THE LOGIC & UTILITY OF MATHEMATICS
CONTENTS CHAPTER 1: AN EMERGENT SOCIAL, CULTURAL, POLITICAL APPROACH: SKETCHING A THEORETICAL LANDSCAPE 1 MATHEMATICS EDUCATION AFTER APARTHEID? 2 FOUR STRANDS OF A SOCIAL, CULTURAL, POLITICAL APPROACH 21 A CRITICAL MATHEMATICS EDUCATION FOR ALL 22 A “CRITICAL ETHNOMATHEMATICS” EDUCATION 23 DIMENSIONS OF DIVERSITY: A CRITICAL PERSPECTIVE IN MATHEMATICS EDUCATION THROUGH A FOCUS ON GENDER 24 A CRITICAL PERSPECTIVE IN THE SOUTH AFRICAN CONTEXT: PEOPLE’S MATHEMATICS 3 PULLING THE THEORETICAL STRANDS TOGETHER THROUGH EDUCATIONAL PRACTICE: THE CASE OF PROJECT WORK 4 CONTEXTUALISING THIS LANDSCAPE CHAPTER 2: METHODOLOGICAL “THEORETICAL TOOLS” FOR RESEARCHING A SOCIAL, CULTURAL, POLITICAL APPROACH 1 A RESEARCH JOURNEY 2 THE ACTUAL CURRENT SITUATION 21 TEACHER EDUCATION, STUDENT TEACHERS AND TEACHING PRACTICE 22 SCHOOL MATHEMATICS CURRICULA AND REFORMS 3 THE IMAGINED HYPOTHETICAL SITUATION 31 INITIATING STUDENT TEACHERS’ HYPOTHETICAL IMAGINATION – DURING COURSEWORK 32 DEVELOPING STUDENT TEACHERS’ HYPOTHETICAL IMAGINATION – GETTING READY FOR PRACTICE 4 THE ARRANGED SITUATION 41 IN THE ARRANGED SITUATION 42 AFTER THE ARRANGED SITUATION 5 REFLECTIONS ON THE SITUATIONS 51 POTENTIALITY 52 INTERVENTION, IMPLEMENTATION OR IMPOSITION 53 CONNECTING THE SITUATIONS 54 TRANSFORMACY 6 CONCLUSION CHAPTER 3: METHODOLOGICAL CHALLENGES AND CRITERIA FOR RESEARCHING A SOCIAL, CULTURAL, POLITICAL APPROACH 1 INTRODUCTION: RESEARCH PARADIGMS 2 A CRITICAL APPROACH TO RESEARCH VERSUS A CRITICAL APPROACH TO EDUCATION 3 SOURCES FOR DEVELOPING A RESEARCH METHODOLOGY FOR A CRITICAL PERSPECTIVE IN MATHEMATICS EDUCATION 31 THE SEARCH INSIDE MATHEMATICS EDUCATION 32 THE SEARCH OUTSIDE MATHEMATICS EDUCATION 4 THE RESEARCHER; RESEARCH PARTICIPANTS; AND THE RESEARCH PROCESS 41 RESEARCHER AND THE RESEARCH PARTICIPANTS 42 RESEARCH PARTICIPANTS AND THE RESEARCH PROCESS 43 THE RESEARCHER AND THE RESEARCH PROCESS 5 IS MY RESEARCH CRITICAL RESEARCH? 6 CRITERIA IN A RESEARCH METHODOLOGY FOR A CRITICAL PERSPECTIVE IN MATHEMATICS EDUCATION 61 VALIDITY IN TRANSFORMATION AND IN ACTION 62 VALIDITY CONCERNS IN MY RESEARCH 63 DEMOCRATIC PARTICIPATORY VALIDITY 64 GENERALISABILITY AND GENERATIVITY 7 CONTEXT IN A RESEARCH METHODOLOGY FOR A CRITICAL PERSPECTIVE IN MATHEMATICS EDUCATION 8 CONCLUSION: CRITIQUE INWARD AND OUTWARD CHAPTER 4: CRUCIAL DESCRIPTIONS: TOWARD CRITIQUE OF THEORY, PRACTICE AND RESEARCH 1 INTRODUCTION 2 CRUCIAL