EBOOK: NUMERACY AND BEYOND

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Publisher : McGraw-Hill Education (UK)
ISBN 13 : 033523187X
Total Pages : 136 pages
Book Rating : 4.3/5 (352 download)

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Book Synopsis EBOOK: NUMERACY AND BEYOND by : Martin Hughes

Download or read book EBOOK: NUMERACY AND BEYOND written by Martin Hughes and published by McGraw-Hill Education (UK). This book was released on 2000-05-16 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the fundamental problems in education is that of applying skills and knowledge which learners have gained in one context to problems they encounter in another. This is particularly so in mathematics, where the problems encountered by learners in applying mathematical knowledge are well documented. Using and applying mathematics has been a central component of the National Curriculum in mathematics. However, the National Numeracy Strategy has adopted a new approach, in which 'using and applying' is integrated throughout the mathematics curriculum. This book aims to help teachers develop their understanding and practice in this crucial area. It is based on the findings of a major research study, funded by the Nuffield Foundation, in which a group of primary teachers worked closely with the research team to develop their thinking and practice. The book provides a clear conceptual analysis of the problem of application, together with extensive examples of ways in which teachers can address it in their classrooms at Key Stages 1 and 2. A novel feature of the book is that it includes first-hand accounts of practice in Japanese classrooms, and outlines what teachers in the UK and elsewhere may learn from Japanese methods.

Math, Better Explained

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Publisher :
ISBN 13 : 9781519711540
Total Pages : 98 pages
Book Rating : 4.7/5 (115 download)

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Book Synopsis Math, Better Explained by : Kalid Azad

Download or read book Math, Better Explained written by Kalid Azad and published by . This book was released on 2015-12-04 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Math, Better Explained is an intuitive guide to the math fundamentals. Learn math the way your teachers always wanted.

Beyond the Numbers: a Student-Centered Approach for Learning Statistical Reasoning

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Publisher :
ISBN 13 : 9781617408144
Total Pages : pages
Book Rating : 4.4/5 (81 download)

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Book Synopsis Beyond the Numbers: a Student-Centered Approach for Learning Statistical Reasoning by : Rayens

Download or read book Beyond the Numbers: a Student-Centered Approach for Learning Statistical Reasoning written by Rayens and published by . This book was released on 2021-08-04 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numeracy in Authentic Contexts

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Publisher : Springer
ISBN 13 : 9811057362
Total Pages : 451 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Numeracy in Authentic Contexts by : Maura Sellars

Download or read book Numeracy in Authentic Contexts written by Maura Sellars and published by Springer. This book was released on 2017-10-25 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the notion that there are many ways in which mathematics learning can be achieved for students and that not all of them are focused on the mathematics classroom. It explores the foundational numeracy principles of the non-mathematical subject areas and aligns these to the Australian numeracy-learning continuum. It demonstrates, in detail, the extent to which numeracy competencies underpin successful learning in all the subject areas of the curricula. It validates a focus of developing numeracy competencies through learning in the arts, science and other discipline areas with which school students to engage with in order develop holistically, but which are not subjected to national assessment practices. It is developed around the notion of ‘praxis’, putting theory into practice in order to respond to the urgent need for students to be supported in their efforts to increase their numeracy capabilities in a world where extensive amounts of new information are often presented in graphical or data based formats. Additionally, it offers perspectives on developing all students’ capacities to become numerate in school contexts and presents inclusive, differentiated lesson examples as an alternative way of exploring numeracy in the context of teaching and learning in real-world classroom contexts.

Strengths-Based Teaching and Learning in Mathematics

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Publisher : Corwin Press
ISBN 13 : 1544374925
Total Pages : 189 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Strengths-Based Teaching and Learning in Mathematics by : Beth McCord Kobett

Download or read book Strengths-Based Teaching and Learning in Mathematics written by Beth McCord Kobett and published by Corwin Press. This book was released on 2020-02-27 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful.

Helping Children Learn Mathematics

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Publisher : National Academies Press
ISBN 13 : 0309131987
Total Pages : 53 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Helping Children Learn Mathematics by : National Research Council

Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.

