Developing Primary Mathematics Teaching: Reflecting on Practice with the Knowledge Quartet

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Tim Rowland, Fay Turner, Anne Thwaites & Peter Huckstep

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  • Front Matter
  • Subject Index
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    List of Figures

    List of Tables

    • Table 2.1 Some suggestions for improving your knowledge for teaching mathematics 25
    • Table 2.2 The codes of the Knowledge Quartet 29
    • Table 2.3 Guidelines for observing, supporting and assessing the level of trainee teachers teaching mathematics 35
    • Table 3.1 Resources for mathematics teaching 43
    • Table 7.1 The different structures of subtraction 166
    • Table 8.1 The lessons 197
    • Table 8.2 Knowledge Quartet lesson reflection proforma 225

    Index of Teachers and Lessons

    Acknowledgements

    We acknowledge with thanks and gratitude the assistance of the many people who have contributed to the development and production of this book. In particular we thank Jane Warwick for her contribution to the research which is at the heart of the book, David Thwaites for expert help with video editing, and Jamie Turner for his imaginative work on the cover photographs. The book would never have come into being without the collaboration of the many teacher-participants whose lessons are featured in it. Their willingness to offer their practice for others to reflect on, warts and all, demonstrates their commitment to the improvement of mathematics teaching – their own, and that of the readers of this book.

    Introduction

    This book differs, in some significant ways, from other books on primary mathematics teaching. A short explanation of who the book was written for, what it is intended to do, and how best to use it, may therefore be helpful.

    The book is for primary mathematics teachers and those who support their professional development in schools, local authorities and universities. It will be especially useful to student teachers (sometimes called ‘trainees’ in England) and early-career teachers, for whom the information in the book is likely to be novel. But the heart of this book is not so much information, as a process of structured reflection whereby teachers – at any stage of their career – can take control of the development of their expertise in teaching mathematics. The reflective process is the outcome of five years of research at the University of Cambridge. It is built on a framework which enables teachers and teacher educators to engage critically with actual lessons and teaching episodes – their own, or others' – with the aim of learning from teaching-in-action. We call our framework The Knowledge Quartet: because it is in four parts, and because it is a way of building up professional knowledge for mathematics teaching. A full explanation is given in Chapter 2.

    Theory and practice are interwoven throughout the book. In each chapter you will find:

    • justification for the focus of the chapter;
    • some exposition related to the topic, or some illuminating aspect of it;
    • tasks – things for you to think about and discuss, where possible, with colleagues;
    • descriptions of actual lessons, or episodes from lessons, for you to consider, discuss and analyse. Some of these episodes can be viewed as video clips on the book's companion website;
    • our own reflections and analytical comments on these lessons and episodes.

    The final chapter is devoted to accounts, tasks and analyses relating to a wide range of classroom scenarios, all taken from actual lessons taught by beginning or early-career teachers.

    Each chapter can be read on its own, but you will gain most from the book if you read Chapters 1 and 2 first. Chapter 2, in particular, explains the Knowledge Quartet, the framework for reflection which features throughout Chapters 3 to 8.

    Of course, the book can be read at home, or on the bus or the train. It is also recommended as a stimulus for group work and plenary discussion in teacher education settings and in continuing professional development. The Knowledge Quartet framework is also ideally suited for use in the improvement of teaching through lesson observation, both within initial teacher education and ongoing teaching development. In these various settings, the observer could be a mentor, tutor, colleague, subject coordinator or school manager of some kind. We would add, however, that we wrote this book so that teachers at different career stages might be encouraged and supported, and not as a means for them to be judged. The key to this positive, critical support is to allow time – if only 15 minutes – for post-lesson review and discussion, shared by teacher and observer, and structured by the Knowledge Quartet.

    We hope that readers will find the book enjoyable, useful and informative: we welcome any feedback on the content, and on the ways that the book is being used.

    TimRowland, FayTurner, AnneThwaites, PeterHuckstep.
    Cambridge, 2008

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