Teaching Mathematics

Author: Paul Chambers

Publisher: SAGE

ISBN: 1446245403

Category: Education

Page: 264

View: 3191

Reflective practice is at the heart of effective teaching, and this book helps you develop into a reflective teacher of mathematics. Everything you need is here: guidance on developing your analysis and self-evaluation skills, the knowledge of what you are trying to achieve and why, and examples of how experienced teachers deliver successful lessons. The book shows you how to plan lessons, how to make good use of resources and how to assess pupils' progress effectively. Each chapter contains points for reflection, which encourage you to break off from your reading and think about the challenging questions that you face as a new teacher. The book is supplemented by a companion website, with: " Videos of real lessons so you can see the skills discussed in the text in action " Links to a range of sites that provide useful additional support " Extra planning and resource materials. If you are training to teach mathematics this book will help you to improve your classroom performance, by providing you with practical advice, but also by helping you to think in depth about the key issues. It also provides examples of the research evidence that is needed in academic work at Masters level, essential for anyone undertaking an M-level PGCE. Paul Chambers was formerly course leader for PGCE mathematics at Edge Hill University.

Teaching Mathematics in the Secondary School

Author: Paul Chambers,Robert Timlin

Publisher: SAGE

ISBN: 1446280942

Category: Education

Page: 296

View: 9631

'Chambers and Timlin write with clarity and purpose. The authors link the theory of teaching mathematics with simple reflective questions and interesting maths tasks. There is practical advice on planning, assessment and differentiations, amongst other pertinent themes' -Jacqueline Oldham, PGCE Secondary Mathematics Course Tutor, St Mary's University College 'This is a very practical guide for learning to teach mathematics for student teachers on all training routes. Chapters are focused and readable but succeed in tackling issues in depth giving the reader strong academic support' -Anne Haworth, PGCE Secondary Mathematics Course Tutor, University of Manchester This book is an essential companion for anyone training to teach mathematics in secondary education. It offers clear and engaging coverage of all major aspects of mathematics teaching that you will need to engage with in order to successfully train for the classroom. This Second Edition includes: a new chapter exploring different teaching approaches including active learning, effective group work and creative mathematics teaching expanded coverage of assessment, using resources in the classroom and metacognition and learning updated coverage of recent developments in education policy and the 2012 Teachers' Standards This is essential reading for anyone training to teach secondary mathematics including postgraduate (PGCE, SCITT) and school-based routes into teaching. Free digital resources for extra support is available in the book's companion website. It includes: Web links and further reading for each chapter A video series of a sample classroom lesson filmed in a real-life setting Visit www.sagepub.co.uk/chamberstimlin

Aspects of Teaching Secondary Mathematics

Perspectives on Practice

Author: Linda Haggarty

Publisher: Routledge

ISBN: 1134500963

Category: Education

Page: 312

View: 3405

If learners in the classroom are to be excited by mathematics, teachers need to be both well informed about current initiatives and able to see how what is expected of them can be translated into rich and stimulating classroom strategies. The book examines current initiatives that affect teaching mathematics and identifies pointers for action in the classroom. Divided into three major sections, it looks at: the changing mathematics classroom at primary, secondary and tertiary level major components of the secondary curriculum practical pedagogical issues of particular concern to mathematics teachers. Each issue is explores in terms of major underpinnings and research in that area, and practical ideas can be drawn from the text and implemented in the reader's classroom practice. Each chapter has been written by a well-respected writer, researcher and practitioner in their field and all share a common goal: to look thoughtfully and intelligently at some of the practical issues facing mathematics teachers and offer their perspectives on those issues.

Teaching and Learning Geometry

Author: Doug French

Publisher: A&C Black

ISBN: 082647361X

Category: Education

Page: 169

View: 3567

This fascinating title reviews the teaching and learning of school geometry from the perspective of both the new teacher and the more experienced teacher. It is designed to extend and deepen subject knowledge and to offer practical advice and ideas for the classroom in the context of current practice and research. Particular emphasis is given to the following elements: •understanding the key ideas of the geometry curriculum •learning geometry effectively: lessons from research and current practice •misconceptions and errors •the role of technology in learning geometry.