Advanced Problems in Mathematics

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Publisher :
ISBN 13 : 9781783747764
Total Pages : 188 pages
Book Rating : 4.7/5 (477 download)

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Book Synopsis Advanced Problems in Mathematics by : Stephen Siklos

Download or read book Advanced Problems in Mathematics written by Stephen Siklos and published by . This book was released on 2019-10-16 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

Mathematics and Computation

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Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

What Teachers Need to Know about Numeracy

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Publisher : Aust Council for Ed Research
ISBN 13 : 0864319045
Total Pages : 114 pages
Book Rating : 4.8/5 (643 download)

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Book Synopsis What Teachers Need to Know about Numeracy by : Peter S. Westwood

Download or read book What Teachers Need to Know about Numeracy written by Peter S. Westwood and published by Aust Council for Ed Research. This book was released on 2008 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an increasing need for numeracy skills in all aspects of life. This book explores the issues that are emerging regarding the teaching of these skills, beginning with preschool and the early years of primary school through to adults with poor numeracy skills. It draws on research and relevant literature from several different countries to provide a comprehensive overview of the subject and contains many links to other sources of information and additional resources.

Building Thinking Classrooms in Mathematics, Grades K-12

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Publisher : Corwin Press
ISBN 13 : 1544374844
Total Pages : 454 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Building Thinking Classrooms in Mathematics, Grades K-12 by : Peter Liljedahl

Download or read book Building Thinking Classrooms in Mathematics, Grades K-12 written by Peter Liljedahl and published by Corwin Press. This book was released on 2020-09-28 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.

EBOOK: Teaching Adult Numeracy: Principles & Practice

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Publisher : McGraw-Hill Education (UK)
ISBN 13 : 0335246834
Total Pages : 329 pages
Book Rating : 4.3/5 (352 download)

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Book Synopsis EBOOK: Teaching Adult Numeracy: Principles & Practice by : Graham Griffiths

Download or read book EBOOK: Teaching Adult Numeracy: Principles & Practice written by Graham Griffiths and published by McGraw-Hill Education (UK). This book was released on 2013-09-16 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers friendly guidance on how to work with adult learners to develop their numeracy and mathematics skills. It brings together current research and practice on teaching adult numeracy into one handy volume and covers the major issues faced by teachers of adult numeracy such as current policy perspectives and implications for teaching practice. There are reflective tasks throughout, which encourage you to develop and apply your theoretical knowledge to your own experiences. Key features include: Reviews of existing policy and research and implications for practice Reflective tasks with commentary, encouraging you to develop and apply your knowledge Case studies of real student experiences Practical activities and ideas to support the planning, teaching and assessment of adult numeracy Drawing on the substantial experience of the contributors, who have a wealth of experience as practitioners and researchers in the field, this book is an essential resource for trainee and practising teachers of adult numeracy and mathematics. It is also an ideal textbook to support teacher training courses leading to a subject specific qualification in teaching numeracy to adults. Contributors: Jackie Ashton, John Barton, Carolyn Brooks, Martyn Edwards, Janette Gibney, David Holloway, David Kaye, Beth Kelly, Barbara Newmarch, Helen Oughton, David Prinn, Diana Spurr, Rebecca Woolley "This is a quite unique book about teaching adult numeracy, which will be invaluable to the many practitioners in this field. The chapters, contributed by a group of experienced and successful lecturers and practitioners, include all aspects of this field, from methods of teaching specific mathematical topics to more general explorations of dyscalculia and emotional factors in adult learners. Each chapter includes research findings and thoughtful presentation of ideas with practical ideas for teaching, and tasks for the reader. This is a market which has not been served well in the past, so it is good to see the gap filled at last." Margaret Brown, Emeritus Professor of Mathematics Education, King's College London, UK "The editors of this book set out to produce a text that would support teacher-education programmes for adult numeracy, and their book does that and more. The content covers different types of learners, different settings, different understandings of what numeracy actually is; and ranges from commentary on research through case studies to "how to" hints and tips for teaching. Chapters 7 (on provoking mathematical thinking) and 8 (attitudes, beliefs and teaching) should be a required read for any adult numeracy teacher. The book would be at home on any numeracy teacher's desk, and would make an excellent set text for numeracy teacher training courses." Carol Randall, course co-ordinator for numeracy in the department of Lifelong Learning Teacher Education, University of Greenwich, UK "This book is a welcome addition to the growing literature on adult numeracy. It should be essential reading for trainee and practising adult numeracy educators. It brings together relevant research and professional wisdom on a wide variety of aspects of adult numeracy teaching and learning in an accessible way, with well-focussed tasks for readers to extend their knowledge and understanding. While the book is born out of UK concerns and issues, it is also relevant to international readers. Highly recommended." Professor Diana Coben PhD, Director, National Centre of Literacy & Numeracy for Adults, University of Waikato, New Zealand, and Hon. Trustee, Adults Learning Mathematics - A Research Forum (ALM -- www.alm-online.net/)

