IMPACT: Interweaving Mathematics Pedagogy and Content for Teaching – serie

Filled with practical learning activities to adopt within your classroom, The Learning and Teaching of Statistics and Probability places reasoning about quantities and quantification at the core of learning and teaching statistics. A companion website to this book is also available at https://neilhatfield.github.io/IMPACT_Statistics/, allowing readers to access a directory of resources – data collections and web-based applets – used in some of the instructional activities featured within this book.Through its presentation of conceptual analyses and resources for teaching with statistical data, the book’s five chapters establish key concepts and foundational ideas in statistics and probability, emphasizing the development of learner understanding and coherence, for example:Individual cases and their attributesData collections, sub-collections, and relevant operations to quantify their attributesSamples, population, and quantifying variationTypes of processes, meanings of randomness, and probability as a measure of stochastic tendencySampling distributions and statistical inference.This highly informative yet practical book is an indispensable resource for teachers of secondary school mathematics, mathematics subject leads, and mathematics and statistics educators within the wider field of education.

Filled with practical learning activities to adopt within your classroom, The Learning and Teaching of Statistics and Probability places reasoning about quantities and quantification at the core of learning and teaching statistics. A companion website to this book is also available at https://neilhatfield.github.io/IMPACT_Statistics/, allowing readers to access a directory of resources – data collections and web-based applets – used in some of the instructional activities featured within this book.Through its presentation of conceptual analyses and resources for teaching with statistical data, the book’s five chapters establish key concepts and foundational ideas in statistics and probability, emphasizing the development of learner understanding and coherence, for example:Individual cases and their attributesData collections, sub-collections, and relevant operations to quantify their attributesSamples, population, and quantifying variationTypes of processes, meanings of randomness, and probability as a measure of stochastic tendencySampling distributions and statistical inference.This highly informative yet practical book is an indispensable resource for teachers of secondary school mathematics, mathematics subject leads, and mathematics and statistics educators within the wider field of education.

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education.The Learning and Teaching of Algebra provides a pedagogical framework for the teaching and learning of algebra grounded in theory and research. Areas covered include:• Algebra: Setting the Scene• Some Lessons From History• Seeing Algebra Through the Eyes of a Learner• Emphases in Algebra Teaching• Algebra Education in the Digital EraThis guide will be essential reading for trainee and qualified teachers of mathematics, graduate students, curriculum developers, researchers and all those who are interested in the "problématique" of teaching and learning algebra. It allows you to get involved in the wealth of knowledge that teachers can draw upon to assist learners, helping you gain the insights that mastering algebra provides.

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education.The Learning and Teaching of Algebra provides a pedagogical framework for the teaching and learning of algebra grounded in theory and research. Areas covered include:• Algebra: Setting the Scene• Some Lessons From History• Seeing Algebra Through the Eyes of a Learner• Emphases in Algebra Teaching• Algebra Education in the Digital EraThis guide will be essential reading for trainee and qualified teachers of mathematics, graduate students, curriculum developers, researchers and all those who are interested in the "problématique" of teaching and learning algebra. It allows you to get involved in the wealth of knowledge that teachers can draw upon to assist learners, helping you gain the insights that mastering algebra provides.

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education.The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach for design research on secondary geometry instruction.Areas covered include:teaching and learning secondary geometry through history;the representations of geometric figures;students’ cognition in geometry;teacher knowledge, practice and, beliefs;teaching strategies, instructional improvement, and classroom interventions;research designs and problems for secondary geometry.Drawing on a team of international authors, this new text will be essential reading for experienced teachers of mathematics, graduate students, curriculum developers, researchers, and all those interested in exploring students’ study of geometry in secondary schools.

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education.The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach for design research on secondary geometry instruction.Areas covered include:teaching and learning secondary geometry through history;the representations of geometric figures;students’ cognition in geometry;teacher knowledge, practice and, beliefs;teaching strategies, instructional improvement, and classroom interventions;research designs and problems for secondary geometry.Drawing on a team of international authors, this new text will be essential reading for experienced teachers of mathematics, graduate students, curriculum developers, researchers, and all those interested in exploring students’ study of geometry in secondary schools.

