Appendix E reveals that in a sample of 14 schools there were 100 learners who enrolled in HG mathematics in comparison to 788 learners who enrolled in SG mathematics in 2002. Even though it may seem as if more than a 1 000 learners were enrolled for SG mathematics for AS schools, but there were 22 AS schools compared to 14 CD schools in the same year.

109 Table 6.6: 2003·2004 Enrolment in CD Schools

2003 Statistics Summary of Enrolment SG HG Mean 91.271 Mean 10.136 Mode 100 Mode N/A Standard Deviation 9.679 Standard Deviation 8.965 Range 31.4 Range 30.3 Min:68.6; Max: 100 Min: 0; Max: 31.4 Count 14 Count 11 2004 Statistics Summary of Enrolment SG HG Mean 89.49286 Mean 13.37273 Median 94.5 Median 10 Mode 100 Mode #N/A Standard Deviation 11.74023 Standard Deviation 11.7059 Range 37.9 Range 30.3 Count 14 Count 11

As shown, Table 6.6 indicates that not much changed in 2003; some change occurred in 2004. The 13% enrolment in HG was the highest thus far. In actual numbers of learners who enrol for HG mathematics CD had more than AS learners. In 2002, 100 learners enrolled for HG mathematics, in 2003, the number dropped to 97. But in 2004, the number increased to 109 and reached its peak of 135 in 2005, a year after the intervention ceased.

In terms of the actual learners, a look into Appendix E shows a drop from 100 learners enrolled in HG mathematics in the year 2002 compared to 97 in the year 2002. Even though it is not a very big drop, a steady increase in HG enrolment as a result of CD intervention would have been expected!

110 Table 6.7: 2005 -2006 Enrolment Statistics in CD Schools

2005 Statistics Summary SG HG Mean 88.42 Mean 12.47 Median 92.7 Median 7.8 Mode 89.4 Mode 10.6 SO 11.99 SO 11.99 Range 42.2 Range 40.5 Minimum 57.8 Minimum 1.7 Maximum 100 Maximum 42.2 Number ofSchools 14 Number of Schools 13 2006 Statistics Summary SG HG Mean 92.8 Mean 10.07 Median 93.35 Median 9.6 Mode 100 Mode Not Applicable SO 6.2 SO 4.9 Range 17.2 Range 13.8 Minimum 82.8 Minimum 3.4 I Maximum 100 Maximum 17.2 Count 14 Count 10

Table 6.7 shows the statistics of enrolment in mathematics for two years after the intervention was stopped. Not much can be concluded about the trend of the enrolment as a result of the interventions since during the intervention enrolment in HG mathematics dropped from 91.27% in 2003 to 89.49% in 2004. Interestingly in the absence of the CD intervention, the mean enrolment % increased from 88.4% in 2005, to 92.8% in 2006.

6.3.2.1 Discussion of Learner Enrolment in Mathematics in CD Schools.

The mode for enrolment in mathematics standard grade for learners firmly remained at 100% throughout the implementation period of CD, that is, 2002 111 2004. This meant that the majority of schools registered all their learners in Standard Grade Mathematics. This was also confirmed by the mean over the same period which revealed that the overwhelming majority of learners, more than 89% were registered for standa rd grade mathematics.

Figure 6.2 presents a summa ry of enrolment of learners both in Higher and Standard Grade mathematics resulting from a CD intervention for the period 2002-2006. This showed a consistent large discrepancy between the enrolm ent in Standard and Higher Grade Mathematics over the years of intervention.

F igure 6 .2 CD Matric Enrolment in Mathemat ics

1 0 0 -.------..... 90 -r--r-r-- -r-, 80 - 70 - 60 SG 50 - 4 0 - . H G 30 - 2 0 10 - o - ~----.,.-'-...... --.,.-'--= 2002 2003 2004 2005 2006 Time (2002-2006)

~------Figure 6.2: CD Matric Enrollement in mathematics

Finally, the statistics for enrolment in mathematics by learners in EF intervention is presented. Since EF is a national flagship intervention which is ongoing, a five year period statistics will be presented.

6.3.3 RESULTS ON ENROLMENT IN MATHEMATICS IN EF SCHOOLS

In section 6.2.2 it was indicated that one school was dropped from the sample as it was an outlier.

112 Table 6.8 is a presentation of Higher and Standard Grade mathematics enrolment of learners in 2002 for eleven high schools that participated in EF intervention. EF was initiated and implemented in 2001 in twelve Gauteng schools. The mean enrolment in SG mathematics is 94.5 % and 7.7% in HG mathematics.

Table 6.8: 2002 Enrolment in Mathematics for EF Schools

Schools % SG Enrolment % HG Enrolment SG StatisticsSummary 1 90.9 9.9 Mean = 94.5 and Mode = 100 2 100 0 Std dev =4.9 3 95.3 4.7 Sample Variance = 24.2 4 100 0 Minimum =85.8 Max =100 5 96.2 3.8 Count = 11 6 90.1 9.9 7 100 0 HG Statistics Summary 8 96 4 Mean = 7.7and Mode = 9.9 9 85.8 14.2 Standard Deviation 4.1 10 96.1 3.9 Sample Variance 16.9

11 88.6 11.4 Minimum =3.8 Maxi = 14.2 Count 8

In 2002, after a year of EF implementation, three high schools, namely, schools 2, 4 and 7 did not enrol any learners in HG mathematics. However, four schools, namely, 1, 6, 9 and 11 have enrolment percentage higher than the mean percentage enrolment of 7.7. However, it is noted that from Appendix E, the corresponding actual number of learners to these higher than mean percentages are 5, 9, 28 and 4 learners! Hence, the only impressive number of learners in HG mathematics was found in school 9!

113 Table 6.9: 2003 Enrolment in Mathematics for EF Schools

Schools % SG Enrolment % HG Enrolment SG Statistics Summary 1 93.2 6.8 Mean = 80.7 Mode = N/A 2 87 13 Standard Deviation 23.8 3 92.5 7.5 Sample Variance 564.4 ~ 64.3 35.7 Minimum = 16.3 Maximum = 100 IS 71.3 28.7 Count 11 16 86.9 13.1 e 100 0 HG Statistics Summary 8 90.6 9.4 Mean = 21.3 Mode =N/A l!j 16.3 83.7 Standard Deviation 24.1 10 90.8 9.2 Sample Variance 581.5 91 94.6 5.4 Minimum = 5.4 Maximum = 83.7 Count 10

a substantial improvement in the percentage mean enrolment of learners in HG mathematics was observed in 2003. The mean percentage enrolment in HG mathematics increased from 7.7% in 2002 to 21.3% in 2003. This is also confirmed by Appendix E which reveals that the actual number of learners enrolled in HG mathematics increased from 59 in the year 2002 to 115 in the year 2003.

With the exception of three schools, 1, 7 and 11, all schools increased in percentage enrolment of learners in HG mathematics. School 2 increased from 0% in 2002, to 13% in 2003. School 3 increased moderately from 4.7% in 2002, to 7.5% in 2003. School 4 had a substantial improvement of 35.7%. The most improvement was observed from school 9 which jumped from 14.2% in 2002 to 83.7% in 2003.

114 Table 6.10: 2004 Enrolment in Mathematics for EF Schools

Schools % SG Enrolment % HG Enrolment SG Statistics Summary h1 86.8 13.2 Mean =79.4 Mode = N/A i2 90.6 9.4 Std dev = 23.81246809 S3 91.8 8.2 Sample Var 567.0336364 4 79.3 20.7 Minimum =11.7 Max =92.5 5 91.7 8.3 Count 11 6 85.2 14.8 1.-.. 7 91.5 8.5 HG Statistics Summary ~8 65.3 34.7 Mean = 13.3 Mode = N/A 9 88.9 11.1 Std dev 8.0846 /810 92.5 7.5 Sample Var 65.360 ~11 90 10 Min =7.5 Max = 34.7 ~ Count 11

An increase in the mean enrolment in HG is also supported by a drop in SG enrolment mean percentage during from 2002 through 2004.

While in 2003 EF schools had gains in learners enrolling in HG mathematics, the opposite was observed in 2004. A decline in the percentage mean enrolment of learners in HG mathematics from 21.3 % in 2003 to 13.3% in 2004 was shown.

A similar trend is found among individual schools participating in EF. The number of learners enrolled in HG mathematics in school 1, declined from 6.8% in the year 2003 to 13.2% in the year 2004. Also in school 2 , learners enrolled in HG mathematics decreased from 13% in 2003 to 9.4% in the year 2004. In school 3 HG mathematics learner enrolment dropped from 7.5% in 2003 to 8.2% in 2004, in school 4 the decline was from 35.7% in 2003 to 20.75% in 2004. In school 5 the drop was 28.7% in 2003 to 8.3% in 2004 and in school 9 from 83.7% to 11.1%.

115 Only schools 3, 6 and 11 showed slight improvements in HG enrolment through the years 2003 and 2004. School 3 improved the HG learner enrolment from 7.5% in the year 2003 to 8.2% in the year 2004. School 6 improved from 13.1% HG learner enrolment in the year 2003 to 14.8% in the year 2004. Finally, school 11 increased from 5.4% HG enrolment IN 2003 to 10% enrolment in 2004.

Table 6.11 shows that the mean percentage enrolment in HG mathematics for sample schools dropped to 10.8% in the year 2005 from 13.3% in the year 2004. This was not caused by the majority of schools having declines in the number of learners enrolling in HG mathematics since only five schools, namely schools 2, 4, 7, 8 and 11 had decline in HG learner enrolment from the year 2004 through 2005.

But the decline in mean percentage enrolment seemed to have been the result of large declines in some schools. For example, schools 4,8 and 11 dropped from 20.7%,34.7% and 10% respectively in the year 2004 to 12.5%,15.1% and 2.9% respectively in the year 2005.

116 Table 6.11: 2005 Enrolment in Mathematics for EF

Schools % SG Enrolment %HG Enrolment SG Statistics Summary ~ 84.4 15.6 Mean = 89.3 Mode = N/A ,..2 91.9 8.1 Std dey 4.7764 3 90.5 9.5 Sample Va. 22.8141 4 87.5 12.5 Min = 81.2 Max= 97 ~5 91.8 9.2 Count 11 6 81.2 18.8 P7 95 5 HG Statistics Summary i 8 84.9 15.1 Mean = 10.8 Mode = N/A n Standard Jl 87 13 Deviation 4.75044 10 91.4 8.6 Sample Variance 22.5667 11 97 2.9 Min = 2.9 Max = 18.8 Count 11 v table 6:12, the mean percentage enrolment improved from 10.8% in 2005 to 14.5% in 2006. However, as the last year of observation a trend of improvement is expected as the EF intervention continue to be implemented in the sample schools over the period of five years, that from the year 2002 through the year 2006. That does not seem to be the case.

The mean percentage enrolment of learners in HG mathematics improved from 7.7% in the year 2002 to 21.3% in 2003, however, it declined in the year 2004 to 13.3% and declined further in the year 2005 to 10.8%. The improvement was observed again from 10.8% to 14.5% in the year 2006. The learner enrolment in HG mathematics lacks a clear trend which would be the impact of the EF intervention. However, schools 1, 3 and 6 show a steady improvement in the learner enrolment in HG mathematics during the observed period from 2002 through 2006.

117 Table 6.12: 2006 Enrolment in Mathematics for EF

Schools % SG Enrolment % HG Enrolment SG StatisticsSummary 1 64.2 35.8 Mean = 86.4 Mode = N/A 2 92.1 7.9 Std dev 10.4148 3 94.9 15.1 Sample Var 108.4696 4 94.7 5.3 Min= 64.2 Max = 96.7 5 96.7 3.3 Count 11 6 72.6 27.4 7 84.5 15.5 HG Statistics Summary 8 78.8 21.2 Mean = 14.5 Mode = N/A 9 89.2 10.8 Std dev 10.0261 10 89.6 10.4 Sample Var 100.5241 11 92.9 7.1 Min= 3.3 Max= 35.8 Count 11

Discussion of Learner Enrolment in Mathematics in EF Schools Statistics in EF was slightly different from that of previous interventions in that lowest means of SG enrolment were achieved in 2003 and 2006; these were 80.7 and 79.4 respectively. This was tantamount to more learner enrolment in HG which translated to highest means of HG enrolment, which was 21.3% and 14.5% in 2003 and 2006 respectively. Figure 6.3 presents this improvement that illustrated this improvement, which was random.

118 EF Matric Enrolment in Mathematics

100 rn 90 j 80 70 -- -- i 60 ~ c 50 W 40 30 20 f 10 0 2002 2003 2004 2005 2006 Years

Figure 6.3 : EF Matric Enrolment in Mathematics

6.3.4 Summary of Participation in Mathematics

Table 6.13: Enrolment Time Series for Interventions

SG Enrol in AS schools SG Enrol in CD schools SG Enrolment in EF schools Year % Enrolment Yea r % Enrolment Year % Enrolment 2002 97.6 2002 90.9 2002 94.5 2003 96 2003 91.27 2003 80.7 2004 94.4 2004 89.5 2004 79.4 2005 96.4 2005 88.4 2005 89.3 2006 93.8 2006 92.8 2006 86.4

HG Enrol in AS schools HG Enrol in CDschools HG Enrol in EFschools Year % Enrolment Year % Enrolment Year % Enrolment 2002 2.8 2002 9.264 2002 7.7 2003 5.8 2003 10.1 4 2003 21.2 2004 6.27 2004 13.4 2004 13.3 2005 5.27 2005 12.5 2005 10.8 2006 8.5 2006 10.1 2006 14. 5 119 Statistics on participation of learners in mathematics through the period of three interventions is summarized by the time series Table 6.13. From the time series, it was clear that there was no consistent pattern for increase or decrease in enrolment for all intervention schools. Lack of increase or decrease in participation in mathematics where interventions were being implemented was tantamount to lack of quantitative impact on mathematics participation. However, the data allowed the exploration of whether interventions performed equally.

6.3.5 Conclusions on the Impact of Interventions on Participation

The analysis of participation in mathematics for learners whose schools participated in interventions was a strategy of answering the research question: What is the impact of mathematics interventions on the high school learner participation in mathematics? The construct of participation in mathematics was defined as enrolment of learners in HG mathematics since it is through enrolment in HG mathematics that learners are able to access the majority of mathematical related professions (see also definition of terms in section 1.7). "Access to technological and professional careers requiring a strong basis in mathematics and science is denied to all but a fraction of the age cohort" (Department of Education and Training, 1995:18). Institutions and organizations that participated in mathematics interventions were very much aware of this. For example, Dinaledi specified an increase in HG enrolment as one of their objectives (section 4.6.3). However, the results presented indicated that only an average of 10% learners was enrolled in Higher Grade mathematics over the observed period of three mathematics interventions. In view of very small number of learners who enrolled for mathematics throughout the five year period in all three interventions, statistical analysis of performance in HG would be nonsensical (Devey, 2009). Therefore, descriptive

120 statistics and Devey's opinion pointed to the conclusion that very low enrolment of learners in HG mathematics despite the implementation of interventions implied that mathematics interventions did not have the desired impact on learner participation in mathematics. In view of low learner enrolment in HG mathematics statistical analysis for learner performance in mathematics was done for combined SG and HG learners.

6.4 DATA ON PERFORMANCE IN MATHEMATICS

The same mathematics results used in the previous section was used for data on performance. In this section, the variable of interest, performance was given by pass in SG and HG mathematics. Raw data in appendix C was analysed using SPSS. The number of students enrolled in mathematics SG and HG are sufficient to conduct inferential statistical analysis and hence hypothesis testing.

6.4.1 Descriptive Statistical Analysis of Data

Descriptive analysis of data was conducted as groundwork for inferential statistical analysis. Table 6.14 provides descriptive statistics of the combined pass rates of learners in SG and HG mathematics for all three interventions over a period of 2002-2006.

By observation from descriptive statistics, throughout the period of observation the % mean performance of learners in intervention schools was below 50%. Considering that the majority of learners were doing mathematics on a lower level, that is standard grade, this was not good at all.

121 Table 6.14: Descriptive Statistics for Learner Performance in Three Interventions

Intervention & Years N Mean Std. Deviation Min Max 2002 percent passed 5G & HG 11 44.607 21.6004 17.92 83.64 2003 percent passed 5G & HG 11 40.911 16.1468 23.96 70.69 2004 percent passed 5G &HG 11 39.893 17.0321 13.93 63.77 2005 percent passed HG & HG 11 46.948 15.040 25.77 73.33 EF 2006 percent passed 5G & HG 11 37.721 17.1971 12.07 66.18 2002 percent passed 5G & HG 14 36.423 25.0498 6.56 90.91 2003 percent passed 5G & HG 14 40.853 23.2779 10.29 83.91 2004 percent passed 5G & HG 14 31.931 27.4873 5.1 93.22 2005 percent passed 5G & HG 14 29.059 22.5375 8.21 90.74 CD 2006 percent passed 5G & HG 14 32.149 28.7057 7.79 98.51 2002 percent passed 5G & HG 22 34.333 22.5549 0 84.62 2003 percent passed 5G & HG 22 33.616 18.5772 6.86 75.68 2004 percent passed 5G & HG 22 32.798 17.9186 9 72.22 2005 percent passed 5G & HG 22 32.3699 19.7282 10.34 75.61 AS 2006 per cent passed 5G & HG 22 21.777 13.7761 7.41 66.67

122 Table 6. 15: Shapiro-Wilkinson Test of Normality

Interventions and years Statistic df SiQ P2002all 2002 per cent EF .924 11 .358 passed standard and higher grade CD .911 14 .168 AS .921 22 .079 P2003all 2003 per cent EF .895 11 .161 Passed standard and Higher grade CD .884 14 .067

AS .956 22 .412

P2004all 2005 per cent EF .937 11 .488 Passed standard and Higher grade CD .846 14 .019 AS .928 22 .110 P2005all 2005 per cent Passed EF .967 11 .860 standard and CD .781 14 .003 Hioher qrade AS .892 22 .021 P2006all 2006 per cent Passed EF .996 11 .843 standard and Higher grade CD .819 14 .009 AS .802 22 .001

6.4.2 Testing the Normality of Data Distribution

In order to investigate the trend of performance in mathematics for different interventions, hence the impact of interventions over a given period of time, inferential statistics was used. The main hypothesis testing techniques are parametric, for example, t and F tests, and they required the data distribution to be normally distributed (Keller, 2006:726). Hence data was tested for normality using the Shapiro-Wilkinson test of normality. The result is displayed in Table 6.15 above.

The assumption is that data distribution throughout the years for all three interventions are normal, which is a null hypothesis (Ho). The alternative

hypothesis (H1) is that at least one data distribution is not normal.

123 Table 6.15 presents the Shapiro Wilkinson test for normality for 15 data distributions, this was done using SPSS.

In 2002 the test statistics for EF, CD and AB were .924, .911 and .921 respectively. These were all at the significance levels .358, .163 and .079. The first two significance levels are above 0.1, that is, p» 0.1, indicating no evidence to reject the null hypothesis of normality. However, the significance level on AB data is below 0.1 p<0.1 which indicates an evidence, though very weak to infer an alternative hypothesis is true, thus the null hypothesis must be rejected. Therefore in 2002, data distribution was almost 311 normal.

In 2003 only the data from CD had significance level below 0.1, otherwise both EF and AB had data distribution with p>0.1 which means normal distribution for the data from EF and AB. However, non-normal distribution exists in CD data. In 2004 the same situation applies, that is, CD again has non-normal distribution. In 2005 and 2006, both AB and CD have non-normal data distributions.

In view of six distributions which are not normal, that is, null hypothesis (Ha), that data distribution is normal for the given period for all interventions throughout the period of observation is rejected. Hence, the alternative hypothesis that the data distribution is not normal is accepted.

Therefore, a non-parametric test had to be conducted to find out whether there was an impact over the years on the learner performance in mathematics.

124 6.4.3 Hypothesis Testing

One of the questions (section 1.3) the qualitative phase seeks to address is: What is the impact of interventions on learner performance? In translating this to hypothesis testing, the null and alternate hypotheses for EF is

H EFO: (f.12=f.13=f.14=f1S=f16) HEn: (f12*f.13*f14*f1S*f16)

For CD the null and alternate hypotheses are:

H CD 0: (f12=f13=f.14=f1S=f.l6) H CDI: (f12*J13*f14*f1S*f16)

Finally, for AS hypothesis testing will be according to the following:

H ABO: (f12=f13=f14=f1S=f.l6) H AB1: (J12*f13*f.14*f1S*f16)

The mean performances for EF, CD and AS for 2002, 2003, 2004 2005 and

2006 are given by f12,f1 3,f14,f1S&f16 respectively. The null hypothesis Ho means there was no difference in the mean performances of learners in mathematics over the observation period in all three interventions, hence they are equal.

However, the alternative hypothesis (H1) means there was a difference in mean performance of learners.

Friedman test for non-parametric hypothesis testing was used in which case , like other non-parametric tests, utilises the ranks of the means. SPSS was used for the computations. Table 6.16 presents the results of mean ranks for each intervention for the observation period. Subsequently, these were used in the Friedman tests for non-parametric hypothesis testing which uses the Chi-Square test statistics. Table 6.17 presents the Friedman tests.

125 Table 6.16: Mean Ranks performance for Interventions

Intervention Year Mean Rank EF p2002 all2002 percentage passed 5G & HG 3.14 p2003 all2003 percentage passed 5G & HG 2.82 p2004 all2004 percentage passed 5G & HG 2.68 p2005 all2005 percentage passed 5G & HG 3.64 p2006 all2006 percentage passed 5G & HG 2.73 CD p2002 all2002 percentage passed 5G & HG 3.14 p2003 all 2003 percentage passed 5G & HG 3.57 p2004 all2004 percentage passed 5G & HG 2.93 p2005 all2005 percentage passed 5G & HG 2.79 p2006 all 2006 percentage passed 5G & HG 2.57 AS p2002 all 2002 percentage passed 5G & HG 3.27 p2003 all 2003 percentage passed 5G & HG 3.36 p2004 all2004 percentage passed 5G & HG 3.14 p2005 all2005 percentage passed 5G & HG 3.05 p2006 all2006 percentage passed 5G & HG 2.18

The test statistics for EF is 2.795 and .593 significance level. This means there is no evidence (p>0.1) for an alternate hypothesis. Hence, the null hypothesis is accepted.

For CD, the test statistics for EF is 3.257 and .516 significance level. This is still above 0 .1, therefore the null hypothesis is accepted. This means there was no significance difference between the mean performances over the observation period.

Finally, the significance level of AS, 0.096 is much lower than what has been obtained thus far. However, this falls within the range 0.05

126 Table 6.17: Friedman Test Statistics

EF N 11 Chi-Square 2.795 df 4 Significance Level .593 CD N 14 Chi-Square 3.257 df 4

.516 Significance Level AS N 22 Chi-Square 7.891 df 4 Significance Level .096

6.4.4 The Impact of Interventions on Learner Performance

In view of the above hypothesis testing, there was no significant evidence that the three interventions EF, CD and AS had an impact on learner performance over the five year observation period.

6.5 CONCLUSIONS ON QUANTITATIVE DATA ANALYSIS

The quantitative impact in terms of a number of learners participating in mathematics was measured using enrolment of learners in Standard Grade and Higher Grade matric mathematics. Descriptive statistics revealed that a very large majority of learners, about 90% of all learners enrolled in mathematics, consistently participated in lower level mathematics. These situations occurred during the implementation of mathematics interventions including a well publicized and well funded intervention CD.

127 It was also revealed that the mean performance of this large majority of learners remained below 50% pass rate through out the interventions. It was also noted that the pass mark in the South African School System was 33.3% but, at least a 50% in HG for senior certificate was the requirement for tertiary mathematical studies.

In view of the above, there was no observable quantitative impact of AS and CD interventions on learner performance and participation in mathematics. Even though at face value, performance and participation in EF schools was slightly above those in AS and CD, statistically there is no significant difference in the impact of these interventions on the performance and participation of learners in mathematics.

6.6 IMPLICATIONS FOR THE QUALITATIVE PHASE

The interventions whose impact was being investigated were flagship interventions where much resources and input had been invested. Hence, there must be some impact which could not be detected by quantitative methods used. Qualitative inquiry was useful in exploring the undetected impact that uncovered reasons for its failure to translate to increased pass rates and the desired participation in mathematics.

6.7 SUMMARY

This chapter presented and analysed quantitative data on two variables of interest, namely, learner participation in mathematics and learner performance in mathematics. Analysis of the impact of mathematics interventions was done separately for each variable. Investigation on the first variable was constrained to descriptive statistical analysis as a result of very small numbers of higher grade learner enrolment. The final analysis entailed hypothesis testing on the impact of each intervention over the observation period. In both analyses the

128 conclusion was that there is no significant impact of mathematics interventions. The following chapter will illuminate these findings and explore the possibility of impact by mathematics interventions that were not detected by quantitative methods.

129 CHAPTER 7

7 PRESENTATION AND ANALYSIS OF QUALITATIVE DATA ON THE IMPACT OF MATHEMATICS INTERVENTIONS

7.1 INTRODUCTION

In this chapter, qualitative data and its analysis is presented within the context of quantitative findings in the previous chapter. This is in accordance with the model of the mixed method design of the study, espoused in chapter 5. This alluded that qualitative methods will be used to explain quantitative findings. Therefore, this chapter is a continuation of the previous chapter. It is also the final presentation and analysis of data analysis for the study.

7.2 SAMPLE AND DATA COLLECTION

Intensity sampling was used to select a sample of three high schools and this meant these schools had experienced a high intensity of mathematics interventions (section 5.6.2.2).

Effective interventions recognize teachers as the key implementers of change (Hofmeyer and Hall, 1996) and therefore, teachers in sample schools were targeted for qualitative interviews. In any case, learners whose results were analysed in the quantitative phase had graduated from high school.

The sample of three schools was reduced to two schools that had participated in AS, CD and EF as result of teacher attrition of some of those who participated in these interventions. Both schools were township schools which were under the

130 control of former Department of Education and Training. Hence, they were the product of Bantu Education Act of 1954. As has been indicated in chapter 5, focus group interviewing was used to collect data. In both schools, focus groups of three teachers were set up. However, in one school, the third teacher excused herself from the interviews as she had never participated in any of the interventions. A facilitator of CD was also interviewed. Interviews were conducted until data reached saturation. This took two days per school and three days for the facilitator.

According to Johnson (2001:104), eagerness to seek deep information can be misconstrued by the informant as the interviewer wanting to hear specific information which has nothing to do with the experiences of the former. In an effort to avoid this scenario informants were encouraged to discuss spontaneously about their experiences and perceptions of the interventions. Guiding the discussions were the last two research questions. However, these were modified to suit an open focus group by saying:

• I would like you to discuss your experiences and perceptions of mathematics interventions;

• I would like you to discuss the manifestation of learner -centred teaching or learning in mathematics interventions.

• The above-mentioned questions were also asked of the CD facilitator.