How Children Learn

Author: John Holt

Publisher: Da Capo Press

ISBN: 0786746904

Category: Education

Page: 320

View: 7151

This enduring classic of educational thought offers teachers and parents deep, original insight into the nature of early learning. John Holt was the first to make clear that, for small children, “learning is as natural as breathing.” In this delightful yet profound book, he looks at how we learn to talk, to read, to count, and to reason, and how we can nurture and encourage these natural abilities in our children.”


Higher Education in the Age of Artificial Intelligence

Author: Joseph E. Aoun

Publisher: MIT Press

ISBN: 0262344327

Category: Education

Page: 216

View: 3994

Driverless cars are hitting the road, powered by artificial intelligence. Robots can climb stairs, open doors, win Jeopardy, analyze stocks, work in factories, find parking spaces, advise oncologists. In the past, automation was considered a threat to low-skilled labor. Now, many high-skilled functions, including interpreting medical images, doing legal research, and analyzing data, are within the skill sets of machines. How can higher education prepare students for their professional lives when professions themselves are disappearing? In Robot-Proof, Northeastern University president Joseph Aoun proposes a way to educate the next generation of college students to invent, to create, and to discover -- to fill needs in society that even the most sophisticated artificial intelligence agent cannot. A "robot-proof" education, Aoun argues, is not concerned solely with topping up students' minds with high-octane facts. Rather, it calibrates them with a creative mindset and the mental elasticity to invent, discover, or create something valuable to society -- a scientific proof, a hip-hop recording, a web comic, a cure for cancer. Aoun lays out the framework for a new discipline, humanics, which builds on our innate strengths and prepares students to compete in a labor market in which smart machines work alongside human professionals. The new literacies of Aoun's humanics are data literacy, technological literacy, and human literacy. Students will need data literacy to manage the flow of big data, and technological literacy to know how their machines work, but human literacy -- the humanities, communication, and design -- to function as a human being. Life-long learning opportunities will support their ability to adapt to change. The only certainty about the future is change. Higher education based on the new literacies of humanics can equip students for living and working through change.

The Art of Proof

Basic Training for Deeper Mathematics

Author: Matthias Beck,Ross Geoghegan

Publisher: Springer Science & Business Media

ISBN: 9781441970237

Category: Mathematics

Page: 182

View: 3890

The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.

Mathematical Olympiad Challenges

Author: Titu Andreescu,Razvan Gelca

Publisher: Springer Science & Business Media

ISBN: 9780817646110

Category: Mathematics

Page: 283

View: 7763

Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory Historical insights and asides are presented to stimulate further inquiry Emphasis is on creative solutions to open-ended problems Many examples, problems and solutions, with a user-friendly and accessible style Enhanced motivatio References

Proofs from THE BOOK

Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer

ISBN: 3662572656

Category: Mathematics

Page: 326

View: 8725

This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters. From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition" “... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.” From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011

Are You Sure...It's ADHD?

Author: Sharon Oberne

Publisher: Buzzing Light

ISBN: 9780595394074

Category: Family & Relationships

Page: 63

View: 7508

This book is a wonderful resource for parents, students and educators wanting to learn more about hidden disabilities. Each of my three children was mislabeled as having ADHD. As I discovered by doing my own research, not one of my children had ADHD. Along with sharing my children's personal history, my book provides additional insight from my experience as an educator working with students having various disabilities, some having ADHD and others with a different disorder. In addition to offering information about the proper procedures in determining a disability, my book provides information about individual educational plans, descriptions of successful adaptations to use with ALL students, an educator's guide for improving classroom climate and a hand-out for college students requesting accommodations.

Proofs and Refutations

The Logic of Mathematical Discovery

Author: Imre Lakatos

Publisher: Cambridge University Press

ISBN: 1316425339

Category: Science

Page: N.A

View: 3941

Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.

Understanding Machine Learning

From Theory to Algorithms

Author: Shai Shalev-Shwartz,Shai Ben-David

Publisher: Cambridge University Press

ISBN: 1107057132

Category: Computers

Page: 409

View: 970

Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage.

