Teaching Mathematics At Secondary Level

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Teaching Mathematics at Secondary Level

Author : Tony Gardiner
Publisher : Open Book Publishers
ISBN 13 : 1783741406
Total Pages : 334 pages
Book Rating : 4.7/5 (837 download)

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Book Synopsis Teaching Mathematics at Secondary Level by : Tony Gardiner

Download or read book Teaching Mathematics at Secondary Level written by Tony Gardiner and published by Open Book Publishers. This book was released on 2016-02-08 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present.This study is aimed at anyone who would like to think more deeply about the discipline of ‘elementary mathematics’, in England and Wales and anywhere else. By analysing and supplementing the current curriculum, Teaching Mathematics provides food for thought for all those involved in school mathematics, whether as aspiring teachers or as experienced professionals. It challenges us all to reflect upon what it is that makes secondary school mathematics educationally, culturally, and socially important.

Learning to Teach Mathematics in the Secondary School

Author : Sue Johnston-Wilder
Publisher : Routledge
ISBN 13 : 1134291868
Total Pages : 459 pages
Book Rating : 4.1/5 (342 download)

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Book Synopsis Learning to Teach Mathematics in the Secondary School by : Sue Johnston-Wilder

Download or read book Learning to Teach Mathematics in the Secondary School written by Sue Johnston-Wilder and published by Routledge. This book was released on 2005-01-14 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learning to Teach Mathematics in the Secondary School covers a wide range of issues in the teaching of mathematics and gives supporting activities to students to enable them to translate theory into practice. Topics covered include: mathematics in the National Curriculum different teaching approaches using ICT mathematics education for pupils with special needs in mathematics assessment and public examinations teaching mathematics post-16 professional development.

Teaching Secondary Mathematics

Author : Alfred S. Posamentier
Publisher : Pearson Higher Ed
ISBN 13 : 013380898X
Total Pages : 750 pages
Book Rating : 4.1/5 (338 download)

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Book Synopsis Teaching Secondary Mathematics by : Alfred S. Posamentier

Download or read book Teaching Secondary Mathematics written by Alfred S. Posamentier and published by Pearson Higher Ed. This book was released on 2014-02-17 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: Note: This is the loose-leaf version of Teaching Secondary Mathematics and does not include access to the Pearson eText. To order the Pearson eText packaged with the loose-leaf version, use ISBN 0133783677. Teaching Secondary Mathematics, 9/e combines methods of teaching mathematics, including all aspects and responsibilities of the job, with a collection of enrichment units appropriate for the entire secondary school curriculum spectrum to give teachers alternatives for making professional judgments about their teaching performance–and ensuring effective learning. The book is divided into two parts designed to ensure effective teaching and learning: Part I includes a focus on the job of teaching mathematics and Part II includes enrichment activities appropriate for the entire secondary school curriculum. Both the Common Core State Standards and The National Council of teachers of Mathematics Principles and Standards for School Mathematics are referred to throughout the book. The new Ninth Edition features an alignment with the Common Core State Standards (CCSS), with special focus on the mathematical practices, an updated technology chapter that shows how current tools and software can be used for teaching mathematics, and an updated chapter on assessment showing show to provide targeted feedback to advance the learning of every student.

High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice

Author : Robert Q. Berry III
Publisher : Corwin Press
ISBN 13 : 1071806467
Total Pages : 328 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice by : Robert Q. Berry III

Download or read book High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice written by Robert Q. Berry III and published by Corwin Press. This book was released on 2020-03-09 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empower students to be the change—join the teaching mathematics for social justice movement! We live in an era in which students have —through various media and their lived experiences— a more visceral experience of social, economic, and environmental injustices. However, when people think of social justice, mathematics is rarely the first thing that comes to mind. Through model lessons developed by over 30 diverse contributors, this book brings seemingly abstract high school mathematics content to life by connecting it to the issues students see and want to change in the world. Along with expert guidance from the lead authors, the lessons in this book explain how to teach mathematics for self- and community-empowerment. It walks teachers step-by-step through the process of using mathematics—across all high school content domains—as a tool to explore, understand, and respond to issues of social injustice including: environmental injustice; wealth inequality; food insecurity; and gender, LGBTQ, and racial discrimination. This book features: Content cross-referenced by mathematical concept and social issues Downloadable instructional materials for student use User-friendly and logical interior design for daily use Guidance for designing and implementing social justice lessons driven by your own students’ unique passions and challenges Timelier than ever, teaching mathematics through the lens of social justice will connect content to students’ daily lives, fortify their mathematical understanding, and expose them to issues that will make them responsive citizens and leaders in the future.

