This brand new series puts learners in charge with an exploratory inquiry-led approach to MYP Mathematics. Each full-colour book and accompanying eBook contains detailed worked examples, reflections, differentiated exercises, and check your knowledge questions to put learning into practice. Clear links to key concepts, related concepts and global contexts in addition to statements of inquiry and inquiry questions for each chapter. ATLs identified throughout. Investigations encourage learners to seek knowledge and develop ATL skills. Written by an international team of highly experienced authors and teachers, and led by Series Editor, Ibrahim Wazir, this new series matches the 2020 Subject Guide.

Creativity of an Aha! Moment and Mathematics Education introduces bisociation, the theory of Aha! moment creativity into mathematics education. It establishes relationships between Koestler's bisociation theory and constructivist learning theories. It lays down the basis for a new theory integrating creativity with learning to describe moments of insight at different levels of student development. The collection illuminates the creativity of the eureka experience in mathematics through different lenses of affect, cognition and conation, theory of attention and constructivist theories of learning, neuroscience and computer creativity. Since Aha! is a common human experience, the book proposes bisociation as the basis of creativity for all. It discusses how to facilitate and assess Aha! creativity in mathematics classrooms. Contributors are: William Baker, Stephen Campbell, Bronislaw Czarnocha, Olen Dias, Gerald Goldin, Peter Liljedahl, John Mason, Benjamin Rott, Edme Soho, Hector Soto, Hannes Stoppel, David Tall, Ron Tzur and Laurel Wolf.

Success Ahead is an exciting new series of Study Guides designed to help you excel in your Grade 12 exams! The series is aligned to the Grade 12 syllabus and helps you to practise and develop core skills. It also helps you to revise and prepare thoroughly for your exams. The Success Ahead Study Guides are user-friendly and can be used in the classroom or for independent practice at home. They can also be used as a quick reference for challenging content. Practise Revise Pass Excel Succeed!

Teaching and learning mathematics is a political act in which children, teachers, parents, and policy makers are made visible as subjects. As they learn about mathematics, children are also learning about themselves - who they are, who they might become. We can choose to listen or not to what children have to say about learning mathematics. Such choices constitute us in relations of power. Mathematical know-how is widely regarded as essential not only to the life chances of individuals, but also to the health of communities and the economic well-being of nations. With the globalisation of education in an increasingly market-oriented world, mathematics has received intensified attention in the first decade of the twenty-first century with a shifting emphasis on utilitarian aspects of mathematics. This is reflected in the reconceptualisation of mathematical competence as mathematical literacy, loosely conceived as those ways of thinking, reasoning and working "mathematically" that allow us to engage effectively in everyday situations, in many occupations, and the cut and thrust of world economies as active, empowered and participatory citizens. It is no surprise then that mathematics has become one of the most politically charged subjects in primary school curricula worldwide. We are experiencing an unprecedented proliferation of regional and national strategies to establish benchmarks, raise standards, enhance achievement, close gaps, and leave no child behind in mathematics education. Industries have sprung up around the design, administration and monitoring of standardised assessment to measure and compare children's mathematical achievement against identified benchmarks and each other.

This edited book promotes thinking, dialogue, research and theorisation on multiple ways of making connections in mathematics teaching and learning in early childhood education. The book addresses some key challenges in research, policy and practice in early childhood mathematics education. It examines diverse ways for learning experiences to connect young children to mathematics, and the importance of forging connections between mathematics and young children's lives as key elements in their engagement with mathematics. Each chapter provides research or theoretical provocations and pedagogical implications for connecting children's lived experiences and ways of learning in mathematics teaching. The chapters are drawn from a range of international authors who raise important ideas within the overall context of current research and consider the theoretical and practical implications of their research. As such, the book advances current thinking on mathematics teaching and learning for children in the early years from birth to eight years with an emphasis on children aged birth to 5 years. It considers the purpose and value in connecting mathematics teaching and learning to children's lives, and provides provocations for both educators and researchers on the many under-researched and under-represented aspects of early years mathematics teaching and learning.