7.3 DATA ANALYSIS

Henning's (2004: 109) global analysis of qualitative data was employed. According to Henning (2004: 109) the global analysis of qualitative data looks at data in an integrated manner as opposed to fragmented codes. Hence, the very structure of data from interviews and accompanying notes is seen as the organising logic or themes for data. In other words, the priority in data analysis was placed on understanding the participants' voice not just finding themes. This

131 represents a shift from organizing transcripts into themes right away (Chase, 2008:73). Also, this is an attempt to avoid the conflict between researcher's interpretation and what participants said (Borland, 2004: 522).

In line with the research design of the study, emerging findings will be linked to qualitative findings. Finally, theorizing will entail linking holistic findings to relevant theory review of the study (Grbich, 2004:185).

7.4 EMERGING THEMES

Data was transcribed by the researcher. Most literature assert that transcription is best done by the researcher conducting the study as she or he has a better understanding of the data (Niewenhuis, 2007: 104). After a global analysis of the participants' voice, translation of these into themes was finally done. Without any intention to do so, these themes were confirmed by the interviews with the facilitator. Unlike teachers who participated in the intervention, the facilitator was an implementing agent. The emerging themes are discussed in the following section. In keeping with the confidential ethical issue (section 5.6.1.7), the names for interventions will not be revealed even in the quotations by teachers which originally mentioned these.

7.4.1 Interventions are for Schools that Perform Well

For teachers, the concept of 'the impact of mathematics interventions' is misplaced because participating in inte rvention EF was regarded as some form of reward for high performance in mathematics.

"Well, firstly when I knew that my school was one of the schools chosen to participate in the intervention, I was speaking to one of the educators and he explained to me that schools participating in

132 the intervention are doing well in terms of performance in mathematics."

"I heard that my school was chosen to be part of the intervention because of the best performance in maths and science and this made me proud that I teach in such a school."

However, there was a condition for participating in the intervention. "Another condition for participation was like they mustn't drop at their percentage rate for metric results. If the school has been selected, at about percentage of 80, it encourages the school that it must stay there or above that percentage. "

Another teacher reiterated the same criteria for schools, but expressed this as a weakness and offered a suggestion. "I don't know the criteria that they actually use for selecting the schools into this intervention. Because as it is right now, it looks like they were actually focusing on schools which are better performing compared to the other schools rather than focusing attention on low performers so as to upgrade them to the level of the other schools. So that's my main worry there. I would rather suggest that they include the schools which are low performing. "

Not only do teachers perceive mathematics interventions to be targeting schools with good results in mathematics, but they actually propose the inclusion of those schools that are in serious need for mathematics interventions! Targeting well performing schools does not auger well with the following aim of mathematics interventions by the 1995 White Paper of Education and Training: "An appropriate mathematics, science and technology education initiative is essential to stem the waste of talent, and make up the chronic national deficit, in these fields of learning, which are crucial to

133 human understanding and to economic advancement" (Department of Education and Training, 1995: 22). Well performing schools in mathematics are not likely to waste talent in mathematics! However, targeting well performing schools could be a special criteria to prepare students for subjects in short supply as indicated by the 1995 White Paper: "Special criteria will be needed to prepare students for subjects in short supply, particularly mathematics... " (Department of Education and Training, 1995:30).

Section 1.1.2 viewed interventions as responses to policies of change. Therefore, it is expected that interventions are implemented when mathematics achievement needs to change.

7.4.2 The Impact on Teachers' Mathematical Content Knowledge

Teachers regarded the impact of EF workshops to be the enhancement of their mathematical content knowledge.

"The impact is actually there because it looks like most of the educators in South Africa are not well acquainted with the mathematics topics in the NCS. Most mathematics topics which are in the new curriculum were never dealt with at college or university. So the intervention is actually boosting educators on such topics.

Another teacher reiterated: "Je, we have got these guys from Zimbabwe. They are the ones who are saying, we did all these mathematics topics in our curriculum in Zimbabwe. They are helping us a lot. Otherwise for most of us here, this is all new. For the first time we are seeing this, we have not been trained about them at university level. "

134 "Actuelty, these workshops are helping us a lot in the difficult topics in mathematics that we have to teach." In perceiving the impact of mathematics interventions to be enhancing their content knowledge, teachers seem to point out that the focus of interventions. Indeed the following theme affirms this.

7.4.3 The Focus of Interventions on Content Knowledge

In claiming that the impact made by interventions is to enhance content knowledge for teachers, in the previous theme, teachers implicitly indicated the focus of interventions. This was true for all three interventions.

This was supported by the CD facilitator: "First of all questionnaires were developed to find out which mathematics content/topics were viewed to be difficult by teachers. These are administered to teachers in target schools. The most problematic topics for teaches were calculus and trigonometry. Facilitators would then develop materials on these topics and conduct teacher workshops based on these. However, one always found teachers who were really good in some parts of the curriculum. This meant teachers ended up helping one another in handling difficult mathematics topics. But, yes interventions had a focus on content knowledge because this is what teachers want."

According to Weimer (2002:46), "strong allegiance to content blocks the road to more learners -centred teaching... the content barrier explicitly impedes faculty". In the South African context, while the content knOWledge is essential for teachers, the preoccupation of interventions with the enhancement of content knowledge ignores the Norms and Standards for teachers (Department of Education, 1997b:89), such as;

135 • Motivate learners to seek growth and achievement

• Facilitate individual growth

• Promote a positive learning atmosphere

• Adjust strategies to the developmental stages of learners

The last one is in sync with the espoused developmental stage of high school learners in chapter 2.

The Norms and Standards for teachers are also supported by literature on teacher education. For example, Moore (2009:1-28) regards setting the stage for successful learning as an effective strategy for teaching and this is in line with promoting a positive learning atmosphere. Hewitt (2008:66) argues that the teacher constructs the world for the learners in classroom through the employment of different teaching styles.

Therefore, focusing on the content and omitting the other essential requirements for successful learning provides some explanation of the lack of evidence of successful learning in mathematics, that is, high participation and achievement in higher grade mathematics in chapter 6.

7.4.4 Preparation for the New Curriculum

The inclination of mathematics interventions such as EF which ran workshops for teacher development in mathematics teaching seems to have been preparing teachers to implement the new mathematics curriculum of the National Curriculum Statements (NCS). However, preparing teachers to implement the new curriculum again, emphasized mathematical content.

136 "Maar, if I could talk about this issue of giving... workshops to make us comply with the NC5. We have been attending the workshop since last year and we are helping each other, maar especially with the new chapters. 50 somewhere, somehow it is a good project. It also develops educators as far as this new curriculum is concerned. "

The above implies preparing teachers to implement the new curriculum meant helping them with the content they are unfamiliar with. However, the new curriculum was not only about mathematical content. For example, Mwakapenda (2008:189) argues; "the new South African curriculum provides opportunities for educator and researchers to see mathematics in ways that present mathematics as a discipline that has connections: it has links within itself and other disciplines."

The researcher probed further to find out whether any more issues, apart from the new topics in the curriculum, were dealt with at these workshops.

"You see, the problem we have as teachers is content. 50 that is what interventions deal with, namely, subject matter and nothing else. Methodology is not discussed in our workshops because as teachers, that is not a problem at all. Some of us have been teaching for years now. We are quite comfortable with methodology. "

It seems as the teachers are 'comfortable with the methodology' since they have been teaching for many years. Such 'comfort with methodology' is at odds with the principle of life long learning which is advocated for education in the new dispensation (van Wyk and Mothata, 1999: 4).

137 The principle of life long learning implies that teachers "should have the desire and ability to continue to learn, to adapt and develop new knowledge, skills ... and to take responsibility for personal performance." (van Wyk and Mothata, 1999:4).

Over and above the ignored principle of life long learning, the comfort zone expressed by teachers contradicts what literature regards as elements of effective teachers such as growing (Warfield,2008:57), fostering change (Fontaine,2008: 108) development (Hammerness, Darling-Hammond, Bransford, Berliner, Cochran-Smith, McDonald and Zeichner,2005:358) .

7.4.5 The Impact on Resources

The support materials provided by EF intervention are of great help in supporting teachers' classroom activities.

"It gives us some materials, the relevant materials that we must focus on. Maybe the examinable topics, those modules that we are work-shopped on are the ones that can help us even in the classroom situation. "

The same teacher continues about the pressure that has been taken off as a result of support materials.

"We are not suffering, anymore we just look at the topic we are treating and you find what to do in the materials. And when we want to teach something you just go to the printers and make photocopies for learners. "

138 This indicates the relief from the burden of spending time preparing for lessons. Now the teacher just picks the topic to be taught and everything required for the lesson is there! However, this seems to indicate that this teacher is only concerned about her/his survival. According to (Fuller, 1969, Richardson & Placier, 2001 and Conway & Clark, 2003) a survival stage is the lowest developmental stage for a teacher. These researchers assert that the highest developmental stage is when the teacher is concerned about the student's results and mastery; "at this stage teachers assume responsibility for student learning" (Arends, 2009:31).

Another reiterated the advantages provided by the support materials, such as adding confidence and enjoyment in their teaching. "The materials themselves contain worksheets that we can give to learners. That helps you in a way such that you don't spend much time developing that worksheet. You can add more time for lesson plans; you can have more time for preparing tests, based on the worksheets. It really helps me to do the job in that way, so it brings about confidence. In fact I can tell you it helps you to enjoy what you're doing". Also, the materials provide stability in the midst of the ever changing textbooks.

"You see each and every year textbooks change. Now with this intervention we stick to one track of the topics we are supposed to teach. It gives you a clear direction on what you are working on. "

This teacher clearly has replaced textbooks which change every year! The reason is; 'worksheets are one dimensional'! However, research has shown that high performing learners in mathematics and science are reported to have access to a number of books at home (Beaton, Mullis, Martin, Gonzalez, Kelly and Smith, 1996:101). Hence, the availability and use of textbooks is very important.

139 Therefore, schools can fill in the gap by availing books for learners from disadvantaged backgrounds who may not have access to books at home (Oakes and Sanders, 2004: 1973). It is highly likely that a number of learner s who may not have access to books at home since section 2.4.2.1 noted that South Africa still has numerous families who live in poverty . This is one of the factors why some researchers assert that socio economic status impact on mathematics achievement in high schools, for example, Ozturk and Singh (2006:25-34).

It must also be noted that there is growing literature that is critical of worksheets and rather regard effective actions such as purposeful teaching or fundamental instruction as having the potential to have more impact on learning and achievement (Coney, 2005; Marzano, 2007 and Schmoker, 2006). This view alleges that worksheets can waste time of good teaching and sometimes are of low quality (Schmoker, 2009:524). Textbooks were not the only resources that came with the mathematics interventions.

"Not only do we get resources such as calculators, we also get textbooks for learners. Every year we are given a certain amount of money that is allocated to the school to be used particularly for resources for learners. So as a school you have to say how many books you want for grade 10. We even have got two additional teachers paid by this budqet".

Unlike, the previous teachers' perception of worksheets versus textbooks, calculators are part of technology which has been cited as having a positive impact on mathematics learning ( Bleich, Ledford, Orril and Polly, 2006:22, Frost and Wiest, 2007:31 and Polly, 2006:14-21). Also extra teachers are not contradictory to literature on teacher development.

140 7.4.6 Extra Mathematics Lessons for Bright Learners.

This theme was related to AB which provided extra mathematics lessons for grade 12 learners during weekends and school holidays. One respondent said:

"The intervention was making a difference. Underperforming schools were forced to send their bright learners to extra classes in the afternoons, Saturdays and holidays. Three subjects were dealt with at these classes, English, Physical Science and Mathematic".

It is not clear which role is played by this intervention, if already bright learners are targeted for the interventions. According to section 3.1.1 the role of mathematics interventions is to break the cycle of mediocrity. It may well be that these bright learners are under achievers!

In view of section 7.4.1 which indicated that interventions were perceived to be for high performing schools, targeting bright learners makes sense. One respondent reiterated the theme in section 7.4.1 "I was one of the teachers selected to teach mathematics in extra classes. Teachers were selected to teach in the intervention based on their good results in the subject they were teaching. But, the school they are from had to have good matric results".

Another said: "They used to say any school that has produced less than 70% we don't take a teacher from there to go and teach. They take teachers from schools that are excelling. Like in our case we have been getting more than 90%, 80% every year."

This respondent continued to site the reason why he was chosen to teach in this intervention:

141 " So that is why a teacher can qualify to teach in that programme. But the moment you go down less than 80% then they say you can't teach there. And then those learners' results really improved. Even the principal phoned, saying my learners were talking about me saying the teacher who came in the afternoons and on Saturdays helped us a lot. "

In this intervention the bright learners and the teachers from well performing schools put together. With this combination, high learner achievement in mathematics would be expected. However, chapter 6 did not show this!

7.4.7 Problematic Learners

For the best part of the interview, teachers eagerly lauded interventions with compliments of enhancing their mathematical content knowledge, helping with resources and helping bright students from poor performing schools. When the issue of impact on learner participation and performance in mathematics was raised, a different problem was introduced by teachers.

"The intervention is very good and is helping us with extra materials to use in the class, but the problem is with the learners. Learners have a negative attitude towards their work and this is demotivating to us. They also struggle about the language. Like, I can show you something. I was looking at the books yesterday and the learner has written invisible region and I've never talked about invisible region. I have talked about feasible region in finding the optimum solution in linear programming problems. They don't want to listen. "

142 If learners are not listening, it means they cannot cognitively engaged, thus active learning would be impossible (Conderman, Bresnahan and Pedersen, 2009: 106). The negative attitude of learners which in turn demotivate teachers may be explained by Hewit (2008:35)'s theory; "the hidden curriculum which contains information which can motivate or demotivate both learners and teachers",

According to this theory, it would seem that mathematics interventions have not been able to assist the teachers in implementing the mathematics curriculum that motivates both learners and teachers. Ar.other possible explanation for learners' lack of interest in listening to their teachers, is that interventions have not been able to assist teachers with the tools of inspiring learners and activate among learners the desire to learn (Kryza, Stephens and Duncan, 2007 and Sullo, 2007).

Proving this is the continued lamentations by teachers: "Learners also do not want to work. They do not do their homework; they do not want to participate in lessons in the classroom. You know, we have a serious problem with learners".

This seems to be classic case of lack of motivation from these mathematics learners! Literature on motivation has continued to correlate students' motivation with task engagement and achievement (Martin,2009:101-114 and Meyer, McClure, Walkey, Weir and McKenzie, 2009:273-293) and approaches in mathematics learning (Cano and Berben,2009:131-153). Hence, students' poor participation in mathematics lessons may be an indication of their lack of motivation!

The question was raised about these problems of learners' learning at the workshops: "Do you bring up these problems at the workshops"? The response was that:

143 "At the workshops there is no time to talk about problems we experience with learners in mathematics classrooms because the focus is on the mathematical content."

This is a serious flaw for mathematics interventions in view of the learner centred approaches of learning (section 2.3). If learners are giving teachers a challenge in classrooms, these have to be central to interventions' activities. For example research based strategies to ignite student teaching (Willis, 2006) could be utilised by interventions to assist teachers to motivate their learners. However, it seems the content is viewed to be the major problem in mathematics education. Therefore, all else is ignored.

Literature has also raised the parental role in motivating learners to learn mathematics, for example, Kim, Schallert and Kim (2010:418-437) and Gotfried, Marcoulides, Gotfried & Oliver (2009:729-739). But more importantly, teacher motivational strategies are known to enhance student self determination (Taylor and Ntoumas,2007:747) and teacher expectation bias are related to students' motivation (de Boer, Bosker, Roel and van der Werf,201 0:168).

Still on the issue of learners learning mathematics in classroom, another teacher commented: "What I've also noticed in terms of the learners is that these new NCS topics are difficult for them. What I am saying is, in the past there was higher grade then there was standard grade. So, but now it's all the same level. I think learners were not considered for that. This goes against learner centred approach in teaching if learners are not taken in consideration; because, only a few are coping, most are failing".

144 At face value, 'not considering learners' is a serious indictment on the curriculum developers who seem to have ignored the guiding principle of 'putting learners first" and acknowledge that they have different capacities of learning mathematics. However, this could also be viewed as the teachers' belief in students' fixed intelligence (section 2.6.1). As one teacher claimed:

"So I think the level of mathematics is the same but learners are not the same. I think they are going to have continuous problems, because the level is the same but we don't consider learners because we say learners are all the same. "

Accordingly the level of mathematics students learn must befit their intelligence. This is in contrast to malleable intelligence which is dependent on effort (Dweck, 2000:2). This also showed negative perception of their students' competence in mathematics. Chapter 2 discussed such views as havinq an impact on how students perform (Bouchey & Harter, 2005:673 and Klem & Connel, 2004). Either of the two explanations for the 'different levels of mathematical capacities for learners' does not auger well with achievement in mathematics.

7.4.8 Poor Participation of Teachers in Interventions

Raising a question of impact on achievement in mathematics by CD also brought another problem.

"I don't want to lie, I only attended a few workshops and then we got the certificates and then they gave us some grade 10, grade 11, grade 12 materials. This was on the old syllabus, not the new one. Workshops for mathematics teachers were based on the methodologies and the strategies to attack the difficult topics like trigonometry and calculus. "

145 Since motivation determines the time spent in different activities as well as account for goal orientation (Gage and Berliner, 1998:315), it seems like teachers lacked motivation to attend CD workshops! Teachers were also asked about what their reasons were for attending only a few workshops. They responded by saying:

"This intervention took place a long time ago, we have forgotten about it. But the main reason why we stop attending workshops is when we feel they are not useful for us. This is also true for all interventions."

Indeed teachers confirmed their lack of goal orientation, that is, the conviction that they by attending CD workshops they were "going somewhere"(Gage and Berliner, 1998:314) did not exist. Logically, whatever improvements that may have happened could not be linked to CD. "So I do not think there was any improvement in mathematics achievement for learners that I can say was because of this intervention. "

The CD Facilitator confirmed the poor attendance of CD workshops when he said that. "A large majority of teachers never attended the workshops on requler basis. For example, if you have forty six schools to look after, the likelihood was that the number would be reduced to twelve educators and eventually you will end up with only five educators attending workshops."

This theme seems to bring back Hewitt's (2008:35) theory, that is, the interventions' hidden curriculum may have been demotivating for teachers!

146 7.4.9 Improvement Caused by Teachers

The separation of interventions from the possible impact on mathematics learning and achievement was articulated by teachers when asked if there was an improvement in mathematics pass rate which could be attributed to the intervention. Three respondents on different articulated this:

"What I can say, it seems I can't say it's the interventions that produce good results, but also it's helping me. You see, where I've been teaching I've been producing good results and I was not in this intervention. When I came here I found poor mathematics results."

"Performance depends on individuals, teachers and their approach. Since I came here performance has improved, for 2006 and 2007. Maths was a problem, but since I came here the problem was solved in those years. "

"From my experience, most interventions prefer good teachers to participate in their workshops. It means you have already been producing good results and improving every year. I do not see being a good teacher to be a result of any intervention. You as a teacher have to work hard, that is all".

In view of the perceptions that interventions target well performing schools (section 7.4.1) and bright learners (section 7.4.6) as well as poor participation of teachers in interventions (section 7.4.8), it is only logical for teachers not to link interventions with an improvement in mathematics achievement.

147 7.4.10 Discrepancy between Claimed Success and Reality

CD was published as the panacea for the ills in mathematics learning and learner performance in the subject. Its evaluation claimed the accomplishments of the interventions' intentions for example Kanjee & Prinsloo (2005:2) contend the intervention had the following outcomes:

• Improved learner participation in class;

• Improved learner performance in mathematics.

However, the facilitator who monitored changes in classrooms for CD participants had a different opinion and experience.

"In visiting mathematics classrooms, we found that teachers do not bother to implement what had been done at workshops. The reason they gave was that facilitators had 'very little knowledge of their learners".

Contrary to Kanjee & Prins/oo's (2005) claim, this indicates that the pattern of classroom activities never changed as teachers were not convinced they should change these. The CD facilitator had experiences and perceptions which were at odds with the CD's claims of success. She had this to say:

"The intervention model was good, but it was too big and therefore its implementation was very poor. "

On exploring the reasons for not improving the poor implementation for CD, the facilitator gave the following reasons:

148 "You see the problem was the management of the implementing organization had made a lot of noise about the capability of the organization to solve mathematics problems in South Africa. So, as facilitators we spent more time and energy writing reports that would impress the sponsors. Attending the real problems we encountered in implementing the intervention was not an issue. Convincing sponsors that we were doing a good job became our focus. "

One aspect of poor implementation seems to illuminate the poor participation by teachers:

"The pressure placed on the interventions facilitators resulted in their high attrition rate. This in turn created lack of continuity among teachers as they had to meet several facilitators with different styles. There was no opportunity for teachers and facilitators to establish rapport which made teachers not to feel attached to the intervention. But, this made continuity in what was happening difficult as new people came in at each and every workshop".

The facilitator's perception about the impact of CD also contradicted the claimed accomplishments. "The impact was therefore minimal, however we reported glowingly about the implementation of the intervention, never citing the actual problems. We only discussed problems at our own staff development workshops, but never in publications. In fact, we exaggerated every thing we did. "

149 The above also illuminate the reason behind, the published non-existing accomplishments for CD by evaluators. CD deliberately misled everyone about the realities of the intervention. It makes sense for evaluators to use reports of the intervention as the point of departure for their evaluation.

7.4.11 Learner Centred Approach Limitations

The issue of learner centred approach was not raised to explain any of the findings in the qualitative findings. But it is viewed to be complementary to the study since chapter 2 discussed learning opportunities endowed by adolescence stage prevalent among high school learners. It is to this end that the researcher asked whether intervention activities were content or teacher or learner based.

• "Doh! Definitely learner centred." • "Ya... of course learner centred." • "Since the introduction of Outcomes Based Education, all workshops were learner centred. " • "Yes, I agree, learner centred workshop."

When it was probed what distinguished learner centred workshop translated, the following responses were given:

• "Workshops do everything to demonstrate to us learner centred approach of teaching, so that we can take this to our classrooms. This means we work in groups. " • "I think it means working as teams. "

According to teachers participating in interventions learner centred approach means working in groups or working as teams.

The facilitator had a broader view of learner centred approaches to teaching and learning. His comments were that: 150 "Yes we ran our workshops in a learner centred fashion with the hope that we were modelling this approach to teachers."

When asked what activities were modelled, the facilitator had this to say: "All activities were learner driven. In the case of workshops for teachers, it meant teacher driven. For example, whenever we tackled a mathematics topic, we made sure that we use the textbooks used by teachers in their classrooms. We also gave them a lot of time to discuss among themselves problematic mathematics concepts. As a result of this discussion, most of the problems were resolved by teachers. This happened because teachers shared different strategies of teaching problematic topics. The only problem that could not be resolved was when disciplinary problems were brought in. But, I must say group work does not necessarily mean learner centred."

In response to this, the researcher asked if teachers were told this and this was the response: "Unfortunately no!. We just hoped that teachers were going to implicitly understand learner centred teaching from what we do at workshops as facilitators."

Learner centred learning and teaching was the rhetoric of the interventions. However, teachers have experienced group work to be synonymous with learner centred learning and teaching. In the same breath, high school teachers were aware that their learners were more challenging. The facilitator, who has a broader understanding of learner centred approaches. acknowledged that learner centred has been limited to group work.

151 7.4.12 Learners' Lack of Ability for Higher Grade Mathematics

The finding from quantitative studies prompted the researcher to find the explanation from the teachers' perspective about why did the majority of learners enrol mathematics on a standard grade level and not on the higher grade. "Like we have said, learners are very lazy and don't want to work. Another thing is most students are not capable. The cannot cope with higher grade mathematics. They even struggle with standard grade mathematics, how much more with higher grade?"

"In fact, this NCS did not consider the students. Now, in NCS there is no standard grade. Everyone has to do the same mathematics. And, eey! This is going to be a big problem with these learners. Ya! They were not thinking about the students when they introduced this new curriculum."

"I also agree with him because not all learners can understand mathematics. "

In view of this consensus on the lack of mathematical ability on the part of the students, the researcher asked if the problem of mathematical ability of learners was brought to forward at the workshops. The following response was given:

"Look, workshops are for serious business like getting to understand the topics that are difficult for teachers. Nothing can change the ability of our students. Some can do mathematics, but others find it very difficult. That is the way things are really!!"

Clearly, teachers believe in the entity theory or fixed intelligence (section 2.6.1). Their learners either have it in them to succeed in higher grade mathematics or they do not. 152 Therefore, the findings in the quantitative phase, that is, an overwhelming majority of about 90% of learners enrolling in standard grade, indicate that these learners are not capable of higher grade mathematics!

Apparently, mathematics interventions or workshops do not have the time to deal with such issues as the content knowledge seems to be more important.

7.5 EXPLAINING THE QUANTITATIVE RESULTS

This section uses the qualitative findings presented in the preceding sections of this chapter to explain quantitative findings in chapter 6. This is in accordance with the study's research design model (section 5.6).

Quantitative data measured the impact of mathematics interventions in terms of learner participation and performance in mathematics. In general, the quantitative findings revealed very little impact across the three interventions (See Tables 6.13 and 6.14).

All the themes that emerged from qualitative interviews will now be used to reveal implicit reasons and factors for the minimal impact interventions.

7.5.1 Perceived Aims and other Aims of Interventions

Interviews with participants revealed that their experiences with mathematics interventions were relatively positive. However, they did not perceive mathematics interventions as the catalyst for learner participation and performance in mathematics. All participants regarded well performing schools in mathematics as targets for interventions as one respondent remarks:

153 "It looks like they were actually focusing on schools which are better performing compared to the other schools rather than focusing attention on low performers so as to upgrade them to the level of the other schools. "

So much so that a recommendation by one participant was made:

"I would rather suggest that they include the schools which have low performance. "

The expected aim of interventions by the participants was to maintain good performance in mathematics and hence interventions were viewed as rewards for well performing schools.

Discussion of South African mathematics interventions in chapter 4, revealed a silence on the explicit learner performance and participation as the goal for the majority of interventions. The discrepancy between the aims of the interventions and its perceived implemented aims was in line with this silence.

For example, common goals for interventions discussed in chapter 4 are: The need for an application based mathematics curriculum;

• Provision of in-service training for teachers;

• Addressing the problem of wasted potential;

• Selecting the best students for extra support.

154 The lack of explicitness on improving poor performance and participation in mathematics was at odds with the explicit national concern about participation and periormance in mathematics. For example, "The number of passes in higher grade mathematics has seen little improvement over the years. The number of higher grade mathematics passes is not enough to satisfy the needs of science, engineering and technology and the financial professions. Few achieve higher grade A, B or C in mathematics, C being the minimum accepted by most universities" (Lawless, 2005:79).

Explicit citation of increased periormance and participation is however, applicable in EF intervention. To a less extent, Mathematics Centre for Primary schools also indicated improvement in mathematical achievement of learners as one of its goals.

Without a clear articulation of what the intervention seeks to achieve, not much can be achieved. If there is no agreed destination at the start of a journey, then the journey is aimless and lacks focus. Any destination reached is good. In this case, teachers only perceive the impact of the intervention in terms of resources and enhancement of their mathematical content knowledge.

7.5.2 Content Based Versus Learner Based Programmes

Literature review in chapter 2 discussed the internationally low participation and periormance in mathematics by adolescent learners. This placed the adolescent at the centre of this challenge. In other words, factors that inhibit and enhance mathematics learning for these learners should be viewed as pivotal in turning the low periormance and participation around.

