Discovering Mathematics is adapted from the leading Singapore course to fully match the English Key Stage 3 National Curriculum. This groundbreaking series harnesses authentic mastery principles through a Concrete-Pictorial-Abstract (CPA) approach, and use of precise mathematical language. Students learn by discovery, an approach pioneered by this course. Written by an experienced UK/Singapore team, this engaging book provides progression and practice for Middle tier students in Year 7 . Topics are introduced through inclusive whole-class activities. Worked examples give clear steps of how to present solutions, with hints and discussion points to encourage paired, group and whole-class working. Practice exercises are differentiated into three levels, progressing from basic fluency to application to problem solving, with consolidation through end-of-chapter exercises. Short answers in the back of the book help students quickly check their understanding, with fully-worked solutions containing GCSE grades in the Teacher Guide. Exercises incorporate 'intelligent practice', with careful variation of the numbers to reinforce and deepen learning. Problem-solving skills are identified throughout, with two dedicated problem-solving sections to support skills development. Students are also encouraged to reflect upon and embed their learning through a Write in Your Journal in every chapter. This Student Book will help students discover the underlying principles of mathematics and set them on the road to mastery.

This book provides a one-stop resource for mathematics educators, policy makers and all who are interested in learning more about the why, what and how of mathematics education in Singapore. The content is organized according to three significant and closely interrelated components: the Singapore mathematics curriculum, mathematics teacher education and professional development, and learners in Singapore mathematics classrooms. Written by leading researchers with an intimate understanding of Singapore mathematics education, this up-to-date book reports the latest trends in Singapore mathematics classrooms, including mathematical modelling and problem solving in the real-world context.

Discovering Mathematics is adapted from the leading Singapore course to fully match the English Key Stage 3 National Curriculum. This groundbreaking series harnesses authentic mastery principles through a Concrete-Pictorial-Abstract (CPA) approach, and use of precise mathematical language. Students learn by discovery, an approach pioneered by this course. Written by an experienced UK/Singapore team, this engaging book provides progression and practice for Foundation tier students in Year 8. Topics are introduced through inclusive whole-class activities. Worked examples give clear steps of how to present solutions, with hints and discussion points to encourage paired, group and whole-class working. Practice exercises are differentiated into two levels, progressing from basic fluency to problem solving, with consolidation through end-of-chapter exercises. Short answers are in the back of the book to help students quickly check their understanding, with fully-worked solutions containing GCSE grades in the Teacher Guide. Exercises incorporate 'intelligent practice', with careful variation of the numbers to reinforce and deepen learning. Problem-solving skills are identified throughout, with two dedicated problem-solving sections to support skills development. Students are also encouraged to reflect upon and embed their learning through a Write in Your Journal in every chapter. This Student Book will help students discover the underlying principles of mathematics and set them on the road to mastery.

Discovering Mathematics is adapted from the leading Singapore course to fully match the English Key Stage 3 National Curriculum. This groundbreaking series harnesses authentic mastery principles through a Concrete-Pictorial-Abstract (CPA) approach, and use of precise mathematical language. Students learn by discovery, an approach pioneered by this course. Written by an experienced UK/Singapore team, this engaging book provides progression and practice for Middle tier students in Year 8. Topics are introduced through inclusive whole-class activities. Worked examples give clear steps of how to present solutions, with hints and discussion points to encourage paired, group and whole-class working. Practice exercises are differentiated into three levels, progressing from basic fluency to application to problem solving, with consolidation through end-of-chapter exercises. Short answers in the back of the book help students quickly check their understanding, with fully-worked solutions containing GCSE grades in the Teacher Guide. Exercises incorporate 'intelligent practice', with careful variation of the numbers to reinforce and deepen learning. Problem-solving skills are identified throughout, with two dedicated problem-solving sections to support skills development. Students are also encouraged to reflect upon and embed their learning through a Write in Your Journal in every chapter. This Student Book will help students discover the underlying principles of mathematics and set them on the road to mastery.