Teaching Mathematics in the Visible Learning Classroom, High School

Author : John Almarode
Publisher : Corwin Press
ISBN 13 : 1544333129
Total Pages : 278 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Teaching Mathematics in the Visible Learning Classroom, High School by : John Almarode

Download or read book Teaching Mathematics in the Visible Learning Classroom, High School written by John Almarode and published by Corwin Press. This book was released on 2018-08-17 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Select the right task, at the right time, for the right phase of learning It could happen in the morning during homework review. Or perhaps it happens when listening to students as they struggle through a challenging problem. Or maybe even after class, when planning a lesson. At some point, the question arises: How do I influence students′ learning—what’s going to generate that light bulb "aha" moment of understanding? In this sequel to the megawatt best seller Visible Learning for Mathematics, John Almarode, Douglas Fisher, Joseph Assof, John Hattie, and Nancy Frey help you answer that question by showing how Visible Learning strategies look in action in the mathematics classroom. Walk in the shoes of high school teachers as they engage in the 200 micro-decisions-per-minute needed to balance the strategies, tasks, and assessments seminal to high-impact mathematics instruction. Using grade-leveled examples and a decision-making matrix, you’ll learn to Articulate clear learning intentions and success criteria at surface, deep, and transfer levels Employ evidence to guide students along the path of becoming metacognitive and self-directed mathematics achievers Use formative assessments to track what students understand, what they don’t, and why Select the right task for the conceptual, procedural, or application emphasis you want, ensuring the task is for the right phase of learning Adjust the difficulty and complexity of any task to meet the needs of all learners It’s not only what works, but when. Exemplary lessons, video clips, and online resources help you leverage the most effective teaching practices at the most effective time to meet the surface, deep, and transfer learning needs of every student.

Mathematics for High School Teachers

Author : Zalman Usiskin
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 616 pages
Book Rating : 4.X/5 (4 download)

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Book Synopsis Mathematics for High School Teachers by : Zalman Usiskin

Download or read book Mathematics for High School Teachers written by Zalman Usiskin and published by Prentice Hall. This book was released on 2003 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: For algebra or geometry courses for teachers; courses in topics of mathematics; capstone courses for teachers or other students of mathematics; graduate courses for practicing teachers; or students who want a better understanding of mathematics. Filling a wide gap in the market, this text provides current and prospective high school teachers with an advanced treatment of mathematics that will help them understand the connections between the mathematics they will be teaching and the mathematics learned in college. It presents in-depth coverage of the most important concepts in high school mathematics: real numbers, functions, congruence, similarity, and more.

Mathematics for Secondary School Teachers

Author : Elizabeth G. Bremigan
Publisher : MAA
ISBN 13 : 0883857731
Total Pages : 444 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis Mathematics for Secondary School Teachers by : Elizabeth G. Bremigan

Download or read book Mathematics for Secondary School Teachers written by Elizabeth G. Bremigan and published by MAA. This book was released on 2011 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses topics of central importance in the secondary school mathematics curriculum, including functions, polynomials, trigonometry, exponential and logarithmic functions, number and operation, and measurement. This volume is primarily intended as the text for a bridge or capstone course for pre-service secondary school mathematics teachers.

Strengths-Based Teaching and Learning in Mathematics

Author : Beth McCord Kobett
Publisher : Corwin
ISBN 13 : 1544374909
Total Pages : 273 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. This book was released on 2020-02-27 with total page 273 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.

Teaching and Learning Mathematics Online

Author : James P. Howard, II
Publisher : CRC Press
ISBN 13 : 1351245570
Total Pages : 439 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Teaching and Learning Mathematics Online by : James P. Howard, II

Download or read book Teaching and Learning Mathematics Online written by James P. Howard, II and published by CRC Press. This book was released on 2020-05-10 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Online education has become a major component of higher education worldwide. In mathematics and statistics courses, there exists a number of challenges that are unique to the teaching and learning of mathematics and statistics in an online environment. These challenges are deeply connected to already existing difficulties related to math anxiety, conceptual understanding of mathematical ideas, communicating mathematically, and the appropriate use of technology. Teaching and Learning Mathematics Online bridges these issues by presenting meaningful and practical solutions for teaching mathematics and statistics online. It focuses on the problems observed by mathematics instructors currently working in the field who strive to hone their craft and share best practices with our professional community. The book provides a set of standard practices, improving the quality of online teaching and the learning of mathematics. Instructors will benefit from learning new techniques and approaches to delivering content. Features Based on the experiences of working educators in the field Assimilates the latest technology developments for interactive distance education Focuses on mathematical education for developing early mathematics courses

