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Cambridge University Press978-1-108-45646-3 — Primary Mathematics3rd EditionFrontmatterMore Information

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PRIMARY MATHEMATICSIntegrating Theory with Practice

3rd

edition

Primary Mathematics: Integrating Theory with Practice provides a

comprehensive introduction to teaching and learning mathematics in

today’s classrooms. Closely aligned with the Australian Curriculum:

Mathematics, this text covers the core learning areas of measurement,

space and geometry, early number concepts, data and statistics, chance

and probability, and patterns and algebra. The text also addresses key

considerations for teachers, such as planning, assessment, diversity and

teaching outside traditional contexts.

This third edition has been thoroughly revised and features three new

chapters focusing on the general capabilities and cross-curricular

priorities, implementing STEM strategies in the primary setting, and

transition to practice. Each chapter highlights how the theory of teaching

mathematics can be put into practice effectively and includes new guided

reflective questions and student tasks. Learning is also supported through

key term definitions, snapshot case studies and reflection points, while

activities throughout each chapter inspire readers to put their knowledge

into practice.

Written by an expert author team, Primary Mathematics remains an

essential resource that will prepare and excite pre-service teachers for their

future as mathematics educators.

Penelope Serow is Associate Professor in the School of Education at the

University of New England.

Rosemary Callingham is Adjunct Associate Professor in the Faculty of

Education at the University of Tasmania.

Tracey Muir is Associate Professor in the Faculty of Education at the

University of Tasmania.

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3edition

PrimaryMathematicsIntegrating Theory with Practice

rd

Penelope SerowRosemary CallinghamTracey Muir


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© Cambridge University Press 2014, 2016, 2019

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primarymathematics

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Contents

ABOUT THE AUTHORS X

HOW TO USE HOTMATHS WITH THIS BOOK XI

ACKNOWLEDGEMENTS XV

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 1 Teaching mathematics today with tomorrow in mind 1

Today’s classroom 2

The TPACK framework 3

Summary of chapters 6

How to use this book 9

CHAPTER 2 Exploring early mathematical development 10

Introduction 10

Early childhood mathematics pedagogy 12

Transition to school 13

The importance of play 14

Early number concepts 14

Linking with curriculum documents 18

Early number activities and strategies 20

Early operations with number 31

Extending early mathematical development beyond number 36

Conclusion 39

Guided student tasks 39

Further reading 40

CHAPTER 3 Exploring measurement 41

Introduction 41

Learning sequence for measurement 41

Establishing formulae for areas and volumes 47

Estimation 49

Conservation 52

Measurement topics 53

Using inquiry to develop an understanding of measurement 67

Conclusion 69


Further reading 70

CHAPTER 4 Exploring geometry 71

Introduction 71

Geometric concepts 71

Theoretical framework 74

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Geometry in the primary classroom 79

The van Hiele teaching phases 96

Conclusion 102


Further reading 103

CHAPTER 5 Exploring whole number computation 104

Introduction 104

Developing number sense 105

Operations with whole numbers 107

Conclusion 122


Further reading 123

CHAPTER 6 Part-whole numbers and proportional reasoning 125

Introduction 125

Background 126

Parts and wholes 127

Conclusion 140


Further reading 141

CHAPTER 7 Exploring patterns and algebra 142

Introduction 142

Linking with curriculum 143

Pattern and structure 143

Developing an understanding of relationships 150

Equals and equivalence 151

Generalisation in upper primary 157

Conclusion 164


Further reading 165

CHAPTER 8 Exploring data and statistics 166

Introduction 166

Development of statistical understanding 168

Asking questions (problems) 169

Collecting and recording data (plan, data) 170

Analysing and representing data (analyse) 175

Telling a story from the data (conclusions) 183

Conclusion 187


Further reading 188

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CHAPTER 9 Exploring chance and probability 189

Introduction 189

Why is probability important? 189

Understanding probability 191

Developing understanding of uncertainty 196

Conclusion 209


Further reading 210

CHAPTER 10 Capitalising on assessment for, of and as learning 211

Introduction 211

Assessment 212

Quality of student responses 216

Construction of assessment tasks 222

National testing 223

Designing assessment items for different levels of complexity 229

Conclusion 231


Further reading 232

CHAPTER 11 Planning for mathematics teaching in the 21st century

classroom 233

Introduction 233

Planning considerations 233

Considering digital technologies when planning for mathematics

lessons 238

Suggestions for capitalising on ICT in the classroom 241

Developing an understanding of place value 244

Planning for an integrated unit 247

Conclusion 252


Further reading 253

CHAPTER 12 Diversity in the primary mathematics classroom 254

Introduction 254

Why is it important to recognise diversity? 254

The impact of teachers’ understanding and beliefs 257

Practical aspects of addressing diversity in the mathematics classroom 259

Conclusion 274


Further reading 275

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CHAPTER 13 General capabilities and cross-curriculum priorities 276