Also, South Africa has embraced Outcomes Based Education whose centre is the learner. Confirming this is the OBE paradigm; 'What and whether students

155 learn is more than when, how and where they learn (Spady, 1994:8). Hence, teachers are advised to choose teaching and learning methods to suit learners and their learning styles.

However, qualitative interviews revealed an absolute focus of interventions on mathematical content. The CD facilitator confirmed the content based intervention:

"First of all, a questionnaire is developed to find out which mathematics content/topics were viewed to be difficult by teachers. The most problematic topics were calculus and trigonometry. We then developed materials on those topics and ran workshops on them. "

The teacher participants supported this by applauding the intervention for boosting educators on the new mathematical topics in the curriculum. The assumption by these interventions seemed to be, all that mathematics teachers needed to be effective, was a strong repertoire of mathematical content knowledge. While teachers cannot teach what they do not know, they need more than content knowledge.

Research in mathematics education has an array of issues that effective mathematics teachers have to deal with; a few of these are cited as follows: • Creating the culture that enhances mathematics learning (Goos, Galbraith & Renshaw, 2004:91); • Communicating in a manner that invites and welcomes all as mathematics learners in the classrooms (Zevenbergen, 2004: 119); • Mathematics teachers learning to act as midwives in their classrooms (Sinclair, 2008:33); • Building relationships with students (Gutstein, 2008:189).

156 • More importantly, applied knowledge of the cognitive, social and psychological capabilities endowed by the developmental stage of high school learners espoused in chapter 2, is essential.

In view of the disregard of issues related to the mathematics learner, it makes sense to have very little impact related to the learner achievement in mathematics.

7.5.3 Interventions Target Bright Students

Interviews revealed that two of the interventions that dealt directly with learners, did so in a highly selective manner. Only a few bright students were selected to participate in extra classes conducted on weekends. Also, literature review in chapter 4 indicated that interventions that deal directly with learners only select the best performing learners (sections 4.6.1 and 4.6.5).

By their design, such interventions only aim to impact on the few learners. Analysis of results in chapter 6 was for the entire classes in schools that participated in interventions.

7.6 EXPLANATION FOR SPECIFIC INTERVENTIONS

The above section gave a general explanation on the overall findings of little impact of all interventions. This section will tease out some explanation related to specific interventions.

7.6.1 Impact for Intervention AB

AB had the least impact on both learner enrolment and achievement in higher grade and standard grade mathematics. Minimal impact made sense in view of the select few learners that participated in AB.

157 Also, learners in these extra classes were taught by teachers from other schools. This makes it hard for teachers to control regular attendance of learners which in turn limits the scope of the intervention. According to teachers who participated in AB, results for learners who attended extra classes improved. But, improvement was in accordance with the framework of AB which had a focus on an overall pass in matric. Mathematics was just one of the subjects offered in AB.

The goal for AB was to improve general pass rates in matric, not necessarily mathematics performance. Hence, the positive impact of AB was regarded as a general improvement on the pass rate, regardless of the possible accompanying failure in mathematics. Accordingly, AB had a positive impact on a different variable from the one considered in quantitative phase.

7.6.2 Impact for Intervention CD

CD intervened through teacher development workshops and classroom support. Hence, this intervention not only had the potential of impacting learning and teaching in mathematics, but it had a mechanism of sustaining its impact. However, impact had to be made first. Its economic achievement overtook the goal to intervene for the better in mathematics learning. Pretence for the latter to have been achieved was thus made. Hence, both quantitative and qualitative findings are synergistic on the little impact of CD. Qualitative methods also revealed that very limited intervention was actually implemented, against the backdrop of a lot of misleading publication about its achievements. This was to justify the millions of rands CD got from big cooperatives.

158 7.6.3 Impact for Intervention EF

Compared to AB and CD, EF had more impact. It had 13.5% as mean of enrolment in higher grade mathematics throughout the five year period. In fact, it was only in 2002, where HG enrolment had a mean below 10%. Otherwise throughout 2003-2006 its mean enrolment was above 10%.

The percentage performance in both standard grade and higher grade mathematics was higher than the other interventions. Even though, it was not as high as the mean enrolment percentage over the five year period. See Table 6.20.

Qualitative methods revealed that EF did have an impact, though this was in different variables. Unlike, CD, literature on EF acknowledges that the intervention had not accomplished its desired impact that is, increasing participation and performance in mathematics. EF had explicit documented intended goals which are in sync with dependent variables in the quantitative phase. However, these did not seem to have been communicated to the intervention's participants.

7.7 IMPACT DETECTED BY QUALITATIVE METHODS

One of the values of mixed methods studies is the complimentary effect on the findings of the study. In the quantitative phase two independent variables were investigated; the participation and performance of learners in mathematics. Based on these variables, there is very little impact made by mathematics interventions. However, qualitative research revealed that interventions had made quite an impact on the mathematical content knowledge of teachers. It also had made an impact on the resources such as calculators, extra textbooks for mathematics. Finally, EF also improved human resources by employing and paying extra teachers. 159 7.8 CHALLENGES FACING INTERVENTIONS

The qualitative research revealed problems encountered by interventions that seem to explain their little impact. Low and irregular participation of teachers in the planned workshops meant the intervention was very limited in its implementation. However, implementing agents for interventions do not publish any limitations. Challenges were swept under the carpet, and exaggerated reports on what had been accomplished were published. Meanwhile, the implementing agents knew about the impediments that were compromising the impact of interventions (see section 7.4.10).

7.9 SUMMARY

This chapter has presented qualitative results and their analysis in terms of emerging themes, which were then used to illuminate and explain quantitative findings in the previous chapter. In doing so, it has provided factors and possible reasons for the little impact of mathematics interventions on learner participation and performance in mathematics. This has put in place a framework for the conclusion and recommendations for the whole study. This is dealt with in the next chapter.

160 CHAPTER 8

8 SUMMARY, DISCUSSIONS, CONCLUSION AND RECOMMENDATIONS

8.1 INTRODUCTION

This chapter is a culmination and conclusion of the study whose purpose was to investigate the impact of mathematics interventions in high schools. The first section of the chapter will recap the study by summarising the essence of the background of the study (chapter 1), literature review (chapters 2, 3 and 4) and the research design of the study (chapter 5). This will be followed by a discussion of the findings (chapters 6 & 7) as they relate to the aims and objectives of the study. Then, applications of the findings and consequent recommendations will be discussed. Final remarks will form part of the conclusion of the study.

8.2 SUMMARY OF THE STUDY

The summary of the study is divided into three subsections; the rationale of the study, literature reviews as well as the research design and data collection.

8.2.1 Rationale for the Study

The background (section 1.1) identified mathematics interventions as catalysts for policy implementation (section1.1.1). Consequently, governmental and non governmental mathematics interventions have been implemented in schools for more than a decade (section 1.1.2).

Despite these, the cycle of mediocrity in mathematics participation and performance in high schools has persisted. (1.1.3). this has resulted into calls for

161 new mathematics interventions (section 1.1.3.4). However, there is no shred of research on why·more than a decade of interventions did not deliver the expected outcomes.

8.2.2 Summary on Literature Review

In view of the learner being the centre of the research problem and questions, literature reviewed included adolescent learners in mathematics (chapter 2). The core literature reviewed was on mathematics interventions globally (chapter 3) and nationally (chapter 4).

8.2.2.1 Summary on Adolescent Learners in Mathematics

Research reviewed at the beginning of chapter 2 indicates decrease in participation of learners in mathematics as they enter high schools. However, literature on adolescence revealed that high school learners have an advantage in mathematics learning as a result of traits associated with their developmental stage, adolescence. These include cognitive growth (section2.3) which is crucial, as mathematics learning is mainly a cognitive activity (Ellis, 2007:3 and Rasmussen & Marrongelle, 2006:5).

Another adolescents' trait is identity formation (section 2.5) which could be exploited in mathematics learning as identity formation (2.5.3). Finally, the study of coping strategies by adolescents in 22 countries (section 2.4.2.1) placed the South African adolescents between those from Hong Kong and Czech Republic.

According to 1995 Third International Mathematics and Science Study (TIMSS) Hong Kong and Czech republic are among the top six high achieving countries in mathematics (http://4brevard.com/choice/international).This seems to suggest that South African's adolescents may have the untapped potential in learning mathematics.

162 8.2.2.2 Summary on Mathematics Interventions

Mathematics interventions were viewed to be efforts to correct and break the vicious cycle of mediocrity in mathematics learning (Adey and Shayer ,1994: 2 and Stoll, 1995: 12) and to improve in general mathematics education system (Adey & Shayer, 1994:2). Literature showed that mathematics interventions should not take longer than two years to demonstrate positive impact (section 3.1.2). Review was classified into international and national perspectives.

8.2.2.3 International Perspective

International literature in chapter 3, revealed three categories of interventions, namely cognitive, comprehensive school reform and mathematics curriculum based interventions (sections 3.2, 3.3 and 3.4 respectively). Common to all these are their purpose to enhance learner achievement in mathematics. Cognitive and comprehensive school reforms do not only improve mathematics achievement, but more importantly these reforms ensure that the improvement is sustained. This is because these interventions take into consideration underlying enablers for achievement in mathematics (sections 3.4.1, 3.4.2 and 3.5.1).

The mathematics curriculum interventions are based on the implementation of the new standards/mathematics curriculum in North America. Four interventions selected for review were Connected Mathematics Project (CMP), Mathematics in Context (CiP), Core Plus Mathematics Project (CPMP) and Systemic Initiative for Montana Mathematics and Science project (SIMMS) (sections 3.4.1, 3.4.2, 3.4.3 &3.4.4). All four interventions aim to increase learner achievement in mathematics. Research on the effectiveness of these interventions was conducted and published (sections 3.4.1.2, 3.4.2.2, 3.6.3.3, 3.4.3.3, 3.4.3.4 & 3.4.4.2).

163 8.2.2.4 National Perspective

Mathematics interventions were geared towards correcting the legacy of excluding the majority of blacks from pursuing mathematical related careers (see section 4.3). Their classifications are in accordance with areas they attempt to improve for example, school curriculum and related materials, teacher development, teacher preparation and learner enrolment in mathematics and science related programs at tertiary level (section 4.5).

Implementation of mathematics interventions spans across the 1980s (section 4.3), through the 21st century (section 4.5). However, there is a deficit of research on their effectiveness. Literature on mathematics interventions is dominated by the input made on the interventions. Their desired output is only used as a rationale for initiating interventions. (sections 4.5.1-4.5.5). As interventions progress, their output becomes foreign. The desired output or the impact of interventions only emerges when new interventions are desired and justified (Bernstein,2005:230-231). However, the Dinaledi intervention was an exception in that it continue to build on its experience.

8.2.3 Influence of Literature Review on the Study

Literature on adolescent learners indicated that learner centred practices that incorporate attributes for these learners may enhance learning in mathematics. Qualitative methods probed whether this type of learner centred was practiced by mathematics interventions.

Review of literature on mathematics interventions confirmed learner achievement in mathematics to be the key dependent variable for mathematics interventions. Participation was not as prominent as achievement. But, both these were dependent variables (chapter 6).

164 What was also revealed by international literature was the central role of specific innovative mathematics curricula in the interventions. Nationally, no special mathematics curriculum was designed for interventions. Hence, curriculum was excluded as an area of investigation.

8.2.4 Summary of Research Design and Data Collection

To address the research questions and the objectives for the study, a sequential mixed method research design was chosen. The purpose of the latter is; "to use the qualitative findings to help clarify the quantitative results" (Ivankova, Creswell, & Plano Clark, 2007: 264). Hence this explanatory mixed method study started with a quantitative phase and was followed by a qualitative phase. The following table illustrates how research questions and objectives were addressed by each phase.

Table 8.1 Research questions and objectives intwo research phases Phase Research Question Objective What is the impact of mathematics interventions onlearner performance inmathematics? What is the impact of mathematics interventions 1. Investigate th~ impact of Quantitative on learner participation in mathematics? mathematics interventions in high schools What is the trend of impact of mathematics interventions over a five-year-period? What are the experiences and perceptions of 2. Explore and explain the impact of Qualitative mathematics interventions byteachers? mathematics interventions from i teachers' point ofview. I ! What learner centred practices are promoted by 3. Investigate the perceived learner I I interventions? centred practices byteachers. I What is the general overview of mathematics 4. Identify the strengths and interventions? weaknesses of mathematics interventions.

165 Nested samples from two phases were selected (section 7.2), that is the qualitative sample was a subset of the sample schools and interventions in the quantitative phase (Onwuebuzie &Collins, 2007: 292). Quantitative phase had two types of samples, three non-randomly selected mathematics interventions (section 6.2.1) and 37 randomly selected high schools from 220 that participated in at least one of the sample interventions (section 6.2.2). Three mathematics interventions were given pseudo names, AS, CD and EF (5.6.17).

Quantitative data was collected from government's database of grade 12 mathematics results through the five year period (2002-2006) in Gauteng from a random sample of schools which had participated in sample interventions (section 6.3). Qualitative data was collected from five mathematics teachers who experienced mathematics interventions from two sample schools (section 7.2).

8.3 KEY FINDINGS RELATED TO THE OBJECTIVES OF THE STUDY

8.3.1 Findings Related to Objective 1: Investigation of the Impact

In relation to the first objective to investigate the impact of mathematics interventions, the following were the key findings:

• Quantitative methods found no impact of mathematics interventions on both learner participation and performance in mathematics;

• Qualitative methods found mathematics interventions to have an impact on resources and the enhancement of mathematical content knowledge for teachers.

The following section briefly discusses these findings.

166 8.3.1.1 Lack of Impact through Quantitative Methods

Table 8.2: National learner enrolment in HG mathematics (Source: Education statistics in South Africaat a glance,2003,2005 &2007) Year Number of learners %learner enrolment 2002 35465 15.7 2003 35956 16.2 2004 39939 16.9 2005 44053 17 2006 46945 17.3 2007 46125 15.3

Quantitative findings indicated no consistent pattern for either increase or decrease in learner participation in mathematics throughout the period of three sample interventions (figures 6.1, 6.2 & 6.3). Throughout the five-year-period (2002-2006) the mathematics HG enrolment percentage (Table 6.13) for learners in

• AS remained below 10%; • CD averaged 10.1%; • EF averaged 13.5%. Corresponding national averages are shown in the following table.

A similar trend was found regarding the learner performance in mathematics (figures 6.4, 6.5 & figure 6.6). Throughout the five-year-period, learner performance in HG mathematics for three interventions (Table 6.20) was as follows:

• AS's average % was 41.0, the range was 38-43.9; • CD's average % was 51.6 and the range was 42.5-58.1; • EF's average % was 54.6 and the range was 39.5-68.8.

167 Similarly, the corresponding national averages are shown in the table below.

Table 8.3: National learner performance in HG mathematics (Source: Education statistics in South Africaat a glance,2003,2005 & 2007) Year Number oflearners who passed % oflearners who passed 2002 25515 71.9 2003 28693 79.8 2004 30086 75.3 2005 32112 72.9 2006 33112 70.5 2007 32783 71.1

The learner enrolment and periormance in interventions is below the national average as shown above. Hence, quantitative methods showed no impact on learner participation and periormance in mathematics as a result of these interventions.

8.3.1.2 The Impact through Qualitative Methods

Despite the above quantitative findings, qualitative methods which do not prescribe any variable, found that teachers that participated in interventions perceived interventions as having some impact (section 7.5.2, 7.5.4 and 7.5.5). The impact in qualitative phase is in terms of variables not considered in the quantitative phase.

Mathematics interventions have improved the content knowledge of mathematics teachers (see sections 7.5.2 & 7.5.3). They have assisted teachers to come to grips with new content knowledge in the new curriculum, namely, National Curriculum Statements. Finally, interventions have provided additional resources essential for mathematics learning, such as teacher support materials and extra teachers, where required (see sections 7.5.5).

168 8.3.2 An explanation of Findings Related to Objective 2

Qualitative phase provided possible reasons for the quantitative findings, namely, the aim of mathematics interventions and the limited implementation of the interventions.

8.3.2.1 The Aim and the Role of Mathematics Interventions

Section 7.6 explained the quantitative findings as being the outcome of the discrepancy between the perceived aims of the interventions by participants and the theoretical aims for interventions (section 7.6.1). Also, literature on national mathematics interventions reveals that these do not explicitly cite their aim to be learner achievement (sections 4.7.1,4.7.2,4.8.1 & 4.8.2). Only a few do (sections 4.7.4 & 4.8.3). In view of their target participants, some interventions seem to have an aim to help achievers to achieve more or maintain their achievement.

This is illustrated by interventions that target well performing schools (section 7.5.1) and bright learners (sections 7.5.6 & 7.6.3). This choice of participants was also revealed in literature review of South African interventions, for example, PROTEC and Star schools (sections 4.7.1 & 4.7.5).

8.3.2.2 Focus on Increasing the Matric Pass Rate

Intervention AS includes mathematics as a subject of interest, but interviews with teacher participants revealed that the achievement for the project is measured by the increased pass rate for learner participants (sections 7.7.1). This is confirmed by the regular cited goal and achievement for the increase in pass rates in grade 12, resulting from interventions (Gauteng Department of Education Annual reports 2002/2003, 2003/2004 and 2007/2008).

169 8.3.2.3 Limited Implementation of Some Mathematics Interventions

Interviews revealed that at least one intervention had very limited implementation as a result of poor participation of teachers and high attrition of facilitators (sections 7.5.8 & 7.9). Consequently, the outcomes should also be limited.

8.3.3 Finding Related to Objective 3: Learner Centred Practices

Teachers perceived learner centred practices by mathematics interventions to be limited to group work (section 7.5.6). This indicates a limited view of the meaning of learner centred learning. The perception that poor performance in mathematics is caused solely by problematic learners (see section 7.5.7) indicates a deficit of knowledge about learners on the part of teachers, as literature review highlighted potential and not problems for high school learners (section 2.3).

8.3.4 Findings related to objective 4: Strengths and Weaknesses

8.3.4.1 Strengths for the Interventions

8.3.4.1.1 Improving Mathematical Content Knowledge for Teachers

The reported positive impact of mathematics interventions on content knowledge for mathematics teachers (section 8.3.1.2) was found to be the strength of the interventions. Much as this was not measured in any way except reported by the teachers, it was seen as the achievement of one of the aims for the National Strategy for Mathematics and Science. Since, competence in content knowledge for mathematics teachers is one of the expected outcomes for the Strategy (Department of Education, 2001 and 2004).

170 More importantly, one of the seven roles for educators promulgated by the Norms and Standards for Educators (2000:14) is the requirement for a teacher to be a specialist in particular subject or learning area. Being a specialist in a subject entail, among other things being "well grounded in the knowledge relevant to the subject ..." (Norms and Standards for Educators, section 3). Finally, research also reveals that teacher quality is a function of adequate knowledge about the subject matter (Kaplan and OWings, 2003:687).

8.3.4.1.2 Improving Resources for Mathematics Teaching

The impact on resources (section 7.4.5) was found to be a strength for the interventions as this is one of the pillars of interventions. For example, "increase the human resource capacity and learning support materials to deliver mathematics education" (Department of Education, 2001 and 2004). Also research has shown that in almost all countries that participated in 1995 TIMSS, one of the factors that distinguished highest from lowest achieving schools in mathematics was; "students in the high achieving schools had higher levels of study aids... " (Martin, Mullis, Gregory, Hoyle and Shen, 2000:10). Therefore, improving resources for students in mathematics seems to be the right road to achievement in the subject.

8.3.4.2 Weaknesses of the Interventions

The following are viewed as the weaknesses for mathematics interventions.

8.3.4.2.1 Lack of Clarity on the Aimed Objectives for Interventions

Redressing the deficit in mathematics achievement for the majority of the South African youth is part of the post apartheid policy in education (Department of Education and Training, 1995:17,22 & 30).

171 Hence, the main objective for mathematics interventions must be to increase learner participation and achievement in mathematics (section 1.1.1), particularly for the African child disadvantaged by the Bantu Education Act of 1954.

Learner participation and achievement are quantifiable variables. These should have been easily detected through quantitative methods in chapter 6. However, qualitative findings indicate a prevalent lack of clarity on the objectives for mathematics interventions (section 7.4.1 and 7.4.4). This is viewed as a basic weakness for mathematics interventions as this leads to fuzzy meaning on their effectiveness to all stakeholders. Learner achievement in mathematics is attributed to teachers (section 7.4.9) because mathematics interventions are not viewed as aiming to achieve the same goal.

8.3.4.2.2 Selecting Bright Learners: Pros and Cons

Selecting bright learners for extra classes (section 7.5.6) is both a strength and a weakness for interventions. It is a strength because this practice fits in with gifted education research which regards bright learners as the resource for the country (Clark,2007; Esquivel and Oades-Sese,2007:125 and Van Tassel Baska & Brown, 2007:342-358 ).

Targeting only bright learners is a weakness since it seems these interventions have no alternate interventions for average and weak learners. Yet, bright learners are only a minority of their group (Bailey, 2007: 127; Child, 2004:253 and Worrel, 2007:122). The selection of bright learners confirms the cry from the teachers of problematic learners (section 7.4.7) and learners' lack of ability for higher grade mathematics (section 7.12). This may be the outcome of the interventions' high inclination towards the minority brilliant which leaves the majority neglected.

172 8.4 APPLICATIONS FOR FINDINGS

Key findings have implications for application of effective mathematics interventions. In the South African context, the latter being those with an aim of correcting the legacy of Bantu Education by increasing learner achievement in mathematics (section 4.3). Applications for findings are discussed in the following section.

8.4.1 Achievement Based Mathematics Interventions

The findings on the impact of mathematics interventions in high schools (section 8.3.1) have implications for the focus and practices of mathematics interventions, if these are to be effective.

The study viewed learner achievement or performance in mathematics as the key independent variable for mathematics interventions. This was encapsulated in the policy (section 1.1.1) and articulated by all global educational and mathematics interventions (sections 3.4, 3.5 &3.6). Also the role of mathematics interventions also points towards the enhancement of achievement by breaking the erosion of mathematics education (section 8.1.2.2).

Albeit, mathematics interventions impacting on other variables (section 8.3.1.2), lack of impact on learner achievement in mathematics implies practices of mathematics interventions need adjustment of their focus. Practices ensued from mathematics interventions that do not emanate from learner achievement, cannot replace their primary aim and role. In a nut shell, mathematics interventions should be based on learner achievement in mathematics through and through.

173 8.4.2 Independent Research of Interventions' Impact

In promoting achievement based mathematics interventions, independent research on the interventions should confirm or dispute the reported gains by implementing agents of interventions. For example, What Works Clearinghouse (2006:1) disputed the gains claimed by the implementers of Connected Mathematics Project (section 3.6.1.2).

In a similar manner this study has findings contrary to Kanjee and Prinsloo (2005:2) who claimed gains in mathematics learner achievement (section 7.5.10).

8.4.3 Broadening Learner Centred Practices in High Schools

Learner centred teaching and learning has become a cliche in the current system of education for example, in mathematics education (section 7.5.11) reveals learner centred learning to be synonymous to simple group learning or teaching. Such a narrow view on learner centred practices held by mathematics teachers as a result of mathematics interventions has one implication.

There is an untapped perspective of learner centred teaching in high schools which entails infusing all the positive characteristics of the high school learner in defining learner centred teaching in high schools and the adolescent learner (chapter 2) . Section 2.4 argued that adolescence is the golden age for learning, hence exploring adolescent centred teaching may just be what is needed to enhance mathematics participation and achievement (section 2.8).

More importantly, this would be in line with the recommendation by the Ministry of Education. "Educational and management processes must therefore put the learner first, recognizing and building on their knowledge and experience, and responding to their needs" (Department of Education and Training, 1995).

174 8.4.4 Extending Group Work to Cooperative Peer Learning

While the previous section discusses the potential for viewing learner centred learning differently from group work lens, group work can be extended to a higher level of cooperative learning. Section 4.2.3 discussed the recommendations made during the zo" century for group work strategies as suitable for African students.

In view of the group work being an integral part of the Outcomes Based education, teachers work in teams (section 7.4.11 ).However, the essence of group work is cooperative learning (Arends, 2009) whose outcomes include academic achievement (Joyce, Calhoun and Hopkins, 2009: 74). More importantly, for adolescents peers playa very important role in their development (Peterson,2004), therefore there is a potential of extending group work to cooperative learning in peer groups can be utilised to optimise their learning.Therefore group work can be extended beyond the narrow view of learning to work together as teams (SAQA, 1997) to cooperative learning.

8.4.5 Building on the Strengths and Rectifying Weaknesses

The study revealed the strengths and weaknesses for mathematics interventions (section 8.3.3.1 & 8.3.3.2). Both these are important for mathematics interventions, especially for the forthcoming interventions (section 1.1.3.4). Weaknesses and strengths are indications of what works and what is not working. Therefore, in planning for the new generation of mathematics interventions, strategies to eliminate or avoid what does not work should be thought through and adopted. Strengths of mathematics interventions should be used as foundation for these new interventions.

175 8.5 RECOMMENDATIONS FOR FURTHER RESEARCH

8.5.1 Closing the Gap between Research and Interventions

There is a gap between research on mathematics education and research on interventions and their impact. Chapter 4 on South African mathematics interventions revealed this gap. The application for findings (sections 8.4.1 & 2) suggest more research needs to be undertaken, which is related to effective mathematics interventions.

The research problem also suggested the scarcity of this research (section1.2) and this is different from evaluation of intervention (Rossi, Lipsey & Freeman, 2004). It is research that eventually leads to what works rather than what worked in this particular intervention. Therefore, a recommendation is made for research geared on mathematics interventions which has a focus on what works. A distinction must be made between evaluation research of specific educational interventions (section 4 .7) which are commissioned by sponsors and research on mathematics interventions as catalysts of policy implementation (section 1.1.1).

8.5.2 Extension of the Study

In view of the geographical limitation and observation periods of this study, an extension of the study along two dimensions is recommended.

8.5.2.1 Extension to other Provinces

Mathematics interventions are a national priority as vehicles for transformation in mathematics education. But the findings for this study are only relevant to one province. Hence, a recommendation for the extension of this study to other provinces is made, so as to confirm or dispute the findings of this study.

176 8.5.2.2 Surveys on the Emerging Variables on the Impact of Interventions

Qualitative methods found that low levels of participation of teachers in mathematics interventions' activities (section 7.4.8) and high attrition of implementing agents which could influence the impact of mathematics interventions (section 7.4.10). Levels of participation and stability of service providers seem to be two emerging variables that have the potential of impacting negatively on the interventions. Hence, a recommendation is made to conduct surveys and experiments to explore and test the impact of these variables on mathematics interventions.

8.5.3 Grounding Research on Mathematics Interventions on Dewey's Pragmatism

In view of the dynamic nature of mathematics interventions, Dewey's pragmatism is viewed to be more suitable to similar studies recommended above. According to Siesta & Surbules (2003: 11) Dewey's pragmatism on educational research means: "... what is constructed over and over again is the dynamic balance or organism and environment, which manifests itself both in specific changes in the environment and specific changes in the patterns of action of the organism."

