Key Ideas in Teaching Mathematics

Research-based guidance for ages 9-19
Author: Anne Watson,Keith Jones,Dave Pratt
Publisher: OUP Oxford
ISBN: 0191643424
Category: Mathematics
Page: 272
View: 2573

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Big ideas in the mathematics curriculum for older school students, especially those that are hard to learn and hard to teach, are covered in this book. It will be a first port of call for research about teaching big ideas for students from 9-19 and also has implications for a wider range of students. These are the ideas that really matter, that students get stuck on, and that can be obstacles to future learning. It shows how students learn, why they sometimes get things wrong, and the strengths and pitfalls of various teaching approaches. Contemporary high-profile topics like modelling are included. The authors are experienced teachers, researchers and mathematics educators, and many teachers and researchers have been involved in the thinking behind this book, funded by the Nuffield Foundation. An associated website, hosted by the Nuffield Foundation, summarises the key messages in the book and connects them to examples of classroom tasks that address important learning issues about particular mathematical ideas.

A Practical Guide to Teaching Mathematics in the Secondary School


Author: Clare Lee,Sue Johnston-Wilder,Robert Ward-Penny
Publisher: Routledge
ISBN: 0415508207
Category: Education
Page: 129
View: 8181

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A Practical Guide to Teaching Mathematics in the Secondary School offers straightforward advice, inspiration and support for mathematics teachers whether in training or newly qualified. Based on the best research and practice available, it offers a wide range of tried and tested approaches that succeed in secondary classrooms. Each chapter contains a wealth of tasks and ideas that allow teachers to reflect on the approaches and make plans for using them in their own classrooms, and offers ideas for lesson plans, learning activities and suggested further reading and development. Illustrated throughout with case studies and practical insights from classroom observations and experience, this book covers key aspects of mathematics teaching, including: managing the class and learning environment; teaching the topics of mathematics; encouraging mathematical thinking; choosing and using resources; using multi-media technology; assessing work in mathematics. A Practical Guide to Teaching Mathematics in the Secondary School is an essential companion to the core textbook Learning to Teach Mathematics in the Secondary School. Written by expert professionals, it supports you in your development of imaginative and effective lessons on a variety of curriculum topics in different teaching situations.

Debates in Mathematics Education


Author: Dawn Leslie,Heather Mendick
Publisher: Routledge
ISBN: 1134483724
Category: Education
Page: 232
View: 393

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Debates in Mathematics Education explores the major issues that mathematics teachers encounter in their daily lives. It engages with established and contemporary debates, promotes and supports critical reflection and aims to stimulate both novice and experienced teachers to reach informed judgements and argue their point of view with deeper theoretical knowledge and understanding. Written by experts in the field of mathematics education, it investigates and offers fresh insight into topics of central importance, including: Gender, social inequality and mathematics Mathematics, politics and climate change The history and culture of mathematics Using popular culture in the mathematics classroom The concept of ‘ability’ and its impact on learning What we mean by ‘teaching for understanding’ Choosing and using examples in teaching The fitness of formal examinations. Designed to stimulate discussion and support you in your own research, writing and practice, Debates in Mathematics Education will be a valuable resource for any student or practising teacher engaged in initial teacher training, continuing professional development or Masters level study. It also has much to offer to those leading initial teacher education programmes, and to beginning doctoral students looking for a survey of the field of mathematics education research.

