MasterClass in Mathematics Education provides accessible links between theory and practice and encourages readers to reflect on their own understanding of their teaching context. Each chapter, written by an internationally respected authority, explores the key concepts within the selected area of the field, drawing directly on published research to encourage readers to reflect on the content, ideas and ongoing debates. Using international case studies, each chapter will encourage readers to think about ways that the teaching and learning of mathematics reflect different cultural traditions and expectations and enable them to evaluate effective strategies for their own contexts.

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.

The mathematics education community continues to contribute research-based ideas for developing and improving problem posing as an inquiry-based instructional strategy for enhancing students' learning. A large number of studies have been conducted which have covered many research topics and methodological aspects of teaching and learning mathematics through problem posing. The Authors' groundwork has shown that many of these studies predict positive outcomes from implementing problem posing on: student knowledge, problem solving and posing skills, creativity and disposition toward mathematics. This book examines, in-depth, the contribution of a problem posing approach to teaching mathematics and discusses the impact of adopting this approach on the development of theoretical frameworks, teaching practices and research on mathematical problem posing over the last 50 years.

This volume presents a set of studies that explore significant questions about mathematics teaching and learning, and illustrate new methodologies for the analysis of new questions about mathematics education. The data from the "Second International Mathematical Study" (SIMS) is the starting point for all of the material in this work. SIMS was one of the largest and most comprehensive data-collection effort on mathematics teaching and learning ever undertaken. Because of its scale, comparative cross-cultural perspective, conceptualization and design, its data offer an indispensable beginning point for the exploration of many of the fundamental questions that circle around mathematics teaching and learning, not only internationally, but in the United States as well.

Research on the preparation and continued development of mathematics teachers is becoming an increasingly important subset of mathematics education research. Such research explores the attributes, knowledge, skills and beliefs of mathematics teachers as well as methods for assessing and developing these critical aspects of teachers and influences on teaching.

"Research Trends in Mathematics Teacher Education" focuses on three major themes in current mathematics teacher education research: mathematical knowledge for teaching, teacher beliefs and identities, and tools and techniques to support teacher learning. Through careful reports of individual research studies and cross-study syntheses of the state of research in these areas, the book provides insights into teachers' learning processes and how these processes can be harnessed to develop effective teachers. Chapters investigate bedrock skills needed for working with primary and secondary learners (writing relevant problems, planning lessons, being attentive to student learning) and illustrate how knowledge can be accessed, assessed, and nurtured over the course of a teaching career. Commentaries provide context for current research while identifying areas deserving future study. Included among the topics: Teachers' curricular knowledgeTeachers' personal and classroom mathematicsTeachers' learning journeys toward reasoning and sense-makingTeachers' transitions in noticingTeachers' uses of a learning trajectory as a tool for mathematics lesson planning

A unique and timely set of perspectives on the professional development of mathematics teachers at all stages of their careers, "Research Trends in Mathematics Teacher Education" brings clarity and practical advice to researchers as well as practitioners in this increasingly critical arena."

Packed with realistic exam-style questions for every topic, this newly updated Exam Practice Workbook is perfectly matched to the Higher Level Edexcel GCSE Maths course. Handy grade stamps indicate the difficulty level of each question, and problem-solving stamps highlight those that require a bit of extra thought. There are also plenty of helpful exam tips throughout the book. Plus, it comes with complete step-by-step solutions (with a full mark scheme) at the back of the book, so it's simple for students to check and correct their work - and there are even QR codes to access brilliant new worked video solutions! And finally, the book is rounded off with a full set of mock exam papers - the answers to these are available to download from the CGP website. CGP's range for Higher Level Edexcel GCSE Maths also includes a matching Revision Guide (9781782944041), Workbook (9781782944072) and Grade 8-9 Targeted Exam Practice Workbook (9781782944157).

Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its value in the mathematical community. The writing is expository, not technical, and should be accessible and informative to a diverse audience. The primary readership includes all those in departments of mathematical sciences in two or four year colleges and universities, and their administrators, as well as graduate students. Researchers in education may also find topics of interest. Other potential readers include those doing work in mathematics education in schools of education, and teachers of secondary or middle school mathematics as well as those involved in their professional development.

