Nathalie Sinclair - Böcker

A majority of the chapters in this book first saw the light of day as talks at a conference organised and held at Queen’s University in Kingston, Ontario, Canada in April 2001. This small, invitational meeting, tellingly entitled Beauty and the Mathematical Beast, brought together a range of academics int- ested in and committed to exploring connections between mathematics and aesthetics. The enthusiastic response of participants at this gathering enco- aged the presenters to expand upon their initial contributions and persuaded the organisers to recruit further chapters in order to bring a greater balance to the whole. The timing of this event was not arbitrary. The preceding decade had seen a resurgence in serious writing dealing with deeper relations between mathematics (and science) and ‘the beautiful’. In many ways, we the editors of this volume found these contributions to the literature were revisiting and drawing on themes that had been prominent over two thousand five h- dred years ago, in certain writings of the Pythagoreans. While not intending to offer a historical reappraisal of these ancient thinkers here, we have none the less chosen to invoke this profound interweaving of the mathematical and the aesthetic to which this reputedly secretive philosophical sect was ext- sively attuned. This book is divided into three sections comprising three chapters each, each with its own short introduction discussing the particular chapters within.

In this innovative book, Nathalie Sinclair makes a compelling case for the inclusion of the aesthetic in the teaching and learning of mathematics. Using a provocative set of philosophical, psychological, mathematical, technological, and educational insights, she illuminates how the materials and approaches we use in the mathematics classroom can be enriched for the benefit of all learners. While ranging in scope from the young learner to the professional mathematician, there is a particular focus on middle school, where negative feelings toward mathematics frequently begin. Offering specific recommendations to help teachers evoke and nurture their students’ aesthetic abilities, this book:Features powerful episodes from the classroom that show students in the act of developing a sense of mathematical aesthetics.Analyzes how aesthetic sensibilities to qualities such as connectedness, fruitfulness, apparent simplicity, visual appeal, and surprise are fundamental to mathematical inquiry.Includes examples of mathematical inquiry in computer-based learning environments, revealing some of the roles they play in supporting students’ aesthetic inclinations.

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.

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.

This book explores alternative ways to consider the relationship between mathematics and the material world. Drawing on the philosophy of Gilles Châtelet and the post-humanist materialism of Karen Barad, the authors present an 'inclusive materialist' approach to studying mathematics education. This approach offers a fresh perspective on human and nonhuman bodies, challenging current assumptions about the role of the senses, language, and ability in teaching and learning mathematics. Each chapter provides empirical examples from the classroom that demonstrate how inclusive materialism can be applied to a wide range of concerns in the field. The authors analyze recent studies on students' gestures, expressions, and drawings in order to establish a link between mathematical activity and mathematical concepts. Mathematics and the Body expands the landscape of research in mathematics education and will be an essential resource for teachers, students, and researchers alike.

Responding to widespread interest within cultural studies and social inquiry, this book addresses the question 'what is a mathematical concept?' using a variety of vanguard theories in the humanities and posthumanities. Tapping historical, philosophical, sociological and psychological perspectives, each chapter explores the question of how mathematics comes to matter. Of interest to scholars across the usual disciplinary divides, this book tracks mathematics as a cultural activity, drawing connections with empirical practice. Unlike other books in this area, it is highly interdisciplinary, devoted to exploring the ontology of mathematics as it plays out in different contexts. This book will appeal to scholars who are interested in particular mathematical habits - creative diagramming, structural mappings, material agency, interdisciplinary coverings - that shed light on both mathematics and other disciplines. Chapters are also relevant to social sciences and humanities scholars, as each offers philosophical insight into mathematics and how we might live mathematically.

In Disrupting Boundaries in Education and Research, six educational researchers explore together the potentialities of transdisciplinary research that de-centres human behaviour and gives materiality its due in the making of educational worlds. The book presents accounts of what happens when researchers think and act with new materiality and post-human theories to disrupt boundaries such as self and other, human and non-human, representation and objectivity. Each of the core chapters works with different new materiality concepts to disrupt these boundaries and to consider the emotive, sensory, nuanced, material and technological aspects of learning in diverse settings, such as in mathematics and learning to swim, discovering the bio-products of 'eco-sustainable' building, making videos and contending with digital government and its alienating effects. When humans are no longer at the centre of the unfolding world it is both disorienting and exhilarating. This book is an invitation to continue along these paths.