DESCRIPTIONS AND THEORY-PRACTICE RELATIONS 3 CRUCIAL DESCRIPTIONS AND RESEARCH 31 TRANSPARENCY 32 TRANSFORMACY 33 GENERATIVITY 34 EXEMPLARITY 4 CONCLUSION CHAPTER 5: CRUCIAL DESCRIPTION OF A SOCIAL, CULTURAL, POLITICAL APPROACH: PART I – SUMAIYA AND THE IMAGINED HYPOTHETICAL SITUATION 2 ABOUT SUMAIYA 3 SUMAIYA IN HER THIRD YEAR: INTRODUCTION TO A NEW CURRICULUM APPROACH 4 SUMAIYA IN HER FOURTH YEAR: PREPARING FOR TEACHING PRACTICE 41 AN IMAGINED HYPOTHETICAL TEACHER 42 IMAGINED HYPOTHETICAL PUPILS 43 IMAGINED HYPOTHETICAL PROJECT IDEAS 44 IMAGINED HYPOTHETICAL PROJECT WORK ISSUES 5 SUMAIYA IN THE ACTUAL CURRENT SITUATION: THE SCHOOL, THE TEACHER, AND THE CLASS CHAPTER 6: CRUCIAL DESCRIPTION OF A SOCIAL, CULTURAL, POLITICAL APPROACH: PART 2 – SUMAIYA AND THE ARRANGED SITUATION 2 PROJECT WORK BEGINS 21 REFLECTIONS OF DAY 3: PROJECT WORK ISSUES 22 REFLECTIONS OF DAY 3: GROUP WORK ISSUES 23 REFLECTIONS OF DAY 3: TEACHING AND LEARNING MATHEMATICS ISSUES 3 GROUP 1: TIME SPENT AFTER SCHOOL 31 REFLECTIONS ON GROUP 1: GROUP WORK ISSUES 32 REFLECTIONS ON GROUP 1: PROJECT WORK ISSUES 33 REFLECTIONS ON GROUP 1: TEACHING AND LEARNING MATHEMATICS ISSUES 4 GROUP 2: DEVELOPING A MATHEMATICS NEWSLETTER 41 REFLECTIONS ON GROUP 2: GROUP WORK ISSUES 42 REFLECTION ON GROUP 2: PROJECT WORK AND MATHEMATICS TEACHING AND LEARNING ISSUES 5 GROUP 4: THE SPORTS SURVEY 51 REFLECTION ON GROUP 4: GROUP WORK ISSUES 52 REFLECTION ON GROUP 4: PROJECT WORK AND MATHEMATICS TEACHING AND LEARNING ISSUES 6 GROUPS 3 AND 5: MONEY SPENT ON MY EDUCATION 61 GROUP 3: MONEY SPENT ON MY EDUCATION 62 GROUP 5: MONEY SPENT ON MY EDUCATION 63 REFLECTIONS ON GROUP 3 AND 5: GROUP WORK ISSUES 64 REFLECTIONS ON GROUP 3 AND GROUP 5: PROJECT WORK ISSUES 65 REFLECTIONS ON GROUP 3 AND GROUP 5: MATHEMATICS TEACHING AND LEARNING ISSUES CHAPTER 7: FROM DESCRIPTION TO THEMES 2 STRUCTURE AND FREEDOM 3 AUTHORITY AND DEMOCRACY 4 MATHEMATICS AND CONTEXT 5 DIFFERENTIATION AND EQUITY 6 ACTUALITY AND POTENTIALITY CHAPTER 8: FROM THEMES TO THEORETICAL LANDSCAPE 2 COMPLEMENTARITY 3 FREEDOM AND STRUCTURE 4 DEMOCRACY AND AUTHORITY 5 CONTEXT AND MATHEMATICS 6 EQUITY AND DIFFERENTIATION 7 POTENTIALITY AND ACTUALITY CHAPTER 9: A PEDAGOGY OF CONFLICT AND DIALOGUE 2 PEDAGOGY, THEORY AND PRACTICE 3 CONFLICT IN A MATHEMATICS PEDAGOGY 4 DIALOGUE IN A MATHEMATICS PEDAGOGY 5 COMPLEMENTARITY IN A PEDAGOGY OF CONFLICT AND DIALOGUE 6 STRENGTHS AND WEAKNESSES; LIMITATIONS AND DREAMS REFERENCES