A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaPaul Ernest's name is synonymous with social constructivism as a philosophy ofmathematics. His contributions to mathematics education have occurred at a veryfundamental level and to an extent shaped theory development in this field. Hisresearch addresses fundamental questions about the nature of mathematics and how itrelates to teaching, learning and society. For the last three decades Paul has been aprolific scholar who has published in a wide array of topics such as the relationshipbetween the philosophy of mathematics and mathematics education, and moregenerally the philosophy of mathematics education, ethics and values in mathematics education, and the philosophy ofresearch methodology.The title of this Festschrift is meant to be a pun to convey the sometimes relativistic dimension to mathematical certaintythat Paul argued for in developing his philosophy, and also a play on words for the fact that absolute "earnestness" mayperhaps be a Platonic construct, and not possible in the realm of language and human discourse Paul Ernest's scholarlyevolution and life can best be summarized in the words of Walt Whitman "Do I contradict myself? Very well then Icontradict myself" (I am large, I contain multitudes). Indeed his presence has beenlarge and multitudinous and this Festschrift celebrates his 65th Birthday withnumerous contributions coming from the mathematics, philosophy and mathematicseducation communities around the world.

The Key Stage 2 Maths series covers mathematical technique for SATs and all other styles of mathematical test. This series of books is designed to be used in sequence from Workbook 1 onwards. The workbook series is complemented by a testbook that reinforce a child's mathematical technique and knowledge. Answers, Progress Charts and a Certificate of Achievement are included at the end of every book. All our materials have been rigorously classroom tested. The methodologies have been successfully used in AE Tuition classes for over 30 years.

Mixing dinosaurs, counting and bedtime, children will love this brilliantly fun board book with a shiny silver foiled cover! Once upon a bedtime, these children could not sleep, so their helpful mums and daddies said that they should count some sheep. Though children think that sheep are nice, there's something they like more, so instead of counting lots of sheep, they counted DINOSAURS! What's the best way to help little ones fall asleep? Introduce them to super cute dinosaurs, of course! And with stomping, laughing and mischievous dinosaurs on every page, and a fun story showing children how to count from one to twenty, this chunky, child-friendly board book is set to become every child's new favourite. The perfect board book for children, especially dinosaur-loving ones! Chunky board book with shiny silver on the cover Helps children learn how to count from one to twenty Brilliantly fun story and beautiful, full-colour illustrations The perfect first-gift for children Encourages children to love counting as much as they love dinosaurs!

This book presents a literature review of and a state-of-the-art glimpse into current research on affect-related aspects of teaching and learning in and beyond mathematics classrooms. Then, research presented at the MAVI 25 Conference, which took place in Intra (Italy) in June 2019, is grouped in thematic strands that capture cutting-edge issues related to affective components of learning and teaching mathematics. The concluding chapter summarises the main messages and sketches future directions for research on affect in mathematics education. The book is intended for researchers in mathematics education and especially graduate students and PhD candidates who are interested in emotions, attitudes, motivations, beliefs, needs and values in mathematics education.

Offering a proven, high-quality, step-by-step approach that builds students' confidence, these texts give students the rigorous practice they need to get better results in the two-tier exams. Clearly organised, easy-to-use and carefully structured main texts provide thorough preparation for students on either a 1-year or 2-year course with clear, student-friendly language used throughout Fully worked examples with explanatory notes and commentary followed by carefully graded exercises offer gradual progression Exam and exam-style questions, presented in non-calculator and calculator section reviews, give further opportunities to consolidate skills acquired over a number of chapters Further compilations of exam and exam-style questions, which reflect how the examiners will assess the new two-tier specifications are provided to give thorough preparation for the exams.

A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaThe word "critical" in the title of this collection has three meanings, all of which are relevant. One meaning, as applied toa situation or problem, is "at a point of crisis." A second meaning is "expressing adverse or disapproving comments orjudgments." A third is related to the verb "to critique," meaning "to analyze the merits and faults of." The authorscontributing to this book pose challenging questions, from multiple perspectives, about the roles of mathematics insociety and the implications for education. Traditional reasons for teaching mathematics include: preparing a newgeneration of mathematics researchers and a cadre of technically competent users of mathematics; training students tothink logically; and because mathematics is as much part of cultural heritage as literature or music. These reasons remainvalid, though open to critique, but a deeper analysis is required that recognizes the roles of mathematics in framing manyaspects of contemporary society, that will connect mathematics education to the lived experiences of students, theircommunities, and society in general, and that acknowledges the global ethical responsibilities of mathematicians andmathematics educators.The book is organized in four sections (1) Mathematics education: For what and why?(2) Globalization and cultural diversity, (3) Mathematics, education, and society and (4) Social justice in, and through, mathematics educationThe chapters address fundamental issues such as the relevance of school mathematics in people's lives; creating a sense of agency for the field of mathematics education, and redefining the relationship between mathematics as discipline, mathematics as school subject and mathematics as part of people's lives.