Hence, Dewey's pragmatism is recommended as a philosophical foundation for further studies on interventions. In other words, mixed methods studies are recommended as means to provide holistic solution to the persistent problem of lack of impact.

177 8.5.4 Longitudinal Studies

In the background, it was mentioned that deficit in mathematics achievement blocks access to professional careers related to mathematics, such as engineering. It is therefore recommended that further studies that will include access to and success to professional careers, as other dependent variables of mathematics interventions, be undertaken.

8.5.5 Exploring the Role of Implementing Agents of Interventions

Studies that incorporate the role of implementing agents as highlighted by the findings (sections 8.3.2.3) are recommended.

8.6 FINAL REMARKS

The country has experienced more than two decades of mathematics interventions in high schools (sections1.3.2, 4.4 and 4.5). More are being implemented and many more are in the pipeline (Bernstein, 2005:11). However, the past and present interventions have one common denominator, namely, they lack evidence of their effectiveness (sections 4.4 & 4.5) and this was confirmed by the findings of the study (sections 8.3.1 & 8.3.2). Without such evidence, interventions are like fashions that are in and out at the whim of fashion designers (Slavin & Fashola, 1998:2).

In her zealous proposal for a new mathematics intervention, Bernstein (2007: 11) is silent about what works in South African mathematics classroom. Her articulation of the deficit in learner achievement in mathematics is typical to what Guiterrez (2008:357) claims to have been the focus of research in mathematics education. However, Guiterrez (2008) proposes a new focus for research, that is, investigation of interventions for gains and excellence.

178 How many more mathematics interventions will be implemented without any consideration of the impact hey are making? Ironically, the process of stringing along an array of perpetual, non-effective mathematics interventions is tantamount to sustaining the legacy of the past we all begrudge (Jansen, 2008) and apartheid mathematics education (Khuzwayo, 2005: 307).

It is the view of this study that South Africa can still shift towards effective mathematics interventions that can transform the chronic deficit in mathematics learning , if mathematics interventions are based on achievement backed by research as opposed to input and report based.

During this study the mathematics curriculum changed. In 2008, grade 12 learners wrote end of the year mathematics examination with no designation to standard or higher grade as a result of the implementation of the National Curriculum Statements, a streamlined version of OBE.

However, the researcher asserts that the findings from this study are still relevant because mathematics will always remain mathematics regardless of the name change of its curriculum. Hence, achievement and participation in mathematics also remain the same.

8.7 CONCLUSION

In concluding the study, the question whether the research problem has been resolved was answered succinctly. The essence of the research problem was the scarcity of research knowledqe concerned about the effectiveness of mathematics interventions. This was against the backdrop of the role of mathematics interventions as vehicles for policy implementation and improvement of mathematics education in high schools.

179 Through the findings of this study, factors that may be limiting the effectiveness of mathematics interventions were uncovered and these were interwoven into a base knowledge that can influence practices and research related to mathematics interventions. The researcher is under no illusion that the knowledge produced in this study provides an ultimate solution to the revolving door type mathematics interventions in the country, but it is a start. Building on this study, can further illuminate on what works in mathematics interventions and hence ameliorate the deficit in mathematics participation and achievement for the youth in high schools.

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224 .A-pp~ ~d( "j. ·ft

GAUTENG DEPARTMENT OF EDUCATION

RESEARCH REQUEST FORM

REQUEST TO CONDUCT RESEARCH IN INSTITUTIONS AND/OR OFFICES OF THE GAUTENG DEPARTMENT OF EDUCATION

1. PARTICULARS OF THE RESEARCHER 1.1 Details of the Researcher Surname and Initials: Mkhize D.R. First Name/s: Duduzile Rosemary Title (Prof/Dr/ Mr/ Mrs / Ms): Ms Student Number (if relevant): 920319425 ID Number 5808080752089

Private Contact Details 1.2 Home Address Postal Address (if different) 506 Zianetta 506 Zianetta 344 Kent Avenue 344 Kent Avenue Ferndale Ferndale

Postal Code: 2194 Postal Code: 2194 I Tel: ( 011) 5190200 I Cell: 0846200292 I Fax: ( 011 ) 5190201 E-mail:[email protected] ,! I

- 1 ------==_..=._- 2. PURPOSE & DETAILS OF THE PROPOSED RESEARCH

2.1 IPurpose of the Research (Place cross where appropriate) Undergraduate Study - Self Postgraduate Study - Self X Private Company/Agency - Commissioned by Provincial Government or Department Private Research by Independent Researcher Non-Governmental Organisation NauonalDeparlmentofEducation Commissions and Committees Independent Research Agencies Statutory Research Agencies Higher Education Institutions

2.2 IFull title of Thesis I Dissertation I Research Project The Impact Of Mathematics Interventions On Learning

and Achievement in High Schools Mathematics: A Mixed Method Study

2.3 IValue of the Research to Education (Attach Research Proposal) The study will contribute on the theory of mathematics interventions as it relates to participation and performance in mathematics of high school learners.

The study will set up the benchmark for transformation in mathematics education in the country, thereby creating the tool against which mathematics interventions could be evaluated.

2.5 IStudent and Postgraduate Enrolment Particulars (if applicable) l i Name ofinstitution where enrolled: University of Johannesburg I I Degree / Qualification: OEd I ! Education/ Curriculum Studies I Faculty and Discipline / Area ofStudy: i i I I Name ofSupervisor/ Promoter: Dr 8. Nduna I

- 2 - 2.6 Employer (w here applicable) Jones & Wagener Consulting Civil Name ofOrganisation: Encineers Position in Organisation: Manager Head ofOrganisation: Board of Directors 59 Bevan Road Street Address: Rivonia Postal Code: 2128 Telephone Number (Code + Ext): (011) 5190200 Fax Number: (011) 519 0201 E-mail:

12.7 IPERSAL Number (where applicable) I

I I I II I

3. PROPOSED RES EARCH METHOD/S

(Please indicate by placing a cross in the appropriate block whether the following modes would be adopted)

3.1 Questionnaifie/s (If Yes, supply copies of each to be used)

YES I I NO I X I

3.2 Interview/s (If Yes, provide copies of each schedule)

YES I X [ NO I I 3.3 Use ofofficiaI documents

YES NO I X

If Yes, please specify the document/s: I i I !

- - 3 - 3.4 Wt:u:ksh&pls-I Group Discussions (If Yes, Supply details) YES I X I NO I Filed work will employ focus group interviews

3.5 Standardised Tests (e.g. Psychometric Tests)

YES I I NO I X If Yes, please specify the testis to be used and provide a copy/ies

4. INSTITUTIONS TO BE INVOLVED IN THE RESEARCH

4.1 Type of Institutions (Please indicate by placing a cross alongside all types ofinstitutions to be researched)

Mark with X INSTITUTIONS here Primary Schools

Secondary Schools X

ABET Centres

ECD Sites

LSEN Schools

Further Education & Training Institutions

Other

4.2 Number of institution/s involved in the study (Kindly place a sum and the total in the spaces provided)

-4- Type of Institution Total

Primary Schools

Secondary Schools 4

ABET Centres

ECD Sites

LSEN Schools

Further Education & Training Institutions

Other

GRAND TOTAL 4

4.3 Name/s ofinstitutions to be researched (Please complete on a separate sheet ifspace is found to be insufficient)

Name/s of Institution/s

Altmont Technical High School

Edenpark High School

Minerva Senior Secondary School

Residensia High School

- 5 - 4.4 Districtls where the study is to be conducted. (Please indicate byplacing a cross alongside the relevant district/s)

District

Johannesburg East

Johannesburg South X

Johannesburg West

Johannesburg North X

Gauteng North

Gauteng West

Tshwane North

Tshwane South

Ekhuruleni South X

Ekhuruleni West

Sedibeng East X

Sedibeng West

If Head Office/s (Please indicate Directorate/s)

NOTE:

If you have not as yet identified your sample/s, a list of the names and addresses of all the institutions and districts under the jurisdiction of the GDE is available from the department at a small fee.

4.5 Number of learners to be involved per school (Please indicate the number by gender)

Grade 1 2 3 4 5 6 I

Gender B G B G B G B G B G 8 G 1 i Number I I

- 6 - Grade 7 8 9 10 11 12 Gender B G 8 G B G 8 GBG B G Number 6 6 6 6

4.6 Number ofeducators/officials involved in the study (Please ndicate the number in the relevant column) Office Type of Deputy Educators HODs Principal Lecturers Based staff Principals Officials

Number 12

4.7 Are the participants to be involved in groups or individually?

Participation

Groups X

Individually

4.8 Average period of time each participant will be involved in the test or other research activities (Please indicate time in minutes)

Participantls Activity Time Learners & Group Interviews 60 educators Learners & Individual educators Interviews

4.9 T.ime ofday that you propose to conduct your research.

After School School Hours During Break Hours I X

4.10 School termls during which the research would be undertaken

First Term Second Term Third Term

- 7 - E ------==..= DECLARATION BY THE RESEARCHER 1. I declare that all statements made by myself in this application are tru« and accurate. 2. I have taken note of all the conditions associated with the granting of approval to conduct research and undertake toebide by them.

Signature: ~0vv(:;~ C!yrc'A~ Date: (() rllt ~t:) <9tf"

- 8 - wn u: DECLARATION BY SUPERVISOR I PROMOTER I LECTURER

I declare that: - 1. The applicant is enrolled at the institution / employed by the organisation to which the undersign~di§ attached. 2. The questionnaires / structured interviews /-test» meet tire cliteria of: • Educational Accountability • Proper Research Design • Sensitivity towards Participants • Correct Content and Terminology • Acceptable Grammar • Absence ofNon-essential/Superfluous items Surname: N])L1I'fA-

First Name/s: g~v\ cf! Vv0'v\M\-( '2/ Institution I Organisation: LArf\J 0(Cft1{/) 0 ( ~ tflq-,Jr/c ~u£ c-

Faculty I Department (where relevant): £j)ucfr77~

Telephone: 0(( .- t;~ 0; 3:J-S7 Fax: O{(-r;~1 J-OU/K

E-mail: hhe(l-\V'llA e U,f-CtC- 2q

r-l---iLt--\7J\ " Signature: ~- \ I, _-1If-Y---

. ~\ Date: /U f'I1,1P-c (1 d-c)ug-

N.B. This form (and all other relevant documentation where available) may be completed and forwarded electronically Nomvula Ubisi ([email protected]). The last 2 pages of this document must however contain the original signatures of both the researcher and his/her supervisor or promoter. These pages may therefore be faxed or hand delivered. Please mark fax - For Attention: NomvuJa 011 355 0512 (fax) or hand deliver (in closed envelope) to Nomvula Ubisi (Room 525), 111 Commissioner Street, Johannesburg.

- 9 ------_.==-~-- UMnyango WezeMfundo Lefapha la Thuto Department of Education Departement van Onderwys

Date: 11 March 2008 Name of Researcher: Mkhize Duduzile Rosemary Address of Researcher: 506 Zianetta 344 Kent Avenue Ferndale Telephone Number: 0115190200/0846200292 Fax Number: 0115190201 The impact of mathematics interventions on learning and Research Topic: achievement in high schools mathematics: A mixed method study Number and type of schools: 4 Secondary Schools Johannesburg South & North, Districtls/HO Ekurhuleni South and Sedibeng East

Re: Approval in Respect of Request to Conduct Research

This letter serves to indicate that approval is hereby granted to the above-mentioned researcher to proceed with research in respect of the study indicated above. The onus rests with the researcher to negotiate appropriate and relevant time schedules with the schoolls and/or offices involved to conduct the research. A separate copy of this letter must be presented to both the School (both Principal and SGB) and the District/Head Office Senior Manager confirming that permission has been granted for the research to be conducted.

Permission has been granted to proceed with the above study subject to the conditions listed below being met, and may be withdrawn should any of these conditions be flouted:

1. The District/Head Office Senior Managerls concerned must be presented with a copy of this letter that would indicate that the said researcher/s has/have been granted permission from the Gauteng Department of Education to conduct the research study. 2. The District/Head Office Senior Managerls must be approached separately, and in Writing, for permission to involve District/Head Office Officials in the project. 3. A copy of this letter must be forwarded to the school principal and the chairperson of the School Governing Body (SGB) that would indicate that the researcher/s have been granted permission from the Gauteng Department of Education to conduct the research study.

______~=""1L.!X1

Director: Knowledge Management and Research Room 525, 111 Commissioner Street, Johannesburg, 2001 P.O. Box 7710, Johannesburg, 2000 Tel: (011) 355-0488 Fax: (all) 355-0286 4. A letter / document that outlines the purpose of the research and the anticipated outcomes of such research must be made available to the principals, SGBs and District/Head Office Senior Managers of the schools and districts/offices concerned, respectively. 5. The Researcher will make every effort obtain the goodwill and co-operation of all the GDE officials, principals, and chairpersons of the SGBs, teachers and learners involved. Persons who offer their co-operation will not receive additional remuneration from the Department while those that opt not to participate will not be penalised in any way. 6. Research may only be conducted after school hours so that the normal school programme is not interrupted. The Principal (if at a school) and/or Director (if at a district/head office) must be consulted about an appropriate time when the researcher/s may carry out their research at the sites that they manage. 7. Research may only commence from the second week ofFebruary and must be concluded before the beginning of the last quarter of the academic year. 8. Items 6 and 7 wifl not apply to any research effort being undertaken on behalf of the GDE. Such research will have been commissioned and be paid for by the Gauteng Department ofEducation. 9. It is the researcher's responsibility to obtain written parental consent of all learners that are expected to participate in the study. 10. The researcher is responsible for supplying and utilising his/her own research resources, such as stationery, photocopies, transport, faxes and telephones and should not depend on the goodwifl of the institutions and/or the offices visited for supplying such resources. 11. The names of the GDE officials, schools, principals, parents, teachers and learners that participate in the study may not appear in the research report without the written consent of each ofthese individuals and/or organisations. 12. On completion of the study the researcher must supply the Director: Knowledge Management & Research with one Hard Cover bound and one Ring bound copy of the final, approved research report. The researcher would also provide the said manager with an electronic copy ofthe research abstract/summary and/or annotation. 13. The researcher may be expected to provide short presentations on the purpose, findings and recommendations of his/her research to both GDE officials and the schools concerned. 14. Should the researcher have been involved with research at a school and/or a district/head office level, the Director concerned must also be supplied with a brief summary of the purpose, findings and recommendations of the research study.

The Gauteng Department of Education wishes you well in this important undertaking and looks forward to examining the findings of your research study.

Kin~egarqs

r0?'l vvaspe I crJlEF INFORMATION OFFICER

i The contents of this letter has been read and understood by the researcher. z. Signature ofResearcher:

Date: /1 /Y(c.r'c-h ~OOJ? APPENDIX C

Enrolment and Performance in Mathematics SG & HG during 2002·2006 for three interventions

Total Number of Interventions: 3

Total number of high schools: 47

Total number of learners: 24 509

EF INTERVENTION FOR 10 057 LEARNERS IN 11 HIGH SCHOOLS

2002 Passed 2002 Wrote 2003 Passed 2003 Wrote 2004 Passed 2004 Wrote 2005 Passed 2005 Wrote 2006 Passed 2006 Wrote Schools 5G HG 5G HG SG HG 5G HG 5G HG 5G HG 5G HG 5G HG SG HG 5G HG 1 42 4 50 5 38 3 54 4 29 3 46 7 29 4 38 7 21 8 34 19 2 34 0 101 0 54 15 119 18 69 11 116 12 64 9 137 12 62 8 127 11 3 16 3 101 5 26 3 49 4 23 6 89 8 25 8 86 9 13 5 44 8 4 17 0 24 (1 4 3 18 10 11 0 23 6 10 2 28 4 8 0 18 1 5 41 2 100 4 23 2 62 24 48 3 99 8 45 4 89 7 28 0 86 3 6 50 8 77 9 24 5 70 11 43 6 115 20 37 9 132 31 11 10 124 50 7 17 0 55 0 23 0 83 0 15 2 111 11 20 5 92 5 12 5 89 16 8 11 0 47 2 14 2 48 5 6 5 32 17 31 5 61 10 15 3 51 14 9 87 20 165 28 33 23 143 28 121 15 304 38 152 33 254 38 112 22 223 27 10 18 2 50 2 21 2 87 9 16 0 61 5 29 4 73 6 19 3 76 10 11 9 1 31 4 13 2 35 2 39 5 62 7 58 3 97 3 40 5 63 5 Totals 342 40 801 59 323 60 768 115 420 56 1058 139 500 86 1087 132 341 69 935 164

1 CD INTERVENTION FOR 7 495 LEARNERS IN 14 HIGH SCHOOLS

2002 Passed 2002 Wrote 2003 Passed 2003 Wrote 2004 Passed 2004 Wrote 2005 Passed 2005 Wrote 2006 Passed 2006 Wrote Schools SG HG SG HG SG HG SG HG SG HG SG HG SG HG SG HG SG HG SG HG 12 15 1 22 1 6 2 31 9 8 9 41 25 13 11 67 21 25 4 85 14 13 9 2 24 8 18 2 46 2 7 a 44 3 14 1 83 7 33 2 77 2 14 32 8 34 10 61 12 73 14 47 8 48 11 41 8 41 13 58 8 59 8 15 13 a 21 a 25 4 63 6 22 3 122 5 18 a 105 5 19 129 a 16 19 a 55 0 10 0 24 0 3 25 a 5 49 0 6 77 a 17 8 0 92 2 17 a 89 1 5 a 91 7 9 1 49 1 7 88 a 18 16 a 71 0 6 a 34 0 6 1 43 1 10 1 54 1 7 50 a 19 9 1 31 4 13 2 35 2 39 5 63 7 58 3 97 3 40 5 65 5 20 8 0 112 10 7 0 64 4 5 70 0 19 2 74 9 8 3 99 19 21 12 1 36 1 15 3 21 5 16 83 a 14 2 42 5 15 4 24 5 22 16 1 27 2 29 1 35 1 22 4 26 9 7 a 26 19 25 6 49 7 23 12 3 52 5 25 2 77 4 37 3 100 4 13 1 69 5 12 2 86 3 24 16 1 130 51 39 6 105 48 25 5 226 36 13 4 165 42 14 2 186 12 25 19 1 81 6 53 1 134 1 38 1 82 1 36 4 90 4 18 3 128 10 Totals 204 19 788 100 324 35 831 97 280 39 1064 109 270 38 1011 135 287 39 1202 85

2 AS INTERVENTION FOR 6 957 LEARNERS IN 22 HIGH SCHOOLS

2002 Passed 2002 Wrote 2003 Passed 2003 Wrote 2004 Passed 2004 Wrote 2005 Passed 2005 Wrote 2006 Passed 2006 Wrote Schools SG HG SG HG SG HG SG HG SG HG SG HG SG HG SG HG SG HG SG HG 26 13 0 24 0 3 0 19 1 13 0 32 2 6 1 25 2 3 1 12 2 27 9 0 27 0 6 0 10 0 5 0 17 0 19 0 41 0 4 0 31 0 28 17 0 28 0 16 3 81 12 21 3 74 3 35 2 118 2 29 0 136 6 29 16 1 20 1 13 0 31 0 23 3 38 3 40 4 59 4 40 6 62 7 30 10 0 60 1 11 0 62 1 18 2 89 2 33 1 94 6 16 6 93 6 31 18 0 55 0 18 4 40 5 25 0 52 1 29 2 39 2 40 1 83 2 32 4 0 57 0 6 1 52 1 19 0 49 0 11 0 36 0 13 0 61 0 33 3 0 35 1 15 1 42 1 18 1 52 1 12 0 87 1 9 0 61 0 34 29 0 76 0 32 4 116 11 24 0 129 2 22 5 123 11 16 5 104 14 35 21 0 73 2 23 0 64 1 21 1 97 5 16 4 132 13 26 1 79 8 36 31 0 79 3 40 0 100 2 10 6 80 17 31 2 188 7 22 1 213 5 37 20 4 92 5 31 1 59 1 36 0 67 0 51 6 106 9 38 2 122 2 38 11 0 58 0 6 1 83 19 16 1 114 1 17 0 129 1 27 0 98 0 39 14 0 74 4 11 2 64 3 21 2 76 2 24 0 163 0 20 1 147 2 40 0 0 54 11 9 0 32 1 6 1 23 2 3 0 28 1 5 0 34 0 41 18 0 63 0 9 99 0 9 0 91 9 12 0 97 0 9 2 54 8 42 15 0 70 0 23 0 68 1 12 0 126 3 23 0 150 2 17 1 241 2 43 11 0 33 0 11 0 28 0 8 0 36 0 21 37 0 5 1 39 10 44 14 0 21 0 26 2 35 2 13 1 18 4 22 4 66 0 10 1 53 11 45 20 2 24 2 27 0 41 0 23 3 29 7 24 36 4 8 1 37 6 46 27 0 78 0 11 0 34 0 13 1 35 1 15 0 47 0 5 0 39 0 47 22 0 82 0 18 0 90 0 15 2 86 9 34 1 110 2 8 1 114 3 Totals 343 7 1183 30 365 19 1250 62 369 27 1410 74 500 32 1911 67 370 31 1913 94

3 APPENDIX D

MEAN RANKS FOR SG & HG % PASS OF THREE INTERVENTIONS Intervention Mean Rank EF p2002all 2002 percent passed SG & HG 3.14

p2003all 2003 percent passed SG & HG 2.82

p2004all 2004 percent passed SG & HG 2.68

p2005all 2005 percent passed SG & HG 3.64

p2006all 2006 percent passed SG & HG 2.73

CD p2002all 2002 percent passed SG & HG 3.14

p2003all 2003 percent passed SG & HG 3.57

p2004all 2004 percent passed SG & HG 2.93

p2005all 2005 percent passed SG & HG 2.79

p2006all 2006 percent passed SG & HG 2.57

AS p2002all 2002 percent passed SG & HG 327

p2003all 2003 percent passed SG & HG 336

p2004all 2004 percent passed SG & HG 3.14

p2005all 2005 percent passed SG & HG 3.05

p2006all 2006 percent passed 5G & HG 2.18 APPENDIX E

Mean Ranks for SG percent pass of three interventions Intervention Mean Rank EF p2002sg 2002 percent passed SG 3.18

p2003sg 2003 percent passed SG 2.73 p2004sg 2004 percent passed SG 2.91

p2005sg 2005 percent passed SG 3.64 p2006sg 2006 percent passed SG 2.55

CD p2002sg 2002 percent passed SG 3.14

p2003sg 2003 percent passed SG 3.57

p2004sg 2004 percent passed SG 2.89

p2005sg 2005 percent passed SG 2.89

p2006sg 2006 percent passed SG 2.50

AS p2002sg 2002 percent passed SG 3.27

p2003sg 2003 percent passed SG 3.18

p2004sg 2004 percent passed SG 3.27

p2005sg 2005 percent passed SG 3.09

p2006sg 2006 percent passed SG 2.18 APPENDIX F

GRADE 12 MATHEMATICS RESULTS FOR ALL HIGH SCHOOLS IN GAUTENG

Subject Total Total Pass Centre Name description entered wrote subject CULTURA HIGH SCHOOL MATHEMATICS HG 19 19 8 GEKOMBINEERDE SKOOL CULLINAN MATHEMATICS HG 18 18 14 HOERSKOOLERASMUS MATHEMATICS HG 16 16 8 CHIPA-TABANE SEC SCHOOL MATHEMATICS HG 2 2 1 DAN KUTUMELA SEC SCHOOL MATHEMATICS HG 17 17 3 MPHUMELOMMUHLE SEC SCHOOL MATHEMATICS HG 2 2 1 EDENDALE PEPPS COLLEGE MATHEMATICS HG 3 3 1 STAR OF HOPE SCHOOL MATHEMATICS HG 7 7 1 ABBOTT'S COLLEGE SILVERLAKES MATHEMATICS HG 8 8 8 AHMED TIMOL SEC MATHEMATICS HG 8 8 3 HOER TEGNIESE SKOOL N DIEDERICHS MATHEMATICS HG 9 9 7 HOERSKOOL BASTION MATHEMATICS HG 19 19 14 HOERSKOOL BEKKER MATHEMATICS HG 9 9 7 HOERSKOOL JAN DE KLERK MATHEMATICS HG 4 3 3 HOERSKOOLMONUMENT MATHEMATICS HG 59 59 56 HOERSKOOL NOORDHEUWEL MATHEMATICS HG 56 56 55 KRUGERSDORP HIGH SCHOOL MATHEMATICS HG 47 47 47 TOWNVlEW HIGH SCHOOL MATHEMATICS HG 1 1 1 MADIBA SCHOOL MATHEMATICS HG 3 3 2 KAGISO SEC SCHOOL MATHEMATICS HG 3 3 2 MATLA COMBINED SCHOOL MATHEMATICS HG 8 7 2 MOSUPATSELA SEC SCHOOL MATHEMATICS HG 39 39 13 SG MAFAESA SEC SCHOOL MATHEMATICS HG 7 7 5 THUTO LEFA SEC SCHOOL MATHEMATICS HG 4 4 1 MANDISA SHICEI<'A SEC SCHOOL MATHEMATICS HG 15 15 10 AZAADVILLE MUSLIM SCHOOL MATHEMATICS HG 10 10 10 CARLETON JONES HIGH SCHOOL MATHEMATICS HG 23 23 18 HOERSKOOL CARLETONVILLE MATHEMATICS HG 9 9 9 J

1 HOERSKOOL JAN VILJOEN MATHEMATICS HG 13 13 13 HOERSKOOL RIEBEECKRAND MATHEMATICS HG 34 34 33 HOERSKOOL WESTONARIA MATHEMATICS HG 16 16 6 HOERSKOOL WONDERFONTEIN MATHEMATICS HG 16 16 8 RANDFONTEIN HIGH SCHOOL MATHEMATICS HG 25 24 11 AB PHOKOMPE SEC SCHOOL MATHEMATICS HG 6 6 1 BADIRILE SEC SCHOOL MATHEMATICS HG 4 4 4 KGOTHALANG SEC SCHOOL MATHEMATICS HG 7 6 6 THUTO LEHAKWE SEC SCHOOL MATHEMATICS HG 7 7 1 PHAHAMA SEC SCHOOL MATHEMATICS HG 11 11 8 TSWASONGU SEC SCHOOL MATHEMATICS HG 26 26 11 TM lETLHAKE SEC SCHOOL MATHEMATICS HG 8 8 7 RELEBOGILE SEC SCHOOL MATHEMATICS HG 12 12 4 ITHUTENG SEC SCHOOL MATHEMATICS HG 2 2 1 CLAPHAM HIGH SCHOOL MATHEMATICS HG 21 21 21 GEREFORMEERDE SKOOL DIRK POSTMA MATHEMATICS HG 9 9 9 HOER TEGNIESE SKOOl JOHN VORSTER MATHEMATICS HG 43 43 43 HOERSKOOL OOS-MOOT MATHEMATICS HG 50 50 48 HOERSKOOL STAATSPRESIDENT CR SWART MATHEMATICS HG 14 13 9 HILLVIEW HIGH SCHOOL MATHEMATICS HG 15 14 13 HOER TEGNIESE SKOOL PRETORIA-TUINE MATHEMATICS HG 10 10 5 HOERSKOOLELANDSPOORT MATHEMATICS HG 11 11 2 HOERSKOOL HENDRIK VERWOERD MATHEMATICS HG 20 19 15 HOERSKOOLHERCULES MATHEMATICS HG 3 3 3 HOERSKOOLLANGENHOVEN MATHEMATICS HG 16 16 7 HOERSKOOl PRETORIA-WES MATHEMATICS HG 3 0 ° HOERSKOOL TUINE MATHEMATICS HG 19 19 18 HOERSKOOLWONDERBOOM MATHEMATICS HG 38 38 37 IONA CONVENT MATHEMATICS HG 7 7 7 PRINCESS PARK SEC SCHOOL & COLLEGE MATHEMATICS HG 9 9 1 SA COLLEGE SCHOOL MATHEMATICS HG 4 4 21 TARGET HIGH SCHOOL MATHEMATICS HG 5 5 °1 LOTUS GARDENS SEC SCHOOL MATHEMATICS HG 8 8 61 I CONFIDENCE COLLEGE MATHEMATICS HG 10 10 6! I I C-PROGRESSIVE SCHOOL MATHEMATICS HG 3 3 ~

