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Helping Children Learn Mathematics, 2nd Australian Edition

Helping Children Learn Mathematics, 2nd Australian Edition

ISBN: 978-0-730-32778-3

Nov 2016

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Description

Helping Children Learn Mathematics 2e is a practical resource for undergraduate students of primary school teaching, rich in ideas, tools and stimulation for lessons during teaching rounds or in the classroom. This second edition provides a clear understanding of how to navigate the Australian curriculum, with detailed coverage on how to effectively use Information and Communications Technology (ICT) in the classroom. The WileyPLUS Learning Space interactive textbook facilitates an engaging learning experience and showcases excellent pedagogy and best e-learning practices.

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About the authors x

Preface xii

Features of this text xiii

About this text xiv

chapter 1 School mathematics in a changing world 1

1.1 What is mathematics? 3

1.2 What determines the mathematics being taught? 4

1.3 Where can you turn? 11

chapter 2 Helping children learn mathematics with understanding 17

2.1 How can we support the diverse learners in our classrooms? 18

2.2 Meaningful connections between procedural and conceptual knowledge 24

2.3 How do children learn mathematics? 26

2.4 How can we help children make sense of mathematics? 31

chapter 3 Planning and teaching 46

3.1 Effective planning and preparation for teaching: using strategic questions to inform teaching practice 47

3.2 Planning for effective teaching 62

3.3 Levels of planning 63

3.4 Planning different types of lessons 64

3.5 Meeting the needs of all students 72

3.6 Assessment and analysis in planning 76

chapter 4 Enhancing learning and teaching through assessment and feedback 82

4.1 Enhancing learning and teaching 84

4.2 Gathering information on student learning 87

4.3 Ways to assess students’ learning and dispositions 89

4.4 Keeping records and communicating about assessments 104

chapter 5 Processes of doing mathematics 116

5.1 Problem solving 118

5.2 Reasoning and proof 123

5.3 Communication 128

5.4 Connections 129

5.5 Representations 131

chapter 6 Helping children with problem solving 141

6.1 What is a problem and what is problem solving? 143

6.2 Teaching mathematics through problem solving 145

6.3 Strategies for problem solving 156

6.4 The importance of looking back 166

6.5 Helping all students with problem solving 167

chapter 7 Counting and number sense in early childhood and primary years 177

7.1 Developing number sense 179

7.2 Counting principles 193

7.3 Counting strategies 196

7.4 Cardinal, ordinal and nominal numbers 207

7.5 Writing numerals 208

chapter 8 Extending number sense: place value 216

8.1 Our numeration system 219

8.2 Nature of place value 220

8.3 Beginning place value 227

8.4 Consolidating place value 230

8.5 Extending place value 237

8.6 Reading and writing numbers 244

8.7 Rounding 248

chapter 9 Operations: meanings and basic facts 257

9.1 Helping children develop number sense and computational fluency 260

9.2 Developing meanings for the operations 263

9.3 Mathematical properties 271

9.4 Overview of learning the basic facts 273

9.5 Thinking strategies for basic facts 281

chapter 10 Mental computation, calculators and estimation 305

10.1 Calculators 310

10.2 Mental computation 314

10.3 Estimation 322

chapter 11 Solving problems with written strategies 339

11.1 Learning strategies that lead to understanding 342

11.2 Addition 344

11.3 Subtraction 351

11.4 Multiplication 357

11.5 Division 365

11.6 Finding the balance between practice and proficiency 372

chapter 12 Fractions and decimals: meanings and operations 382

12.1 Conceptual development of fractions 385

12.2 Operations with fractions 406

12.3 Conceptual development of decimals 413

12.4 Operations with decimals 418

chapter 13 Ratio, proportion and percentages: meanings and applications 428

13.1 Ratios 431

13.2 Proportions 434

13.3 Percentages 442

chapter 14 Extending students with number theory 457

14.1 Number theory in primary school mathematics 459

14.2 Number theory topics for primary school students 463

14.3 Other number theory topics 475

chapter 15 Algebraic thinking 485

15.1 Problems, patterns and relations 488

15.2 Language and symbols of algebra 495

15.3 Modelling, generalising and justifying 498

chapter 16 Geometry 516

16.1 The geometry of 2-dimensional shapes and 3-dimensional objects 519

16.2 Locations and spatial relationships 543

16.3 Transformations 546

16.4 Visualisation and spatial reasoning 549

chapter 17 Measurement 557

17.1 The measurement process 561

17.2 Identifying attributes and comparing 563

17.3 Measurement concepts for all units 576

17.4 Measuring with informal units 579

17.5 Measuring with formal units 583

17.6 Applications including formulae 593

17.7 Comparing and converting measurements 598

17.8 Estimating measurements 601

17.9 Connecting attributes 603

chapter 18 Data analysis, statistics and probability 612

18.1 Formulating questions and collecting data 617

18.2 Organising and representing data 619

18.3 Analysing data: descriptive statistics 631

18.4 Interpreting results 638

18.5 Probability 641

Appendix A 655

Appendix B 665

Appendix C 674

  • Local Relevance: Reys’ second edition provides a clear understanding of how to navigate the Australian curriculum, plus detailed coverage on how to effectively use ICT in the classroom
  • Focus on Understandings: This resource is rich in ideas, tools and stimulation for primary maths lessons, with a focus on students’ understanding of mathematics
  • Best Practices: Students can experience firsthand the value of ICT in education with this digital resource which showcases excellent pedagogy and best e-learning practices.
  • Practice Modules: ‘In The Classroom’ modules ask students to apply their learning to address how they would teach a maths learning objective
  • Interactive Online Textbook: The WileyPLUS Learning Space interactive textbook is full of rich media, videos, animation and interactives embedded at the point of learning
  • Branched Animations: Animated case scenarios ask students “what would you do” in realistic classroom scenarios, with branched narratives demonstrating the impact of their actions