Introduction 276

General capabilities 277

Cross-curriculum priorities 289

Conclusion 291


Further reading 292

CHAPTER 14 STEM in the primary setting 293

Introduction 293

STEM in schools 293

STEM and primary mathematics 295

Problem-based learning and STEM 297

The United Kingdom experience 299

Implementing STEM in the primary classroom 300

Conclusion 305


Further reading 306

CHAPTER 15 Surviving as an ‘out of field’ teacher of mathematics 307

Introduction 307

Community beliefs about mathematics teaching and related issues 308

Secondary lesson structures 311

Issues to think about in the secondary context within each strand 316

Conclusion 321


Further reading 322

CHAPTER 16 Teaching mathematics beyond the urban areas 323

Introduction 323

Rural and remote areas 324

Considering classroom structures 329

National testing 332

Conclusion 339


Further reading 340

CHAPTER 17 Considerations for implementing ICT in the mathematics

classroom 341

Introduction 341

The TPACK framework 341

The SAMR model 343

Auditing your ICT skills 345

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Leading the teaching of ICT within your school 347

Conclusion 354


Further reading 355

CHAPTER 18 Becoming a teacher of mathematics 356

Introduction 356

Mathematics anxiety and the challenge of tests 357

Evidence-based teaching 362

Professional learning and communities 367

Conclusion 370


Further reading 371. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .

REFERENCES 372

INDEX 384

ixContents


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About the authors

PENELOPE SEROW is Associate Professor of Mathematics Education at the University of

New England. She has worked on various development projects in Pacific Island contexts

and is actively involved in research in the areas of primary, secondary and pre-service

mathematics education. Penelope’s research interests include assessment for learning

practices, making the most of available tools in the mathematics classroom to actively

engage students, and providing community-focused opportunities for teacher education in

remote locations.

ROSEMARY CALLINGHAM is an Adjunct Associate Professor at the University of Tas-

mania. She has an extensive background in mathematics education in Australia, at school,

system and tertiary levels, including mathematics curriculum development and imple-

mentation, large-scale testing and pre-service teacher education. Rosemary’s research

interests include teachers’ pedagogical content knowledge, statistical literacy, mental

computation and assessment of mathematics and numeracy.

TRACEY MUIR is an Associate Professor in Mathematics Education at the University of

Tasmania. Her teaching expertise has been recognised through a number of Teaching

Merit Certificate awards, a VC Team Award for Teaching Excellence, an Office for

Learning and Teaching Team Award for Teaching Excellence and a VC Citation for

Outstanding Contribution to Student Learning. Tracey is an Executive Member of the

Mathematics Association of Tasmania, a previous editor of APMC, and a past VP

(Development) of the Mathematics Education Research Group of Australasia. Her

research interests include effective teaching of numeracy, student engagement, flipped

learning and teacher knowledge. Tracey regularly conducts professional learning for

teachers and has delivered workshops, presentations and keynote addresses at national

and international conferences.

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How to use HOTmaths with this book

Once you have registered your HOTmaths access code, found on the inside front cover of

this book, for subsequent visits the below navigation instructions provide a general

overview of the main HOTmaths features used within this textbook.

Log in to your account via www.hotmaths.com.au.

Upon logging in you will automatically arrive at your Dashboard. This screen offers

you access to FUNdamentals (colourful maths games and activities for Foundation to

Year 2 students), Games and the HOTmaths Dictionary. The Dashboard can also be

accessed via the icon on the right-hand side of the toolbar at the top of any HOTmaths

lesson page.

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Different HOTmaths streams can be accessed via the Course list dropdown. You can

change the Course list and Course (year level) using the dropdown on the left-hand side

of the toolbar.

You can then select a Topic, and finally a Lesson.

Most lessons contain a number of interactive and printable activities, which can be

accessed via the links on the right-hand side of the orange toolbar. These include:

Resources, Walkthroughs, Scorcher and Questions.

xii How to use HOTmaths with this book


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The Resources tab within lessons contain widgets (animations) and HOTsheets

(activities). By clicking on the ‘Number bars’ link, you will access the widget below.

Clicking the ‘Addition bingo’ link will give you access to the HOTsheet below.

xiiiHow to use HOTmaths with this book


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The toolbar at the top of each lesson page is also the location for the search function,

where you can enter the name of any widget or HOTsheet for quick access. The results

page will automatically display videos based on the keywords searched, indicated by the

videos tab being highlighted in blue. If you are looking for a widget or a HOTsheet, simply

click onto the required tab and the results will appear. Using the above widget as an

example, searching ‘Number bars’ and clicking on the widget tab will provide you a link to

the Number Bars widget. By clicking locations next to the widget name you can see what

HOTmaths lessons use the resource. You can also narrow your search results to a specific

course, topic or lesson using the dropdown menus.

Throughout this textbook you will find numerous references to resources from HOT-

maths. Please note that given its nature HOTmaths is constantly being updated. All

pathways and references are correct as of May 2019 and every effort has been made to

provide you with an accurate picture of the functions within HOTmaths.

xiv How to use HOTmaths with this book


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Acknowledgements

The authors and Cambridge University Press would like to thank the following for

permission to reproduce material in this book.

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not endorse any product that uses ACARA material or make any representations as to the

quality of such products. Any product that uses material published on this website should

not be taken to be affiliated with ACARA or have the sponsorship or approval of ACARA.

It is up to each person to make their own assessment of the product.

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Grist Photography; 3.2 (top right): © Getty Images/Fernando Trabanco Fotografia;

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