Making Sense of Mathematics for Teaching High School

Author : Edward C. Nolan
Publisher : Solution Tree Press
ISBN 13 : 1942496494
Total Pages : 273 pages
Book Rating : 4.9/5 (424 download)

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Book Synopsis Making Sense of Mathematics for Teaching High School by : Edward C. Nolan

Download or read book Making Sense of Mathematics for Teaching High School written by Edward C. Nolan and published by Solution Tree Press. This book was released on 2016-05-19 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develop a deep understanding of mathematics by grasping the context and purpose behind various strategies. This user-friendly resource presents high school teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Combine student understanding of functions and algebraic concepts so that they can better decipher the world. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, or modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to ensure mathematics instruction is focused, coherent, and rigorous. Gain clarity about the most productive progression of mathematical teaching and learning for high school. Watch short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction Equations and Functions Structure of Equations Geometry Types of Functions Function Modeling Statistics and Probability Epilogue: Next Steps Appendix: Weight Loss Study Data References Index

Teaching Mathematics in Secondary and Middle School

Author : James S. Cangelosi
Publisher : Prentice Hall
ISBN 13 : 9780134392332
Total Pages : 0 pages
Book Rating : 4.3/5 (923 download)

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Book Synopsis Teaching Mathematics in Secondary and Middle School by : James S. Cangelosi

Download or read book Teaching Mathematics in Secondary and Middle School written by James S. Cangelosi and published by Prentice Hall. This book was released on 1996 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For senior-level and graduate courses in Methods of Teaching Mathematics for Secondary and Middle School Teachers. Focused on all the complex aspects of teaching mathematics in today's classroom and the most current NCTM recommendations and standards this text shows students how to creatively incorporate the Standards into their teaching along with inquiry instructional strategies (for leading pupils to do meaningful mathematics) and direct strategies (for developing mathematical skills). Interactive in approach, it includes an abundance of illustrative examples, numerous cases, one expansive case study that follows a mathematics teacher through his first year in the profession, cooperative learning activities, field-based activities, and transitional activities.

Visible Learning for Mathematics, Grades K-12

Author : John Hattie
Publisher : Corwin Press
ISBN 13 : 1506362958
Total Pages : 209 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis Visible Learning for Mathematics, Grades K-12 by : John Hattie

Download or read book Visible Learning for Mathematics, Grades K-12 written by John Hattie and published by Corwin Press. This book was released on 2016-09-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.

The Teaching and Learning of Mathematics at University Level

Author : Derek Holton
Publisher : Springer Science & Business Media
ISBN 13 : 0306472317
Total Pages : 559 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis The Teaching and Learning of Mathematics at University Level by : Derek Holton

Download or read book The Teaching and Learning of Mathematics at University Level written by Derek Holton and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a text that contains the latest in thinking and the best in practice. It provides a state-of-the-art statement on tertiary teaching from a multi-perspective standpoint. No previous book has attempted to take such a wide view of the topic. The book will be of special interest to academic mathematicians, mathematics educators, and educational researchers. It arose from the ICMI Study into the teaching and learning of mathematics at university level (initiated at the conference in Singapore, 1998).

High School Mathematics at Work

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309174732
Total Pages : 191 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis High School Mathematics at Work by : National Research Council