Despite pervading all aspects of educational practice and theory, little scholarship focuses on time in education. This book addresses that lacuna questioning our assumptions about time and their ramifications on theories of learning, issues of equity and diversity, and on the purposes of education itself. The authors examine ideas about time in a wide variety of contexts, from ancient Greek fiction to 19th century theories of evolution and from 20th century indigenous stories to 20th century afro-futurist fiction. They show how pervasive the image of ‘time as an arrow’ has become, an image of time that is one-way, singular and teleological. Through exploring other theories of time, the authors propose alternatives for time in education. They argue that time is one of the key biopolitical tools we think and operate with, but rarely address as a historical, cultural and pedagogical category with which schools reproduce oppressive structures around race, class, and gender in society. The book draws on ideas from the arts and the sciences to illustrate and trouble assumptions of time drawing on artistic and theoretic work from Édouard Glissant, Henri Lefebvre, Giordano Nanni, Denise Ferreira da Silva, Bonnie Honig and others.

Despite pervading all aspects of educational practice and theory, little scholarship focuses on time in education. This book addresses that lacuna questioning our assumptions about time and their ramifications on theories of learning, issues of equity and diversity, and on the purposes of education itself. The authors examine ideas about time in a wide variety of contexts, from ancient Greek fiction to 19th century theories of evolution and from 20th century indigenous stories to 20th century afro-futurist fiction. They show how pervasive the image of ‘time as an arrow’ has become, an image of time that is one-way, singular and teleological. Through exploring other theories of time, the authors propose alternatives for time in education. They argue that time is one of the key biopolitical tools we think and operate with, but rarely address as a historical, cultural and pedagogical category with which schools reproduce oppressive structures around race, class, and gender in society. The book draws on ideas from the arts and the sciences to illustrate and trouble assumptions of time drawing on artistic and theoretic work from Édouard Glissant, Henri Lefebvre, Giordano Nanni, Denise Ferreira da Silva, Bonnie Honig and others.

This volume stages a series of radical provocations that seek to reorient the very conditions under which learning becomes thinkable. Refusing the redemptive pull of schooling as a salvageable public good, the collection foregrounds the necessity of undisciplining education, dislodging it from its colonial grammars, disciplinary enclosures, and anthropocentric imaginaries.Schools, far from neutral spaces of knowledge transmission, are infrastructural technologies of late capitalist governance: disciplining bodies, managing time, and sustaining the ongoing occupation of Indigenous lands under the guise of progress and order. Drawing from grotesque materialisms, Indigenous epistemologies, and speculative philosophies, the volume positions pluriversal indeterminacy as a generative ontological condition, contesting the closure-driven logics of Western educational taxonomy. If schools operate as entropy-displacement machines, maintaining systemic stability through the externalization of collapse, then what is required is not critique alone, but a methodological insurgency capable of abolishing education’s epistemic foundations. To this end, contributors—traversing anthropology, architecture, mathematics, biology, Indigenous studies, art, philosophy, and literature—articulate a constellation of non-disciplined pedagogical experiments that emerge from the current unraveling of education itself. Through deliberate acts of epistemic undoing, authors inhabit a space where fixed categories, such as human/nonhuman, past/future, knowledge/ignorance are rendered inoperative, making room for learning that reconfigures the possible.

A majority of the chapters in this book first saw the light of day as talks at a conference organised and held at Queen’s University in Kingston, Ontario, Canada in April 2001. This small, invitational meeting, tellingly entitled Beauty and the Mathematical Beast, brought together a range of academics int- ested in and committed to exploring connections between mathematics and aesthetics. The enthusiastic response of participants at this gathering enco- aged the presenters to expand upon their initial contributions and persuaded the organisers to recruit further chapters in order to bring a greater balance to the whole. The timing of this event was not arbitrary. The preceding decade had seen a resurgence in serious writing dealing with deeper relations between mathematics (and science) and ‘the beautiful’. In many ways, we the editors of this volume found these contributions to the literature were revisiting and drawing on themes that had been prominent over two thousand five h- dred years ago, in certain writings of the Pythagoreans. While not intending to offer a historical reappraisal of these ancient thinkers here, we have none the less chosen to invoke this profound interweaving of the mathematical and the aesthetic to which this reputedly secretive philosophical sect was ext- sively attuned. This book is divided into three sections comprising three chapters each, each with its own short introduction discussing the particular chapters within.

Lesson play is a novel construct in research and teachers’ professional development in mathematics education. Lesson play refers to a lesson or part of a lesson presented in dialogue form—inspired in part by Lakatos’s evocative Proofs and Refutations—featuring imagined interactions between a teacher and her/his students.

Lesson play is a novel construct in research and teachers’ professional development in mathematics education. Lesson play refers to a lesson or part of a lesson presented in dialogue form—inspired in part by Lakatos’s evocative Proofs and Refutations—featuring imagined interactions between a teacher and her/his students.