Teaching Mathematics in Early Childhood


Author: Sally Moomaw
Publisher: Brookes Publishing Company
ISBN: 9781598571196
Category: Education
Page: 211
View: 3095

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Children who learn math fundamentals in preschool and kindergarten have the best chance of later achievement in school; but all too often, children don't get the effective early math instruction that makes all the difference. Now there's a core early childhood textbook that helps current and future educators teach the most critical math concepts to young students while meeting today's national standards for mathematics education. Developed by Sally Moomaw, a nationally respected expert with more than 20 years of classroom experience, this accessible textbook gives readers a solid theoretical understanding of math concepts and standards and the guidance they need to create and implement their own lessons. Highly readable and practical enough for years of use beyond the classroom, this text: helps teacher plan effective lessons; advances inclusion by giving teachers universal design strategies and adaptations to help them support all learners; targets the critical math skills children will build on for the rest of their lives; focuses on the youngest students (including children wih special needs) so teachers can implement developmentally appropriate math instruction; gives teachers invaluable guidance in weavig math lessons into everyday routines and conversations; and makes teacher preparation clear and easy. Whether used in preservice courses on teaching mathematics or in-service professional development, this comprehensive textbook will help educators give the youngest students a strong foundation of basic math concepts, and prepare them for lifelong academic success.

Learning to Teach Mathematics in the Secondary School

A companion to school experience
Author: Sue Johnston-Wilder,Clare Lee,David Pimm
Publisher: Routledge
ISBN: 1317372360
Category: Education
Page: 318
View: 2467

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Learning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in the secondary school classroom. This fourth edition has been fully updated to reflect the latest changes to the curriculum and research in the field, taking into account key developments in teacher training and education, including examinations and assessment. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, such as: why we teach mathematics??????? the place of mathematics in the National Curriculum ???? planning, teaching and assessing for mathematics learning?????????? how to communicate mathematically???? using digital technology to advance mathematical learning working with students with special educational needs post-16 teaching the importance of professional development the affective dimension when learning mathematics, including motivation, confidence and resilience Already a major text for many university teaching courses, this revised edition features a glossary of useful terms and carefully designed tasks to prompt critical reflection and support thinking and writing up to Masters Level. Issues of professional development are also examined, as well as a range of teaching approaches and styles from whole-class strategies to personalised learning, helping you to make the most of school experience, during your training and beyond. Designed for use as a core textbook, Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all those who aspire to be effective mathematics teachers.

Learning to Teach Mathematics in the Secondary School

A companion to school experience
Author: Sue Johnston-Wilder,Clare Lee,David Pimm
Publisher: Routledge
ISBN: 1317372360
Category: Education
Page: 318
View: 4380

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Learning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in the secondary school classroom. This fourth edition has been fully updated to reflect the latest changes to the curriculum and research in the field, taking into account key developments in teacher training and education, including examinations and assessment. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, such as: why we teach mathematics??????? the place of mathematics in the National Curriculum ???? planning, teaching and assessing for mathematics learning?????????? how to communicate mathematically???? using digital technology to advance mathematical learning working with students with special educational needs post-16 teaching the importance of professional development the affective dimension when learning mathematics, including motivation, confidence and resilience Already a major text for many university teaching courses, this revised edition features a glossary of useful terms and carefully designed tasks to prompt critical reflection and support thinking and writing up to Masters Level. Issues of professional development are also examined, as well as a range of teaching approaches and styles from whole-class strategies to personalised learning, helping you to make the most of school experience, during your training and beyond. Designed for use as a core textbook, Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all those who aspire to be effective mathematics teachers.

The Mathematics Teacher's Handbook


Author: Mike Ollerton
Publisher: A&C Black
ISBN: 1847060110
Category: Education
Page: 176
View: 2549

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A comprehensive handbook for mathematics teachers with practical advice on all aspects of the maths curriculum including developing an effective classroom culture, assessment and progressing mathematical concept development.

Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

The Global Evolution of an Emerging Field of Research and Practice
Author: Carolyn Kieran
Publisher: Springer
ISBN: 3319683519
Category: Education
Page: 443
View: 2042

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This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.

