Rosa Archer - Understanding Lesson Study for Mathematics: A Practical Guide for Improving Teaching and Learning

Using the latest research, this book provides an insight into how learning in mathematics can be improved through a lesson study approach. This highly practical resource explores the research and theory that underpins lesson study, and shows the significant impact it can have on teacher development.

Divided into ten accessible main chapters that focus in depth on an individual mathematics lesson, each chapter provides research and background to the lesson, an outline of key features, a detailed description and analysis of the lesson in practice, post-lesson discussions and reflections which generalise from the experience, as well as links to helpful resources. Some of the key topics explored include:

• Fractions
• Proportional relationships
• Probability and statistics
• Geometry
• Modelling
• Algebra
• Dialogic reasoning.

Understanding Lesson Study for Mathematics is the perfect resource for all mathematics teachers, trainee teachers, and professional developers who are looking to develop the use of lesson study in their own practice or for those simply seeking new inspiring ideas for the mathematics classroom.

Rosa Archer, Manchester University, has worked on lesson study for ten years with colleagues from Japan and from England.

Sin Morgan, Manchester University, is a teacher educator, researcher and professional developer with a passion for mathematics education and lesson study.

David Swanson teaches at Manchester University and researches mathematical and pedagogical concept development and critical social perspectives on education.

First published 2021

by Routledge

2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN

and by Routledge

52 Vanderbilt Avenue, New York, NY 10017

Routledge is an imprint of the Taylor & Francis Group, an informa business

2021 Rosa Archer, Sin Morgan and David Swanson

The right of Rosa Archer, Sin Morgan and David Swanson to be identified as authors of this work has been asserted by them in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.

All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers.

Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library

Library of Congress Cataloging-in-Publication Data

A catalog record has been requested for this book

ISBN: 978-1-138-48571-6 (hbk)

ISBN: 978-1-138-48572-3 (pbk)

ISBN: 978-1-351-04828-6 (ebk)

At the heart of this book are ten chapters that focus in depth on an individual mathematics lesson. Each chapter includes some of the thinking behind the lesson, a description and analysis of the lesson in practice and some general understanding developed from the experience.

Each lesson and chapter has been developed through lesson study (LS). All three authors are former teachers and currently teacher educators and researchers at The University of Manchester, and have worked on using LS as a professional development tool for teachers and for pre-service teachers for several years. We have seen that LS can have a significant impact on teachers development and this book is an attempt to share what we have learned and understood.

The idea of this book was born while we were discussing readings we could share with our pre-service teachers on a particular aspect of mathematics teaching. We could find many densely written academic articles and many descriptions of teaching practice, but very little in between, which related big ideas with classroom practice in a convincing and accessible way. We therefore decided to write our own to share with our pre-service teachers, and we found conducting and reporting on lesson studies to be the perfect vehicle.

The aim of this book is therefore to reflect on research on pedagogy via practical applications and translate research into practice (and vice-versa). Through it we hope readers will develop their understanding of learning and teaching mathematics, and also learn about LS as a method for further development.

LS, as a professional development tool, has become very popular in the UK and in the US in recent years. However, in our experience, LS is interpreted in many different ways, and sometimes in an overly simplistic and not always helpful way. This book aims to provide sufficient reflections and theoretical background on LS to support those wishing to develop it in their own establishments.

The book includes:

• A focus on mathematics pedagogy for mathematics teachers and pre-service teachers
• Ten lessons including the research background, planning, reflections and lesson plans in easily accessible writing
• A focus on difficult to teach topics and curriculum challenges
• Current debates and research translated into practice
• A model for conducting, writing up and sharing lesson studies.

The book can therefore be read at many different levels. Teachers and pre-service teachers wishing to develop their pedagogy or introduce new ideas in the classroom could read the lesson plans and lesson reflections and try the lessons themselves. The research-based background to the lesson will help develop their understanding further and support their reflection and analysis. Pre-service teachers can find practical examples of lesson planning and reflection to assist them in these important areas. Those developing professional development courses could share the lesson plans with colleagues and use some of the activities suggested within. Teacher educators could also use some of the activities suggested and use the lesson plans and evaluations as discussion points with students. Pre-service teachers, masters students and undergraduate students on education courses could use the chapters to support the writing of academic assignments.

Recent changes to the national curriculum in the UK and particularly the greater emphasis on mastery within the classroom and problem solving within public examinations are posing new challenges to the various groups discussed above; we hope that the materials found within this book can offer suggestions to support understanding and reflection.

Each chapter may be read and used independently. However, those who wish to begin with some further background on lesson study should read the introduction to it in . This introductory chapter is also useful in explaining the structure of the lesson chapters, as the sections closely follow the different phases typically found in lesson study. We should also note here that at times we adapt grammatical tense to these phases in later chapters, using present tense when describing the practical experience of the lesson, so the reader can more easily imagine being present as a fly on the wall in the classroom.

Through the chapters of the book we tell three interrelated stories about mathematical understanding, pedagogy and lesson study. Following the ten chapters on each lesson, in we draw together and generalise from the understandings we have developed in relation to each, and add some thoughts on lesson study as a form of research.