This book examines new trends and developments in research related to the mathematical education of pre-service elementary teachers, and explores the implications of these research advances for theory and practice in teacher education. The book is organized around the following four overarching themes: pre-service teachers' mathematics content and mathematics-specific pedagogical preparation; professional growth through activities and assessment tools used in mathematics teacher preparation programs; pre-service mathematics teachers' knowledge and beliefs; and perspectives on noticing in the preparation of elementary mathematics teachers. Including contributions from researchers working in 11 different countries, the book offers a forum for discussing and debating the state of the art regarding the mathematical preparation of pre-service elementary teachers. By presenting and discussing the findings of research conducted in different countries, the book offers also opportunities to readers to learn about varying teacher education practices around the world, such as: innovative practices in advancing or assessing teachers' knowledge and beliefs, similarities and differences in the formal mathematics education of teachers, types of and routes in teacher education, and factors that can influence similarities or differences.

Heinemann Active Maths' bright and lively Pupil Books have been designed to further consolidate children's learning through independent practice. They are closely linked to the Teacher Activity Cards and each Heinemann Active Maths outcome. Each Pupil Book contains: 'I can...' statements to encourage self-assessment. 'Rocket' questions to extend and challenge children's learning. Teacher Activity Card references so you know which card the Pupil Book pages link to. * This component forms part of the Second Level Beyond Number Starter Pack, but can be purchased individually.

Each test should take about 15 minutes, however it is more important that a child completes the test accurately and does not rush their answers. Children will speed up naturally with practice. These tests extend children's learning beyond their expected age-related National Curriculum standard. The testbook provides practice for SATs and all other styles of mathematical test. The testbook is designed to be used in conjunction with the KS2 Maths workbooks as an additional learning tool. Answers, Progress Charts and a Certificate of Achievement are included at the end of the book. All our materials have been rigorously classroom tested. The methodologies have been successfully used in AE Tuition classes for over 30 years.

In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles).

A sampling of the coverage:

• The conjoint origins of proof and theoretical physics in ancient Greece.
• Proof as bearers of mathematical knowledge.
• Bridging knowing and proving in mathematical reasoning.
• The role of mathematics in long-term cognitive development of reasoning.
• Proof as experiment in the work of Wittgenstein.
• Relationships between mathematical proof, problem-solving, and explanation.

Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.

Rhetorical Ways of Thinking focuses on how the co-construction of learning models the interpretation of a mathematical situation. It is a comprehensive examination of the role of sociocultural-historical theory developed by Vygotsky. This book puts forward the supposition that the major assumptions of sociocultural-historic theory are essential to understanding the theory's application to mathematical pedagogy, which explores issues relevant to learning and teaching mathematics-in-context, thus providing a valuable practical tool for general mathematics education research. The most important goal, then, is to exemplify the merging of the theory with practice and the subsequent applications to mathematics teaching and learning. This monograph contains five chapters, including a primer to Vygotsky's sociocultural historic theory, three comprehensive empirical studies examining: prospective teachers' perception of mathematics teaching and learning and the practice of scaffolded instruction to assist practicing teachers in developing their understanding of pedagogical content knowledge. Finally, the book concludes with a contextualization of the theory, linking it to best practices in the classroom.

Discover how space is part of our daily lives with Everyday STEM Science - Space, filled with facts, stories and experiments to try at home! Everyone knows there are planets and stars and space rocks, but how do these, and everything else in space, affect us on Earth? From the beginning of the universe and the origins of the planets, to the latest research and space missions, journey through space and uncover what is really out there . . . Discover how we're made of stars, find out how old you would be if you lived on Mars, and how time travel can happen in space. Plus, meet the explorers, astronomers and scientists whose discoveries have given us this fascinating space knowledge, including Mae Jemison, Stephen Hawking and Cecilia Payne-Gaposchkin. Readers can also carry out cool astronomical experiments at home. With easy-to-understand text written by science communicator and podcaster Izzie Clarke, and lots of colourful artworks, photos and diagrams, readers can best explore where we encounter space and why it's even important at all. The Everyday STEM series makes science relevant to tweens. Instead of telling kids STEM is important and is the key to their future success, these books show readers how we use science, technology, engineering and maths in our everyday lives. While the topics sound high-level and complex, this series makes these concepts age-appropriate and accessible. So, while we can't promise to teach 9 to 11-year-olds quantum physics, we can explain in the simplest terms the practical applications of STEM.