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Helping Children Learn Mathematics, 5th Australian Edition

Reys, Rogers, Keate, Cooke, Fanshawe, Gronow
Print ISBN: 9781394330713, Interactive eText ISBN: 9781394330720

Available from semester 1, 2026. The fifth Australian edition of Helping Children Learn Mathematics equips pre-service teachers with the confidence and practical tools to become effective mathematics educators. Aligned with the Australian Curriculum and NAPLAN, this edition empowers future primary teachers with research-informed strategies and classroom-tested activities—many of which the author team, all current educators, have successfully used in their own teaching.

This streamlined edition is shorter and more focused, allowing readers to concentrate on practical skills and their classroom application.

Key features:
✔ Local ANZ content ✔ Instructor Resource Toolkit
✔ Interactive media and practice quizzes ✔ Local Wiley support
✔ Affordable access models

Table of Contents

Introduction
1.1 What is mathematics?
1.2 What determines the mathematics being taught?
1.3 The role of the teacher
1.4 Where can you turn?
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

2.1 How can we support the diverse learners in our classrooms?
2.2 Meaningful connections between procedural and conceptual knowledge
2.3 How do children learn mathematics?
2.4 How can we help children make sense of mathematics?
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
3.1 Effective planning and preparation for teaching: using strategic questions to inform teaching practice
3.2 Planning for effective teaching
3.3 Levels of planning
3.4 Planning different types of lessons
3.5 Meeting the needs of all children
3.6 Assessment and analysis in planning
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
4.1 Enhancing learning and teaching
4.2 Gathering information on children’s learning
4.3 Ways to assess children’s learning and dispositions
4.4 Keeping records and communicating about assessments
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
5.1 Understanding
5.2 Fluency
5.3 Problem solving
5.4 Reasoning
5.5 Communication
5.6 Representations
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
6.1 What is a problem and what is problem solving?
6.2 Teaching mathematics through problem solving
6.3 Strategies for problem solving
6.4 The importance of looking back
6.5 Helping all children with problem solving
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
7.1 Developing number sense
7.2 Counting principles
7.3 Counting strategies
7.4 Cardinal, ordinal and nominal numbers
7.5 Writing numerals
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
8.1 Our numeration
8.2 Nature of place value
8.3 Beginning place value
8.4 Consolidating place value
8.5 Extending place value
8.6 Reading and writing numbers
8.7 Rounding
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
9.1 Helping children develop number sense and computational fluency
9.2 Developing meanings for the operations
9.3 Mathematical properties
9.4 Overview of learning the basic number facts
9.5 Thinking strategies for basic number facts
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
10.1 Calculators
10.2 Mental computation
10.3 Estimation
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
11.1 Emergent understanding and experiences
11.2 Addition
11.3 Subtraction
11.4 Multiplication
11.5 Division
11.6 Finding the balance between practice and proficiency
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
12.1 Conceptual development of fractions
12.2 Understanding equivalence and ordering fractions
12.3 Operations with fractions
12.4 Conceptual development of decimals
12.5 Operations with decimals
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
13.1 Ratios
13.2 Proportions
13.3 Percentages
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
14.1 Number theory in primary school mathematics
14.1 Number theory topics for primary school children
14.3 Other number theory topics
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
15.1 Problems, patterns and relations
15.2 Language and symbols of algebra
15.3 Modelling, generalising and justifying
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
16.1 The geometry of two-dimensional shapes and three-dimensional objects
16.2 Location, position and spatial relationships
16.3 Transformations
16.4 Visualisation and spatial reasoning
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
17.1 The measurement process
17.2 Identifying attributes and comparing
17.3 Measurement concepts for all units
17.4 Measuring with informal units
17.5 Measuring with formal units
17.7 Comparing and converting measurements
17.8 Estimating measurements
17.9 Connecting attributes
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Introduction
18.1 Formulating questions for data collection
18.2 Organising and representing data
18.3 Analysis data: descriptive statistics
18.4 Interpreting results
18.5 Probability
Concept check
Making connections
A glance at where we’ve been
Things to do: from what you’ve read
Things to do: going beyond this text
References
Acknowledgements

Authors

Robert Reys
Audrey Cooke
Kirsten Everitt
Melissa Fanshawe
Lorraine Gaunt
Mark Gronow
Leicha Keate
Kate Quane
Jessa Rogers

Explore our content

The fifth Australian edition of Helping Children Learn Mathematics prepares pre-service Foundation and Primary teachers to confidently teach mathematics in line with the Australian Curriculum and NAPLAN requirements.

