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Paul Killen - How Big Is a Big Number?: Learning to Teach Mathematics in the Primary School

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Paul Killen How Big Is a Big Number?: Learning to Teach Mathematics in the Primary School
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What, how and why?If you dont really understand the content of the primary mathematics curriculum, how can you teach it? This beautiful full colour book is here to help. It covers all you need to know to be an effective teacher of primary mathematics.It shows you how to explore number, shape and pattern with the children you teach. It examines what we mean by mastery of mathematics and reviews what we can learn from Asian maths teaching methods. It helps you to see how areas of mathematics fit together and how you can support children to build their own understanding of the subject.This book goes beyond showing you how to teach. It shows you that process is as important as product. That getting it wrong can be as useful as getting it right and that children cant really learn the what without understanding the why.

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How Big is a Big Number?
How Big Is a Big Number Learning to Teach Mathematics in the Primary School - image 1
How Big is a Big Number?

Learning to teach mathematics in the primary school

  • Paul Killen
  • Sarah Hindhaugh
How Big Is a Big Number Learning to Teach Mathematics in the Primary School - image 2
How Big Is a Big Number Learning to Teach Mathematics in the Primary School - image 3

Learning Matters

An imprint of SAGE Publications Ltd

1 Olivers Yard

55 City Road

London EC1Y 1SP

SAGE Publications Inc.

2455 Teller Road

Thousand Oaks, California 91320

SAGE Publications India Pvt Ltd

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Mathura Road

New Delhi 110 044

SAGE Publications Asia-Pacific Pte Ltd

3 Church Street

#10-04 Samsung Hub

Singapore 049483

Paul Killen and Sarah Hindhaugh 2018

First published 2018

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may be reproduced, stored or transmitted in any form, or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction, in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers.

Library of Congress Control Number: 2017954851

British Library Cataloguing in Publication Data

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

ISBN 978-1-5264-0413-8

ISBN 978-1-5264-0414-5 (pbk)

Editor: Amy Thornton

Production controller: Chris Marke

Project management: Swales & Willis Ltd, Exeter, Devon

Marketing manager: Dilhara Attygalle

Cover design: Wendy Scott

Typeset by: C&M Digitals (P) Ltd, Chennai, India

Printed and bound in the UK

At SAGE we take sustainability seriously. Most of our products are printed in the UK using FSC papers and boards. When we print overseas we ensure sustainable papers are used as measured by the PREPS grading system. We undertake an annual audit to monitor our sustainability.

Acknowledgements

This book is dedicated to the many wonderful primary trainees we have met and taught over the past years at LJMU. We have learned so much from you and we hope you have learned something from us.

About the authors
Paul Killen After previously working in secondary schools, Further Education and Higher Education, Paul Killen is now Head of Primary Programmes at Liverpool John Moores University and over almost 20 years has taught primary and secondary mathematics education to a vast range of Initial Teacher Training (ITT) courses including PGCE, Undergraduate and School Direct. Paul was also Programme Leader for Teach First in Liverpool and for 7 years delivered mathematics at the Teach First Summer Institutes in Canterbury, Warwick and Leeds.Sarah Hindhaugh began her career teaching in primary schools where she became a school mathematics coordinator and a lead mathematics teacher for Liverpool Education Authority. For the last 17 years she has been a Senior Lecturer in mathematics at Liverpool John Moores University where she manages the mathematics provision across all ITT routes including undergraduate and postgraduate courses.
Introduction

We are passionate about mathematics. We love maths and we love teaching maths.

As such, it upsets us greatly to hear adults say, I cant do maths or I hate maths. It is even worse to hear children make such comments. We believe that through effective teaching, every child has the potential to achieve a high level of mathematical proficiency. We go further. Anyone with a negative mathematical outlook has been failed by their teachers.

Mastery of mathematics is an issue currently high on the education agenda. However, to be able to deliver mastery, teachers need to not only be confident in their curriculum subject knowledge, they must also have a deep understanding of the pedagogical knowledge that will allow any mathematical topic to be taught in the most effective way.

It is our belief that many of us were taught mathematics by being provided with a range of, what we call, rules and their recipes. Very often, such rules were not explained or justified. We want all students and all children to fully understand what they are doing in mathematics and why they are doing it. A mastery approach in mathematics avoids teaching children rules and it presents all new work in the context of childrens existing knowledge.

This book seeks to bring together these three elements of mastery, curriculum knowledge and pedagogy. We trust that by reading this book you will become more secure in your own mathematical understanding and will therefore become a more effective teacher. In the same way that children will deepen their understanding of mathematics by doing it, you will develop your mastery of pedagogy through teaching it.

It has been our pleasure to teach students how to teach mathematics for many years and it is they who have inspired us to write this book. We know that many of our students began their training lacking confidence in their own ability at mathematics. Yet time and again, we have seen them blossom into highly effective teachers with a desire to ensure all children achieve mathematical success.

Contained within each chapter of this book, we offer teaching ideas, as well as opportunities for you to reflect on various aspects of mathematical knowledge and pedagogy. We also include tasks for you to complete in each chapter. There are two types of task: the first type provides you with the opportunity to work through some specific examples related to each theme in the appendix, we provide the solutions to these. However, this is not a mathematics textbook. Rather, we want you to think how each mathematical idea we discuss can be developed in the classroom to promote mastery. Thus, the second type of task we include is designed to offer ideas to stretch and challenge both you and the children in your class.

What maths can you see?

The key to mastering any mathematical topic and its corresponding skills is to be able to apply the new knowledge in a variety of different contexts. Equally, children need to be able to recognise the mathematics in various problems and situations. With this in mind, we will conclude each chapter with a photograph.

For the reader, this is an opportunity to think of the application of mathematics in a wide range of situations. Each image could also be used as a stimulating starter activity with a group of children. For each photograph, we simply invite you to identify, What maths can you see? Sometimes the mathematics is obvious and links directly to elements covered in that chapter. However, sometimes the mathematics is less clear.

Each photograph has the potential to lead to a rich discussion about the mathematics that is all around us and to apply mathematical thinking to a real-life context. We believe that it is through such discussion that children will master different mathematical ideas. There is no right or wrong way to approach this. The teacher will lead this discussion through a series of open questions and children may see connections with aspects of mathematics that you do not. In the appendix to this book, we offer some guidance and possible avenues to explore in relation to each photograph.

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