Geometry has never been funnier! Green, funny aliens will help children to master the knowledge of shapes, formulas and figures. A new, entertaining activity book to challenge young readers joins the worldwide successful "Mad for Math" series with a collection of fun games based on geometry - which can really be fun! Children can be challenged with games of growing complexity throughout this activity book - and all answers can be found at the end. A didactic and educational, yet entertaining book which teaches children that you can not only play with geometry...but also to have fun with it! Includes 8 pages of stickers

This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children's developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.

Part I: Introduction. Challenging Perspectives on Mathematics Classroom Communication: From Representations to Contexts, Interactions and Politics. Part II: Contributed Chapters. Theme I: Communication: register, representations, context(s).

Edexcel's own Student Book for the new 2009 Edexcel International GCSE Mathematics specification. Provides complete coverage of the 2009 Edexcel International GCSE Mathematics specification. Attractive, full-colour design and engaging features makes the title accessible for every student. Contains exam practice throughout, with revision questions and practice exam questions. Linked to additional online material for students and teachers, provided by Edexcel, ensuring that you have as much support as possible. Full answers to the Student Book questions are available to teachers and parents by emailing [email protected] (for UK teachers and parents) or [email protected] (for all other teachers and parents).

Note that the Floris Books editions of Jamie York's books have been completely revised for UK and European notation, language and metric systems. They are also suitable for use in South Africa, Australia and New Zealand. Experienced maths teacher and consultant Jamie York believes that a love of learning comes through the teacher, so his books are committed to supporting teachers in developing their classroom skills and to fostering a love of maths in their students. Unlike conventional maths textbooks, his books are not full of fancy graphics and contrived ways to make maths fun. Rather, they: -- focus on the essentials, so teachers aren't overwhelmed by endless lists of required materials -- are genuinely interesting and challenging, sparking students' enthusiasm for learning maths -- are developmentally appropriate to the age of the child, thereby encouraging inner mathemetical awareness and thinking -- favour depth over superficiality, to avoid teaching blind procedures to solve meaningless problems. This student's workbook for Class 8 contains practice questions, with room for working, on all the topics a student needs to cover in Steiner-Waldorf Class 8 (age 14-15). The book includes number bases, Pythagorean theorem, mensuration, percents and growth, and proportions and dimensional analysis. Note that this workbook is also available in a pack of ten with a teacher's answer booklet.

Heinemann Active Maths: Engages pupils with a bank of stimulating, varied and exciting interactive and print-based activities. Follows an active approach to maths teaching and learning with an emphasis on real-life situations. Helps children develop a concrete understanding of maths concepts through investigation and discussion.

Supporting Early Mathematical Development is an essential text for current Early Years practitioners and students, offering an excellent blend of theory and practice that will enable you to provide successful mathematical education for children from birth to eight years old. Charting the delivery of mathematical development in Playgroups, Children's Centres, Nurseries and Primary Schools, it forges links between current practice and fundamental Early Years principles and makes suggestions for creating effective pedagogies in maths teaching.

Promoting mathematical development through play-based learning, this book presents:

• a wealth of practical multi-sensory teaching strategies
• instructional methodologies
• activity ideas incorporating play, books, songs, cookery and the outdoors
• examples of children's work
• advice on translating theory into practice
• questions for reflective practice.

Throughout the book, Caroline McGrath breaks down the complexity of teaching and learning mathematics into simple steps and guides readers through possible gaps in their knowledge, bringing fresh enthusiasm to teaching mathematics. This is an invaluable resource for practitioners and trainee teachers wishing to strengthen their mathematical teaching and professional practice, or for students on a wide range of Early Years courses.

This book is about how teachers can use classroom mathematics tasks to support student learning, and presents data on the ways in which teachers used those tasks in a particular research project. It is the product of research findings focusing on teacher practice, teacher learning and knowledge, and student learning. It demonstrates how teachers can use mathematics tasks to promote effective student learning.