2 HOERSKOOL AKASIA MATHEMATICS HG 30 30 28 HOERSKOOL GERRIT MARITZ MATHEMATICS HG 33 33 33 HOERSKOOLMONTANA MATHEMATICS HG 39 39 33 HOERSKOOL OVERKRUIN MATHEMATICS HG 62 62 62 HOERSKOOL PRETORIA-NOORD MATHEMATICS HG 20 19 16 AMOGELANG SEC SCHOOL MATHEMATICS HG 3 3 3 BOTSE-BOTSE SEC MATHEMATICS HG 3 3 3 CENTRAL SEC SCHOOL MATHEMATICS HG 2 2 1 FILADELFIA MATHEMATICS HG 4 4 1 HLANGANANI SEC SCHOOL MATHEMATICS HG 3 3 2 HLOMPHANANG SEC SCHOOL MATHEMATICS HG 7 7 6 KGADIME MATSEPE SEC MATHEMATICS HG 13 13 3 KGOMOTSO SEC SCHOOL MATHEMATICS HG 13 13 11 LETHABONG SEC SCHOOL MATHEMATICS HG 3 3 3 MAKHOSINI COMBINED SEC SCHOOL MATHEMATICS HG 4 4 2 MEMEZELO SEC SCHOOL MATHEMATICS HG 1 1 0 REITUMETSE SEC SCHOOL MATHEMATICS HG 27 27 22 SENTHIBELE SENIOR SEC MATHEMATICS HG 6 6 0 SOSHANGUVE SEC SCHOOL MATHEMATICS HG 13 13 6 SOSHANGUVE TECHNICAL CENTRE MATHEMATICS HG 3 3 3 WALLMANSTHAL SEC MATHEMATICS HG 3 3 0 ELIZABETH MATSEMELA SEC SCHOOL MATHEMATICS HG 7 7 7 CHARLTON VOS COLLEGE OF EDUCATION MATHEMATICS HG 5 5 3 HOERSKOOL DIE WILGERS MATHEMATICS HG 52 52 46 HOERSKOOL ELDORAIGNE MATHEMATICS HG 123 123 121 HOERSKOOL GARSFONTEIN MATHEMATICS HG 137 137 117 HOERSKOOLMENLOPARK MATHEMATICS HG 110 110 106 PRO ARTE ALPHEN PARK MATHEMATICS HG 44 43 26 HOERSKOOL UITSIG MATHEMATICS HG 26 26 21 HOERSKOOL CENTURION MATHEMATICS HG 74 74 72 HOERSKOOLVOORTREKKERHOOGTE MATHEMATICS HG 16 15 12 HOERSKOOLWATERKLOOF MATHEMATICS HG 202 202 196 HOERSKOOLZWARTKOP MATHEMATICS HG 79 79 73 L¥TIELTON MANOR HIGH SCHOOL MATHEMATICS HG 49 48 28 SUTHERLAND HIGH SCHOOL MATHEMATICS HG 80 80 77(

3 THE GLEN HIGH SCHOOL MATHEMATICS HG 39 39 34 WILLOWRIDGE HIGH SCHOOL MATHEMATICS HG 69 69 63 THE WAY CHRISTIAN SCHOOL MATHEMATICS HG 2 2 2 EERSTERUST SEC SCHOOL MATHEMATICS HG 5 5 2 PROSPERITUS SEC SCHOOL MATHEMATICS HG 4 4 3 CHRISTIAN BROTHERS' COLLEGE MOUNT EDMUND MATHEMATICS HG 37 37 37 HOERSKOOL F H ODENDAAL MATHEMATICS HG 7 7 6 HOERSKOOL SILVERTON MATHEMATICS HG 15 15 15 CORNERSTONE COLLEGE SEC. SCHOOL MATHEMATICS HG 23 22 21 GATANG SEC SCHOOL MATHEMATICS HG 8 8 5 SOLOMON MAHLANGU FREEDOM SCHOOL MATHEMATICS HG 2 2 1 J KEKANA SEC SCHOOL MATHEMATICS HG 6 6 6 JAFTA MAHLANGU SEC SCHOOL MATHEMATICS HG 5 5 5 LEHLABILE SEC SCHOOL MATHEMATICS HG 6 6 4 LOMPEC SEC SCHOOL MATHEMATICS HG 1 1 0 MAMELODI SEC SCHOOL MATHEMATICS HG 11 11 9 MODIRI TECHNICAL SCHOOL MATHEMATICS HG 2 2 1 PHATENG SEC SCHOOL MATHEMATICS HG 15 15 6 RIBANE-LAKA SEC SCHOOL MATHEMATICS HG 3 3 1 VLAKFONTEIN SEC SCHOOL MATHEMATICS HG 19 19 2 VUKANI MAWETHU SEC SCHOOL MATHEMATICS HG 2 2 2 HIMALAYA SEC SCHOOL MATHEMATICS HG 14 14 10 LAUDIUM SEC SCHOOL MATHEMATICS HG 9 9 9 AFRIKAANSE HOER MEISIESKOOL MATHEMATICS HG 60 60 60 AFRIKAANSE HOER SEUNSKOOL MATHEMATICS HG 96 96 95

CRAWFORD COLLEGE PRETORIA MATHEMATICS HG 70 70 67 I I LORETO CONVENT SCHOOL MATHEMATICS HG 16 16 13 i I PRETORIA BOYS' HIGH SCHOOL MATHEMATICS HG 197 197 173 1 I PRETORIA HIGH SCHOOL FOR GIRLS MATHEMATICS HG 118 116 111 I PRETORIA HOSPITAL SCHOOL MATHEMATICS HG 2 1 1 I TECHNICAL HIGH SCHOOL MATHEMATICS HG 7 7 71 BOKGONI TECHNICAL SEC SCHOOL MATHEMATICS HG 13 13 7 CENTRAL ISLAMIC SCHOOL MATHEMATICS HG 14 14 14 DAVID HELLEN PETA SEC SCHOOL MATHEMATICS HG 6 6 3

4 DR WF NKOMO SEC SCHOOL MATHEMATICS HG 11 11 9 ED-U-COLLEGE SEC SCHOOL MATHEMATICS HG 5 5 2 EDWARD PHATUDI SEC SCHOOL MATHEMATICS HG 3 3 a FLAVIUS MAREKA SEC SCHOOL MATHEMATICS HG 3 3 2 GREENWOOD COLLEGE MATHEMATICS HG 1 1 1 HOFMEYR SEC SCHOOL MATHEMATICS HG 1 1 1 HOLY TRINITY SEC CATHOLIC SCHOOL MATHEMATICS HG 4 4 3 MERIDIAN COLLEGE MATHEMATICS HG 18 18 a PHELINDABA SEC SCHOOL MATHEMATICS HG 4 4 1 TSHWANE MUSLIM SCHOOL MATHEMATICS HG 26 26 25 SAULRIDGE SEC SCHOOL MATHEMATICS HG 9 9 6 DANSA INTERNATIONAL COLLEGE MATHEMATICS HG 3 3 3 PRETORIA HINDU SCHOOL MATHEMATICS HG 3 3 3 ELMAR COLLEGE MATHEMATICS HG 9 9 4 PRETORIA MUSLIM TRUST SUNNI SCHOOL MATHEMATICS HG 9 9 9 BRAINWAVE ACADEMY OF LEARNING MATHEMATICS HG 4 4 a FOUNDERS COMMUNITY SCHOOL MATHEMATICS HG 3 3 a ROSINA SEDIBANE MODIBA SPORT SCHOOL MATHEMATICS HG 9 9 1 CARPE DIEM ACADEMY MATHEMATICS HG 5 5 a AL-ASR EDUCATIONAL INSTITUTE MATHEMATICS HG 8 8 8 BEREA PARK INDEPENDENT HIGH SCHOOL MATHEMATICS HG 2 2 1 ARCADIA INDEPENDENT HIS MATHEMATICS HG 9 9 a GELUKSDAL SEC SCHOOL MATHEMATICS HG 11 11 3 LIVERPOOL SEC SCHOOL MATHEMATICS HG 36 36 32 WILLIAM HILLS SEC SCHOOL MATHEMATICS HG 7 7 3 BENONI HIGH SCHOOL MATHEMATICS HG 98 98 92--j BRAKPAN HIGH SCHOOL MATHEMATICS HG 20 20 31 I GEKOMBINEERDE SKOOl NOORDERLIG MATHEMATICS HG 27 26 51 HOERSKOOL DIE ANKER (HTS i BRAKPAN&HOOGLAN MATHEMATICS HG 23 23 13 I HOERSKOOlBRANDWAG MATHEMATICS HG 42 42 39 HOERSKOOL HANS MOORE MATHEMATICS HG 13 13 13 HOERSKOOLSTOFFBERG MATHEMATICS HG 49 49 24 KATHSTAN COLLEGE MATHEMATICS HG 1 1 1 WILLOWMOORE HIGH SCHOOL MATHEMAT:CS HG 19 19 19

5 WORDSWORTH HIGH SCHOOL MATHEMATICS HG 19 19 13 ABEDNIGO MANANA SEC (BB MYATAZA) MATHEMATICS HG 11 10 5 EPHES MAMKELI SEC SCHOOL MATHEMATICS HG 9 9 4 BENONI EDUCATIONAL COLLEGE MATHEMATICS HG 6 6 2 BUHLEBEMFUNDO SEC SCHOOL MATHEMATICS HG 19 19 6 DINOTO TECHNICAL SEC MATHEMATICS HG 17 17 10 DR HARRY GWALA SEC SCHOOL MATHEMATICS HG 4 4 4 ETWATWA SEC SCHOOL MATHEMATICS HG 5 5 0 HULWAZI SEC SCHOOL MATHEMATICS HG 15 15 10 JE MALEPE SEC SCHOOL MATHEMATICS HG 12 12 7 LESIBA SEC SCHOOL MATHEMATICS HG 6 6 0 MABUYA SEC SCHOOL MATHEMATICS HG 7 7 1 MAMELLONG COMPR MATHEMATICS HG 11 11 3 PHANDIMFUNDO SEC SCHOOL MATHEMATICS HG 4 4 2 THOLULWAZI SEC SCHOOL MATHEMATICS HG 2 2 2 TSAKANE SEC SCHOOL MATHEMATICS HG 13 13 3 UNITY SEC SCHOOL MATHEMATICS HG 7 7 4 ST FRANCIS COLLEGE MATHEMATICS HG 6 6 6 CAIPHUS NYOKA SEC SCHOOL MATHEMATICS HG 5 4 0 VEZUKHONO SEC SCHOOL MATHEMATICS HG 7 7 5 PETIT HIGH SCHOOL MATHEMATICS HG 1 1 1 BENONI MUSLIM SCHOOL MATHEMATICS HG 7 7 4 EAST RAND SCHOOL OF ART MATHEMATICS HG 2 2 0 ALRAPARK SEC SCHOOL MATHEMATICS HG 6 6 1 NIGEL SEC SCHOOL MATHEMATICS HG 1 1 0 SPRINGS SEC SCHOOL MATHEMATICS HG 11 11 91 EUREKA HIGH SCHOOL MATHEMATICS HG 11 10 HOER TEGNIESE SKOaL SPRINGS MATHEMATICS HG 4 4 3~ HOERSKOOLHUGENOTE MATHEMATICS HG 47 46 HOERSKOOLJOHANJURGENS MATHEMATICS HG 26 26 24 HOERSKOOL JOHN VORSTER MATHEMATICS HG 22 22 22 NIGEL HIGH SCHOOL MATHEMATICS HG 22 22 15 SPRINGS BOYS' HIGH SCHOOL MATHEMATICS HG 35 35 31 j SPRINGS GIRLS' HIGH SCHOOL MATHEMATICS HG 20 20 20 I MATHEMATICS HG 3 3 31 SPRINGS MUSLIM SCHOOL I

6 ASSER MALOKA SEC MATHEMATICS HG 6 6 5 ESIBONELWESIHLE SEC MATHEMATICS HG 8 8 5 KENNETH MASEKELA SEC MATHEMATICS HG 3 3 2 LABAN MOTLHABI COMPR SCHOOL MATHEMATICS HG 7 7 7 LEFA-IFA SEC SCHOOL MATHEMATICS HG 1 0 0 MOM SEBONE SEC SCHOOL MATHEMATICS HG 8 8 8 NIMROD NDEBELE SEC SCHOOL MATHEMATICS HG 7 7 4 NKUMBULO SEC SCHOOL MATHEMATICS HG 8 8 2 PHULONG SEC SCHOOL MATHEMATICS HG 3 3 2 TLAKULA SEC SCHOOL MATHEMATICS HG 7 7 5 ZIMISELE SEC SCHOOL MATHEMATICS HG 6 6 5 OOSRAND SEC SCHOOL MATHEMATICS HG 4 4 1 REIGER PARK NR 2 SEC SCHOOL MATHEMATICS HG 2 2 1 AFRIKAANSE HOERSKOOL GERMISTON MATHEMATICS HG 16 15 14 BEDFORDVIEW HIGH SCHOOL MATHEMATICS HG 21 21 7 BOKSBURG HIGH SCHOOL MATHEMATICS HG 74 74 67 DAWNVIEW HIGH SCHOOL MATHEMATICS HG 8 8 8 DINWIDDIE HIGH SCHOOL MATHEMATICS HG 7 7 7 EDENGLEN HIGH SCHOOL MATHEMATICS HG 50 50 50 EDENVALE HIGH SCHOOL MATHEMATICS HG 40 40 35 GERMISTON HIGH SCHOOL MATHEMATICS HG 29 29 16 HOER TEGNIESE SKOOL ELSPARK MATHEMATICS HG 19 18 18 PRIMROSE HIGH SCHOOL MATHEMATICS HG 9 9 8 HOERSKOOL DR E G JANSEN MATHEMATICS HG 72 72 56 HOERSKOOLEDENVALE MATHEMATICS HG 8 8 3 HOERSKOOLELSBURG MATHEMATICS HG 5 5 4 HOERSKOOL GOUDRIF MATHEMATICS HG 16 16 15 HOERSKOOL OOSTERUG MATHEMATICS HG 25 24 20

HOERSKOOLVOORTREKKER MATHEMATICS HG 12 12 51 HOERSKOOL VRYBURGER HIGH SCHOOL MATHEMATICS HG 9 9 41 SUNWARD PARK HIGH SCHOOL MATHEMATICS HG 34 34 32 ERASMUS MONARENG SEC SCHOOL MATHEMATICS HG 14 14 5 FRANCISCAN MATRIC PROJECT MATHEMATICS HG 20 20 15 i GRACELAND EDUCATION CENTRE MATHEMATICS HG 3 3 3 ILUNGE SEC SCHOOL MATHEMATICS HG 8 8 1

7 INSTITUTE STATUS ACRES SEC SCHOOL MATHEMATICS HG 4 4 2 LETHULWAZI COMPR SCHOOL MATHEMATICS HG 10 10 8 MASITHWALISANE SEC SCHOOL MATHEMATICS HG 5 5 1 THUTO-LESEDI SEC SCHOOL MATHEMATICS HG 9 9 9 VOSLOORUS COMPR SEC SCHOOL MATHEMATICS HG 5 5 1 FALCON'S EDUC COLLEGE MATHEMATICS HG 5 5 3 PHINEAS XULU SEC SCHOOL MATHEMATICS HG 3 3 2 HOERSKOOL BIRCHLEIGH MATHEMATICS HG 30 29 19 HOERSKOOLJEUGLAND MATHEMATICS HG 59 59 58 HOERSKOOL KEMPTON PARK MATHEMATICS HG 80 80 75 HOERSKOOL RHODESFIELD MATHEMATICS HG 9 9 8 NORKEM PARK HIGH SCHOOL MATHEMATICS HG 19 19 13 SIR PIERRE VAN RYNEVELD HIGH SCHOOL MATHEMATICS HG 27 27 19 WINDSOR HOUSE ACADEMY MATHEMATICS HG 8 8 6 BOITUMELONG SEC SCHOOL MATHEMATICS HG 2 2 2 BOKOMOSO SEC SCHOOL MATHEMATICS HG 25 24 9 ELITE COLLEGE MATHEMATICS HG 4 4 3 ESSELEN PARK SPORT SCHOOL OF EXCELLENCE MATHEMATICS HG 4 4 4 SPARTAN HIGH SCHOOL MATHEMATICS HG 3 3 2 INQAYIZIVELE SEC SCHOOL MATHEMATICS HG 20 20 10 JIYANA SEC SCHOOL MATHEMATICS HG 2 2 1 MASIQHAKAZE SEC SCHOOL MATHEMATICS HG 7 7 3 MASISEBENZE COMPR SCHOOL MATHEMATICS HG 17 16 3 TEMBISA SEC SCHOOL MATHEMATICS HG 20 20 14 TERSIA KING LEARING ACADEMY MATHEMATICS HG 6 6 5 THUTO-KE-MAATLA COMPR SCHOOL MATHEMATICS HG 9 9 6 ZITIKENI SEC SCHOOL MATHEMATICS HG 28 28 13 OOS-RAND AKADEMIE MATHEMATICS HG 3 3 0 PALMRIDGE SEC SCHOOL MATHEMATICS HG 15 15 3 ALBERTON HIGH SCHOOL MATHEMATICS HG 34 33 31 BRACKEN HIGH SCHOOL MATHEMATICS HG 35 35 35 HOERSKOOL MARAIS VILJOEN MATHEMATICS HG 91 91 55 HOERSKOOLALBERTON MATHEMA IICS HG 32 32 221 HOERSKOOL DINAMIKA MATHEMATICS HG 23 23 21

8 PARKLANDS HIGH SCHOOL MATHEMATICS HG 9 9 4 ALAFANG SEC SCHOOL MATHEMATICS HG 1 1 1 EKETSANG SEC SCHOOL MATHEMATICS HG 2 2 1 FUMANA SEC SCHOOL MATHEMATICS HG 19 19 7 KATLEHONG SEC SCHOOL MATHEMATICS HG 1 0 0 KWADUKATHOLE COMPR SCHOOL MATHEMATICS HG 8 8 2 LANDULWAZI COMPR SCHOOL MATHEMATICS HG 10 10 3 LETHUKUTHULA SEC MATHEMATICS HG 1 1 0 MPILISWENI SEC SCHOOL MATHEMATICS HG 16 16 2 MPONTSHENG SEC SCHOOL MATHEMATICS HG 10 10 1 NTOMBIZODWA SEC MATHEMATICS HG 19 19 0 PHUMLANI SEC SCHOOL MATHEMATICS HG 7 7 6 PONEGO SEC SCHOOL MATHEMATICS HG 4 4 1 SIJABUlILE SEC SCHOOL MATHEMATICS HG 8 8 1 THOKO THABA SEC MATHEMATICS HG 26 26 2 TIISETSONG SEC SCHOOL MATHEMATICS HG 16 15 2 WINILE SEC SCHOOL MATHEMATICS HG 2 2 1 KATLEHONGTECH S S MATHEMATICS HG 6 6 0- - BERTHARRY ENGLISH PRIVATE SCHOOL MATHEMATICS HG 6 6 a OXFORD COMBINED COLLEGE MATHEMATICS HG 6 5 a GLOBAL SEC COLLEGE MATHEMAT!CS HG 11 11 a MICRO LEARNING ACADEMY MATHEMATICS HG 6 4 1 ROSHNEE SEC SCHOOL MATHEMATICS HG 17 16 12 GENERAL SMUTS HIGH SCHOOL MATHEMATICS HG 19 19 19 HOER TEGNIESE SKOOL VEREENIGING MATHEMATICS HG 19 18 16 HOERSKOOL DR MALAN MATHEMATICS HG 17 17 15 HOERSKOOL DRIE RIVIERE MATHEMATICS HG 39 39 36 I HOERSKOOLOVERVAAL MATHEMATICS HG 24 24 221 HOERSKOOL VEREENIGING MATHEMATICS HG 34 34 28 RIVERSIDE HIGH SCHOOL MATHEMATICS HG 37 37 23 ISIZWE-SETJHABA SEC SCHOOL MATHEMATICS HG 15 14 1

LEKOA SHANDU SEC MATHEMATICS HG 5 5 2 , MOHLOLI SEC SCHOOL MATHEMATICS HG 3 3 0 THUTOLORESECSCHOOL MATHEMATICS HG 9 9 4 ASSEMBLIES OF GOD (CEFUPS ACADEMY) MATHEMATICS HG 9 8 1

9 ROSHNEE ISLAMIC SCHOOL MATHEMATICS HG 13 13 13 MEYERTON HIGH SCHOOL MATHEMATICS HG 12 12 2 HOER VOLKSKOOL HEIDELBERG MATHEMATICS HG 33 33 30 SEDAVEN HIGH SCHOOL MATHEMATICS HG 15 15 5 KGORO YA THUTO SEC MATHEMATICS HG 3 3 0 ZIKHETHELE SEC SCHOOL MATHEMATICS HG 10 10 1 EL TABERNACLE ( MATHEMATICS HG 2 2 1 HOER TEGNIESE SKOOL CAREL DE WET MATHEMATICS HG 8 8 8 HOERSKOOL SUIDERLIG MATHEMATICS HG 14 14 12 HOERSKOOL VANDERBIJLPARK MATHEMATICS HG 10 9 8 BOIKGETHELO SEC SCHOOL MATHEMATICS HG 4 4 0 BOTEBO-TSEBO SEC SCHOOL MATHEMATICS HG 6 6 6 ESOKWAZI SEC SCHOOL MATHEMATICS HG 16 16 6 FUNDULWAZI SEC SCHOOL MATHEMATICS HG 19 19 6 JET NTEO SEC SCHOOL MATHEMATICS HG 1 1 0 JORDAN SEC SCHOOL MATHEMATICS HG 4 4 4 KATLEHO-IMPUMELELO SEC SCHOOL MATHEMATICS HG 5 5 5 KHUTLO-THARO SEC SCHOOL MATHEMATICS HG 7 7 4 LAKESIDE SEC SCHOOL MATHEMATICS HG 4 4 2 MAHAR ENG SEC SCHOOL MATHEMATICS HG 11 11 1 BEVERLY HILLS SEC SCHOOL MATHEMATICS HG 20 20 4 MAXEKE SEC SCHOOL MATHEMATICS HG 3 3 1 MOHALADITOE SEC SCHOOL MATHEMATICS HG 5 5 2 MOSHATE SEC SCHOOL MATHEMATICS HG 6 6 1 POELANO SEC SCHOOL MATHEMATICS HG 2 2 0 QEDILlZWE SEC SCHOOL MATHEMATICS HG 9 9 5 RESIDENSIA SEC SCHOOL MATHEMATICS HG 51 50 10

RUTASETJHABA SEC SCHOOL MATHEMATICS HG 20 18 6 1 I SAPPHIRE SEC SCHOOL MATHEMATICS HG 6 6 1 1, SEBOKENG TECH HIGH SCHOOL MATHEMATICS HG 3 3 21 I SEHOPOTSO SEC SCHOOL MATHEMATICS HG 5 5 51 I SETJHABA-SOHLE SEC MATHEMATICS HG 2 2 11 i SIZANANI THUSANANG COMPR SCHOOL MATHEMATICS HG 31 22 22 I TANDUKWAZI SEC SCHOOL MATHEMATICS HG 7 7 1 THARABOLLO SEC SCHOOL MATHEMATICS HG 7 6 2

10 THUTO-TIRO COMPR MATHEMATICS HG 12 11 2 TOKELO SEC SCHOOL MATHEMATICS HG 8 8 4 TSOLO SEC SCHOOL MATHEMATICS HG 7 7 2 EL SHADDAI SCHOOL MATHEMATICS HG 10 5 0 CHRYSTAL SPRINGS PRIVATE SCHOOL MATHEMATICS HG 7 7 0 HOERSKOOL DRIEHOEK MATHEMATICS HG 52 51 47 HOERSKOOL TRANSVALIA MATHEMATICS HG 62 62 61 SUNCREST HIGH SCHOOL MATHEMATICS HG 26 26 12 THE VAAL HIGH SCHOOL MATHEMATICS HG 8 8 0 ATHLONE BOYS' HIGH SCHOOL MATHEMATICS HG 1 1 0 ATHLONE GIRLS' HIGH SCHOOL MATHEMATICS HG 15 15 6 BETH JACOBS GIRLS' HIGH SCHOOL MATHEMATICS HG 7 7 7 CONVENT OF THE HOLY FAMILY MATHEMATICS HG 11 11 8 CRAWFORD COLLEGE JOHANNESBURG MATHEMATICS HG 30 29 12 DOMINICAN CONVENT SCHOOL (BELGRAVIA) MATHEMATICS HG 15 15 7 HIGHLANDS NORTH BOYS HIGH SCHOOL MATHEMATICS HG 9 9 3 HOPE SCHOOUSKOOL MATHEMATICS HG 2 2 1 JEPPE HIGH SCHOOL FOR BOYS MATHEMATICS HG 50 48 42 JEPPE GIRLS' HIGH SCHOOL MATHEMATICS HG 48 48 48 KING EDWARD VII SCHOOL MATHEMATICS HG 81 81 66 MALVERN HIGH SCHOOL MATHEMATICS HG 4 4 3 MARYVALE COLLEGE MATHEMATICS HG 10 10 4 PARKTOWN BOYS' HIGH SCHOOL MATHEMATICS HG 80 80 77 QUEENS HIGH SCHOOL MATHEMATICS HG 49 49 42 RAND MEISIESKOOUGIRLS' SCHOOL MATHEMATICS HG 1 1 1 RAND TUTORIAL COLLEGE MATHEMATICS HG 1 1 1 SANDRINGHAM HIGH SCHOOL MATHEMATICS HG 43 43 36 TORAH ACADEMY PRIMARY & HIGH SCHOOL MATHEMATICS HG 5 5 5 YESHIVATH TORAH EMETH COLLEGE MATHEMATICS HG 5 5 5 CENTURION COLLEGE MATHEMATICS HG 15 15 1 EDUCATIONAL PROGRAMMES CENT. MATHEMATICS HG 3 2 0 NEWGATE COLLEGE MATHEMATICS HG 11 10 4 ST ENDA'S EDUCATION SEC SCHOOL MATHEMATICS HG 6 6 6 ST MARY'S COLLEGE MATHEMATICS HG 5 4 0 SUPREME EDUCATIONAL COLLEGE MATHEMATICS HG 7 7 0 i