EBOOK: Boys and Girls in the Primary Classroom

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Publisher : McGraw-Hill Education (UK)
ISBN 13 : 0335227902
Total Pages : 201 pages
Book Rating : 4.3/5 (352 download)

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Book Synopsis EBOOK: Boys and Girls in the Primary Classroom by : Christine Skelton

Download or read book EBOOK: Boys and Girls in the Primary Classroom written by Christine Skelton and published by McGraw-Hill Education (UK). This book was released on 2003-10-16 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates how gender equity (and inequality) occurs in primary classrooms. It uses the findings of current research to provide teachers with recommendations for promoting equity amongst boys and girls. Each contributor summarizes recent research in the area of specialization before looking specifically at issues relevant to primary teaching and learning. The areas of the primary school covered include the National Curriculum subjects of literacy, numeracy and science, and broader topics such as working with boys, children with special educational needs, primary/secondary transition, playground cultures and children's construction of gender identities. The book uses classroom-based research to provide accessible accounts of investigations into gender and primary schooling. At the same time, it offers a critique of the whole drive towards 'evidence based' research. Boys and Girls in the Primary Classroom is aimed particularly at primary teachers and student teachers although the research will be of interest to academics and undergraduate students.

EBOOK: Adult Literacy, Numeracy and Language: Policy, Practice and Research

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Author :
Publisher : McGraw-Hill Education (UK)
ISBN 13 : 0335228038
Total Pages : 206 pages
Book Rating : 4.3/5 (352 download)

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Book Synopsis EBOOK: Adult Literacy, Numeracy and Language: Policy, Practice and Research by : Lyn Tett

Download or read book EBOOK: Adult Literacy, Numeracy and Language: Policy, Practice and Research written by Lyn Tett and published by McGraw-Hill Education (UK). This book was released on 2006-06-16 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the social practice of literacy, numeracy and language and its implications for teaching and learning adult basic skills. Leading international experts argue that literacy, numeracy and language are more than just a set of skills or techniques, but are shaped by the social and cultural context within which they are taking place; the meanings they have for users; and the purposes they serve. This shifts the focus from a narrow, functional and externally imposed definition of literacy, numeracy and language learning, to more open and numerous definitions that focus on what people do with their knowledge, understanding and skills in a range of contexts. Adult Literacy, Numeracy and Language shows how the social practice approach to learning and teaching can be used to develop more inclusive views of adult literacy, numeracy and language. Bringing together the views of researchers, policy makers and practitioners, it helps readers to develop an understanding of contemporary policy developments and encourages them to examine their own practice as adult basic education teachers, in order to respond more effectively to the needs of their students. This book is a valuable resource for practitioners, researchers and students on courses in adult and continuing education (particularly basic skills), postgraduate students, and researchers in the field of post-compulsory education.

STEM Lesson Essentials, Grades 3-8

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Publisher : Heinemann Educational Books
ISBN 13 : 9780325043586
Total Pages : 0 pages
Book Rating : 4.0/5 (435 download)

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Book Synopsis STEM Lesson Essentials, Grades 3-8 by : Jo Anne Vasquez

Download or read book STEM Lesson Essentials, Grades 3-8 written by Jo Anne Vasquez and published by Heinemann Educational Books. This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Want to know how to implement authentic STEM teaching and learning into your classroom? STEM Lesson Essentials provides all the tools and strategies you'll need to design integrated, interdisciplinary STEM lessons and units that are relevant and exciting to your students. With clear definitions of both STEM and STEM literacy, the authors argue that STEM in itself is not a curriculum, but rather a way of organizing and delivering instruction by weaving the four disciplines together in intentional ways. Rather than adding two new subjects to the curriculum, the engineering and technology practices can instead be blended into existing math and science lessons in ways that engage students and help them master 21st century skills.