Die Nuwe alles-in-een reeks kan nou spog met 'n nuwe lees- en klankprogram vir Gr 1 tot 3 om gedeelde, begeleide en selfstandige lees in die klaskamer te bevorder. Dit is ontwikkel volgens doe beginsels en doelwitte van die Kurrikulum- en assesseringsbeleidsverklaring. Die leerfokus van hierdie boek is om fonemiese bewustheid te bevorder. Leerders moet daarvan bewus wees dat spraak uit 'n reeks klanke bestaan, hulle moet individuele klanke herken, asook die manier waarop klanke woorde en woorde sinne vorm.

Concept Mapping in Mathematics: Research into Practice is the first comprehensive book on concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of concept mapping can be used innovatively and strategically to improve planning, teaching, learning, and assessment at different educational levels. This collection of research articles examines the usefulness of concept maps in the educational setting, with applications and examples ranging from primary grade classrooms through secondary mathematics to pre-service teacher education, undergraduate mathematics and post-graduate mathematics education. A second meta-cognitive tool, called vee diagrams, is also critically examined by two authors, particularly its value in improving mathematical problem solving.

Thematically, the book flows from a historical development overview of concept mapping in the sciences to applications of concept mapping in mathematics by teachers and pre-service teachers as a means of analyzing mathematics topics, planning for instruction and designing assessment tasks including applications by school and university students as learning and review tools. This book provides case studies and resources that have been field tested with school and university students alike. The findings presented have implications for enriching mathematics learning and making problem solving more accessible and meaningful for students.

The theoretical underpinnings of concept mapping and of the studies in the book include Ausubel s cognitive theory of meaningful learning, constructivist and Vygotskian psychology to name a few. There is evidence particularly from international studies such as PISA and TIMSS and mathematics education research, which suggest that students mathematical literacy and problem solving skills can be enhanced through students collaborating and interacting as they work, discuss and communicate mathematically. This book proposes the meta-cognitive strategy of concept mapping as one viable means of promoting, communicating and explicating students mathematical thinking and reasoning publicly in a social setting (e.g., mathematics classrooms) as they engage in mathematical dialogues and discussions.

Concept Mapping in Mathematics: Research into Practice is of interest to researchers, graduate students, teacher educators and professionals in mathematics education.

This book uses the publicly available TEDS-M data to answer such questions as: How does teacher education contribute to the learning outcomes of future teachers? Are there programs that are more successful than others in helping teachers learn to teach mathematics? How does the local and national policy environment contribute to teacher education outcomes? It invites readers to explore these questions across a large number of international settings. The importance of preparing future mathematics teachers has become a priority across many nations. Across the globe nations have allocated resources and expertise to this endeavour. Yet in spite of the importance accorded to teacher education not much is known about different approaches to preparing knowledgeable teachers and whether these approaches do in fact achieve their purpose. The Mathematics Teacher Education and Development Study (TEDS-M) is the first, and to date the only, cross-national study using scientific and representative samples to provide empirical data on the knowledge that future mathematics teachers of primary and secondary school acquire in their teacher education programs. The study addresses the central importance of teacher knowledge in learning to teach mathematics by examining variation in the nature and influence of teacher education programs within and across countries. The study collected data on teacher education programs structure, curriculum and opportunities to learn, on teacher educators' characteristics and beliefs, and on future mathematics teachers' individual characteristics, beliefs, and mathematics and pedagogical knowledge across 17 countries providing a unique opportunity to explore enduring questions in the field.

Abacus Evolve Challenge is perfect for ensuring more able children are being stretched to reach their full potential in maths. Challenge contains a range of enrichment and extension activities with a fourth level of differentiation above that found in other programmes.