Teaching and Learning Stochastics

Advances in Probability Education Research
Author: Carmen Batanero,Egan J Chernoff
Publisher: Springer
ISBN: 3319728717
Category: Education
Page: 384
View: 7543

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This book presents a collection of selected papers that represent the current variety of research on the teaching and learning of probability. The respective chapters address a diverse range of theoretical, empirical and practical aspects underpinning the teaching and learning of probability, curricular issues, probabilistic reasoning, misconceptions and biases, as well as their pedagogical implications. These chapters are divided into THREE main sections, dealing with: TEACHING PROBABILITY, STUDENTS' REASONING AND LEARNING AND EDUCATION OF TEACHERS. In brief, the papers presented here include research dealing with teachers and students at different levels and ages (from primary school to university) and address epistemological and curricular analysis, as well as the role of technology, simulations, language and visualisation in teaching and learning probability. As such, it offers essential information for teachers, researchers and curricular designers alike.

The SIOP Model for Teaching Mathematics to English Learners


Author: Jana Echevarria,MaryEllen Vogt,Deborah Short
Publisher: Allyn & Bacon
ISBN: 9780205627585
Category: Education
Page: 202
View: 6488

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Enhance your Mathematics content instruction with the SIOP Model and transform the academic English and mathematics skills of your English learners. Based on the best-selling resource, Making Content Comprehensible for English Learners: The SIOP Model by acclaimed authors Jana Echevarria, MaryEllen Vogt, and Deborah Short; teachers, coaches, and intervention teachers have access to research-based, SIOP-tested techniques for lessons specifically for the mathematics classroom. This highly anticipated book, The SIOP Model for Teaching Mathematics to English Learners addresses the issues faced in teaching math to English learners (ELs) at each grade-level. SIOP techniques and activities organized around the eight SIOP components guide educators in promoting academic language development along with comprehensible mathematics content. Written for SIOP teachers and those who have learned the SIOP Model, this book includes proven, effective math lessons and comprehensive units designed by SIOP math educators Araceli Avila and Melissa Castillo. In addition, this book provides ideas to adapt the techniques for students at different levels of English proficiency. This book is sure to become an indispensable resource for math educators of English learners. Presents a systematic process for teaching both the academic content of mathematics and its associated academic language to English learners. Offers ideas and activities about teaching mathematics and organizes activities by grade-bands--K-2, 3-5 (or 6), 6-8, and 9-12 and SIOP components. Provides use-tomorrow ideas and activities for implementing the eight components of the SIOP Model in a mathematics classroom. Includes lesson plans and comprehensive units that illustrate how a particular activity can be effective for ALL students, not just English learners. Create the ideal SIOP classroom with other resourcesfrom the SIOP Model Series: 99 Ideas and Activities for Teaching English Learners with the SIOP Model; Implementing the SIOP Model through Effective Coaching and Professional Development; The SIOP Model for Administrators; Making Content Comprehensible for Elementary English Learners; and Making Content Comprehensible for Secondary English Learners ; The SIOP Model for Teaching Math to English Learners; The SIOP Model for Teaching Social Studies to English Learners; and The SIOP Model for Teaching Science to English Learners (all published by Pearson)

Teaching Numeracy

9 Critical Habits to Ignite Mathematical Thinking
Author: Margie Pearse,K. M. Walton
Publisher: Corwin Press
ISBN: 1452238855
Category: Education
Page: 240
View: 5207

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Transform mathematics learning from “doing” to “thinking” American students are losing ground in the global mathematical environment. What many of them lack is numeracy—the ability to think through the math and apply it outside of the classroom. Referencing the new common core and NCTM standards, the authors outline nine critical thinking habits that foster numeracy and show you how to: Monitor and repair students’ understanding Guide students to recognize patterns Encourage questioning for understanding Develop students’ mathematics vocabulary Included are several numeracy-rich lesson plans, complete with clear directions and student handouts.

