Teaching Mathematics Conceptually

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Publisher : Sage Publications UK
ISBN 13 : 1529618177
Total Pages : 268 pages
Book Rating : 4.5/5 (296 download)

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Book Synopsis Teaching Mathematics Conceptually by : Beth L. MacDonald

Download or read book Teaching Mathematics Conceptually written by Beth L. MacDonald and published by Sage Publications UK. This book was released on 2023-04-08 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book expands upon the guiding principles at the heart of Math Recovery® instruction, exploring their connections with learning theory, practical application in the classroom and their wider links to agreed concepts of high-quality mathematics teaching. It provides a well-rounded overview of all major aspects of mathematics teaching including inquiry-based and constructivist approaches, planning and assessment, and strategies that offer children opportunities for reflection, satisfaction and increasing challenge. Particular focus is placed on equitable and inclusive practices in mathematics and how we can develop teaching that connects with the abilities, cultures, and lived experiences of all children. This is essential reading for all teachers familiar with the Math Recovery® approach and classroom mathematics teachers in elementary and primary schools everywhere seeking to enhance their own professional knowledge and understanding. Beth L. MacDonald is an associate professor in Early Childhood Mathematics Education in the School of Teaching and Learning at Illinois State University. Jonathan N. Thomas is an associate professor of mathematics education and the chairperson of the Department of STEM Education at the University of Kentucky.

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.

Concept-Based Mathematics

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Publisher : Corwin Press
ISBN 13 : 150633265X
Total Pages : 307 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis Concept-Based Mathematics by : Jennifer T.H. Wathall

Download or read book Concept-Based Mathematics written by Jennifer T.H. Wathall and published by Corwin Press. This book was released on 2016-01-14 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 show students math’s essential elegance, as well as its practicality—and help them 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 —through a conceptual lens—helping students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and even guides you through an ideal concept-based classroom. Practical tools include: Examples from arithmetic to calculus Inquiry tasks, unit planners, templates, and activities Sample assessments with examples of student work Vignettes from international educators A dedicated companion website with additional resources, including a study guide, templates, exemplars, discussion questions, and other professional development activities. Everyone has the power to understand math. By extending Erickson and Lanning’s work on Concept-Based Curriculum and Instruction specifically to math, this book helps students achieve the deep understanding and skills called for by global standards and be prepared for the 21st century workplace. "Jennifer Wathall’s book is one of the most forward thinking mathematics resources on the market. While highlighting the essential tenets of Concept-Based Curriculum design, her accessible explanations and clear examples show how to move students to deeper conceptual understandings. This book ignites the mathematical mind!" — Lois A. Lanning, Author of Designing Concept-based Curriculum for English-Language Arts, K-12 "Wathall is a master at covering all the bases here; this book is bursting with engaging assessment examples, discussion questions, research, and resources that apply specifically to mathematical topics. Any math teacher or coach would be hard-pressed to read it and not come away with scores of ideas, assessments, and lessons that she could use instantly in the classroom. As an IB Workshop Leader and instructional coach, I want this book handy on a nearby shelf for regular referral – it′s a boon to any educator who wants to bring math to life for students." — Alexis Wiggins, Instructional Coach, IB Workshop Leader and Consultant

Making Sense of Mathematics for Teaching High School

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Publisher : Solution Tree Press
ISBN 13 : 1942496494
Total Pages : 231 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 231 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

Visible Learning for Mathematics, Grades K-12

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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 Problem with Math Is English

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Publisher : John Wiley & Sons
ISBN 13 : 1118237021
Total Pages : 310 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis The Problem with Math Is English by : Concepcion Molina

Download or read book The Problem with Math Is English written by Concepcion Molina and published by John Wiley & Sons. This book was released on 2012-09-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching K-12 math becomes an easier task when everyone understands the language, symbolism, and representation of math concepts Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at a superficial level. Written to inspire ?aha? moments, this book enables teachers to help students identify and comprehend the nuances and true meaning of math concepts by exploring them through the lenses of language and symbolism, delving into such essential topics as multiplication, division, fractions, place value, proportional reasoning, graphs, slope, order of operations, and the distributive property. Offers a new way to approach teaching math content in a way that will improve how all students, and especially English language learners, understand math Emphasizes major attributes of conceptual understanding in mathematics, including simple yet deep definitions of key terms, connections among key topics, and insightful interpretation This important new book fills a gap in math education by illustrating how a deeper knowledge of math concepts can be developed in all students through a focus on language and symbolism.