Never Work Harder Than Your Students and Other Principles of Great Teaching

Author: Robyn R. Jackson

Publisher: ASCD

ISBN: 1416612262

Category: Education

Page: 249

View: 3561

Is great teaching a gift that only a few of us are born with, or is it a skill that can be learned? In Never Work Harder Than Your Students, Robyn Jackson makes a radical assertion: Any teacher can become a master teacher by developing a master teacher mindset. The master teacher mindset can be achieved by rigorously applying seven principles to your teaching until they become your automatic response to students in the classroom. The more you practice these seven principles, the more you begin to think like a master teacher: 1. Start where your students are. 2. Know where your students are going. 3. Expect to get your students to their goal. 4. Support your students along the way. 5. Use feedback to help you and your students get better. 6. Focus on quality rather than quantity. 7. Never work harder than your students. Using these principles, Jackson shows you how to become a master teacher no matter where you are in your practice. Each chapter provides a detailed explanation of one of the mastery principles, the steps you need to take to apply them to your own practice, and suggestions for how you can begin practicing the principle in your classroom right away. Jackson offers stories from her own teaching practice, as well as from other teachers she has helped, to show you how each principle works. Teaching is a hard job, but using Jackson’s principles will help you and your students reap the rich rewards of that hard work.

How to Prove It

A Structured Approach

Author: Daniel J. Velleman

Publisher: Cambridge University Press

ISBN: 1139450972

Category: Mathematics

Page: N.A

View: 8178

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

Proofs Without Words

Exercises in Visual Thinking

Author: Malcolm Scott MacKenzie,Roger B. Nelsen

Publisher: MAA

ISBN: 9780883857007

Category: Mathematics

Page: 140

View: 5570

Proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: Geometry and algebra; Trigonometry, calculus and analytic geometry; Inequalities; Integer sums; and Sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.

Offer of Proof

Author: Robert Heilbrun

Publisher: Harper Collins

ISBN: 9780061900112

Category: Fiction

Page: 384

View: 4904

A riveting thriller, the debut novel of a high–profile Manhattan public defender with a gift for writing about the law in ways that are vastly entertaining, witty, sardonic and wise. A beautiful young businesswoman is murdered on the streets of New York after shopping for art in Chelsea, and in her final words to the police, she identifies her assailant. Or does she? Arch Gold, dedicated public defender, gets the biggest case of his life when he's assigned to represent the accused killer, Damon Tucker, a young black kid from Harlem. Damon claims he's innocent, and Gold puts his reputation on the line to save his client and find the real killer.

Burden of Proof

Author: DiAnn Mills

Publisher: NavPress

ISBN: 1496427076

Category: Fiction

Page: 416

View: 7232

Reeling from a negotiation gone wrong, FBI Special Agent April Ramos is caught off guard when a frazzled young woman shoves a crying baby into her arms, then disappears. Worry for the child’s safety quickly turns to fear when a man claiming to be the girl’s father abducts them at gunpoint. April puts her hostage negotiation skills to use to learn more about who she’s dealing with: Jason Snyder, a fugitive accused of murder. As Jason spins a tall tale about being framed for the killing of his business partner, April must sort through his claims to find the truth. A truth that becomes all the more evident after April overhears a conversation between Jason and the local sheriff and realizes something more sinister may be happening in their small town of Sweet Briar, Texas. But aligning herself with a known fugitive to uncover the burden of proof could cost April her job . . . or worse, her life and the lives of other innocent people.

The Art of Asking

How I Learned to Stop Worrying and Let People Help

Author: Amanda Palmer

Publisher: Grand Central Publishing

ISBN: 1455581070

Category: Self-Help

Page: 224

View: 4915

FOREWORD BY BRENE BROWN and POSTSCRIPT FROM BRAIN PICKINGS CREATOR MARIA POPOVA Rock star, crowdfunding pioneer, and TED speaker Amanda Palmer knows all about asking. Performing as a living statue in a wedding dress, she wordlessly asked thousands of passersby for their dollars. When she became a singer, songwriter, and musician, she was not afraid to ask her audience to support her as she surfed the crowd (and slept on their couches while touring). And when she left her record label to strike out on her own, she asked her fans to support her in making an album, leading to the world's most successful music Kickstarter. Even while Amanda is both celebrated and attacked for her fearlessness in asking for help, she finds that there are important things she cannot ask for-as a musician, as a friend, and as a wife. She learns that she isn't alone in this, that so many people are afraid to ask for help, and it paralyzes their lives and relationships. In this groundbreaking book, she explores these barriers in her own life and in the lives of those around her, and discovers the emotional, philosophical, and practical aspects of THE ART OF ASKING. Part manifesto, part revelation, this is the story of an artist struggling with the new rules of exchange in the twenty-first century, both on and off the Internet. THE ART OF ASKING will inspire readers to rethink their own ideas about asking, giving, art, and love.