Download or read book High School Mathematics at Work written by National Research Council and published by National Academies Press. This book was released on 1998-05-27 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally, vocational mathematics and precollege mathematics have been separate in schools. But the technological world in which today's students will work and live calls for increasing connection between mathematics and its applications. Workplace-based mathematics may be good mathematics for everyone. High School Mathematics at Work illuminates the interplay between technical and academic mathematics. This collection of thought-provoking essaysâ€"by mathematicians, educators, and other expertsâ€"is enhanced with illustrative tasks from workplace and everyday contexts that suggest ways to strengthen high school mathematical education. This important book addresses how to make mathematical education of all students meaningfulâ€"how to meet the practical needs of students entering the work force after high school as well as the needs of students going on to postsecondary education. The short readable essays frame basic issues, provide background, and suggest alternatives to the traditional separation between technical and academic mathematics. They are accompanied by intriguing multipart problems that illustrate how deep mathematics functions in everyday settingsâ€"from analysis of ambulance response times to energy utilization, from buying a used car to "rounding off" to simplify problems. The book addresses the role of standards in mathematics education, discussing issues such as finding common ground between science and mathematics education standards, improving the articulation from school to work, and comparing SAT results across settings. Experts discuss how to develop curricula so that students learn to solve problems they are likely to encounter in lifeâ€"while also providing them with approaches to unfamiliar problems. The book also addresses how teachers can help prepare students for postsecondary education. For teacher education the book explores the changing nature of pedagogy and new approaches to teacher development. What kind of teaching will allow mathematics to be a guide rather than a gatekeeper to many career paths? Essays discuss pedagogical implication in problem-centered teaching, the role of complex mathematical tasks in teacher education, and the idea of making open-ended tasksâ€"and the student work they elicitâ€"central to professional discourse. High School Mathematics at Work presents thoughtful views from experts. It identifies rich possibilities for teaching mathematics and preparing students for the technological challenges of the future. This book will inform and inspire teachers, teacher educators, curriculum developers, and others involved in improving mathematics education and the capabilities of tomorrow's work force.

Teaching Math to Multilingual Students, Grades K-8

Author : Kathryn B. Chval
Publisher : Corwin
ISBN 13 : 1071810812
Total Pages : 249 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis Teaching Math to Multilingual Students, Grades K-8 by : Kathryn B. Chval

Download or read book Teaching Math to Multilingual Students, Grades K-8 written by Kathryn B. Chval and published by Corwin. This book was released on 2020-12-21 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using strengths-based approaches to support development in mathematics It’s time to re-imagine what’s possible and celebrate the brilliance multilingual learners bring to today’s classrooms. Innovative teaching strategies can position these learners as leaders in mathematics. Yet, as the number of multilingual learners in North American schools grows, many teachers have not had opportunities to gain the competencies required to teach these learners effectively, especially in disciplines such as mathematics. Multilingual learners—historically called English Language Learners—are expected to interpret the meaning of problems, analyze, make conjectures, evaluate their progress, and discuss and understand their own approaches and the approaches of their peers in mathematics classrooms. Thus, language plays a vital role in mathematics learning, and demonstrating these competencies in a second (or third) language is a challenging endeavor. Based on best practices and the authors’ years of research, this guide offers practical approaches that equip grades K-8 teachers to draw on the strengths of multilingual learners, partner with their families, and position these learners for success. Readers will find: • A focus on multilingual students as leaders • A strength-based approach that draws on students’ life experiences and cultural backgrounds • An emphasis on maintaining high expectations for learners’ capacity for mastering rigorous content • Strategies for representing concepts in different formats • Stop and Think questions throughout and reflection questions at the end of each chapter • Try It! Implementation activities, student work examples, and classroom transcripts With case studies and activities that provide a solid foundation for teachers’ growth and exploration, this groundbreaking book will help teachers and teacher educators engage in meaningful, humanized mathematics instruction.

Teaching Mathematics in the Secondary School

Author : Paul Chambers
Publisher : SAGE
ISBN 13 : 1446290956
Total Pages : 298 pages
Book Rating : 4.4/5 (462 download)

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Book Synopsis Teaching Mathematics in the Secondary School by : Paul Chambers

Download or read book Teaching Mathematics in the Secondary School written by Paul Chambers and published by SAGE. This book was released on 2013-03-31 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: ′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

Teaching Mathematics

Author : Pamela Cowan
Publisher : Routledge
ISBN 13 : 1134310838
Total Pages : 272 pages
Book Rating : 4.1/5 (343 download)

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Book Synopsis Teaching Mathematics by : Pamela Cowan

Download or read book Teaching Mathematics written by Pamela Cowan and published by Routledge. This book was released on 2006-02-13 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical introduction to Maths teaching designed specifically for beginning teachers in primary and secondary schools. It brings together the latest DfES and TTA guidelines and requirements with authoritative guidance, ensuring that readers feel confident about how to approach their role as a teacher. This book explores key issues in maths teaching today, including: planning and classroom management assessment, recording and reporting information and communication technology investigative mathematics equal opportunities, special needs and differentiation key skills and alternative mathematics qualifications being an effective maths teacher personal and professional development in the early stages of a teaching career.