The Second Handbook of Research on the Psychology of Mathematics Education

The Journey Continues
Author: Ángel Gutiérrez,Gilah C. Leder,Paolo Boero
Publisher: Springer
ISBN: 9463005617
Category: Education
Page: 558
View: 1006

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Since its establishment in 1976, PME (The International Group for the Psychology of Mathematics Education) is serving as a much sought after venue for scientific debate among those at the cutting edge of the field, as well as an engine for the development of research in mathematics education. A wide range of research activities conducted over the last ten years by PME members and their colleagues are documented and critically reviewed in this handbook, released to celebrate the Group’s 40 year anniversary milestone. The book is divided into four main sections: Cognitive aspects of learning and teaching content areas; Cognitive aspects of learning and teaching transverse areas; Social aspects of learning and teaching mathematics; and Professional aspects of teaching mathematics. The selection for each chapter of a team of at least two authors, mostly located in different parts of the world, ensured effective coverage of each field. High quality was further enhanced by the scrupulous review of early chapter drafts by two leaders in the relevant field. The resulting volume with its compilation of the most relevant aspects of research in the field, and its emphasis on trends and future developments, will be a rich and welcome resource for both mature and emerging researchers in mathematics education.

Education for Life and Work

Developing Transferable Knowledge and Skills in the 21st Century
Author: Committee on Defining Deeper Learning and 21st Century Skills,Center for Education,Board on Testing and Assessment,Division of Behavioral and Social Sciences and Education,National Research Council
Publisher: National Academies Press
ISBN: 030925650X
Category: Education
Page: 229
View: 1952

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Americans have long recognized that investments in public education contribute to the common good, enhancing national prosperity and supporting stable families, neighborhoods, and communities. Education is even more critical today, in the face of economic, environmental, and social challenges. Today's children can meet future challenges if their schooling and informal learning activities prepare them for adult roles as citizens, employees, managers, parents, volunteers, and entrepreneurs. To achieve their full potential as adults, young people need to develop a range of skills and knowledge that facilitate mastery and application of English, mathematics, and other school subjects. At the same time, business and political leaders are increasingly asking schools to develop skills such as problem solving, critical thinking, communication, collaboration, and self-management - often referred to as "21st century skills." Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century describes this important set of key skills that increase deeper learning, college and career readiness, student-centered learning, and higher order thinking. These labels include both cognitive and non-cognitive skills- such as critical thinking, problem solving, collaboration, effective communication, motivation, persistence, and learning to learn. 21st century skills also include creativity, innovation, and ethics that are important to later success and may be developed in formal or informal learning environments. This report also describes how these skills relate to each other and to more traditional academic skills and content in the key disciplines of reading, mathematics, and science. Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century summarizes the findings of the research that investigates the importance of such skills to success in education, work, and other areas of adult responsibility and that demonstrates the importance of developing these skills in K-16 education. In this report, features related to learning these skills are identified, which include teacher professional development, curriculum, assessment, after-school and out-of-school programs, and informal learning centers such as exhibits and museums.

Science Education

An International Course Companion
Author: Keith S. Taber,Ben Akpan
Publisher: Springer
ISBN: 9463007490
Category: Education
Page: 606
View: 6796

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"This book comprises a wide range of scholarly essays introducing readers to key topics and issues in science education. Science education has become a well established field in its own right, with a vast literature, and many active areas of scholarship. Science Education: An International Course Companion offers an entry point for students seeking a sound but introductory understanding of the key perspectives and areas of thinking in science education. Each account is self-contained and offers a scholarly and research-informed introduction to a particular topic, theme, or perspective, with both citations to key literature and recommendations for more advanced reading. Science Education: An International Course Companion allows readers (such as those preparing for school science teaching, or seeking more advanced specialist qualifications) to obtain a broad familiarity with key issues across the field as well as guiding wider reading about particular topics of interest. The book therefore acts as a reader to support learning across courses in science education internationally. The broad coverage of topics is such that that the book will support students following a diverse range of courses and qualifications. The comprehensive nature of the book will allow course leaders and departments to nominate the book as the key reader to support students – their core ‘course companion’ in science education."