Discovering Mathematics is adapted from the leading Singapore course to fully match the English Key Stage 3 National Curriculum. This groundbreaking series harnesses authentic mastery principles through a Concrete-Pictorial-Abstract (CPA) approach, and use of precise mathematical language. Students learn by discovery, an approach pioneered by this course. Written by an experienced UK/Singapore team, this engaging book provides progression and practice for Foundation tier students in Year 7. Topics are introduced through inclusive whole-class activities. Worked examples give clear steps of how to present solutions, with hints and discussion points to encourage paired, group and whole-class working. Practice exercises are differentiated into two levels, progressing from basic fluency to problem solving, with consolidation through end-of-chapter exercises. Short answers are in the back of the book to help students quickly check their understanding, with fully-worked solutions containing GCSE grades in the Teacher Guide. Exercises incorporate 'intelligent practice', with careful variation of the numbers to reinforce and deepen learning. Problem-solving skills are identified throughout, with two dedicated problem-solving sections to support skills development. Students are also encouraged to reflect upon and embed their learning through a Write in Your Journal in every chapter. This Student Book will help students discover the underlying principles of mathematics and set them on the road to mastery.

This book offers a detailed look into the how and what of mathematics instruction in Singapore. It presents multiple aspects of mathematics instruction in schools, ranging from the unique instructional core, practices that promote mastery, development of conceptual knowledge through learning experiences, nurturing of positive attitudes, self-regulation of learning and development and use of instructional materials for making connections across mathematical ideas, developing mathematical reasoning, and developing fluency in applying mathematical knowledge in problem solving.The book presents a methodology that is successful in documenting classroom instruction in a comprehensive manner. The research findings illuminate instruction methods that are culturally situated, robust and proven to impact student learning. It demonstrates how a unique data source can be analysed through multiple lenses and provides readers with a rich portrait of how the school mathematics instruction is enacted in Singapore secondary schools.

Discovering Mathematics is adapted from the leading Singapore course to fully match the Engilsh Key Stage 3 National Curriculum. This groundbreaking series harnesses authentic mastery principles through a Concrete-Pictorial-Abstract (CPA) approach, and use of precise mathematical language. Students learn by discovery, an approach pioneered by this course. Written by an experienced UK/Singapore team, this engaging book provides progression and practice for Higher tier students in Year 8. Topics are introduced through inclusive whole-class activities. Worked examples give clear steps of how to present solutions, with hints and discussion points to encourage paired, group and whole-class working. Practice exercises are differentiated into three levels, progressing from basic fluency to application to problem solving, with consolidation through end-of-chapter exercises. Short answers in the back of the book help students quickly check their understanding, with fully-worked solutions containing GCSE grades in the Teacher Guide. Exercises incorporate 'intelligent practice', with careful variation of the numbers to reinforce and deepen learning. Problem-solving skills are identified throughout, with two dedicated problem-solving sections to support skills development. Students are also encouraged to reflect upon and embed their learning through a Write in Your Journal in every chapter. This Student Book will help students discover the underlying principles of mathematics and set them on the road to mastery.

This book offers a detailed look into the how and what of mathematics instruction in Singapore. It presents multiple aspects of mathematics instruction in schools, ranging from the unique instructional core, practices that promote mastery, development of conceptual knowledge through learning experiences, nurturing of positive attitudes, self-regulation of learning and development and use of instructional materials for making connections across mathematical ideas, developing mathematical reasoning, and developing fluency in applying mathematical knowledge in problem solving.The book presents a methodology that is successful in documenting classroom instruction in a comprehensive manner. The research findings illuminate instruction methods that are culturally situated, robust and proven to impact student learning. It demonstrates how a unique data source can be analysed through multiple lenses and provides readers with a rich portrait of how the school mathematics instruction is enacted in Singapore secondary schools.

Discovering Mathematics is adapted from the leading Singapore course to fully match the Engilsh Key Stage 3 National Curriculum. This groundbreaking series harnesses authentic mastery principles through a Concrete-Pictorial-Abstract (CPA) approach, and use of precise mathematical language. Students learn by discovery, an approach pioneered by this course. Written by an experienced UK/Singapore team, this engaging book provides progression and practice for Middle tier students in Year 9. Topics are introduced through inclusive whole-class activities. Worked examples give clear steps of how to present solutions, with hints and discussion points to encourage paired, group and whole-class working. Practice exercises are differentiated into three levels, progressing from basic fluency to application to problem solving, with consolidation through end-of-chapter exercises. Short answers in the back of the book help students quickly check their understanding, with fully-worked solutions containing GCSE grades in the Teacher Guide. Exercises incorporate 'intelligent practice', with careful variation of the numbers to reinforce and deepen learning. Problem-solving skills are identified throughout, with two dedicated problem-solving sections to support skills development. Students are also encouraged to reflect upon and embed their learning through a Write in Your Journal in every chapter. This Student Book will help students discover the underlying principles of mathematics and set them on the road to mastery.