This volume investigates the evolution of the geometry curriculum in the United States over the past 150 years. A primary goal is to increase awareness of the shape and nature of the current geometry curriculum by explaining how things have come to be as they are.Given the limited access to first-hand accounts of the enacted geometry curriculum during the past 150 years, the monograph relies on textbooks to provide a record of the implemented curriculum at any given point in time. Policy documents can provide insight into the choices made in textbooks by hinting at the issues considered and the recommendations made.The monograph is organized in a chronological sequence of "notable events" leading to discernable changes in thinking about the geometry curriculum over the past century and a half—roughly the extent of time during which geometry has been taught in American schools. Notable events include important reports or commissions, influential texts, new schools of thought, and developments in learning technologies. These events affected, among other things: content and aims of the geometry curriculum; the nature of mathematical activity as construed by both mathematicians and mathematics educators; and, the resources students are given for engaging in mathematical activity. Before embarking through the notable events, it is necessary to consider the "big bang" of geometry, namely the moment in time that shaped the future life of the geometry curriculum. This corresponds to the emergence of Euclidean geometry. Given its influence on the shape of the geometry curriculum, familiarity with the nature of the geometry articulated in Euclid’s Elements is essential to understanding the many tensions that surround the school geometry curriculum.Several themes emerge over the course of the monograph, and include: the aims and means of the geometry curriculum, the importance of proof in geometry, the role of visualization and tactile experiences, the fusion between solid and plane geometry, the curricular connections between geometry and algebra, and the use of motion and continuity.The intended audience would include curriculum developers, researchers, teachers, and curriculum supervisors.

This volume investigates the evolution of the geometry curriculum in the United States over the past 150 years. A primary goal is to increase awareness of the shape and nature of the current geometry curriculum by explaining how things have come to be as they are.Given the limited access to first-hand accounts of the enacted geometry curriculum during the past 150 years, the monograph relies on textbooks to provide a record of the implemented curriculum at any given point in time. Policy documents can provide insight into the choices made in textbooks by hinting at the issues considered and the recommendations made.The monograph is organized in a chronological sequence of "notable events" leading to discernable changes in thinking about the geometry curriculum over the past century and a half—roughly the extent of time during which geometry has been taught in American schools. Notable events include important reports or commissions, influential texts, new schools of thought, and developments in learning technologies. These events affected, among other things: content and aims of the geometry curriculum; the nature of mathematical activity as construed by both mathematicians and mathematics educators; and, the resources students are given for engaging in mathematical activity. Before embarking through the notable events, it is necessary to consider the "big bang" of geometry, namely the moment in time that shaped the future life of the geometry curriculum. This corresponds to the emergence of Euclidean geometry. Given its influence on the shape of the geometry curriculum, familiarity with the nature of the geometry articulated in Euclid’s Elements is essential to understanding the many tensions that surround the school geometry curriculum.Several themes emerge over the course of the monograph, and include: the aims and means of the geometry curriculum, the importance of proof in geometry, the role of visualization and tactile experiences, the fusion between solid and plane geometry, the curricular connections between geometry and algebra, and the use of motion and continuity.The intended audience would include curriculum developers, researchers, teachers, and curriculum supervisors.

It is a significant reference book for those involved with teaching mathematics or using mobile technologies in education, while also offering insights and examples that are applicable to the use of digital technologies in education generally.

This book brings together international research on school teachers’, and university lecturers’ uses of digital technology to enhance teaching and learning in mathematics.

This book brings together international research on school teachers’, and university lecturers’ uses of digital technology to enhance teaching and learning in mathematics.

Mobile technologies influence the way that we interact with the world, the way that we live. We use them for communication, entertainment, information and research. In education settings, there has been substantial investment in mobile devices, often without a concomitant investment in developing pedagogy and practices. With mobile technologies evolving rapidly, and the number of educational apps growing, there is a need for research into how they facilitate mathematics learning. Such research is of particular importance regarding how such devices may be used to open up new ways of envisaging mathematics and mathematics education, and to help develop conceptual rather than procedural or declarative knowledge. This volume draws upon international research and reports on a range of research projects that have incorporated mobile technologies for mathematics education. It presents research on the use of mobile technologies, such as iPads, iPods, iPhones, Androids,and Tablets, across a diverse range of cultures, year levels and contexts. It examines the ways in which mobile technologies, including apps, might influence students’ engagement, cognition, collaboration and attitudes, through the reshaping of the learning experience. In addition, the book presents appropriate ways to integrate mobile technologies into teaching and learning programmes. It is a significant reference book for those involved with teaching mathematics or using mobile technologies in education, while also offering insights and examples that are applicable to the use of digital technologies in education generally.