Teaching Mathematics Meaningfully

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Author :
Publisher : Brookes Publishing Company
ISBN 13 :
Total Pages : 316 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Teaching Mathematics Meaningfully by : David H. Allsopp

Download or read book Teaching Mathematics Meaningfully written by David H. Allsopp and published by Brookes Publishing Company. This book was released on 2007 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making mathematics concepts understandable is a challenge for any teacher--a challenge that's more complex when a classroom includes students with learning difficulties. With this highly practical resource, educators will have just what they need to teach mathematics with confidence: research-based strategies that really work with students who have learning disabilities, ADHD, or mild cognitive disabilities. This urgently needed guidebook helps teachers Understand why students struggle.Teachers will discover how the common learning characteristics of students with learning difficulties create barriers to understanding mathematics. Review the Big Ideas. Are teachers focusing on the right things? A helpful primer on major NCTM-endorsed mathematical concepts and processes helps them be sure. Directly address students' learning barriers. With the lesson plans, practical strategies, photocopiable information-gathering forms, and online strategies in action, teachers will have concrete ways to help students grasp mathematical concepts, improve their proficiency, and generalize knowledge in multiple contexts. Check their own strengths and needs. Educators will reflect critically on their current practices with a thought-provoking questionnaire. With this timely book--filled with invaluable ideas and strategies adaptable for grades K-12--educators will know just what to teach and how to teach it to students with learning difficulties.

Making Sense of Mathematics for Teaching, Grades 3-5

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Publisher : Solution Tree Press
ISBN 13 : 1942496435
Total Pages : 386 pages
Book Rating : 4.9/5 (424 download)

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Book Synopsis Making Sense of Mathematics for Teaching, Grades 3-5 by : Juli K. Dixon

Download or read book Making Sense of Mathematics for Teaching, Grades 3-5 written by Juli K. Dixon and published by Solution Tree Press. This book was released on 2016-04-11 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develop a deep understanding of mathematics. This user-friendly resource presents grades 3–5 teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Focus on an understanding of and procedural fluency with multiplication and division. Address how to learn and teach fraction concepts and operations with depth. Thoroughly teach plane and solid geometry. 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. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, and 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. Use charts and diagrams for classifying shapes, which can engage students in important mathematical practices. Access short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction 1 Place Value, Addition, and Subtraction 2 Multiplication and Division 3 Fraction Concepts 4 Fraction Operations 5 Geometry 6 Measurement Epilogue Next Steps Appendix A Completed Classification of Triangles Chart Appendix B Completed Diagram for Classifying Quadrilaterals

What is Mathematics: School Guide to Conceptual Understanding of Mathematics

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Publisher : PhilScience Press
ISBN 13 : 9731991980
Total Pages : 315 pages
Book Rating : 4.7/5 (319 download)

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Book Synopsis What is Mathematics: School Guide to Conceptual Understanding of Mathematics by : Catalin Barboianu

Download or read book What is Mathematics: School Guide to Conceptual Understanding of Mathematics written by Catalin Barboianu and published by PhilScience Press. This book was released on 2021-01-18 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is not a mathematics book, but a book about mathematics, which addresses both student and teacher, with a goal as practical as possible, namely to initiate and smooth the way toward the student's full understanding of the mathematics taught in school. The customary procedural-formal approach to teaching mathematics has resulted in students' distorted vision of mathematics as a merely formal, instrumental, and calculatory discipline. Without the conceptual base of mathematics, students develop over time a "mathematical anxiety" and abandon any effort to understand mathematics, which becomes their "traditional enemy" in school. This work materializes the results of the inter- and trans-disciplinary research aimed toward the understanding of mathematics, which concluded that the fields with the potential to contribute to mathematics education in this respect, by unifying the procedural and conceptual approaches, are epistemology and philosophy of mathematics and science, as well as fundamentals and history of mathematics. These results argue that students' fear of mathematics can be annulled through a conceptual approach, and a student with a good conceptual understanding will be a better problem solver. The author has identified those zones and concepts from the above disciplines that can be adapted and processed for familiarizing the student with this type of knowledge, which should accompany the traditional content of school mathematics. The work was organized so as to create for the reader a unificatory image of the complex nature of mathematics, as well as a conceptual perspective ultimately necessary to the holistic understanding of school mathematics. The author talks about mathematics to convince readers that to understand mathematics means first to understand it as a whole, but also as part of a whole. The nature of mathematics, its primary concepts (like numbers and sets), its structures, language, methods, roles, and applicability, are all presented in their essential content, and the explanation of non-mathematical concepts is done in an accessible language and with many relevant examples.

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.