Discovering Mathematics is adapted from the leading Singapore course to fully match the English Key Stage 3 National Curriculum. This groundbreaking series harnesses authentic mastery principles through a Concrete-Pictorial-Abstract (CPA) approach, and use of precise mathematical language. Students learn by discovery, an approach pioneered by this course. Written by an experienced UK/Singapore team, this engaging book provides progression and practice for Higher tier students in Year 9. Topics are introduced through inclusive whole-class activities. Worked examples give clear steps of how to present solutions, with hints and discussion points to encourage paired, group and whole-class working. Practice exercises are differentiated into three levels, progressing from basic fluency to application to problem solving, with consolidation through end-of-chapter exercises. Short answers in the back of the book help students quickly check their understanding, with fully-worked solutions containing GCSE grades in the Teacher Guide. Exercises incorporate 'intelligent practice', with careful variation of the numbers to reinforce and deepen learning. Problem-solving skills are identified throughout, with two dedicated problem-solving sections to support skills development. Students are also encouraged to reflect upon and embed their learning through a Write in Your Journal in every chapter. This Student Book will help students discover the underlying principles of mathematics and set them on the road to mastery.

Discovering Mathematics is adapted from the leading Singapore course to fully match the English Key Stage 3 National Curriculum. This groundbreaking series harnesses authentic mastery principles through a Concrete-Pictorial-Abstract (CPA) approach, and use of precise mathematical language. Students learn by discovery, an approach pioneered by this course. Written by an experienced UK/Singapore team, this engaging book provides progression and practice for Higher tier students in Year 7 . Topics are introduced through inclusive whole-class activities. Worked examples give clear steps of how to present solutions, with hints and discussion points to encourage paired, group and whole-class working. Practice exercises are differentiated into three levels, progressing from basic fluency to application to problem solving, with consolidation through end-of-chapter exercises. Short answers in the back of the book help students quickly check their understanding, with fully-worked solutions containing GCSE grades in the Teacher Guide. Exercises incorporate 'intelligent practice', with careful variation of the numbers to reinforce and deepen learning. Problem-solving skills are identified throughout, with two dedicated problem-solving sections to support skills development. Students are also encouraged to reflect upon and embed their learning through a Write in Your Journal in every chapter. This Student Book will help students discover the underlying principles of mathematics and set them on the road to mastery.

This book contributes towards the literature in the field of mathematics education, specifically on aspects of empowering learners of mathematics. The book, comprising eighteen chapters, written by renowned researchers in mathematics education, provides readers with approaches and applicable classroom strategies to empower learners of mathematics.The chapters in the book can be classified into four sections. The four sections focus on how learners could be empowered in their learning, cognitive and affective processes, through mathematical content, purposefully designed mathematical tasks, whilst developing 21st century competencies.

The aim of this book is to contribute towards literature in the field of mathematics education, specifically the development of 21st century competencies amongst learners of mathematics.The book comprising fourteen chapters, written by renowned researchers in mathematics education, provides readers with approaches and applicable classroom strategies to foster skills and dispositions that will enable learners to thrive in the fast-changing and complex world that we live in today.The chapters in the book can be classified into three broad themes. The first is an examination of what is meant by 21st century competencies and how they can be developed within the context of the mathematics curriculum. The second is an in-depth discussion of evidence-based practices aimed at fostering specific competencies like metacognition and reflective thinking, critical thinking and communication skills. The last and third theme is about teaching approaches that are likely to feature increasingly in the 21st century classroom, for example flipped learning or the use of comics and storytelling.

This sixth volume, in the series of yearbooks by the Association of Mathematics Educators in Singapore, entitled Learning Experiences to Promote Mathematics Learning is unique in that it focuses on a single theme in mathematics education. The objective is for teachers and researchers to advance the learning of mathematics through meaningful experiences.Several renowned international and Singapore scholars have published their work in this volume. The fourteen chapters of the book illustrate evidence-based practices that school teachers and researchers can experiment with in their own classrooms to bring about meaningful learning outcomes. Three broad themes, namely fundamentals for active and motivated learning, learning experiences for developing mathematical processes, and use of ICT tools for learning through visualizations, simulations and representations, shape the ideas in these chapters. The book makes a significant contribution towards the learning of mathematics. It is a good resource for mathematics teachers, educators and research students.

