Why does it matter whether we state definitions carefully when we all know what particular geometric figures look like? What does it mean to say that a reflection is a transformation—a function? How does the study of transformations and matrices in high school connect with later work with vector spaces in linear algebra? How much do you know… and how much do you need to know? Helping your students develop a robust understanding of geometry requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry. It is organised around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently. Move beyond the mathematics you expect your students to learn. Students who fail to get a solid grounding in pivotal concepts struggle in subsequent work in mathematics and related disciplines. By bringing a deeper understanding to your teaching, you can help students who don’t get it the first time by presenting the mathematics in multiple ways. The Essential Understanding Series addresses topics in school mathematics that are critical to the mathematical development of students but are often difficult to teach. Each book in the series gives an overview of the topic, highlights the differences between what teachers and students need to know, examines the big ideas and related essential understandings, reconsiders the ideas presented in light of connections with other mathematical ideas, and includes questions for readers’ reflection.

Exploring the ways in which maths skills can be learned through cross-curricular activities based on visual arts and music, this text presents maths as a meaningful and exciting subject which holds no fears for children. The authors recognize that while maths-phobia prevails in our increasingly mathematicized world, attitudes and approaches to teaching the subject need to be reviewed, and issues such as gender stereotyping, which encourage maths-apathy, need to be tackled at an early age. Within this collection of classroom-based stories are detailed examples of intergrative mathematic projects.

This book shows how creative maths can really work. Exploring the ways in which maths skills can be learned through cross-curricular activities based on visual arts and music, the book presents maths as a meaningful and exciting subject which holds no fears for children.
The authors recognise that while maths-phobia prevails in our increasingly mathematicised world, attitudes and approaches to teaching the subject need to be reviewed, and issues such as gender stereotyping, which encourage maths-apathy, need to be tackled at an early stage.
Within this collection of classroom-based stories are detailed examples of integrative mathematic projects; these will give teachers the confidence to try out cross-curricular activities in their classes. The book also provides support with difficult areas such as assessment, planning and development.
Fascinating to read in its own right this book will appeal to the specialist and non-specialist alike.

First published in 1987, this book examines mathematics school teaching from the perspective that it is a language - arguing that this can illuminate many events that occur in classes and highlight issues that may not have previously seemed important. The central concern is with the processes of communication as they are shaped by school conventions and the fact that it is mathematics being discussed. Speaking, listening, writing and reading are examined and analysed with the first half focusing on verbal interactions and the second half examining aspects of pupil written mathematics. Also explored is the nature of the mathematical writing system itself and how pupils gain access to it.

Symbols and Meanings in School Mathematics explores the various uses and aspects of symbols in school mathematics and also examines the notion of mathematical meaning. It is concerned with the power of language which enables us to do mathematics, giving us the ability to name and rename, to transform names and to use names and descriptions to conjure, communicate and control our images. It is in the interplay between language, image and object that mathematics is created and can be communicated to others. The book also addresses a set of questions of particular relevance to the last decade of the twentieth century, which arise due to the proliferation of machines offering mathematical functioning.

First published in 1987, this book examines mathematics school teaching from the perspective that it is a language - arguing that this can illuminate many events that occur in classes and highlight issues that may not have previously seemed important. The central concern is with the processes of communication as they are shaped by school conventions and the fact that it is mathematics being discussed. Speaking, listening, writing and reading are examined and analysed with the first half focusing on verbal interactions and the second half examining aspects of pupil written mathematics. Also explored is the nature of the mathematical writing system itself and how pupils gain access to it.

Symbols and Meanings in School Mathematics explores the various uses and aspects of symbols in school mathematics and also examines the notion of mathematical meaning. It is concerned with the power of language which enables us to do mathematics, giving us the ability to name and rename, to transform names and to use names and descriptions to conjure, communicate and control our images. It is in the interplay between language, image and object that mathematics is created and can be communicated to others.
The book also addresses a set of questions of particular relevance to the last decade of the twentieth century, which arise due to the proliferation of machines offering mathematical functioning.

Learning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in the secondary school classroom. This fourth edition has been fully updated to reflect the latest changes to the curriculum and research in the field, taking into account key developments in teacher training and education, including examinations and assessment. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, such as: why we teach mathematics the place of mathematics in the National Curriculum planning, teaching and assessing for mathematics learning how to communicate mathematically using digital technology to advance mathematical learning working with students with special educational needs post-16 teaching the importance of professional development the affective dimension when learning mathematics, including motivation, confidence and resilience Already a major text for many university teaching courses, this revised edition features a glossary of useful terms and carefully designed tasks to prompt critical reflection and support thinking and writing up to Masters Level. Issues of professional development are also examined, as well as a range of teaching approaches and styles from whole-class strategies to personalised learning, helping you to make the most of school experience, during your training and beyond. Designed for use as a core textbook, Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all those who aspire to be effective mathematics teachers.

This book explores the connection between the ways people speak in mathematics classrooms and their opportunities to learn mathematics. The words spoken, heard, written and read in mathematics classrooms shape students' sense of what mathematics is and of what people can do with mathematics. The authors employ multiple perspectives to consider the means for transformative action with respect to increasing opportunities for traditionally marginalized students to form mathematical identities that resonate with their cultural, social, linguistic, and political beings.

This book explores the connection between the ways people speak in mathematics classrooms and their opportunities to learn mathematics. The words spoken, heard, written and read in mathematics classrooms shape students sense of what mathematics is and of what people can do with mathematics. The authors employ multiple perspectives to consider the means for transformative action with respect to increasing opportunities for traditionally marginalized students to form mathematical identities that resonate with their cultural, social, linguistic, and political beings."

Learning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in the secondary school classroom. This fourth edition has been fully updated to reflect the latest changes to the curriculum and research in the field, taking into account key developments in teacher training and education, including examinations and assessment. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, such as: why we teach mathematics the place of mathematics in the National Curriculum planning, teaching and assessing for mathematics learning how to communicate mathematically using digital technology to advance mathematical learning working with students with special educational needs post-16 teaching the importance of professional development the affective dimension when learning mathematics, including motivation, confidence and resilience Already a major text for many university teaching courses, this revised edition features a glossary of useful terms and carefully designed tasks to prompt critical reflection and support thinking and writing up to Masters Level. Issues of professional development are also examined, as well as a range of teaching approaches and styles from whole-class strategies to personalised learning, helping you to make the most of school experience, during your training and beyond. Designed for use as a core textbook, Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all those who aspire to be effective mathematics teachers.

Why are there so many formulas for area and volume, and why do some of them look alike? Why does one quadrilateral have no special name while another has several, like square, rectangle, rhombus, and parallelogram-and why are all these names useful? How much do you know ... and how much do you need to know? Helping your students develop a robust understanding of geometry requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry. It is organized around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students-and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students' understanding of the topic.