A Volume in International Perspectives on Mathematics Education - Cognition, Equity & Society Series Editor Bharath Sriraman, The University of Montana and Lyn English, Queensland University of Technology Why a book on gender issues in mathematics in the 21st century? Several factors have influenced the undertaking of this project by the editors. First, an international volume focusing on gender and mathematics has not appeared since publication of papers emerging from the 1996 International Congress on Mathematical Education (Keitel, 1998). Surely it was time for an updated look at this critical area of mathematics education. Second, we have had lively discussion and working groups on gender issues at conferences of the International Group for the Psychology of Mathematics Education [PME] for the past four years, sessions at which stimulating and ground-breaking research has been discussed by participants from many different countries. Some publication seemed essential to share this new knowledge emerging from a wider variety of countries and from different cultural perspectives. Third, some western countries such as Australia and the USA have experienced in recent years a focus on the "boy problem," with an underlying assumption that issues of females and mathematics have been solved and are no longer worthy of interest. Thus it seemed timely to look more closely at the issue of gender and mathematics internationally. When the idea for this volume first emerged, invitations were issued to those regularly attending the working and discussion groups at PME. Potential authors were charged to focus on gender issues in mathematics and were given wide scope to hone in on the issues that were central to their own research efforts, or were in receipt or in need of close attention in their own national or regional contexts.

Children's Fractional Knowledge elegantly tracks the construction of knowledge, both by children learning new methods of reasoning and by the researchers studying their methods. The book challenges the widely held belief that children's whole number knowledge is a distraction from their learning of fractions by positing that their fractional learning involves reorganizing-not simply using or building upon-their whole number knowledge. This hypothesis is explained in detail using examples of actual grade-schoolers approaching problems in fractions including the schemes they construct to relate parts to a whole, to produce a fraction as a multiple of a unit part, to transform a fraction into a commensurate fraction, or to combine two fractions multiplicatively or additively. These case studies provide a singular journey into children's mathematics experience, which often varies greatly from that of adults. Moreover, the authors' descriptive terms reflect children's quantitative operations, as opposed to adult mathematical phrases rooted in concepts that do not reflect-and which in the classroom may even suppress-youngsters' learning experiences. Highlights of the coverage: Toward a formulation of a mathematics of living instead of being Operations that produce numerical counting schemes Case studies: children's part-whole, partitive, iterative, and other fraction schemes Using the generalized number sequence to produce fraction schemes Redefining school mathematics This fresh perspective is of immediate importance to researchers in mathematics education. With the up-close lens onto mathematical development found in Children's Fractional Knowledge, readers can work toward creating more effective methods for improving young learners' quantitative reasoning skills.

Study & Master Mathematics has been specially developed by an experienced author team to support the Curriculum and Assessment Policy Statement (CAPS). The comprehensive Learner's Book provides: * activities that develop learners' skills and understanding in each of the topics specified by the Mathematics curriculum * stimulating Mental Maths activities for all relevant topics * examples based on learners' own experiences. Also provides and innovative Teacher's Guide.

Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. Mathematical Thinking and Writing teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point.
Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure.
After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas.
* Covers the full range of techniques used in proofs, including contrapositive, induction, and proof by contradiction
* Explains identification of techniques and how they are applied in the specific problem
* Illustrates how to read written proofs with many step by step examples
* Includes 20% more exercises than the first edition that are integrated into the material instead of end of chapter
* The Instructors Guide and Solutions Manual points out which exercises simply must be either assigned or at least discussed because they undergird later results

The 2015 TIMSS Grade 9 study was administered in August 2015 by a team of researchers at the Human Sciences Research Council (HSRC) in collaboration with the Department of Basic Education (DBE) and the International Association for the Evaluation of Educational Achievement (IEA). This was the fifth time that South Africa has participated in TIMSS since 1995. In addition to the learner assessment data, the study also collected contextual information from learners, teachers and school principals, making it possible to explore the factors that are related to Grade 9 mathematics and science achievement. This report was written to provide some perspective about how the results of international assessments can be used to provide meaningful national insights. Sections of the report bring together the main findings based on descriptive, inferential and psychometric analysis of the data. The report concludes with recommendations of how the results relate to policy and practice for improving educational quality.