How People Learn

Brain, Mind, Experience, and School: Expanded Edition
Author: National Research Council,Division of Behavioral and Social Sciences and Education,Board on Behavioral, Cognitive, and Sensory Sciences,Committee on Developments in the Science of Learning with additional material from the Committee on Learning Research and Educational Practice
Publisher: National Academies Press
ISBN: 0309131979
Category: Education
Page: 384
View: 8694

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First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methods--to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education.

Developing Thinking in Algebra


Author: John Mason
Publisher: SAGE
ISBN: 9781412911719
Category: Mathematics
Page: 324
View: 7843

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By integrating pedagogy and subject knowledge through experiencing a variety of tasks for learners, this book makes it possible for all learners to succeed in thinking algebraically.

Concept-Based Mathematics

Teaching for Deep Understanding in Secondary Classrooms
Author: Jennifer T.H. Wathall
Publisher: Corwin Press
ISBN: 150633265X
Category: Education
Page: 296
View: 4480

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Give math students the connections between what they learn and how they do math—and suddenly math makes sense If your secondary-school students are fearful of or frustrated by math, it’s time for a new approach. When you teach concepts rather than rote processes, you help students discover their own natural mathematical abilities. This book is a road map to retooling how you teach math in a deep, clear, and meaningful way to help students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and there’s even a companion website with additional resources.

Researching Your Own Practice

The Discipline of Noticing
Author: John Mason
Publisher: Routledge
ISBN: 1134536593
Category: Education
Page: 288
View: 6399

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Central to caring professions such as teaching is the need to notice and be sensitive to the experiences of pupils and teachers. Starting from this position, Researching Your Own Practice demonstrates that in order to develop your professional practice you must first develop your own sensitivities and awareness. One must be attuned to fresh possibilities when they are needed and be alert to such a need through awareness of what is happening at any given time. By giving a full explanation of this theory and a guide to its implementation, this book provides a practical approach to becoming more methodical and systematic in professional development. It also gives the reader a basis for turning professional development into practitioner research, as well as giving advice on how noticing can be used to improve any research, or be used as a research paradigm in its own right. The discipline of noticing is a groundbreaking approach to professional development and research, based upon noticing a possibility for the future, noticing a possibility in the present moment and reflecting back on what has been noticed before in order to prepare for the future. John Mason, one of the discipline's most authoritative exponents, provides us here with a clear, persuasive and practical guide to its understanding and implementation.

About Teaching Mathematics: A K-8 Resource (4th Edition)


Author: Marilyn Burns
Publisher: Math Solutions Publications
ISBN: 9781935099321
Category: Education
Page: 536
View: 8940

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In this fourth edition of her signature resource, Marilyn presents her current thinking and insights and includes ideas from her most recent teaching experiences. Part 1, “Starting Points,” reflects the major overhaul of this book and addresses twenty-three issues important to thinking about teaching mathematics today. Part 2, “Problem-Solving Investigations,” opens with how to plan problem-solving lessons; followed by whole-class, small-group, and individual investigations organized into five areas of the curriculum: Measurement, Data, Geometry, Patterns and Algebraic Thinking, and Number and Operations. Part 3, “Teaching Arithmetic,” focuses on the cornerstone of elementary mathematics curriculum, offering ideas and assessments that build students' understanding, confidence, and competence in arithmetic. In Part 4, “Questions Teachers Ask,” features Marilyn's responses to pedagogical questions she's received from teachers over the years. What's in the Fourth Edition: Features more than 250 problem-solving investigations; Includes Marilyn's personal teaching notes throughout Reproducibles that are also available in a downloadable, printable format

Response to Intervention in Math


Author: Paul J. Riccomini,Bradley S. Witzel
Publisher: Corwin Press
ISBN: 1412966353
Category: Education
Page: 151
View: 5952

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Provides educators with instructions on applying response-to-intervention (RTI) while teaching and planning curriculum for students with learning disabilities.