This fifth volume in the series of yearbooks by the Association of Mathematics Educators in Singapore entitled Nurturing Reflective Learners in Mathematics is unique in that it focuses on a single theme in mathematics education. The objective is to encourage teachers and researchers to advance reflection among students and teachers in mathematics classrooms.Several renowned international and Singapore researchers in the field have published their work in this volume. The fifteen chapters of the book illustrate evidence-based practices that school teachers and researchers can experiment with in their own classrooms to bring about meaningful learning outcomes. Three broad themes, namely fundamentals, instructional tools, and approaches to teaching for nurturing reflective learners in mathematics classrooms, shape the ideas in these chapters. The book makes a significant contribution towards the learning of mathematics. It is a good resource for mathematics teachers, educators and research students.

This fourth volume in the series of yearbooks by the Association of Mathematics Educators in Singapore entitled Reasoning, Communication and Connections in Mathematics is unique in that it focuses on a single theme in mathematics education. The objective is to encourage teachers and researchers to advance reasoning, communication and connections in mathematics classrooms.Several renowned international researchers in the field have published their work in this volume. The fifteen chapters of the book illustrate evidence-based practices that school teachers and researchers can experiment with in their own classrooms to bring about meaningful learning outcomes. Three major themes: mathematical tasks, classroom discourse, and connectivity within and beyond mathematics, shape the ideas underpinning reasoning, communication and connections in these chapters. The book makes a significant contribution towards mathematical processes essential for learners of mathematics. It is a good resource for mathematics educators and research students.

Low Attainers in Primary Mathematics focuses on data from students in Singapore schools. It is widely acknowledged that students from Singapore do well in mathematics in international studies. This book provides readers with a glimpse of students from Singapore who are at the other end of the ability spectrum.The book is based on a study that explored the mathematics content knowledge of Primary 4 low attainers in mathematics, their behaviours, affects and home backgrounds, and learning experiences. Based on the findings of the study, the book has recommendations for teachers of low attainers in primary mathematics.This book serves as a must-have resource for teachers and graduate students in Singapore who are working with or studying low attainers in primary mathematics. It also makes a worthy contribution towards literature on low attainers in the field of mathematics education.

The third in the series of yearbooks by the Association of Mathematics Educators in Singapore, Assessment in the Mathematics Classroom is unique as it addresses a focused theme on mathematics education. The objective is to encourage teachers and researchers to include assessment of non-cognitive attributes and to use techniques in addition to paper-and-pencil tests that focus on typical problems.

Several renowned international researchers in the field have published their work in the book. The thirteen chapters of the book illustrate evidence-based practices that school teachers and researchers can experiment in their lessons to bring about meaningful learning outcomes. A recurring theme in most chapters is the widely circulated notions of formative assessment and assessment for learning. The book makes a significant contribution towards assessment in mathematics and is a must-read for graduate research students and mathematics educators.

Mathematical Applications and Modelling is the second in the series of the yearbooks of the Association of Mathematics Educators in Singapore. The book is unique as it addresses a focused theme on mathematics education. The objective is to illustrate the diversity within the theme and present research that translates into classroom pedagogies.

The book, comprising of 17 chapters, illuminates how application and modelling tasks may help develop the capacity of students to use mathematics in their present and future lives. Several renowned international researchers in the field of mathematical modelling have published their work in the book. The chapters are comprehensive and laden with evidence-based examples for both mathematics educators and classroom teachers. The book is an invaluable contribution towards the emerging field of research in mathematical applications and modelling. It is a must-read for graduate research students and mathematics educators.

This book is the first in the series of the yearbooks of the Association of Mathematics Educators in Singapore. It is highly unique as it addresses a focused theme of mathematics education. The chapters of the book, illustrate the immense diversity within the theme and presents research that translates into classroom pedagogies.

The thirteen chapters of the book illustrate how mathematical problems may be crafted and infused in classroom teaching. Several novel pedagogies, such as learning mathematics through productive failure, problem posing and generative activities are presented in the book. The chapters are comprehensive and laden with evidence-based examples for both mathematics educators and classroom teachers of mathematics. The book is an invaluable contribution towards the already established field of research of mathematical problem solving. It is also a must read for graduate research students and mathematics educators.

This comprehensive book is a state-of-the-art review of research and practices of mathematics education in Singapore. It traces the fascinating journey from the original development of the Singapore mathematics curriculum in the 1950s to the present day, and reports on diverse findings about the Singapore experience that are not readily available in print. All of the authors are active mathematics educators or senior mathematics teachers in Singapore, thus adding authenticity and distinctiveness to the stories covered in this book. The issues they so earnestly explore in this book will undoubtedly be of interest to graduate students, mathematics educators, and the international mathematics education community.