This book is for people who teach calculus – and especially for people who teach student teachers, who will in turn teach calculus. The calculus considered is elementary calculus of a single variable. The book interweaves ideas for teaching with calculus content and provides a reader-friendly overview of research on learning and teaching calculus along with questions on educational and mathematical discussion topics.Written by a group of international authors with extensive experience in teaching and research on learning/teaching calculus both at the school and university levels, the book offers a variety of approaches to the teaching of calculus so that you can decide the approach for you. Topics covered includeA history of calculus and how calculus differs over countries todayMaking sense of limits and continuity, differentiation, integration and the fundamental theorem of calculus (chapters on these areas form the bulk of the book)The ordering of calculus concepts (should limits come first?)Applications of calculus (including differential equations)The final chapter looks beyond elementary calculus. Recurring themes across chapters include whether to take a limit or a differential/infinitesimal approach to calculus and the use of digital technology in the learning and teaching of calculus. This book is essential reading for mathematics teacher trainers everywhere.

This book is for people who teach calculus – and especially for people who teach student teachers, who will in turn teach calculus. The calculus considered is elementary calculus of a single variable. The book interweaves ideas for teaching with calculus content and provides a reader-friendly overview of research on learning and teaching calculus along with questions on educational and mathematical discussion topics.Written by a group of international authors with extensive experience in teaching and research on learning/teaching calculus both at the school and university levels, the book offers a variety of approaches to the teaching of calculus so that you can decide the approach for you. Topics covered includeA history of calculus and how calculus differs over countries todayMaking sense of limits and continuity, differentiation, integration and the fundamental theorem of calculus (chapters on these areas form the bulk of the book)The ordering of calculus concepts (should limits come first?)Applications of calculus (including differential equations)The final chapter looks beyond elementary calculus. Recurring themes across chapters include whether to take a limit or a differential/infinitesimal approach to calculus and the use of digital technology in the learning and teaching of calculus. This book is essential reading for mathematics teacher trainers everywhere.

Typically, most people don’t realize when and how they can use the mathematics they were taught in high school – yet many of the mathematical ideas and skills can be a powerful tool for understanding how the world works. Learning and Teaching for Mathematical Literacy addresses this situation, offering practical strategies for developing a broader vision of mathematical literacy in the classroom and recognising the importance of maintaining these skills into adult life. Linked to the material explored throughout this book, classroom activities and lesson materials are freely available for use via the QR codes included in each chapter.Filled with case studies and classroom activities, chapters tackle several topics:Describing a framework for a broader vision of mathematical literacy – what is it, and why is it important?Teaching mathematical literacy in the classroomApplying mathematical literacy to ‘real life’ scenarios: My dad is buying a new dishwasher. Should he buy the extended warranty on offer? My phone works fine but I've been offered an upgrade. How should I decide whether to take it?The role of technology in teaching mathematical literacyDesigning mathematical measures for real-word quantitiesFirmly grounded by practical applications for the classroom and beyond, this is an essential handbook for any teacher, teaching assistant, or mathematics subject lead who wishes to develop their students’ mathematical literacy skills. This is also an ideal resource for those delivering or enrolled in teacher preparation courses.

Typically, most people don’t realize when and how they can use the mathematics they were taught in high school – yet many of the mathematical ideas and skills can be a powerful tool for understanding how the world works. Learning and Teaching for Mathematical Literacy addresses this situation, offering practical strategies for developing a broader vision of mathematical literacy in the classroom and recognising the importance of maintaining these skills into adult life. Linked to the material explored throughout this book, classroom activities and lesson materials are freely available for use via the QR codes included in each chapter.Filled with case studies and classroom activities, chapters tackle several topics:Describing a framework for a broader vision of mathematical literacy – what is it, and why is it important?Teaching mathematical literacy in the classroomApplying mathematical literacy to ‘real life’ scenarios: My dad is buying a new dishwasher. Should he buy the extended warranty on offer? My phone works fine but I've been offered an upgrade. How should I decide whether to take it?The role of technology in teaching mathematical literacyDesigning mathematical measures for real-word quantitiesFirmly grounded by practical applications for the classroom and beyond, this is an essential handbook for any teacher, teaching assistant, or mathematics subject lead who wishes to develop their students’ mathematical literacy skills. This is also an ideal resource for those delivering or enrolled in teacher preparation courses.

Linear algebra is a cornerstone of mathematics, yet its teaching and learning present unique challenges. This book invites readers to explore how linear algebra concepts can be introduced and developed through engaging activities, real-world applications, and the integration of technology in the classroom.Delving into key topics such as systems of linear equations, linear transformations, determinants, eigen theory, and vector spaces, the book bridges theory and practice. It provides field-tested activities that engage student thinking, offering instructors adaptable tools to foster conceptual understanding. Additionally, it presents recent research findings, making them accessible to educators and researchers alike. By focusing on task design, student interaction, and instructor facilitation, the book demonstrates how these elements can work together to enhance learning. Researchers will also find a comprehensive overview of studies on linear algebra education, with a focus on tasks and tools that promote meaningful engagement.This highly practical book is an indispensable resource for educators, researchers, and general readers looking to transform linear algebra instruction and enhance student engagement.

