Developing Essential Understanding Of Algebraic Thinking For Teaching Mathematics In Grades 3 5
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Developing Essential Understanding Of Algebraic Thinking For Teaching Mathematics In Grades 3 5
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Author : Maria L. Blanton
language : en
Publisher:
Release Date : 2011
Developing Essential Understanding Of Algebraic Thinking For Teaching Mathematics In Grades 3 5 written by Maria L. Blanton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Algebra categories.
Like algebra at any level, early algebra is a way to explore, analyse, represent and generalise mathematical ideas and relationships. This book shows that children can and do engage in generalising about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3-5. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships and functional thinking to generalise relationships between covarying quantities. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.
Developing Essential Understanding Of Rational Numbers For Teaching Mathematics In Grades 3 5
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Author : Carne Barnett-Clarke
language : en
Publisher: National Council of Teachers of English
Release Date : 2010
Developing Essential Understanding Of Rational Numbers For Teaching Mathematics In Grades 3 5 written by Carne Barnett-Clarke and has been published by National Council of Teachers of English this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know… and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organised around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.
Planting The Seeds Of Algebra 3 5
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Author : Monica Neagoy
language : en
Publisher: Corwin Press
Release Date : 2014-12-05
Planting The Seeds Of Algebra 3 5 written by Monica Neagoy and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-05 with Education categories.
Give your students a foundation of algebra for math success – now and in the future! Algebra is not something to be feared, but something to be embraced with a sense of wonder. Planting the Seeds of Algebra, 3-5, introduces algebra as an accessible way of seeing the world that is necessary to our students’ futures. Students and teachers must become friendly with algebraic foundations, as they have increasingly become the gateway to careers in the STEM fields. Monica Neagoy empowers teachers with theoretical and practical ways to introduce Algebra to 3-5 grade students, making vital connections to concepts they will encounter in middle school and beyond. You’ll discover Four explorations to help you weave key algebraic ideas into everyday mathematics Step-by-step lessons from real classrooms that will guide you in teaching concepts and in establishing their relevance and applicability New teaching methods that break down difficult algebraic concepts and build a critical foundation for higher math Awaken new awareness and change attitudes by sowing the seeds for a vibrant, useful, and rich experience with mathematics. "While reading this book I experienced the sense of wonder and aha moments alongside the students themselves. This book will move your faculty to new depths of understanding about mathematics and will instill the passion to explore a myriad of algebraic concepts." — Bob Weiman, Director St. Stephen’s & St. Agnes School "She’s done it again! Monica Neagoy has authored another book that deftly presents important foundations of algebra while celebrating mathematics through carefully crafted explorations, all of which include student and teacher vignettes and comments about the mathematics they have learned and are teaching. Wow. When I read this book I felt like I was in a classroom!" — Francis (Skip) Fennell, McDaniel College Past President of the National Council of Teachers of Mathematics
Developing Essential Understanding Of Expressions Equations And Functions For Teaching Mathematics In Grades 6 8
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Author : Gwendolyn M. Lloyd
language : en
Publisher: National Council of Teachers of English
Release Date : 2011
Developing Essential Understanding Of Expressions Equations And Functions For Teaching Mathematics In Grades 6 8 written by Gwendolyn M. Lloyd and has been published by National Council of Teachers of English this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Effective teaching categories.
Why do some equations have one solution, others two or even more solutions and some no solutions? Why do we sometimes need to ""switch"" the direction of an inequality symbol in solving an inequality? What could you say if a student described a function as an equation? How much do you know...and how much do you need to know? Helping your students develop a robust understanding of expressions, equations and functions requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about expressions, equations and functions. It is organised around five big ideas, supported by multiple smaller, interconnected ideas - essential understandings. Taking you beyond a simple introduction to expressions, equations and functions, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students - and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students' understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.
Developing Essential Understanding Of Number And Numeration For Teaching Mathematics In Prekindergarten Grade 2
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Author : Barbara J. Dougherty
language : en
Publisher:
Release Date : 2010
Developing Essential Understanding Of Number And Numeration For Teaching Mathematics In Prekindergarten Grade 2 written by Barbara J. Dougherty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Number concept categories.
How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organised around one big idea and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining this understanding is essential because numbers and numeration are building blocks for other mathematical concepts and for thinking quantitatively about the real-world. Essential Understanding series topics include: Number and Numeration for Grades Pre-K-2 Addition and Subtraction for Grades Pre-K-2 Geometry for Grades Pre-K-2 Reasoning and Proof for Grades Pre-K-8 Multiplication and Division for Grades 3-5 Rational Numbers for Grades 3-5 Algebraic Ideas and Readiness for Grades 3-5 Geometric Shapes and Solids for Grades 3-5 Ratio, Proportion and Proportionality for Grades 6-8 Expressions and Equations for Grades 6-8 Measurement for Grades 6-8 Data Analysis and Statistics for Grades 6-8 Function for Grades 9-12 Geometric Relationships for Grades 9-12 Reasoning and Proof for Grades 9-12 Statistics for Grades 9-12
Planting The Seeds Of Algebra Prek 2
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Author : Monica Neagoy
language : en
Publisher: Corwin Press
Release Date : 2012-04-20
Planting The Seeds Of Algebra Prek 2 written by Monica Neagoy and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-20 with Education categories.
The subject of algebra has always been important in American secondary mathematics education. However, algebra at the elementary level has been garnering increasing attention and importance over the past 15 years. There is consequently a dire need for ideas, suggestions and models for how best to achieve pre-algebraic instruction in the elementary grades. Planting the Seeds of Algebra will empower teachers with theoretical and practical knowledge about both the content and pedagogy of such instruction, and show them the different faces of algebra as it appears in the early grades. The book will walk teachers of young children through many examples of K-6 math lessons and unpack, step by step, the hidden connections to higher algebra. After reading this book, teachers will be better equipped ...
Teaching And Learning Algebraic Thinking With 5 To 12 Year Olds
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Author : Carolyn Kieran
language : en
Publisher: Springer
Release Date : 2017-12-04
Teaching And Learning Algebraic Thinking With 5 To 12 Year Olds written by Carolyn Kieran and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-04 with Education categories.
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.
Developing Essential Understanding Of Proof And Proving For Teaching Mathematics In Grades 9 12
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Author : Amy B. Ellis
language : en
Publisher: National
Release Date : 2012
Developing Essential Understanding Of Proof And Proving For Teaching Mathematics In Grades 9 12 written by Amy B. Ellis and has been published by National this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Education categories.
Focuses on essential knowledge for teachers about proof and the process of proving. It is organised around five big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to proof and the activities involved in proving, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students...and teachers.
Early Algebraization
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Author : Jinfa Cai
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-24
Early Algebraization written by Jinfa Cai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-24 with Education categories.
In this volume, the authors address the development of students’ algebraic thinking in the elementary and middle school grades from curricular, cognitive, and instructional perspectives. The volume is also international in nature, thus promoting a global dialogue on the topic of early Algebraization.
Early Algebra
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Author : Carolyn Kieran
language : en
Publisher: Springer
Release Date : 2016-07-11
Early Algebra written by Carolyn Kieran and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-11 with Education categories.
This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this volume reveals the nature of the research that has been carried out in early algebra and how it has shaped the growth of the field. The survey, in presenting examples drawn from the steadily growing research base, highlights both the nature of algebraic thinking and the ways in which this thinking is being developed in the primary and early middle school student. Mathematical relations, patterns, and arithmetical structures lie at the heart of early algebraic activity, with processes such as noticing, conjecturing, generalizing, representing, justifying, and communicating being central to students’ engagement.