This edition combines current research with classroom-tested strategies, including ready-made lesson plans, In the Classroom activities, and guidance on problem-solving and assessment. This streamlined edition focuses on practical skills, with detailed support for ICT integration and an interactive eText featuring videos, exercises, and quizzes.

Authored by practising educators, the text includes empirical activities drawn directly from their teaching experience, ensuring relevance and immediate classroom application.

What’s in Helping Children Learn Mathematics, 5th Edition?

New to this edition:

  • Curriculum alignment: Fully updated to reflect the latest Australian Curriculum V9, ensuring all content meets current national standards for mathematics education.
  • Professional standards mapping: Each chapter now highlights relevant Australian Professional Standards for Teachers, supporting professional development and accreditation pathways.
  • Contemporary research base: References have been reviewed and updated, with most drawn from post-2020 research to ensure content remains current and evidence-based.

Key features:

  • Ready-made lesson plans: Includes clear, classroom-ready lesson plans designed to save preparation time and support effective instruction.
  • ‘In the Classroom’ activities: Features practical, tried-and-tested activities developed by the expert author team to enhance hands-on learning.
  • Problem solving and assessment focus: Provides strategies for planning instruction with a strong emphasis on problem-solving approaches and effective assessment techniques.
  • ICT integration: Offers comprehensive guidance on using Information and Communications Technology to enrich mathematics teaching and enhance student engagement.
  • Interactive eText: Delivers an engaging digital learning experience, with features that support flexible study and reinforce key concepts.
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Interactives and key features ​

Available as a digital eText or printed textbook, this title enables every student to master concepts and succeed in assessment. Lecturers are supported with an extensive, easy-to-use teaching and learning package.

Our digital eText includes animated case studies based on real classroom scenarios, accompanied by questions that test and deepen your knowledge and understanding.

Branching animations (eText)

Included in our eText are excerpts from real classroom lessons across a range of year levels and mathematical topics. These snapshots illustrate effective teaching practices and classroom dialogue, helping pre-service teachers connect theory to practice.

'Snapshot of a lesson' videos (eText)

Our digital eText features end-of-chapter multiple-choice quizzes that provide instant feedback, helping to reinforce understanding and support learning.

Concept check questions ​(eText)

Our digital eText features interactive activities that let you match, categorise, or sequence concepts by moving elements on-screen, actively reinforcing learning with immediate feedback.

Interactivities (eText)

Encourages pre-service teachers to explore cross-cultural issues and diverse perspectives in the mathematics classroom. Also covers key components of the Australian Curriculum, including proficiency standards, diversity, and general capabilities.

Making connections

Focuses on the unique teaching and learning needs of early childhood students, offering comprehensive applications of mathematical concepts in real-world classroom scenarios during this critical stage of development.

Spotlight on early childhood

This boxed feature has practical, tried-and-tested activities developed by the expert author team. These provide a wealth of ideas and strategies for teaching the mathematical concepts covered in each chapter.

Featured: ‘In the classroom’ activities

Embodies the text’s active approach to learning and teaching mathematics. Divided into two parts, these activities engage students in inquiry, investigation, and reflective thinking to develop the understanding and insight needed to become effective educators.

'Things to do' feature

Featured throughout this text are clear, classroom-ready lesson plans designed to reduce preparation time and support effective teaching practice.

Ready made lesson plans

Students can personalise their eText by highlighting and taking notes, as well other useful tools like the read aloud or flash card creation features.

Personalisation features (eText)

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Instructor Resource Toolkit

Our Instructor Resource Toolkit is designed to seamlessly integrate the text content into your teaching, saving you time and boosting student engagement. It includes a variety of customisable tools, guides and assessment.*

Pre-made PowerPoint slides save you time in your course set-up, while the ability to customise the content means you can build it to suit your courses learning outcomes.

The Manual offers suggested exemplar answers or guidance from the authors or SME on approaching the “From Theory to Practice” questions, that require personal reflection.

Access to a comprehensive LMS-ready test bank. This collection of customisable exam and quiz questions are designed to assess students’ understanding of key concepts and learning objectives.

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This text is proudly published and supported by a local team dedicated to enriching learning experiences for ANZ based students and instructors.

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*The Instructor Resource Toolkit is only available to educators in Australian, New Zealand & Pacific Universities. Our team will verify all requests for access. Once your request is verified, you will be able to login and download the resources from the Instructor Companion site. ​