Linear algebra is a cornerstone of mathematics, yet its teaching and learning present unique challenges. This book invites readers to explore how linear algebra concepts can be introduced and developed through engaging activities, real-world applications, and the integration of technology in the classroom.Delving into key topics such as systems of linear equations, linear transformations, determinants, eigen theory, and vector spaces, the book bridges theory and practice. It provides field-tested activities that engage student thinking, offering instructors adaptable tools to foster conceptual understanding. Additionally, it presents recent research findings, making them accessible to educators and researchers alike. By focusing on task design, student interaction, and instructor facilitation, the book demonstrates how these elements can work together to enhance learning. Researchers will also find a comprehensive overview of studies on linear algebra education, with a focus on tasks and tools that promote meaningful engagement.This highly practical book is an indispensable resource for educators, researchers, and general readers looking to transform linear algebra instruction and enhance student engagement.

Numbers are the backbones of mathematics. From 1 to infinity, numbers accompany and underlie the learning of mathematics and research. While perceived as familiar and understood, numbers present fascinating and often mysterious patterns, relationships and pedagogical issues. The Learning and Teaching of Number explores how mathematics education research has addressed issues related to the structure of numbers and number operations and provides a classroom context. It invites readers to explore less-travelled paths through a well-trodden terrain of number. This fascinating book combines mathematical content with pedagogical ideas and research results. Focusing on number, the book illustrates central ideas related to numbers via a variety of tasks at different levels of complexity. The Learning and Teaching of Number will allow the reader to examine and develop personal understanding of number sets and the relationships among them; enhance personal understanding of familiar topics associated with number operations; engage in a variety of tasks and strengthen personal problem-solving skills; enrich their repertoire of mathematical tasks and pedagogical actions; and consider research ideas and results related to teaching numbers, number operations and number relationships.This is a valuable resource for teacher education courses, graduate programs in mathematics education and professional development programs. Teacher trainers and maths teachers will find their personal understanding of numbers and relationships enriched and will draw connections between research and classroom pedagogy which will extend and enhance their teaching.

Numbers are the backbones of mathematics. From 1 to infinity, numbers accompany and underlie the learning of mathematics and research. While perceived as familiar and understood, numbers present fascinating and often mysterious patterns, relationships and pedagogical issues. The Learning and Teaching of Number explores how mathematics education research has addressed issues related to the structure of numbers and number operations and provides a classroom context. It invites readers to explore less-travelled paths through a well-trodden terrain of number. This fascinating book combines mathematical content with pedagogical ideas and research results. Focusing on number, the book illustrates central ideas related to numbers via a variety of tasks at different levels of complexity. The Learning and Teaching of Number will allow the reader to examine and develop personal understanding of number sets and the relationships among them; enhance personal understanding of familiar topics associated with number operations; engage in a variety of tasks and strengthen personal problem-solving skills; enrich their repertoire of mathematical tasks and pedagogical actions; and consider research ideas and results related to teaching numbers, number operations and number relationships.This is a valuable resource for teacher education courses, graduate programs in mathematics education and professional development programs. Teacher trainers and maths teachers will find their personal understanding of numbers and relationships enriched and will draw connections between research and classroom pedagogy which will extend and enhance their teaching.

This book takes stock of the state of affairs of the teaching and learning of mathematical modelling with regard to research, development and practice. It provides a conceptual framework for mathematical modelling in mathematics education at all education levels, as well as the background and resources for teachers to acquire the knowledge and competencies that will allow them to successfully include modelling in their teaching, with an emphasis on the secondary school level. Mathematics teachers, mathematics education researchers and developers will benefit from this book. Expertly written and researched, this book includes a comprehensive overview of research results in the field, an exposition of the educational goals associated with modelling, the essential components of modelling competency and an extensive discussion of didacticopedagogical challenges in modelling. Moreover, it offers a wide variety of illuminating cases and best-practice examples in addition to insights into the focal points for future research and practice. The Learning and Teaching of Mathematical Modelling is an invaluable resource for teachers, researchers, textbook authors, secondary school mathematics teachers, undergraduate and graduate students of mathematics as well as student teachers.