Mathematics for Elementary Teachers

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Publisher : McGraw-Hill Science, Engineering & Mathematics
ISBN 13 : 9780073053707
Total Pages : 0 pages
Book Rating : 4.0/5 (537 download)

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Book Synopsis Mathematics for Elementary Teachers by : Albert B. Bennett

Download or read book Mathematics for Elementary Teachers written by Albert B. Bennett and published by McGraw-Hill Science, Engineering & Mathematics. This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for a mathematics for elementary school teachers course where instructors choose to focus on and/or take an activities approach to learning. It provides inductive activities for prospective elementary school teachers and incorporates the use of physical models, manipulatives, and visual images to develop concepts and encourage higher-level thinking. This text contains an activity set that corresponds to each section of the companion text, Mathematics for Elementary Teachers: A Conceptual Approach which is also by Bennett/Nelson. The Activities Approach text can be used independently or along with its companion volume. The authors are pleased to welcome Laurie Burton, PhD, Western Oregon University to this edition of Mathematics for Elementary Teachers: An Activity Approach.

Mathematical Mindsets

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Publisher : John Wiley & Sons
ISBN 13 : 1118415531
Total Pages : 320 pages
Book Rating : 4.1/5 (184 download)

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Book Synopsis Mathematical Mindsets by : Jo Boaler

Download or read book Mathematical Mindsets written by Jo Boaler and published by John Wiley & Sons. This book was released on 2015-10-12 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.

Conceptual Mathematics

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Author :
Publisher : Cambridge University Press
ISBN 13 : 0521894859
Total Pages : 409 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Conceptual Mathematics by : F. William Lawvere

Download or read book Conceptual Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2009-07-30 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

Concept-rich Mathematics Instruction

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Publisher : ASCD
ISBN 13 : 141660359X
Total Pages : 162 pages
Book Rating : 4.4/5 (166 download)

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Book Synopsis Concept-rich Mathematics Instruction by : Meir Ben-Hur

Download or read book Concept-rich Mathematics Instruction written by Meir Ben-Hur and published by ASCD. This book was released on 2006 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an instructional approach that helps students in every grade level understand math concepts so they can apply them on assessments, across the curriculum, and outside of school. Provides teaching practices and lesson ideas that give students a stronger foundation for reasoning and problem solving.

Understanding and Teaching Primary Mathematics

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Author :
Publisher : Routledge
ISBN 13 : 1317614399
Total Pages : 261 pages
Book Rating : 4.3/5 (176 download)

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Book Synopsis Understanding and Teaching Primary Mathematics by : Tony Cotton

Download or read book Understanding and Teaching Primary Mathematics written by Tony Cotton and published by Routledge. This book was released on 2014-04-29 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: How would you teach the concept of odd and even numbers to a child? What is the probability of throwing a three on a six-sided die? How could you help a child who is confusing ratio and proportion? By seamlessly combining subject knowledge and pedagogy, the second edition of Understanding and Teaching Primary Mathematics will not only build your own confidence in mathematics, but also equip you with the curriculum understanding and pedagogical know-how to excel at teaching maths to children of any age. Written in a clear and accessible way, the book guides you through the fundamental ideas which are at the heart of teaching and learning maths, with special focus on observation and assessment of primary and early years children. Hallmark features Links to the classroom and research are provided throughout to help you relate educational theory to your own teaching practice. Portfolio and audit tasks allow you to assess your own subject knowledge and build up a portfolio of evidence to gain Qualified Teacher Status. The accompanying extra resources offers topic-specific self-audits for you to monitor your progress, exemplar lesson plans, a range of Portfolio Tasks mapped directly to current teacher standards and web-links to up-to-date online resources. New to this edition Resource Inspiration boxes give inviting examples of different activities to do with your class to provide inspiration for your own teaching. High quality videos with corresponding discussion, have been expertly selected from Teachers TV help to widen your skills and develop your practice, offering tips, lesson ideas and classroom resources.

Vital Directions for Mathematics Education Research

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461469775
Total Pages : 212 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Vital Directions for Mathematics Education Research by : Keith R Leatham

Download or read book Vital Directions for Mathematics Education Research written by Keith R Leatham and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a collection of chapters from prominent mathematics educators in which they each discuss vital issues in mathematics education and what they see as viable directions research in mathematics education could take to address these issues. All of these issues are related to learning and teaching mathematics. The book consists of nine chapters, seven from each of seven scholars who participated in an invited lecture series (Scholars in Mathematics Education) at Brigham Young University, and two chapters from two other scholars who are writing reaction papers that look across the first seven chapters. The recommendations take the form of broad, overarching principles and ideas that cut across the field. In this sense, this book differs from classical “research agenda projects,” which seek to outline specific research questions that the field should address around a central topic.

Principles to Actions

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Publisher : National Council of Teachers of Mathematics, Incorporated
ISBN 13 : 9780873537742
Total Pages : 139 pages
Book Rating : 4.5/5 (377 download)

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Book Synopsis Principles to Actions by : National Council of Teachers of Mathematics

Download or read book Principles to Actions written by National Council of Teachers of Mathematics and published by National Council of Teachers of Mathematics, Incorporated. This book was released on 2014-02 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning.