PRIMARY MATHEMATICS - Cambridge University...
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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.
Cambridge University Press978-1-108-45646-3 — Primary Mathematics3rd EditionFrontmatterMore Information
www.cambridge.org© in this web service Cambridge University Press
Cambridge University Press978-1-108-45646-3 — Primary Mathematics3rd EditionFrontmatterMore Information
www.cambridge.org© in this web service Cambridge University Press
3edition
PrimaryMathematicsIntegrating Theory with Practice
rd
Penelope SerowRosemary CallinghamTracey Muir
Cambridge University Press978-1-108-45646-3 — Primary Mathematics3rd EditionFrontmatterMore Information
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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
Guided student tasks 70
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
Guided student tasks 102
Further reading 103
CHAPTER 5 Exploring whole number computation 104
Introduction 104
Developing number sense 105
Operations with whole numbers 107
Conclusion 122
Guided student tasks 122
Further reading 123
CHAPTER 6 Part-whole numbers and proportional reasoning 125
Introduction 125
Background 126
Parts and wholes 127
Conclusion 140
Guided student tasks 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
Guided student tasks 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
Guided student tasks 187
Further reading 188
vi Contents
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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
Guided student tasks 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
Guided student tasks 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
Guided student tasks 253
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
Guided student tasks 274
Further reading 275
viiContents
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CHAPTER 13 General capabilities and cross-curriculum priorities 276
Introduction 276
General capabilities 277
Cross-curriculum priorities 289
Conclusion 291
Guided student tasks 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
Guided student tasks 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
Guided student tasks 322
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
Guided student tasks 340
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
viii Contents
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Leading the teaching of ICT within your school 347
Conclusion 354
Guided student tasks 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
Guided student tasks 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
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