11 BLUE HILLS COLLEGE (ST. PAULS COLLEGE) MATHEMATICS HG 3 3 2 EDEN COLLEGE MATHEMATICS HG 10 10 10 WITS TUTORIAL COLLEGE MATHEMATICS HG 1 1 0 JEPPE ADULT EDUC CENTRE MATHEMATICS HG 4 4 2 MARLBORO GARDENS SEC SCHOOL MATHEMATICS HG 7 7 5 BRYANSTON HIGH SCHOOL MATHEMATICS HG 72 72 69 CHINESE KUO TING SCHOOL MATHEMATICS HG 2 2 2 MIDRAND PARALLEL MEDIUM HIGH SCHOOL MATHEMATICS HG 18 18 12 NORTHVIEW HIGH SCHOOL MATHEMATICS HG 9 9 2 SANDOWN HIGH SCHOOL MATHEMATICS HG 12 12 5 WAVERLEY GIRLS' HIGH SCHOOL MATHEMATICS HG 35 35 25 WENDYWOOD HIGH SCHOOL MATHEMATICS HG 19 19 15 ALEXANDRA SEC SCHOOL MATHEMATICS HG 9 7 3 EAST BANK HIGH SCHOOL MATHEMATICS HG 16 15 1 KWABHEKILANGA SEC SCHOOL MATHEMATICS HG 14 13 7 MINERVA SEC SCHOOL MATHEMATICS HG 17 16 5 REALOGILE SEC SCHOOL MATHEMATICS HG 3 3 3 UNITED SISTERHOOD MITZVAH MATHEMATICS HG 3 3 2 CRAWFORD SCHOOLS LONEHILL MATHEMATICS HG 66 66 66 CRAWFORD SANDTON SCHOOL MATHEMATICS HG 82 82 82 EQINISWENI SEC SCHOOL MATHEMATICS HG 8 8 2 UMQHELE SEC SCHOOL MATHEMATICS HG 8 8 5 IVORY PARK SEC SCHOOL MATHEMATICS HG 16 16 15

EMSHUKANTAMBO SEC SCHOOL MATHEMATICS HG 11 11 11 I MUSI COMPR MATHEMATICS HG 7 7 1 I PROGRESS COMPR SCHOOL MATHEMATICS HG 3 3 1 THABA-JABULA SEC SCHOOL MATHEMATICS HG 23 23 1 JOHANNESBURG SEC SCHOOL MATHEMATICS HG 6 6 3 GREENSIDE HIGH SCHOOL MATHEMATICS HG 95 95 83 HOER TEGNIESE SKOOL LANGLAAGTE MATHEMATICS HG 20 20 10 MCAULEY HOUSE SCHOOL MATHEMATICS HG 11 11 9 PARKTOWN GIRLS' HIGH SCHOOL MATHEMATICS HG 96 96 92 ROOSEVELT HIGH SCHOOL MATHEMATICS HG 14 14 14 BONA COMPR SCHOOL MATHEMATICS HG 6 5 1 BOPHELO-IMPILO PRIVATE SCHOOL MATHEMATICS HG 2 2 1

12 LOFENTSE COMPR SCHOOL MATHEMATICS HG 9 9 1 ORLANDO SEC SCHOOL MATHEMATICS HG 3 3 1 RAUCALL SEC SCHOOL MATHEMATICS HG 34 34 34 SELELEKELA SEC SCHOOL MATHEMATICS HG 5 5 2 TASK ACADEMY SCHOOL MATHEMATICS HG 5 5 1 NEW NATION SCHOOL MATHEMATICS HG 1 1 0 CHRIS J BOTHA SEC SCHOOL MATHEMATICS HG 26 26 5 CORONATIONVILLE SEC SCHOOL MATHEMATICS HG 6 6 2 WESTBURY SEC SCHOOL MATHEMATICS HG 3 2 1 HOERSKOOLVORENTOE MATHEMATICS HG 17 17 11 NORTHCLIFF HIGH SCHOOL MATHEMATICS HG 101 100 100 ST BARNABAS COLLEGE MATHEMATICS HG 43 43 19 FIDELITAS COMPR SCHOOL MATHEMATICS HG 1 1 1 FaNS LUMINIS SEC SCHOOL MATHEMATICS HG 15 15 3 IMMACULATA SEC SCHOOL MATHEMATICS HG 16 16 3 NAMEDI SEC SCHOOL MATHEMATICS HG 6 6 4 FERNDALE HIGH SCHOOL MATHEMATICS HG 14 14 12 FOURWAYS HIGH SCHOOL MATHEMATICS HG 81 81 75 HOERSKOOL LINDEN MATHEMATICS HG 64 64 64 HOERSKOOLRANDBURG MATHEMATICS HG 49 49 49 RAND PARK HIGH SCHOOL MATHEMATICS HG 84 83 82 SEKOLO SA BOROKGO MATHEMATICS HG 28 28 18 ST ANSGAR'S COMBINED SCHOOL MATHEMATICS HG 16 16 5 - DIEPSLOOT COMBINED SCHOOL MATHEMATICS HG 1 1 1 BRANDCLIFF HOUSE PRIVATE SCHOOL MATHEMATICS HG 3 3 1 AZARA SEC SCHOOL MATHEMATICS HG 27 26 3 LENASIA SEC SCHOOL MATHEMATICS HG 43 43 23

SOUTHVIEW HIGH SCHOOL (LENASIA SOUTH) MATHEMATICS riG 18 18 11 1I I LENASIA SOUTH SEC SCHOOL MATHEMATICS HG 22 22 10 I MH JOOSUB TECHNICAL SEC SCHOOL MATHEMATICS HG 2 2 0 NIRVANA SEC SCHOOL MATHEMATICS HG 23 23 19

TRINITY SEC SCHOOL MATHEMATICS HG 2 2 2: GLENVISTA HIGH SCHOOL MATHEMATICS HG 54 53 44 KWADEDANGENDLALE SEC SCHOOL MATHEMATICS HG 5 5 51 AURORA COMPR SCHOOL MATHEMATICS HG 4 4 21 I

13 DR BW VILAKAZI SEC SCHOOL MATHEMATICS HG 11 11 2 EMDENI SEC SCHOOL MATHEMATICS HG 1 1 1 WILLOWMEAD SEC SCHOOL MATHEMATICS HG 1 0 0 LAVELA SEC SCHOOL MATHEMATICS HG 19 19 3 LENZ PUBLIC SCHOOL MATHEMATICS HG 6 6 5 MAPETLA HIGH SCHOOL MATHEMATICS HG 1 1 1 NALEDI SEC SCHOOL MATHEMATICS HG 2 2 1 NGHUNGHUNYANICOMPR MATHEMATICS HG 16 14 1 PRUDENS SEC SCHOOL MATHEMATICS HG 5 5 4 REASOMA SEC SCHOOL MATHEMATICS HG 17 17 10 SEANA MARENA SEC SCHOOL MATHEMATICS HG 1 1 1 SEKANO-NTOANE SEC SCHOOL MATHEMATICS HG 6 6 4 SENAOANE SEC SCHOOL MATHEMATICS HG 19 19 4 TETELO SEC SCHOOL MATHEMATICS HG 8 8 8 THABO SEC SCHOOL MATHEMATICS HG 15 14 12 THOMAS MOFOLO SEC SCHOOL MATHEMATICS HG 7 7 6 VUWANI SEC SCHOOL MATHEMATICS HG 10 10 3 FRED NORMAN SEC SCHOOL MATHEMATICS HG 3 3 3 ZAKARIYYA PARK SEC SCHOOL MATHEMATICS HG 4 4 4 LENASIA MUSLIM SCHOOL MATHEMATICS HG 37 37 35 MOSES MAREN MISSION TECHNICAL SEC MATHEMATICS HG 4 4 3 NUR-UL-ISLAM SCHOOL MATHEMATICS HG 5 5 1 OAKDALE SEC SCHOOL MATHEMATICS HG 3 3 2 AL-AQSA SCHOOL MATHEMATICS HG 15 15 14 EAGLEWISE ACADEMY MATHEMATICS HG 7 7 0 ELDORADO PARK SEC SCHOOL MATHEMATICS HG 6 6 6 KLIPTOWN SEC SCHOOL MATHEMATICS HG 4 4 1 LANCEA VALE SEC SCHOOL MATHEMATICS no 2 2 1 SILVER OAKS SEC SCHOOL MATHEMATICS HG 6 6 3 FOREST HIGH SCHOOL MATHEMATICS HG 12 12 6 HOERSKOOL DIE FAKKEL MATHEMATICS HG 3 3 0 DIVERSITY HOERIHIGH SCHOOL MATHEMATICS HG 3 3 1

HOERSKOOL PRESIDENT MATHEMATICS HG 23 23 20 j MONDEOR HIGH SCHOOL MATHEMATICS HG 28 28 28 SIR JOHN ADAMSON HIGH SCHOOL MATHEMATICS HG 41 40 15

14 THE HILL HIGH SCHOOL MATHEMATICS HG 34 34 24 ALTMONT TECHNICAL HIGH SCHOOL MATHEMATICS HG 14 14 4 BHUKULANI SEC SCHOOL MATHEMATICS HG 14 14 14 IBHONGO SEC SCHOOL MATHEMATICS HG 6 6 0 JABULANI TECHNICAL SEC SCHOOL MATHEMATICS HG 2 2 2 LETARE SEC SCHOOL MATHEMATICS HG 7 6 1 MAFORI MPHAHLELE COMPR SCHOOL MATHEMATICS HG 4 4 2 MOLETSANE SEC SCHOOL MATHEMATICS HG 4 4 4 PACE SEC PRIVATE SCHOOL MATHEMATICS HG 5 5 1 PHAFOGANG SEC SCHOOL MATHEMATICS HG 16 16 2 JOHANNESBURG POLYTECH INSTITUTE MATHEMATICS HG 9 9 5 HIS MAJESTY EDUCATIONAL INSTITUTE MATHEMATICS HG 14 7 0 HORIZON INTERNATIONAL HIGH SCHOOL MATHEMATICS HG 6 6 5 DAMELIN COLLEGE - JOHANNESBURG MATHEMATICS HG 11 11 8 JOHN ORR TECHNICAL HIGH SCHOOL MATHEMATICS HG 7 7 5 NATIONAL SCHOOL OF THE ARTS MATHEMATICS HG 10 10 8 SHEIKH ANTA DIOP COLLEGE MATHEMATICS HG 2 2 0 ABC ACADEMY PRIVATE SCHOOL MATHEMATICS HG 3 3 3 ASTRA COLLEGE MATHEMATICS HG 4 3 0 AVONDALE GIRLS HIGH MATHEMATICS HG 1 1 0 BANTORI COLLEGE MATHEMATICS HG 8 8 3 BASA TUTORIAL INSTITUTE MATHEMATICS HG 5 5 5 DALIWONGA SEC SCHOOL MATHEMATICS HG 19 19 1 EDUCATION ALIVE SCHOOL MATHEMATICS HG 1 1 1 FREEDOM COMMUNITY COLLEGE MATHEMATICS HG 1 1 0 LIBERTY COMMUNITY SCHOOL MATHEMATICS HG 23 23 2 MAHLASEDI HIGH SCHOOL MATHEMATICS HG 1 1 1 MORRIS ISAACSON SEC SCHOOL MATHEMATICS HG 22 21 3 NEW MODEL PRIVATE COLLEGE MATHEMATICS HG 12 12 0 PHOENIX COLLEGE OF JOHANNESBURG MATHEMATICS HG 5 4 0 DR BEYERS NAUDE SEC SCHOOL MATHEMATICS HG 3 3 2 PROVIDENCE ACADEMY MATHEMATICS HG 6 5 3 ROBIN HOOD PRIVATE SEC SCHOOL MATHEMATICS HG 14 11 1 ST MATTHEWS PRIVATE SEC SCHOOL MATHEMATICS HG 16 16 16 VECTOR COMBINED SCHOOL MATHEMATICS HG 11 11 5

15 ADELAIDE TAMBO (J C MERKIN WHITE CITY MATHEMATICS HG 1 1 0 JOHANNESBURG MUSLIM SCHOOL MATHEMATICS HG 21 21 21 JORDAO COLLEGE MATHEMATICS HG 1 1 0 THUSA-SETJHABA SEC SCHOOL MATHEMATICS HG 3 3 2 AHA-THUTO SEC SCHOOL MATHEMATICS HG 29 28 10 ISIKHUMBUZO HIGH SCHOOL MATHEMATICS HG 10 10 0 TSHEBETSO HIGH SCHOOL MATHEMATICS HG 11 9 0 LESHATA SEC SCHOOL MATHEMATICS HG 23 23 13 RAPHELA SEC SCHOOL MATHEMATICS HG 13 13 8 THAMSANQASECSCHOOL MATHEMATICS HG 1 1 0 VULANINDLELA SEC MATHEMATICS HG 4 4 0 JABULILE SEC SCHOOL MATHEMATICS HG 6 6 3 THETHA SEC SCHOOL MATHEMATICS HG 9 9 1 SIYAPHAMBILI HIGH SCHOOL MATHEMATICS HG 1 1 0 IN-TUITION COLLEGE MATHEMATICS HG 1 1 0 ANCHOR COMPR MATHEMATICS HG 7 7 6 EMADWALENI SEC SCHOOL MATHEMATICS HG 4 4 3 ORLANDO WEST SEC SCHOOL MATHEMATICS HG 1 1 1 PHEFENI SEC SCHOOL MATHEMATICS HG 14 14 4 ST MARTIN DE PORRES HIGH SCHOOL MATHEMATICS HG 8 8 0 KELOKITSO COMPR SCHOOL MATHEMATICS HG 5 4 3 KWA-MAHLOBO SEC SCHOOL MATHEMATICS HG 4 4 2 LAMULA JUBILEE SEC SCHOOL MATHEMATICS HG 9 9 4 LETSIBOGO SEC SCHOOL MATHEMATICS HG 14 14 3 MATSELISO SEC SCHOOL MATHEMATICS HG 4 4 4 MEADOWLANDS SEC SCHOOL MATHEMATICS HG 5 5 3 MOKGOME SEC SCHOOL MATHEMATICS HG 2 2 2 THUTOLORE SEC SCHOOL MATHEMATICS HG 7 7 5 VERITAS SEC SCHOOL MATHEMATICS HG 5 4 3 FLORIDA PARK HIGH SCHOOL MATHEMATICS HG 19 19 17 HOERSKOOL DIE ADELAAR MATHEMATICS HG 6 6 6 HOERSKOOL DIE BURGER MATHEMATICS HG 13 13 71 HOERSKOOL FLORIDA MATHEMATICS HG 69 69 69 HOERSKOOLROODEPOORT MATHEMATICS HG 65 65 62 PRINCESS HIGH SCHOOL MATHEMATICS HG 14 14 13

16 WEST RIDGE HIGH SCHOOL MATHEMATICS HG 26 26 23 FORTE SEC SCHOOL MATHEMATICS HG 42 42 20 GEORGE KHOSA SEC SCHOOL MATHEMATICS HG 10 10 4 PJ SIMELANE SEC SCHOOL MATHEMATICS HG 20 20 13 SEBETSA-O-THOLEMOPUTSO MATHEMATICS HG 4 4 4 TULIP SEC SCHOOL MATHEMATICS HG 1 1 1 ALLEN GLEN HIGH SCHOOL MATHEMATICS HG 50 50 33 VICTORY HOUSE PRIVATE SCHOOL MATHEMATICS HG 5 5 3 WISE-UP COMBINED SCHOOL MATHEMATICS HG 1 1 1 DOORNKOP SEN SEC SCHOOL MATHEMATICS HG 9 9 4 CULTURA HIGH SCHOOL MATHEMATICS SG 34 34 21 GEKOMBINEERDE SKOOL CULLINAN MATHEMATICS SG 29 29 25 HOERSKOOLERASMUS MATHEMATICS SG 47 47 35 CHIPA-TABANE SEC SCHOOL MATHEMATICS SG 44 44 30 DAN KUTUMELA SEC SCHOOL MATHEMATICS SG 53 53 4 MPHUMELOMMUHLE SEC SCHOOL MATHEMATICS SG 12 12 3 EDENDALE PEPPS COLLEGE MATHEMATICS SG 33 33 16 WOZANIBONE INTERM SCHOOL MATHEMATICS SG 13 13 7 STAR OF HOPE SCHOOL MATHEMATICS SG 38 38 2 LESEDI HIGH SCHOOL MATHEMATICS SG 17 17 2 ABBOTT'S COLLEGE SILVERLAKES(TEMP NUMBER MATHEMATICS SG 9 9 7 - AHMED TIMOL SEC MATHEMATICS SG 64 64 41 HOER TEGNIESE SKOOL N DIEDERICHS MATHEMATICS SG 27 27 27 HOERSKOOL BASTION MATHEMATICS SG 85 85 62 .- HOERSKOOL BEKKER MATHEMATICS SG 34 33 29 HOERSKOOL JAN DE KLERK MATHEMATICS SG 37 37 31 HOERSKOOLMONUMENT MATHEMATICS SG 77 77 76 j HOERSKOOLNOORDHEUWEL MATHEMATICS SG 87 87 84 KRUGERSDORP HIGH SCHOOL MATHEMATICS SG 115 115 105 TOWNVIEW HIGH SCHOOL MATHEMATICS SG 34 34 19 MADIBA SCHOOL MATHEMATICS SG 69 69 56 KAGISO SEC SCHOOL MATHEMATICS SG 70 68 17 MAGALIESBURG STATE SCHOOL MATHEMATICS SG 24 24 10 MATLA COMBINED SCHOOL MATHEMATICS SG 16 16 4

17 MOSUPATSELA SEC SCHOOL MATHEMATICS SG 125 122 54 SCHAUMBURG COMBINED SCHOOL MATHEMATICS SG 28 27 10 SG MAFAESA SEC SCHOOL MATHEMATICS SG 61 59 41 THUTO LEFA SEC SCHOOL MATHEMATICS SG 55 54 14 MANDISA SHICEKA SEC SCHOOL (EX REA MATHEMATICS SG 110 106 54 AZAADVILLE MUSLIM SCHOOL MATHEMATICS SG 11 11 11 RANDFONTEIN SEC SCHOOL MATHEMATICS SG 31 30 4 CARLETON JONES HIGH SCHOOL MATHEMATICS SG 62 62 52 HOERSKOOL CARLETONVILLE MATHEMATICS SG 63 62 49 HOERSKOOL JAN VILJOEN MATHEMATICS SG 60 59 44 HOERSKOOL RIEBEECKRAND MATHEMATICS SG 75 75 70 HOERSKOOL WESTONARIA MATHEMATICS SG 56 55 25 HOERSKOOL WONDERFONTEIN MATHEMATICS SG 22 22 10 RANDFONTEIN HIGH SCHOOL MATHEMATICS SG 42 42 37 AB PHOKOMPE SEC SCHOOL MATHEMATICS SG 49 47 22 BADIRILE SEC SCHOOL MATHEMATICS SG 49 49 20 KGOTHALANG SEC SCHOOL MATHEMATICS SG 65 64 26 THUTO LEHAKWE SEC SCHOOL MATHEMATICS SG 58 58 11 PHAHAMA SEC SCHOOL MATHEMATICS SG 128 127 62 TSWASONGU SEC SCHOOL MATHEMATICS SG 64 62 16 T M LETLHAKE SEC SCHOOL MATHEMATICS SG 286 273 32 RELEBOGllE SEC SCHOOL MATHEMATICS SG 71 70 24 ITHUTENG SEC SCHOOL MATHEMATICS SG 15 15 9 CLAPHAM HIGH SCHOOL MATHEMATICS SG 62 62 61 GEREFORMEERDE SKOOl DIRK POSTMA MATHEMATICS SG 8 8 8 HOER TEGNIESE SKOOl JOHN VORSTER MATHEMATICS SG 72 72 68 HOERSKOOlOOS-MOOT MATHEMATICS SG 109 109 91 HOERSKOOL STAATSPRESIDENT C R SWART MATHEMATICS SG 28 28 23 I HilLVIEW HIGH SCHOOL MATHEMATICS SG 91 91 75 1 I HOER TEGNIESE SKOOl PRETORIA-TUINE MATHEMATICS SG 49 49 38l i HOERSKOOLELANDSPOORT MATHEMATICS SG 37 35 20l HOERSKOOL HENDRIK VERWOERD MATHEMATICS SG 46 46 33 i HOERSKOOlHERCULES MATHEMATICS SG 21 21 14 HOERSKOOlLANGENHOVEN MATHEMATICS SG 40 40 25 HOERSKOOL PRETORIA-WES MATHEMATICS SG 45 45 36

18 HOERSKOOL TUINE MATHEMATICS SG 116 116 104 HOERSKOOL WONDERBOOM MATHEMATICS SG 124 123 106 IONA CONVENT MATHEMATICS SG 13 13 13 PRINCESS PARK SEC SCHOOL & COLLEGE MATHEMATICS SG 12 12 6 SA COLLEGE SCHOOL MATHEMATICS SG 26 26 20 TARGET HIGH SCHOOL MATHEMATICS SG 20 17 7 LOTUS GARDENS SEC SCHOOL MATHEMATICS SG 81 81 25 CONFIDENCE COLLEGE MATHEMATICS SG 19 19 11 PRINSHOFSKOOL MATHEMATICS SG 8 8 8 C-PROGRESSIVE SCHOOL MATHEMATICS SG 42 42 13 HOERSKOOL AKASIA MATHEMATICS SG 94 94 79 HOERSKOOL GERRIT MARITZ MATHEMATICS SG 105 104 84 HOERSKOOLMONTANA MATHEMATICS SG 71 71 50 HOERSKOOL OVERKRUIN MATHEMATICS SG 101 101 99 HOERSKOOL PRETORIA-NOORD MATHEMATICS SG 71 71 59 AMOGELANG SEC SCHOOL MATHEMI'.TICS SG 154 150 37 BOTSE-BOTSE SEC MATHEMATICS SG 70 70 29 CENTRAL SEC SCHOOL MATHEMATICS SG 136 132 70 FILADELFIA MATHEMATICS SG 13 13 5 HLANGANANI SEC SCHOOL MATHEMATICS SG 60 57 17 HLOMPHANANG SEC SCHOOL MATHEMATICS SG 62 61 40 KGADIME MATSEPE SEC MATHEMATICS SG 93 92 20 I KGOMOTSO SEC SCHOOL MATHEMATICS SG 141 140 46 LETHABONG SEC SCHOOL MATHEMATICS SG 43 43 13-J MAKHOSINI COMBINED SEC SCHOOL MATHEMATICS SG 160 156 35 I I MEMEZELO SEC SCHOOL MATHEMATICS SG 57 56 7i I REITUMETSE SEC SCHOOL MATHEMATICS SG 223 223 112 1 I SENTHIBELE SENIOR SEC MATHEMATICS SG 136 136 29 i ! SOSHANGUVESECSCHOOL MATHEMATICS SG 110 110 55l, SOSHANGUVE TECHNICAL CENTRE MATHEMATICS SG 143 139 50 TIYELELANI SEC SCHOOL MATHEMATICS SG 78 77 13 WALLMANSTHAL SEC MATHEMATICS SG 27 27 12 ELIZABETH MATSEMELA SEC SCHOOL MATHEMATICS SG 80 77 28 CHARLTON VOS COLLEGE OF EDUCATION MATHEMATICS SG 25 25 22 HOERSKOOL DIE WILGERS MATHEMATICS SG 67 66 57

19 HOERSKOOL ELDORAIGNE MATHEMATICS SG 114 114 104 HOERSKOOL GARSFONTEIN MATHEMATICS SG 82 82 71 HOERSKOOLMENLOPARK MATHEMATICS SG 90 90 78 PRO ARTE ALPHEN PARK MATHEMATICS SG 49 48 35 HOERSKOOL UITSIG MATHEMATICS SG 76 76 59 HOERSKOOL CENTURION MATHEMATICS SG 104 102 99 HOERSKOOLVOORTREKKERHOOGTE MATHEMATICS SG 98 97 77 , HOERSKOOLWATERKLOOF MATHEMATICS SG 107 107 100 HOERSKOOL~ARTKOP MATHEMATICS SG 132 132 123 L¥TIELTON MANOR HIGH SCHOOL MATHEMATICS SG 86 86 63 SUTHERLAND HIGH SCHOOL MATHEMATICS SG 111 111 105 THE GLEN HIGH SCHOOL MATHEMATICS SG 83 83 78 WILLOWRIDGE HIGH SCHOOL MATHEMATICS SG 56 56 55 THE WAY CHRISTIAN SCHOOL MATHEMATICS SG 4 4 4 EERSTERUST SEC SCHOOL MATHEMATICS SG 33 33 14 PROSPERITUS SEC SCHOOL MATHEMATICS SG 49 49 26 CHRISTIAN BROTHERS' COLLEGE MOUNT EDMUND MATHEMATICS SG 22 21 19 HOERSKOOL FH ODENDAAL MATHEMATICS SG 29 29 20 HOERSKOOL SILVERTON MATHEMATICS SG 33 33 27 CORNERSTONE COLLEGE SEC. SCHOOL MATHEMATICS SG 71 71 71 GATANG SEC SCHOOL MATHEMATICS SG 45 44 13 SOLOMON MAHLANGU FREEDOM SCHOOL MATHEMATICS SG 48 47 24

J KEKANA SEC SCHOOL MATHEMATICS SG 93 91 16 I JAFTA MAHLANGU SEC SCHOOL MATHEMATICS SG 82 79 45 LEHLABILE SEC SCHOOL MATHEMATICS SG 87 86 31 LOMPEC SEC SCHOOL MATHEMATICS SG 29 29 61 MAMELODI SEC SCHOOL MATHEMATICS SG 69 67 39 I I MATHEMATICS SG MODIRI TECHNICAL SCHOOL 83 83 401I I PHATENG SEC SCHOOL MATHEMATICS SG 101 101 44 STANZA BOPAPE SEC SCHOOL MATHEMATICS SG 23 23 14 RIBANE-LAKA SEC SCHOOL MATHEMATICS SG 89 87 17 TSAKO THABO SEC SCHOOL MATHEMATICS SG 25 25 13 VLAKFONTEIN SEC SCHOOL MATHEMATICS SG 80 79 5 VUKANI MAWETHU SEC SCHOOL MATHEMATICS SG 38 38 26 I I

