Teaching and learning mathematics in Karachi’s low-cost private schools Asyia Kazmi Thesis submitted in fulfilment of the requirements for the degree of Doctor of Education University College London Institute of Education Curriculum, Pedagogy and Assessment July 2019 1 Declaration I, Asyia Kazmi confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. Word count (exclusive of appendices, the list of references and bibliographies but including footnotes, endnotes, glossary, maps, diagrams and tables): 45,096 words. Asyia Kazmi July 2019 2 Abstract To improve learning-outcomes teaching quality matters. However, research into teaching in low- and middle-income countries (L&MIC) is limited, particularly in mathematics and the rapidly rising low-cost private sector (LCPS). The purpose of this research is to study mathematics teaching and learning in Karachi’s LCPS by exploring four related aspects: who attends Karachi’s LCPS- school; the values that underpin LCPS teachers’ instructional and professional practices; the instructional practices teachers use to teach mathematics; and the institutional environment that supports or hinders the development of mathematics teaching practice. Five key components of effective teaching underpinned by communicative pedagogies are explored in this study in relation to LCPS teachers’ practice: planning and preparation; a conducive classroom environment; effective instructional practices; independent practice and summative assessment; and teachers’ role as professionals. Employing a mixed-method case-study approach, this study uses primary data gathered through lesson observations and interviews conducted in five pilot and two in-depth case-study LCPS- schools, and secondary quantitative data. This thesis employs a pragmatic perspective on the school effectiveness and improvement research framework and argues for its greater use in identifying good practice in L&MIC. LCPS teachers are unqualified, untrained and poorly paid but driven by a strong sense of moral purpose underpinned by a transformational view of education. They exhibit a continuum of practice from novice to expert with the latter reflecting the same components of effective practices found in HIC literature. My findings show LCPS teachers can be supported to become expert through a systematic programme of professional development and a supportive accountability framework. Therefore, this study argues for support to be provided to LCPS teachers on developing students’ conceptual understanding, embedding formative assessment and promoting mathematical communication. It concludes with recommendations for policymakers to engage with the LCPS at a systemic level to promote equity and improve learning. 3 Dedicated to my father Syed Abdul Hakeem Kazmi 1936 - 2013 Knowledge exists potentially in the human soul like the seed in the soil; by learning, the potential becomes actual. The teacher must adapt their teaching to the pupils’ capacity and ability. Al-Ghazali (circa 1010) 4 Acknowledgements My heartfelt thanks to my supervisors Dr Clare Bentall and Professor Candia Morgan for their patience and perseverance. I truly appreciated their detailed and challenging supervision of my thesis. Thank you to all my teachers and a sincere thank you to the teachers of my pilot and case-study schools. I valued the time they gave to me and their engagement with my work. Their commitment and enthusiasm continues to inspire me. Undertaking a professional doctorate, it would be remiss of me to not acknowledge the support provided by my colleagues in the DfE, DFID, Ofsted and PwC as well as the amazing tutors and students on the EdD programme. Throughout my doctorate journey I have been blessed with amazing family and friends who encouraged, supported and cajoled: ▪ I would not be where I am today without Teresa Smart, my friend and my mentor ▪ My brothers and sisters, especially Sadyia, thank you ▪ My sons, you can stop lecturing me to finish now ▪ My husband, thank you for your unwavering support. Finally, thank you to my father, who sacrificed so much. He taught us that seeking knowledge is an obligation and he taught us to value knowledge and learning above possessions. May we all continue this legacy. 5 Contents Table of Figures .............................................................................................. 11 List of Acronyms ............................................................................................. 12 Personal Statement ........................................................................................ 13 Chapter 1 Introduction.................................................................................... 19 The rationale for this research ................................................................ 19 A focus on mathematics teaching........................................................... 20 The rapid rise of low-cost private schooling in Pakistan ......................... 21 The case for school effectiveness and improvement research lens ....... 24 Overview of the thesis ............................................................................ 25 Chapter 2 Literature review: Teaching and learning in low- and middle- income countries .................................................................................. 27 Introduction ............................................................................................ 27 2.1.1 Definitions ............................................................................................... 28 Teaching and teachers in L&MIC ........................................................... 28 2.2.1 Improve teaching to improve learning .................................................... 28 2.2.2 The context in which LCPS teachers work ............................................. 29 2.2.3 Summary ................................................................................................ 31 Teaching and pedagogy ......................................................................... 31 2.3.1 Defining teaching .................................................................................... 32 2.3.2 Defining Pedagogy ................................................................................. 33 2.3.3 Summary ................................................................................................ 34 Towards a framework for defining good teaching in L&MIC ................... 35 2.4.1 Knowledge of educational goals, purposes and values; and contexts .... 36 Expectations in mathematics ..................................................... 37 2.4.2 Knowledge of students and their characteristics .................................... 40 Students of mathematics ........................................................... 40 Adapting teaching to meet the needs of students ...................... 41 2.4.3 Curriculum knowledge ............................................................................ 42 2.4.4 Content knowledge ................................................................................. 43 2.4.5 General pedagogical knowledge ............................................................ 45 6 Planning and preparation ........................................................... 46 Classroom environment ............................................................. 46 Instructional practices ................................................................ 48 Independent practice and summative assessment .................... 55 Teachers as professionals ......................................................... 57 Summary ................................................................................... 58 2.4.6 Pedagogical content knowledge ............................................................. 58 2.4.7 Summary ................................................................................................ 61 Conclusion ............................................................................................. 61 2.5.1 Implications for research design ............................................................. 62 Chapter 3 Methodology .................................................................................. 65 Introduction ............................................................................................ 65 3.1.1 Context ................................................................................................... 66 Research methodology overview: mixed-method, case-study research. 66 3.2.1 Overview of data collection approach ..................................................... 68 Quantitative data about the student population ...................................... 70 Qualitative data from pilot and case-study schools ................................ 71 3.4.1 Selection of, and access to, the pilot case-study schools ....................... 71 3.4.2 Observations .......................................................................................... 72 Observations of the context and environment............................ 73 Observation of teaching ............................................................. 74 Observing students’ books......................................................... 80 Field notes ................................................................................. 80 3.4.3 Interviews with teachers and senior leaders ..........................................