ACT For Dummies Two eBook Bundle

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Publisher : John Wiley & Sons
ISBN 13 : 1118596692
Total Pages : 1505 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis ACT For Dummies Two eBook Bundle by : Scott A. Hatch

Download or read book ACT For Dummies Two eBook Bundle written by Scott A. Hatch and published by John Wiley & Sons. This book was released on 2013-01-08 with total page 1505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two complete ebooks for one low price! Created and compiled by the publisher, this ACT bundle brings together two of the bestselling For Dummies ACT guides in one, e-only bundle. With this special bundle, you’ll get the complete text of the following titles: ACT For Dummies, 5th Edition Are you one of the millions of students taking the ACT? Have no fear! This friendly guide gives you the competitive edge by fully preparing you for every section of the ACT, including the optional writing test. You get three complete practice tests, complete with detailed explanations and walk-throughs plus sample questions--all updated--along with proven test-taking strategies to improve your score on the ACT. ACT For Dummies is packed with comprehensive review chapters for all four sections of the exam, including English, math, reading, and writing. It offers updated ACT study tips, tips to stay focused on test day, advice to manage your time wisely, how to make smart guesses and spot test traps, and practice materials that model the most recent ACT test. ACT Math For Dummies The ACT Mathematics Test is a 60-question, 60-minute subtest designed to measure the mathematical skills students have typically acquired in courses taken by the end of 11th grade, and is generally considered to be the most challenging section of the ACT. ACT Math For Dummies is an approachable, easy-to-follow study guide specific to the Math section, complete with practice problems and strategies to help you prepare for exam day. Packed with review chapters for algebra, geometry, and trigonometry and three practice tests modeled from questions off the most recent ACT tests, this is your one-stop guide to learn, review, and practice for the test! About the Authors of ACT For Dummies, 2nd Edition Lisa Zimmer Hatch, MA and Scott A. Hatch, JD have been preparing individuals to excel on standardized tests, gain admission to college, and secure careers since 1987. For nearly 30 years, they have provided their award-winning standardized test preparation throughout the world. About the Author of ACT Math For Dummies Mark Zegarelli is the author of Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies (both from Wiley), and five other books on basic math, calculus, and logic. He holds degrees in both English and math from Rutgers University and is a math tutor and teacher.

EBOOK: Teaching Secondary Mathematics with ICT

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Author :
Publisher : McGraw-Hill Education (UK)
ISBN 13 : 0335225969
Total Pages : 273 pages
Book Rating : 4.3/5 (352 download)

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Book Synopsis EBOOK: Teaching Secondary Mathematics with ICT by : Sue Johnston-Wilder

Download or read book EBOOK: Teaching Secondary Mathematics with ICT written by Sue Johnston-Wilder and published by McGraw-Hill Education (UK). This book was released on 2004-10-16 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: “This is a book all mathematics teachers and teacher educators should read! It brings together a wealth of insights from a range of authors… The major issues confronting teachers of mathematics who wish to use ICT in different domains of mathematics are addressed in a clear and accessible way.” Professor Celia Hoyles OBE, Dean of Research and Consultancy, Institute of Education, University of London Teaching Secondary Mathematics with ICT shows the reader how to use Information and Communication Technology (ICT) effectively to enhance the teaching of mathematics in the secondary school. The book explains which forms of technology can be used to improve mathematics teaching and learning, how to get started and where to go for further information. The first two chapters provide a useful introduction for those new to teaching mathematics with ICT. Further chapters cover topics including: ICT and the curriculum: number, algebra, geometry and statistics Making use of interactive whiteboards in the classroom Using the internet and video-conferencing to enhance teaching The book includes practical classroom scenarios and case studies (for example, the government-funded MathsAlive! Initiative), as well as discussions of general issues, such as the role of feedback and the use of ICT in whole-class teaching. It draws on current research and is supplemented by a linked web site, which provides access to demonstration copies of software and sample files. It also includes a directory of resources with lists of organisations, web sites, projects and further reading. Key reading for Education students specialising in Mathematics and all those teaching secondary mathematics, including non-specialists and those on professional development courses. Visit the text-supporting website: www.openup.co.uk/jwp

Putnam and Beyond

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Author :
Publisher : Springer
ISBN 13 : 3319589881
Total Pages : 857 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Putnam and Beyond by : Răzvan Gelca

Download or read book Putnam and Beyond written by Răzvan Gelca and published by Springer. This book was released on 2017-09-19 with total page 857 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.