20 BONALESEDISECSCHOOL MATHEMATICS SG 73 73 26 MERVYN HARVEY EDUC CENTRE MATHEMATICS SG 17 16 7 HIMALAYA SEC SCHOOL MATHEMATICS SG 55 55 40 LAUDIUM SEC SCHOOL MATHEMATICS SG 100 100 51 AFRIKAANSE HOER MEISIESKOOL MATHEMATICS SG 40 39 39 AFRIKAANSE HOER SEUNSKOOL MATHEMATICS SG 101 101 97 CRAWFORD COLLEGE PRETORIA MATHEMATICS SG 31 31 31 LORETO CONVENT SCHOOL MATHEMATICS SG 21 21 21 PRETORIA BOYS' HIGH SCHOOL MATHEMATICS SG 75 75 65 PRETORIA HIGH SCHOOL FOR GIRLS MATHEMATICS SG 95 95 94 HOSPITAALSKOOL PRETORIA HOSPITAL SCHOOL MATHEMATICS SG 8 5 3 PRETORIA TECHNICAL HIGH SCHOOL MATHEMATICS SG 86 86 83 BOKGONI TECHNICAL SEC SCHOOL MATHEMATICS SG 42 42 38 ..- CENTRAL ISLAMIC SCHOOL MATHEMATICS SG 14 14 12 DAVID HELLEN PETA SEC SCHOOL MATHEMATICS SG 38 38 30 DR WF NKOMO SEC SCHOOL MATHEMATICS SG 35 35 23 ED-U-COLLEGE SEC SCHOOL MATHEMATICS SG 23 23 12 EDWARD PHATUDI SEC SCHOOL MATHEMATICS SG 66 63 11 FLAVIUS MAREKA SEC SCHOOL MATHEMATICS SG 14 14 7 GREENWOOD COLLEGE MATHEMATICS SG 25 24 15 HOFMEYR SEC SCHOOL MATHEMATICS SG 90 90 48 - HOLY TRINITY SEC CATHOLIC SCHOOL MATHEMATICS SG 39 39 25 MERIDIAN COLLEGE MATHEMATICS SG 17 17 2 PHELINDABA SEC SCHOOL MATHEMATICS SG 47 46 21 TSHWANE MUSLIM SCHOOL MATHEMATICS SG 15 15 15 SAULRIDGE SEC SCHOOL MATHEMATICS SG 19 18 9 DANSA INTERNATIONAL COLLEGE MATHEMATICS SG 16 16 15 PRETORIA HINDU SCHOOL MATHEMATICS SG 8 8 8 ELMAR COLLEGE MATHEMATICS SG 15 15 11 PRETORIA MUSLIM TRUST SUNNI SCHOOL MATHEMATICS SG 14 14 1: j BRAINWAVE ACADEMY OF LEARNING MATHEMATICS SG 14 13 PRiNCEFIELD TRUST SCHOOL MATHEMATICS SG 5 5 FOUNDERS COMMUNITY SCHOOL MATHEMATICS SG 16 16 6°1 STEVE TSHWETE SEC SCHOOL MATHEMATICS SG 43 43 29

21 ROSINA SEDIBANE MODIBA SPORT SCHOOL MATHEMATICS SG 25 25 11 NELLMAPIUS SEC SCHOOL MATHEMATICS SG 37 35 5 CARPE DIEM ACADEMY MATHEMATICS SG 3 3 2 AL-ASR EDUCATIONAL INSTITUTE MATHEMATICS SG 7 6 6 BEREA PARK INDEPENDENT HIGH SCHOOL MATHEMATICS SG 17 17 3 ARCADIA INDEPENDENT H/S(TEMP.NUMBER) MATHEMATICS SG 10 9 3 GELUKSDAL SEC SCHOOL MATHEMATICS SG 56 56 20 LIVERPOOL SEC SCHOOL MATHEMATICS SG 64 63 63 WILLIAM HILLS SEC SCHOOL MATHEMATICS SG 63 62 35 BENONI HIGH SCHOOL MATHEMATICS SG 136 136 129 BRAKPAN HIGH SCHOOL MATHEMATICS SG 43 43 20 GEKOMBINEERDE SKOaL NOORDERLIG MATHEMATICS SG 16 16 8 HOERSKOOL DIE ANKER (HTS BRAKPAN&HOOGLAN MATHEMATICS SG 45 45 33 HOERSKOOLBRANDWAG MATHEMATICS SG 87 87 76 HOERSKOOL HANS MOORE MATHEMATICS SG 31 31 31 HOERSKOOLSTOFFBERG MATHEMATICS SG 65 65 40 KATHSTAN COLLEGE MATHEMATICS SG 7 7 6 WILLOWMOORE HIGH SCHOOL MATHEMATICS SG 68 67 56 WORDSWORTH HIGH SCHOOL MATHEMATICS SG 48 48 47 ABEDNIGO MANANA SEC (BB MYATAZA) MATHEMATICS SG 81 79 13 EPHES MAMKELI SEC SCHOOL MATHEMATICS SG 91 89 33 - BENONI EDUCATIONAL COLLEGE MATHEMATICS SG 28 28 26 BUHLEBEMFUNDO SEC SCHOOL MATHEMATICS SG 92 91 17 DAVEY SEC SCHOOL MATHEMATICS SG 61 60 13 DINOTO TECHNICAL SEC MATHEMATICS SG 97 96 ~ DR HARRY GWALA SEC SCHOOL MATHEMATICS SG 54 53 27 I ETWATWA SEC SCHOOL MATHEMATICS SG 53 52 10 HB NYATHI SEC SCHOOL MATHEMATICS SG 151 151 27 ! I HULWAZI SEC SCHOOL MATHEMATICS SG 128 127 451 I JE MALEPE SEC SCHOOL MATHEMATICS SG 109 109 40 I j LESIBA SEC SCHOOL MATHEMATICS SG 137 132 12 ! MABUYA SEC SCHOOL MATHEMATICS SG 66 65 11 MAMELLONG COMPR MATHEMATICS SG 94 92 33 PHANDIMFUNDO SEC SCHOOL MATHEMATICS SG 120 114 14

22 RESHOGOFADITSWE SEC SCHOOL MATHEMATICS SG 44 44 11 RIVONI SEC SCHOOL MATHEMATICS SG 61 56 9 THOLULWAZI SEC SCHOOL MATHEMATICS SG 31 31 8 TSAKANE SEC SCHOOL MATHEMATICS SG 43 43 13 UNITY SEC SCHOOL MATHEMATICS SG 76 76 39 ST FRANCIS COLLEGE MATHEMATICS SG 40 40 37 CAIPHUS NYOKA SEC SCHOOL MATHEMATICS SG 58 53 9 VEZUKHONO SEC SCHOOL MATHEMATI CS SG 46 45 32 PETIT HIGH SCHOOL MATHEMATICS SG 43 43 35 BENONI MUSLIM SCHOOL MATHEMATICS SG 12 12 6 EAST RAND SCHOOL OF ART MATHEMATICS SG 41 38 5 ALRAPARK SEC SCHOOL MATHEMATICS SG 28 28 12 NIGEL SEC SCHOOL MATHEMATICS SG 18 18 8 SPRINGS SEC SCHOOL MATHEMATICS SG 31 31 23 EUREKA HIGH SCHOOL MATHEMATICS SG 67 63 14 HOER TEGNIESE SKOaL SPRINGS MATHEMATICS SG 53 53 13 HOERSKOOLHUGENOTE MATHEMATICS SG 82 81 60 HOERSKOOLJOHANJURGENS MATHEMATICS SG 66 65 44 HOERSKOOL JOHN VORSTER MATHEMATICS SG 31 31 29 NIGEL HIGH SCHOOL MATHEMATI CS SG 89 88 61 SPRINGS BOYS' HIGH SCHOOL MATHEMATICS SG 77 77 54 SPRINGS GIRLS' HIGH SCHOOL MATHEMATICS SG 49 48 45 - SPRINGS MUSLIM SCHOOL MATHEMATICS SG 8 8 7 ASSER MALOKA SEC MATHEMATI CS SG 148 142 24 ESIBONELWESIHLE SEC MATHEMATICS SG 123 118 30 KENNETH MASEKELA SEC MATHEMATICS SG 45 44 27 LABAN MOTLHABI COMPR SCHOOL MATHEMATICS SG 47 47 22 LEFA-IFA SEC SCHOOL MATHEMATICS SG 21 19 11 MOM SEBONE SEC SCHOOL MATHEMATICS SG 33 33 29 NIMROD NDEBELE SEC SCHOOL MATHEMATICS SG 46 46 21 I NKUMBULO SEC SCHOOL MATHEMATICS SG 78 75 12 I I PHULONG SEC SCHOOL MATHEMATICS SG 51 50 34l I TLAKULA SEC SCHOOL MATHEMATICS SG 56 55 19 ZIMISELE SEC SCHOOL MATHEMATICS SG 16 16 7 JAMESON GIRLS HIGH SCHOOL MATHEMATICS SG 24 24 9 I

23 DALPARK LEARNING ACADEMY MATHEMATICS SG 6 6 2 OOSRAND SEC SCHOOL MATHEMATICS SG 73 72 39 REIGER PARK NR 2 SEC SCHOOL MATHEMATICS SG 45 44 18 AFRIKAANSE HOERSKOOL GERMISTON MATHEMATICS SG 44 44 42 BEDFORDVIEW HIGH SCHOOL MATHEMATICS SG 59 59 34 BOKSBURG HIGH SCHOOL MATHEMATICS SG 102 102 93 DAWNVIEW HIGH SCHOOL MATHEMATICS SG 48 48 34 DINWIDDIE HIGH SCHOOL MATHEMATICS SG 45 45 43 EDENGLEN HIGH SCHOOL MATHEMATICS SG 137 137 104 EDENVALE HIGH SCHOOL MATHEMATICS SG 63 62 56 GERMISTON HIGH SCHOOL MATHEMATICS SG 124 124 65 HOER TEGNIESE SKOaL ELSPARK MATHEMATICS SG 32 31 24 PRIMROSE HIGH SCHOOL MATHEMATICS SG 81 77 55 HOERSKOOL DR E G JANSEN MATHEMATICS SG 101 101 86 HOERSKOOLEDENVALE MATHEMATICS SG 30 30 17 HOERSKOOL ELSBURG MATHEMATICS SG 22 22 15 HOERSKOOL GOUDRIF MATHEMATICS SG 56 56 46 HOERSKOOL OOSTERLIG MATHEMATICS SG 48 47 45 HOERSKOOLVOORTREKKER MATHEMATICS SG 22 22 18 HOERSKOOL VRYBURGER HIGH SCHOOL MATHEMATICS SG 27 27 13 SCHOOL OF ACHIEVEMENT/PRESTASIESKOOL MATHEMATICS SG 11 11 11 SUNWARD PARK HIGH SCHOOL MATHEMATICS SG 101 100 77 ERASMUS MONARENG SEC SCHOOL MATHEMATICS SG 104 100 16 FRANCISCAN MATRIC PROJECT MATHEMATICS SG 246 237 168 GRACELAND EDUCATION CENTRE MATHEMATICS SG 86 85 20 ILUNGE SEC SCHOOL MATHEMATICS SG 79 77 26 INSTITUTE STATUS ACRES SEC SCHOOL MATHEMATICS SG 22 20 4 LETHULWAZI COMPR SCHOOL MATHEMATICS ~G 67 66 35 MASITHWALISANE SEC SCHOOL MATHEMATICS SG 46 46 26

RONDEBULT SEC SCHOOL MATHEMATICS SG 81 81 51 I CLADELTON INTERNATIONAL COL(S.A. INTER) MATHEMATICS SG 32 32 7 THUTO-LESEDI SEC SCHOOL MATHEMATICS SG 106 105 71 , VOSLOORUS COMPR SEC SCHOOL MATHEMATICS SG 213 202 22 i I FALCON'S EDUC COLLEGE MATHEMATICS SG 8 8 6l I PHINEAS XULU SEC SCHOOL MATHEMATICS SG 111 110 28 !

24 HOERSKOOL BIRCHLEIGH MATHEMATICS SG 30 30 21 HOERSKOOLJEUGLAND MATHEMATICS SG 140 140 119 HOERSKOOL KEMPTON PARK MATHEMATICS SG 91 90 81 HOERSKOOL RHODESFIELD MATHEMATICS SG 40 40 34 NORKEM PARK HIGH SCHOOL MATHEMATICS SG 92 92 63 SIR PIERRE VAN RYNEVELD HIGH SCHOOL MATHEMATICS SG 103 103 74 WINDSOR HOUSE ACADEMY MATHEMATICS SG 8 8 8 BOITUMELONG SEC SCHOOL MATHEMATICS SG 122 118 38 BOKOMOSO SEC SCHOOL MATHEMATICS SG 150 146 26 ELITE COLLEGE MATHEMATICS SG 24 22 10 ESSELEN PARK SPORT SCHOOL OF EXCELLENCE MATHEMATICS SG 14 14 8 SPARTAN HIGH SCHOOL MATHEMATICS SG 28 28 20 IKUSASA COMPR SCHOOL MATHEMATICS SG 98 92 27 INQAYIZIVELE SEC SCHOOL MATHEMATICS SG 80 79 38 JIYANA SEC SCHOOL MATHEMATICS SG 147 142 20 MASIQHAKAZE SEC SCHOOL MATHEMATICS SG 132 126 34 MASISEBENZE COMPR SCHOOL MATHEMATICS SG 94 93 18 MEHLARENG COMBINED FARM SCHOOL MATHEMATICS SG 18 16 5 SUPERO COMBINED SCHOOL MATHEMATICS SG 5 5 4 SIZWE SEC SCHOOL MATHEMATICS SG 85 84 36 TEMBISA SEC SCHOOL MATHEMATICS SG 135 135 50 TERSIA KING LEARING ACADEMY MATHEMATICS SG 19 19 14 THUTO-KE-MAATLA COMPR SCHOOL MATHEMATICS SG 229 224 135 ZITIKENI SEC SCHOOL MATHEMATICS SG 181 178 35 OOS-RAND AKADEMIE MATHEMATICS SG 4 4 0 EDENPARK SEC SCHOOL MATHEMATICS SG 34 33 5 PALMRIDGE SEC SCHOOL MATHEMATICS SG 34 34 19 ALBERTON HIGH SCHOOL MATHEMATICS SG 103 102 73 BRACKEN HIGH SCHOOL MATHEMATICS SG 103 103 101 HOERSKOOL MARAIS VILJOEN MATHEMATICS SG 111 108 7~ HOERSKOOLALBERTON MATHEMATICS SG 71 68 58 HOERSKOOL DINAMIKA MATHEMATICS SG 73 73 68 PARKLANDS HIGH SCHOOL MATHEMATICS SG 77 74 29 1I MATHEMATICS SG 29 ! ALAFANG SEC SCHOOL 68 67 I

25 BUHLEBUZILE SEC MATHEMATICS SG 85 82 34 EKETSANG SEC SCHOOL MATHEMATICS SG 129 125 13 FUMANA SEC SCHOOL MATHEMATICS SG 311 292 65 KATLEHONG SEC SCHOOL MATHEMATICS SG 217 206 16 KWADUKATHOLE COMPR SCHOOL MATHEMATICS SG 54 49 9 LANDULWAZI COMPR SCHOOL MATHEMATICS SG 86 76 19 LETHUKUTHULA SEC MATHEMATICS SG 74 72 9 MPILISWENI SEC SCHOOL MATHEMATICS SG 63 61 13 MPONTSHENG SEC SCHOOL MATHEMATICS SG 57 57 9 NTOMBIZODWA SEC MATHEMATICS SG 79 77 10 PHUMLANI SEC SCHOOL MATHEMATICS SG 164 163 43 PONEGO SEC SCHOOL MATHEMATICS SG 126 123 42 SIJABULILE SEC SCHOOL MATHEMATICS SG 63 62 9 THOKO THABA SEC MATHEMATICS SG 147 141 12 TIISETSONG SEC SCHOOL MATHEMATICS SG 137 134 10 WINILE SEC SCHOOL MATHEMATICS SG 241 222 17 KATLEHONG SCHOOL FOR THE DEAF AND BLIND MATHEMATICS SG 5 0 0 KATLEHONGTECH SS MATHEMATICS SG 77 76 14 BALMORAL COLLEGE MATHEMATICS SG 16 16 15 BERTHARRY ENGLISH PRIVATE SCHOOL MATHEMATICS SG 11 11 4 OXFORD COMBINED COLLEGE MATHEMATICS SG 17 15 5 GLOBAL SEC COLLEGE MATHEMATICS SG 9 8 1 MICRO LEARNING ACADEMY MATHEMATICS SG 1 1 0 RUST-TER-VAAL COMBINED SCHOOL MATHEMATICS SG 31 29 9 ROSHNEE SEC SCHOOL MATHEMATICS SG 30 28 19 GENERAL SMUTS HIGH SCHOOL MATHEMATICS SG 128 127 92 HOER TEGNIESE SKOaL VEREENIGING MATHEMATICS SG 38 37 32 HOERSKOOL DR MALAN MATHEMATICS SG 100 100 76 HOERSKOOL DRIE RIVIERE MATHEMATICS SG 56 56 48 HOERSKOOL OVERVAAL MATHEMATICS SG 36 36 33J HOERSKOOL VEREENIGING MATHEMATICS SG 43 43 31 RIVERSIDE HIGH SCHOOL MATHEMATICS SG 103 103 67 ISIZWE-SETJHABA SEC SCHOOL MATHEMATICS SG 63 61 7 LEKOA SHANDU SEC MATHEMATICS SG 52 51 18

26 MOHLOLI SEC SCHOOL MATHEMATICS SG 87 86 28 THUTOLORESECSCHOOL MATHEMATICS SG 39 39 16 VAAL ED U COLLEGE PRIVATE MATHEMATICS SG 14 14 13 ASSEMBLIES OF GOD (CEFUPS ACADEMY) MATHEMATICS SG 35 34 14 ROSHNEE ISLAMIC SCHOOL MATHEMATICS SG 12 12 11 AMSTELACADEMY MATHEMATICS SG 8 8 4 MEYERTON HIGH SCHOOL MATHEMATICS SG 51 50 18 HOER VOLKSKOOL HEIDELBERG MATHEMATICS SG 60 59 49 SEDAVEN HIGH SCHOOL MATHEMATICS SG 19 18 12 KGORO YA THUTO SEC MATHEMATICS SG 24 24 7 KHANYA-LESEDI SEC MATHEMATICS SG 126 126 54 KUDUNG MIDDLE SCHOOL MATHEMATICS SG 9 9 7 RATANDA SEC SCHOOL MATHEMATICS SG 18 16 10 ~KHETHELESECSCHOOL MATHEMATICS SG 39 37 5 EL TABERNACLE (TEMPORARY NUMBER) MATHEMATICS SG 15 15 9 HOER TEGNIESE SKOaL CAREL DE WET MATHEMATICS SG 59 59 58 HOERSKOOL SUIDERLIG MATHEMATICS SG 59 59 49 HOERSKOOL VANDERBIJLPARK MATHEMATICS SG 42 41 37 BOIKGETHELO SEC SCHOOL MATHEMATICS SG 28 28 2 BOTEBO-TSEBO SEC SCHOOL MATHEMATICS SG 106 103 41 DINOKANENG SEC SCHOOL MATHEMATICS SG 133 129 19 ED MASHABANE SEC SCHOOL MATHEMATICS SG 77 72 6 ESOKWAZI SEC SCHOOL MATHEMATICS SG 89 83 30 FUNDULWAZI SEC SCHOOL MATHEMATICS SG 82 80 18 JET NTEO SEC SCHOOL MATHEMATICS SG 100 97 21 JORDAN SEC SCHOOL MATHEMATICS SG 69 68 16 KATLEHO-IMPUMELELO SEC SCHOOL MATHEMATICS SG 78 76 29 KGOKARE SEC SCHOOL MATHEMATICS SG 46 45 19 KHUTLO-THARO SEC SCHOOL MATHEMATICS SG 135 133 28 LAKESIDE SEC SCHOOL MATHEMATICS SG 95 94 15 LEBOHANG SEC SCHOOL MATHEMATICS SG 81 80 10 MAHARENG SEC SCHOOL MATHEMATICS SG 53 52 10 BEVERLY HILLS SEC SCHOOL MATHEMATICS SG 120 115 40 MAXEKE SEC SCHOOL MATHEMATICS SG 179 175 18 MOHALADITOE SEC SCHOOL MATHEMATICS SG 64 61 5

27 MOPHOLOSI SEC SCHOOL MATHEMATICS SG 116 112 23 MOQHAKA SEC SCHOOL MATHEMATICS SG 26 25 5 MOSHATE SEC SCHOOL MATHEMATICS SG 37 37 8 POELANO SEC SCHOOL MATHEMATICS SG 33 31 2 QEDILlZWE SEC SCHOOL MATHEMATICS SG 181 174 26 RAMOLELLE INTERMEDIATE MATHEMATICS SG 14 13 1 RAMOSUKULA SEC SCHOOL MATHEMATICS SG 33 33 3 RESIDENSIA SEC SCHOOL MATHEMATICS SG 135 124 11 RUTASETJHABA SEC SCHOOL MATHEMATICS SG 193 180 42 SAPPHIRE SEC SCHOOL MATHEMATICS SG 109 100 12 SEBOKENG TECH HIGH SCHOOL MATHEMATICS SG 50 49 28 SEHOPOTSO SEC SCHOOL MATHEMATICS SG 37 36 10 SETJHABA-SOHLE SEC MATHEMATICS SG 81 76 15 SIZANANI THUSANANG COMPR SCHOOL MATHEMATICS SG 61 59 20 TANDUKWAZI SEC SCHOOL MATHEMATICS SG 152 149 13 THARABOLLO SEC SCHOOL MATHEMATICS SG 168 167 40 THUTO-TIRO COMPR MATHEMATICS SG 186 178 14 TOKELO SEC SCHOOL MATHEMATICS SG 116 109 5 TSHEPO-THEMBA SEC SCHOOL MATHEMATICS SG 119 113 18 TSOLO SEC SCHOOL MATHEMATICS SG 75 75 28 EL SHADDAI SCHOOL MATHEMATICS SG 10 4 0 CHRYSTAL SPRINGS PRIVATE SCHOOL MATHEMATICS SG 31 31 1 HOERSKOOL DRIEHOEK MATHEMATICS SG 68 67 57 HOERSKOOL TRANSVALIA MATHEMATICS SG 67 67 63 SUNCREST HIGH SCHOOL MATHEMATICS SG 59 59 34 THE VAAL HIGH SCHOOL MATHEMATICS SG 54 54 23 SAMELSON COLLEGE MATHEMATICS SG 3 0 0 KENSINGTON SEC SCHOOL MATHEMATICS SG 25 25 22 ATHLONE BOYS' HIGH SCHOOL MATHEMATICS SG 38 38 32 ATHLONE GIRLS' HIGH SCHOOL MATHEMATICS SG 60 60 34 BETH JACOBS GIRLS' HIGH SCHOOL MATHEMATICS SG 7 7 7 CONVENT OF THE HOLY FAMILY MATHEMATICS SG 28 28 23 CRAWFORD COLLEGE JOHANNESBURG MATHEMATICS SG 34 34 22 DOMINICAN CONVENT SCHOOL (BELGRAVIA) MATHEMATICS SG 20 20 11 JULES HIGH SCHOOL (EDITH HINDS) MATHEMATICS SG 35 35 19

28 GRANTLEY COLLEGE MATHEMATICS SG 2 2 2 HIGHLANDS NORTH BOYS HIGH SCHOOL MATHEMATICS SG 32 32 20 HOPE SCHOOUSKOOL MATHEMATICS SG 2 2 2 JEPPE HIGH SCHOOL FOR BOYS MATHEMATICS SG 80 80 48 JEPPE GIRLS' HIGH SCHOOL MATHEMATICS SG 58 58 58 KING EDWARD VII SCHOOL MATHEMATICS SG 75 74 66 MALVERN HIGH SCHOOL MATHEMATICS SG 50 50 32 MARYVALE COLLEGE MATHEMATICS SG 15 15 14 PARKTOWN BOYS' HIGH SCHOOL MATHEMATICS SG 38 38 37 QUEENS HIGH SCHOOL MATHEMATICS SG 71 70 60 RAND MEISIESKOOUGIRLS' SCHOOL MATHEMATICS SG 37 37 34 RAND TUTORIAL COLLEGE MATHEMATICS SG 10 10 5 SANDRINGHAM HIGH SCHOOL MATHEMA"!"ICS SG 82 82 62 THE TORAH ACADEMY PRIMARY AND HIGH SCHOO MATHEMATICS SG 8 8 8 YESHIVATH TORAH EMETH COLLEGE MATHEMATICS SG 1 1 1 CENTURION COLLEGE MATHEMATICS SG 13 13 5 EDUCATIONAL PROGRAMMES CENT. MATHEMATICS SG 5 4 0 NEWGATE COLLEGE MATHEMATICS SG 24 24 6 OLYMPUS INST.OF LEARNING MATHEMATICS SG 22 19 3 SIR ISAAC NEWTON HIGH SCHOOL MATHEMATICS SG 16 15 0 ST ENDA'S EDUCATION SEC SCHOOL MATHEMATICS SG 49 48 36 ST MARY'S COLLEGE MATHEMATICS SG 9 9 2 SUPREME EDUCATIONAL COLLEGE MATHEMATICS SG 21 20 2 BLUE HILLS COLLEGE (ST. PAULS COLLEGE) MATHEMATICS SG 41 40 23 EDEN COLLEGE MATHEMATICS SG 14 14 12 WITS TUTORIAL COLLEGE MATHEMATICS SG 17 13 2 JEPPE ADUL T EDUC CENTRE MATHEMATICS SG 16 16 6 ALLANRIDGE SEC SCHOOL MATHEMATICS SG 34 34 23 MARLBORO GARDENS SEC SCHOOL MATHEMATICS SG 13 13 10 BRYANSTON HIGH SCHOOL MATHEMATICS SG 95 95 88 CHINESE KUO TING SCHOOL MATHEMATICS SG 12 12 9 MIDRAND PARALLEL MEDIUM HIGH SCHOOL MATHEMATICS SG 67 66 49 NORTHVIEW HIGH SCHOOL MATHEMATICS SG 84 82 36 SANDOWN HIGH SCHOOL MATHEMATICS SG 43 42 21

