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THE IMPACT OF MATHEMATICS INTERVENTIONS IN HIGH SCHOOLS: A MIXED METHOD INQUIRY by DUDUZILE ROSEMARY MKHIZE THESIS submitted in fulfillment of the requirements for the degree PHILOSOPHAE DOCTOR in 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