29 WAVERLEY GIRLS' HIGH SCHOOL MATHEMATICS SG 35 34 34 WENDYWOOD HIGH SCHOOL MATHEMATICS SG 65 64 53 ALEXANDRA COMMERCIAL HIGH SCHOOL MATHEMATICS SG 22 22 1 ALEXANDRA SEC SCHOOL MATHEMATICS SG 96 92 31 EAST BANK HIGH SCHOOL MATHEMATICS SG 96 92 10 KWABHEKILANGA SEC SCHOOL MATHEMATICS SG 90 89 21 MINERVA SEC SCHOOL MATHEMATICS SG 93 89 12 REALOGILE SEC SCHOOL MATHEMATICS SG 78 76 20 UNITED SISTERHOOD MITZVAH MATHEMATICS SG 33 33 27 CRAWFORD SCHOOLS LONEHILL MATHEMATICS SG 23 23 23 CRAWFORD SANDTON SCHOOL MATHEMATICS SG 26 26 26 EQINISWENI SEC SCHOOL MATHEMATICS SG 123 118 25 UMQHELE SEC SCHOOL MATHEMATICS SG 157 156 61 IVORY PARK SEC SCHOOL MATHEMATICS SG 117 117 78 EMSHUKANTAMBO SEC SCHOOL MATHEMATICS SG 69 69 36 MUSI COMPR MATHEMATICS SG 80 80 5 PROGRESS COMPR SCHOOL MATHEMATICS SG 136 134 40 THABA-JABULA SEC SCHOOL MATHEMATICS SG 62 61 11 JOHANNESBURG SEC SCHOOL MATHEMATICS SG 49 49 22 GREENSIDE HIGH SCHOOL MATHEMATICS SG 58 57 42 HOER TEGNIESE SKOaL LANGLAAGTE MATHEMATICS SG 166 164 53 MCAULEY HOUSE SCHOOL MATHEMATICS SG 24 24 15 - PARKTOWN GIRLS' HIGH SCHOOL MATHEMATICS SG 73 73 72 ROOSEVELT HIGH SCHOOL MATHEMATICS SG 75 75 67 BONA COMPR SCHOOL MATHEMATICS SG 89 84 26 BOPHELO-IMPILO PRIVATE SCHOOL MATHEMATICS SG 13 13 3 LOFENTSE COMPR SCHOOL MATHEMATICS SG 72 70 22 ORLANDO SEC SCHOOL MATHEMATICS SG 83 77 17 RAUCALL SEC SCHOOL MATHEMATICS SG 40 40 40 SELELEKELA SEC SCHOOL MATHEMATICS SG 67 63 15 TASK ACADEMY SCHOOL MATHEMATICS SG 44 42 1: I NEW NATION SCHOOL MATHEMATICS SG 23 22 CHRIS J BOTHA SEC SCHOOL MATHEMATICS SG 48 47 22 CORONATIONVILLE SEC SCHOOL MATHEMATICS SG 29 27 4 1 NOORDGESIG SEC SCHOOL MATHEMATICS SG 71 70 141 30 R W FICK SEC SCHOOL MATHEMATICS SG 77 75 23 RIVERLEA SEC SCHOOL MATHEMATICS SG 39 39 15 WESTBURY SEC SCHOOL MATHEMATICS SG 114 112 8 HOERSKOOLVORENTOE MATHEMATICS SG 58 58 36 NORTHCLIFF HIGH SCHOOL MATHEMATICS SG 125 124 114 ST BARNABAS COLLEGE MATHEMATICS SG 9 9 6 BOPASENATLA SEC SCHOOL MATHEMATICS SG 43 40 7 DIEPDALE SEC SCHOOL MATHEMATICS SG 61 58 13 FIDELITAS COMPR SCHOOL MATHEMATICS SG 52 52 9 FaNS LUMINIS SEC SCHOOL MATHEMATICS SG 134 132 16 IMMACULATA SEC SCHOOL MATHEMATICS SG 68 68 21 MADIBANE COMPR SCHOOL MATHEMATICS SG 21 21 7 NAMEDI SEC SCHOOL MATHEMATICS SG 117 116 18 FERNDALE HIGH SCHOOL MATHEMATICS SG 57 57 25 FOURWAYS HIGH SCHOOL MATHEMATICS SG 98 98 87 HOERSKOOL LINDEN MATHEMATICS SG 31 31 30 HOERSKOOLRANDBURG MATHEMATICS SG 67 67 61 RAND PARK HIGH SCHOOL MATHEMATICS SG 126 125 117 ITIRELE-ZENZELE COMPR SCHOOL MATHEMATICS SG 101 96 26 KWENA MOLAPO COMPR FARM SCHOOL MATHEMATICS SG 23 22 22 SEKOLO SA BOROKGO MATHEMATICS SG 23 23 19 ST ANSGAR'S COMBINED SCHOOL MATHEMATICS SG 84 82 17 RADLEY COLLEGE MATHEMATICS SG 12 11 10 DIEPSLOOT COMBINED SCHOOL MATHEMATICS SG 19 18 18 BRANDCLIFF HOUSE PRIVATE SCHOOL MATHEMATICS SG 18 18 14 ENNERDALE SEC SCHOOL MATHEMATICS SG 88 85 7 AZARA SEC SCHOOL MATHEMATICS SG 22 22 13 LENASIA SEC SCHOOL MATHEMATICS SG 62 62 42 J SOUTHVIEW HIGH SCHOOL (LENASIA SOUTH NO. MATHEMATICS SG 55 55 32 LENASIA SOUTH SEC SCHOOL MATHEMATICS SG 48 48 29 MH JOOSUB TECHNICAL SEC SCHOOL MATHEMATICS SG 93 91 25 NIRVANA SEC SCHOOL MATHEMATICS SG 105 104 87 TOPAZ SEC SCHOOL MATHEMATICS SG 46 45 25 I TRINITY SEC SCHOOL MATHEMATICS SG 33 33 17 ! I

31 GLENVISTA HIGH SCHOOL MATHEMATICS SG 125 123 100 KWADEDANGENDLALE SEC SCHOOL MATHEMATICS SG 65 63 40 AURORACOMPRSCHOOL MATHEMATICS SG 77 74 33 DR BW VILAKAZI SEC SCHOOL MATHEMATICS SG 149 142 19 EMDENI SEC SCHOOL MATHEMATICS SG 48 46 10 FONTANUS COMPR SEC SCHOOL MATHEMATICS SG 50 47 7 WILLOWMEAD SEC SCHOOL MATHEMATICS SG 45 43 28 LAVELA SEC SCHOOL MATHEMATICS SG 99 98 8 LENZ PUBLIC SCHOOL MATHEMATICS SG 35 34 8 MAPETLA HIGH SCHOOL MATHEMATICS SG 28 27 17 NALEDI SEC SCHOOL MATHEMATICS SG 43 42 10 NGHUNGHUNYANICOMPR MATHEMATICS SG 58 56 6 PRUDENS SEC SCHOOL MATHEMATICS SG 24 24 15 REASOMA SEC SCHOOL MATHEMATICS SG 160 157 56 SEANA MARENA SEC SCHOOL MATHEMATICS SG 87 87 25 SEKANO-NTOANE SEC SCHOOL MATHEMATICS SG 42 42 12 SENAOANE SEC SCHOOL MATHEMATICS SG 73 71 28 TETELa SEC SCHOOL MATHEMATICS SG 101 101 34 THE AFRICA HOUSE COLLEGE MATHEMATICS SG 27 21 10 THABO SEC SCHOOL MATHEMATICS SG 77 73 29 THOMAS MOFOLO SEC SCHOOL MATHEMATICS SG 49 49 25 VUWANI SEC SCHOOL MATHEMATICS SG 128 127 28 FRED NORMAN SEC SCHOOL MATHEMATICS SG 51 51 33 ZAKARIYYA PARK SEC SCHOOL MATHEMATICS SG 18 18 15 LENASIA MUSLIM SCHOOL MATHEMATICS SG 35 35 34 MOSES MAREN MISSION TECHNICAL SEC MATHEMATICS SG 25 25 4 NUR-UL-ISLAM SCHOOL MATHEMATICS SG 7 7 0 OAKDALE SEC SCHOOL MATHEMATICS SG 93 92 40 ELETHU THEMBA SCHOOL MATHEMATICS SG 27 26 6 AL-AQSA SCHOOL MATHEMATICS SG 16 16 16 ELDORADO PARK SEC SCHOOL MATHEMATICS SG 41 41 39 i ! KLiPSPRUIT-WES SEC SCHOOL MATHEMATICS SG 68 68 16 I I KLiPTOWN SEC SCHOOL MATHEMATICS SG 46 46 81 LANCEA VALE SEC SCHOOL MATHEMATICS SG 86 85 3q

MISSOURILAAN SEC SCHOOL MATHEMATICS SG 33 33 11 I !

32 SILVER OAKS SEC SCHOOL MATHEMATICS SG 95 94 16 WILLOW CRESCENT SEC SCHOOL MATHEMATICS SG 44 44 14 FOREST HIGH SCHOOL MATHEMATICS SG 91 91 48 HOERSKOOL DIE FAKKEL MATHEMATICS SG 20 19 13 DIVERSITY HOER/HIGH SCHOOL MATHEMATICS SG 32 32 26 HOERSKOOL PRESIDENT MATHEMATICS SG 38 38 30 MONDEOR HIGH SCHOOL MATHEMATICS SG 126 126 115 SIR JOHN ADAMSON HIGH SCHOOL MATHEMATICS SG 115 115 58 THE HILL HIGH SCHOOL MATHEMATICS SG 65 65 51 ALTMONT TECHNICAL HIGH SCHOOL MATHEMATICS SG 85 85 25 BHUKULANI SEC SCHOOL MATHEMATICS SG 52 50 36 IBHONGO SEC SCHOOL MATHEMATICS SG 100 94 14 JABULANI TECHNICAL SEC SCHOOL MATHEMATICS SG 109 109 50 LETARE SEC SCHOOL MATHEMATICS SG 16 15 1 MAFORI MPHAHLELE COMPR SCHOOL MATHEMATICS SG 32 32 16 MOLETSANE SEC SCHOOL MATHEMATICS SG 72 71 23 PACE SEC PRIVATE SCHOOL MATHEMATICS SG 15 15 4 PHAFOGANG SEC SCHOOL MATHEMATICS SG 65 65 4 SPARROW COMBINED MATHEMATICS SG 7 7 2 JOHANNESBURG POLYTECH INSTITUTE MATHEMATICS SG 16 16 4 HIS MAJESTY EDUCATIONAL INSTITUTE MATHEMATICS SG 70 62 13 HORIZON INTERNATIONAL HIGH SCHOOL MATHEMATICS SG 4 4 3 DAMELIN COLLEGE - JOHANNESBURG MATHEMATICS SG 16 16 11 JOHN ORR TECHNICAL HIGH SCHOOL MATHEMATICS SG 105 103 71 NATIONAL SCHOOL OF THE ARTS MATHEMATICS SG 33 33 31 SHEIKH ANTA DIOP COLLEGE MATHEMATICS SG 15 15 5 ABC ACADEMY PRIVATE SCHOOL MATHEMATICS SG 53 50 16 AFRO-KOMBS COLLEGE MATHEMATICS SG 26 26 7 ASTRA COLLEGE MATHEMATICS SG 20 10 3 AVONDALE GIRLS HIGH MATHEMATICS SG 11 11 7 BANTORI COLLEGE MATHEMATICS SG 34 33 BASA TUTORIAL INSTITUTE MATHEMATICS SG 26 26 ~ BEKEZELA COLLEGE MATHEMATICS SG 8 8 5 DALIWONGA SEC SCHOOL MATHEMATICS SG 56 56 3 EDUCATION ALIVE SCHOOL MATHEMATICS SG 18 18 10

33 FREEDOM COMMUNITY COLLEGE MATHEMATICS SG 42 40 13 KNOWLEDGE IS VIRTUE ACADEMY MATHEMATICS SG 22 21 1 LIBERTY COMMUNITY SCHOOL MATHEMATICS SG 36 36 12 LOBONE SEC SCHOOL MATHEMATICS SG 86 77 8 MAHLASEDI HIGH SCHOOL MATHEMATICS SG 10 7 0 MNCUBE SEC SCHOOL MATHEMATICS SG 86 85 13 MORRIS ISAACSON SEC SCHOOL MATHEMATICS SG 213 208 25 NEW MODEL PRIVATE COLLEGE MATHEMATICS SG 4 4 0 PHOENIX COLLEGE OF JOHANNESBURG MATHEMATICS SG 14 13 6 DR BEYERS NAUDE SEC SCHOOL MATHEMATICS SG 25 24 5 PROVIDENCE ACADEMY MATHEMATICS SG 52 50 23 ROBIN HOOD PRIVATE SEC SCHOOL MATHEMATICS SG 39 26 3 ST MATIHEWS PRIVATE SEC SCHOOL MATHEMATICS SG 43 43 43 UNITED CHURCH PREPARATORY SCHOOL MATHEMATICS SG 17 17 14 VECTOR COMBINED SCHOOL MATHEMATICS SG 98 91 28 ADELAIDE TAMBO (J C MERKIN WHITE CITY MATHEMATICS SG 19 18 2 JOHANNESBURG MUSLIM SCHOOL MATHEMATICS SG 31 31 29 EKUKHANYENI MATHEMATICS SG 28 23 9 JORDAO COLLEGE MATHEMATICS SG 11 11 5 METROPOLITAN COLLEGE MATHEMATICS SG 25 23 7 THUSA-SETJHABA SEC SCHOOL MATHEMATICS SG 86 83 12 AHA-THUTO SEC SCHOOL MATHEMATICS SG 163 162 48 ISIKHUMBUZO HIGH SCHOOL MATHEMATICS SG 42 40 6 TSHEBETSO HIGH SCHOOL MATHEMATICS SG 1 1 0 JOHWETO PRIVATE PRIMARY SCHOOL MATHEMATICS SG 5 4 4 LESHATA SEC SCHOOL MATHEMATICS SG 37 37 19 QOQA SEC SCHOOL MATHEMATICS SG 26 21 18 RAPHELA SEC SCHOOL MATHEMATICS SG 121 116 43 THAMSANQA SEC SCHOOL MATHEMATICS SG 74 74 15 VULANINDLELA SEC MATHEMATICS SG 80 70 11 SAKHISIZWE SEC SCHOOL (WEILERS PUBLIC) MATHEMATICS SG 36 33 19 JABULILE SEC SCHOOL MATHEMATICS SG 81 78 21 THETHA SEC SCHOOL MATHEMATICS SG 41 40 5 SIYAPHAMBILI HIGH SCHOOL MATHEMATICS SG 28 26 7 THULA MNTWANA COMB SCHOOL MATHEMATICS SG 9 9 3

34 MPHETHI MAHLATSI SEC SCHOOL MATHEMATICS SG 60 59 7 IN-TUITION COLLEGE MATHEMATICS SG 8 8 5 ITHUBA-LETHU SEC SCHOOL MATHEMATICS SG 68 65 6 ANCHOR COMPR MATHEMATICS SG 50 49 15 EMADWALENI SEC SCHOOL MATHEMATICS SG 22 21 11 ORLANDO WEST SEC SCHOOL MATHEMATICS SG 51 50 24 PHEFENI SEC SCHOOL MATHEMATICS SG 50 50 11 ST MARTIN DE PORRES HIGH SCHOOL MATHEMATICS SG 19 19 13 KELOKITSO COMPR SCHOOL MATHEMATICS SG 57 57 15 KWA-MAHLOBO SEC SCHOOL MATHEMATICS SG 22 22 8 LAMULA JUBILEE SEC SCHOOL MATHEMATICS SG 44 44 27 LETSIBOGO SEC SCHOOL MATHEMATICS SG 52 51 15 MATSELISO SEC SCHOOL MATHEMATICS SG 100 98 46 MEADOWLANDS SEC SCHOOL MATHEMATICS SG 37 37 15 MOKGOME SEC SCHOOL MATHEMATICS SG 37 37 19 THUTOLORESECSCHOOL MATHEMATICS SG 112 111 27 VERITAS SEC SCHOOL MATHEMATICS SG 25 25 2 FLORIDA PARK HIGH SCHOOL MATHEMATICS SG 124 122 69 HOERSKOOL DIE ADELAAR MATHEMATICS SG 14 14 14 HOERSKOOL DIE BURGER MATHEMATICS SG 49 49 33 HOERSKOOL FLORIDA MATHEMATICS SG 102 102 93 HOERSKOOLROODEPOORT MATHEMATICS SG 112 111 98 LANTERNSKOOL MATHEMATICS SG 7 7 6 PRINCESS HIGH SCHOOL MATHEMATICS SG 113 113 88 WEST RIDGE HIGH SCHOOL MATHEMATICS SG 132 132 97 FORTE SEC SCHOOL MATHEMATICS SG 112 111 53 GEORGEKHOSASECSCHOOL MATHEMATICS SG 41 39 19 PJ SIMELANE SEC SCHOOL MATHEMATICS SG 68 68 48 SEBETSA-O-THOLEMOPUTSO MATHEMATICS SG 29 29 8 TULIP SEC SCHOOL MATHEMATICS SG 14 14 9 ALLEN GLEN HIGH SCHOOL MATHEMATICS SG 100 100 87 VICTORY HOUSE PRIVATE SCHOOL MATHEMATICS SG 7 7 5 WISE-UP COMBINED SCHOOL MATHEMATICS SG 13 12 4 DOORNKOPSENSECSCHOOL MATHEMATICS SG 47 47 11

35 APPENDIXG

HIGH SCHOOLS

THAT PARTICIPATED IN AS INTERVENTION " t $~O04 2005 2006 l'l::lmA ,<, 0/0 Passed % Passed GN 211540 ABEL MOTSHOANE SEC SCHOOL 48.00 25.64 50.00 GN 922475 AHA-THUTO SEC SCHOOL 50.09 GW 271502 ALTMONT TECHNICAL HIGH SCHOOL 41.24 57.36 44 GW 270025 ASSER MALOKA SEC 73.33 80.85 62.50 GW 400120 BOIKGETHELO SEC SCHOOL TN 240895 BOITUMELONG SEC SCHOOL 41.61 54.86 59.49 TN 240929 BONA COMPR SCHOOL 62.96 44.40 45.27 TN 240960 BOPASENATLA SEC SCHOOL 38.93 47.10 48.15 TN 241273 BOTEBO-TSEBO SEC SCHOOL 59.29 51.60 49.28 TW 240747 CORONATIONVILLE SEC SCHOOL 84.03 78.97 63.64 TS 220699 COSMOCITY 57.52 58.78 57.14 TS 221184 D.A. MOKOMA SEC SCHOOL 50.78 38.46 38.78 TS 231639 DAUWONGA SEC SCHOOL 41.86 56.36 56.96 TS 220855 DAVEY SEC SCHOOL 64.71 87.80 67.47 TS 221028 DIEPDALE SEC SCHOOL 49.08 81.25 65.63 GE 310979 DINOKANENG SEC SCHOOL 49.58 57.83 36.36 GE 311464 DR. MOTSUENYANE SEC SCHOOL 30.91 44.34 52.00 EAST BANK HIGH SCHOOL 90.38 GE 350074 68.28 52.10-- GE 350561 ED MASHABANE SEC SCHOOL 55.19 47.24 44.85 ~---- GE 350959 EDENPARK SEC SCHOOL 66.32 36.00 37.70 ES 161752 EDWARD PHATUDI SEC SCHOOL 74.56 65.22 56.59 ES 161802 EKETSANG SEC SCHOOL 45.99 29.95 44.88 ES 162099 EMDEN I SEC SCHOOL 43.09 33.01 22.68 -~ EN 260620 ENNERDALESECSCHOOL 46.32 50.00 57~~ EN 260836 EQINISWENI SEC SCHOOL 42.75 45.81 48.47 EN 260976 ERASMUS MONARENG SEC SCHOOL 70.00 46.11 53.01 EN 261073 EUREKA HIGH SCHOOL 68.75 87.50 57.14 EN 261479 FONTANUS COMPR SEC 50.56 45.39 46.73 FR. SMANGALISO MKHATSHWA SEC. ES 340026 SCHOOL 66.93 38.05 52.12 ES 340331 FUMANA SEC SCHOOL 62.34 63.96 54.88 ES 340562 GA-RANKUWA TECHN. HIGH SCHOOL 48.70 30.04 3~ ES 340604 HL SETLALENTOA SEC SCHOOL 41.78 44.49 46.98 ES 340711 HLOMPHANANG SEC SCHOOL 73.33 39.45 18.75 ES 340802 I.R. LESOLANG SEC SCHOOL 28.36 27.27 41.18 ES 340844 IBHONGO SEC SCHOOL 66.33 51.40 54.61 ES 340984 IKUSASA COMPR SCHOOL 30.81 30.83 35.65 ES 341040 ILUNGE SEC SCHOOL 32.04 32.45 45.19 ES 341123 ISIZWE-SETJHABA SEC SCHOOL 62.57 50.26 57.92 ES 341347 J KEKANA SEC SCHOOL 25.16 27.70 27.96

1 ES 341370 JET NTEO SEC SCHOOL 71.60 47.47 43.92 ES 341511 JIYANA SEC SCHOOL 31.25 42.20 30.13 ES 341594 JOHN ORR TECHNICAL HIGH SCHOOL 44.09 26.29 45.37 ES 160069 JORDAN SEC SCHOOL 60.36 91.95 79.81 EN 261065 KATLEHO-IMPUMELELO SEC SCHOOL 79.31 76.30 63.50 SE 330860 KATLEHONG SEC SCHOOL 75.41 53.47 45.52 GE 351296 KATLEHONG TECH SS 36.67 70.15 41.28 SW 320325 KELOKITSO COMPR SCHOOL 52.78 45.45 41.46 SW 320358 KGADIME MATSEPE SEC 71.28 64.75 43.02 SW 320432 KLiPSPRUIT-WES SEC SCHOOL 45.96 38.58 37.98 SW 320457 KWABHEKILANGA SEC SCHOOL 38.00 23.81 30.39 SW 320663 KWADUKATHOLE COMPR SCHOOL 83.17 34.82 26.62 SW 320671 KWA-MAHLOBO SEC SCHOOL 43.90 46.34 51.22 SW 320689 L.G. HOLELE SEC SCHOOL 70.77 52.94 41.88 SW 320788 LEBOHANG SEC SCHOOL 66.67 51.16 30.69 SW 320895 LENZ PUBLIC SCHOOL 78.57 40.63 45.97 SW 320960 LETARE SEC SCHOOL 70.09 41.44 21.96 SW 321026 LETHABONG SEC SCHOOL 49.65 46.09 26.47 SW 321083 LETHUKUTHULA SEC 77.66 61.06 47.79 SW 321091 LOBONE SEC SCHOOL 64.58 59.04 41.33 SW 321109 M.H. BALOYI SEC SCHOOL 86.02 82.98 66.67 SW 321281 MAHARENG SEC SCHOOL 52.00 48.65 16.67 SW 321307 MAKHOSINI COMBINED SEC SCHOOL 72.85 60.78 47.29 SW 321364 MASISEBENZE COMPR SCHOOL 42.50 28.57 9.09 SW 321380 MAXEKE SEC SCHOOL 73.96 55.66 52.78 SW 321372 MEHLARENG COMBINED FARM SCHOOL 23.91 SW 321406 MEMEZELO SEC SCHOOL 53.13 34.77 35.11 SW 321414 MH JOOSUB TECHNICAL SEC SCHOOL 24.49 38.96 41.98 SW 321430 MINERVA SEC SCHOOL 69.44 33.33 38.46 SW 321455 MNCUBE SEC SCHOOL 49.23 45.87 43.80 SW 321497 MODIRI TECHNICAL SCHOOL 20.37 51.52 54.55 SW 321505 MOHALADITOE SEC SCHOOL 59.84 44.14 48.51 SW 321521 MOPHOLOSI SEC SCHOOL 54.81 23.68 41.47 SW 321570 MOQHAKA SEC SCHOOL 28.02 27.75 28.3_~ MOSHATE SEC SCHOOL 60.95 20.74 16.36 SW 321604 --- SW 321638 MPHETHI MAHLATSI SEC SCHOOL 24.35 25.65 27.88 SW 321703 MPHUMELOMMUHLE SEC SCHOOL 56.80 40.11 2607 JE 152090 MPILISWENI SEC SCHOOL 49.66 40.68 53.08 JE 152207 MUSI COMPR 30.92 48.97 48.51 JE 152264 NAMEDI SEC SCHOOL 40.00 50.00 58.00 JE 260760 NEW NATION SCHOOL 89.69 84.54 72.73 JE 150318 NGHUNGHUNYANICOMPR 96.55 100.00 89.74 IN 121608 NKUMBULO SEC SCHOOL 69.49 55.56 53.13 IN 131961 NOORDGESIG SEC SCHOOL 30.89 21.78 48.83 IN 132670 NTOMBIZODWA SEC 48.39 53.33 40.00 IN 133348 ODI HIGH SCHOOL 37.93 14.75 54.84 IN 140053 ORLANDO SEC SCHOOL 58.14 48.00 45.64

2 IN 140087 PARKLANDS HIGH SCHOOL 76.14 46.09 50.77 IN 140095 POELANO SEC SCHOOL 55.86 46.36 56.77 IN 140111 PONEGO SEC SCHOOL 64.66 64.89 57.39 IN 140137 QEDILlZWE SEC SCHOOL 50.83 62.77 55.64 IN 140426 RWFICK SEC SCHOOL 30.14 34.78 53.45 IN 140434 RAMOLELLE INTERMEDIATE 57.14 46.84 47.06 IN 140848 RAMOSUKULA SEC SCHOOL 59.24 35.93 48.54 IN 152363 RANDFONTEIN SEC SCHOOL 67.59 30.77 52.38 IN 400180 RANTAILANE SEC SCHOOL JC 121210 RAPHELA SEC SCHOOL. 87.12 84.44 74.31 JS 330696 REIGER PARK NR 2 SEC SCHOOL 72.51 84.50 61.29 JC 132043 RESIDENSIA SEC SCHOOL 58.02 80.61 62.83 JS 130708 RIVERLEA SEC SCHOOL 93.20 97.20 86.72 JS 331215 RIVONI SEC SCHOOL 87.65 73.95 61.61 JS 110023 SANDTONVIEW COMBINED SCHOOL 43.48 70.00 44.53 JS 331504 SAPPHIRE SEC SCHOOL 61.33 59.41 40.48 JS 331950 SEBOKENG TECH HIGH SCHOOL 25.00 JC 110247 SEHOPOTSO SEC SCHOOL 64.67 72.29 55.24 JC 110643 SENAOANE SEC SCHOOL 40.54 33.15 59.80 JC 110692 SENTHIBELE SENIOR SEC 24.14 29.79 43.04 JC 110890 SETJHABA-SOHLE SEC 74.60 67.19 57.89 JC 111120 SIMUNYE SEC SCHOOL 30.12 58.67 37.61 JC 111260 SIZANANI THUSANANG COMPR SCHOOL 45.14 57.09 47.37 JC 120188 ST ANSGAR'S COMBINED SCHOOL 65.66 47.41 33.08 JC 121392 STANZA BOPAPE SEC SCHOOL 26.19 36.53 37.60 JC 121491 STRAUSS SEC 63.83 50.00 51.69 JC 132431 TMLETLHAKE SEC SCHOOL 51.65 20.69 38.46 JC 132498 TANDUKWAZI SEC SCHOOL 39.23 30.22 30.50 JW 140665 THARABOLLO SEC SCHOOL 54.84 65.57 59.63 JW 140624 THOKO THABA SEC 79.79 92.65 81.48 TW 910953 THUTO·TIRO COMPR . 59,67 54,84 TW 910553 TIISETSONG SEC SCHOOL --- TW 910007 TIPFUXENI SEC SCHOOL 54,90 TW 914249 TOKELO SEC SCHOOL 38,89 TSHEPO-THEMBA SEC SCHOOL 51,46 TN 912338 --- TW 912270 TSOLO SEC SCHOOL 53,75 TW 910253 TSWAING SEC SCHOOL 55,35 TW 914251 VLAKFONTEIN SEC SCHOOL 39,52 TW 914249 VOSLOORUS COMPR SEC 49,2 TW 910794 VULANINDELA SEC SCHOOL 43,1 TW 911556 WESTBURY SEC SCHOOL 55,4 TW 911749 WINILE SEC SCHOOL 52,8 TW 240762 WINTERVELDT HIGH SCHOOL 56.28 67.79 46.94 TW 914110 ZIKHETHELE SEC SCHOOL 25,4 TN 912139 ZITIKENI SEC SCHOOL 49