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Author: James J. Kaput
Publisher: Routledge
Published: 2008
Total Pages: 562
ISBN-13:
DOWNLOAD EBOOKThis book--the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra--provides a rationale for a stronger and more sustained approach to algebra in school.
Author: James J. Kaput
Publisher: Routledge
Published: 2017-09-25
Total Pages: 496
ISBN-13: 1351577085
DOWNLOAD EBOOKThis volume is the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra. In recent years, the National Council for Teachers of Mathematics has recommended that algebra become a strand flowing throughout the K-12 curriculum, and the 2003 RAND Mathematics Study Panel has recommended that algebra be “the initial topical choice for focused and coordinated research and development [in K-12 mathematics].” This book provides a rationale for a stronger and more sustained approach to algebra in school, as well as concrete examples of how algebraic reasoning may be developed in the early grades. It is organized around three themes: The Nature of Early Algebra Students’ Capacity for Algebraic Thinking Issues of Implementation: Taking Early Algebra to the Classrooms. The contributors to this landmark volume have been at the forefront of an effort to integrate algebra into the existing early grades mathematics curriculum. They include scholars who have been developing the conceptual foundations for such changes as well as researchers and developers who have led empirical investigations in school settings. Algebra in the Early Grades aims to bridge the worlds of research, practice, design, and theory for educators, researchers, students, policy makers, and curriculum developers in mathematics education.
Author: Susan Jo Russell
Publisher: Heinemann Educational Books
Published: 2011
Total Pages: 0
ISBN-13: 9780325041919
DOWNLOAD EBOOK"To truly engage in mathematics is to become curious and intrigued about regularities and patterns, then describe and explain them. A focus on the behavior of the operations allows students starting in the familiar territory of number and computation to progress to true engagement in the discipline of mathematics." -Susan Jo Russell, Deborah Schifter, and Virginia Bastable Algebra readiness: it's a topic of concern that seems to pervade every school district. How can we better prepare elementary students for algebra? More importantly, how can we help all children, not just those who excel in math, become ready for later instruction? The answer lies not in additional content, but in developing a way of thinking about the mathematics that underlies both arithmetic and algebra. Connecting Arithmetic to Algebra invites readers to learn about a crucial component of algebraic thinking: investigating the behavior of the operations. Nationally-known math educators Susan Jo Russell, Deborah Schifter, and Virginia Bastable and a group of collaborating teachers describe how elementary teachers can shape their instruction so that students learn to: *notice and describe consistencies across problems *articulate generalizations about the behavior of the operations *develop mathematical arguments based on representations to explain why such generalizations are or are not true. Through such work, students become familiar with properties and general rules that underlie computational strategies-including those that form the basis of strategies used in algebra-strengthening their understanding of grade-level content and at the same time preparing them for future studies. Each chapter is illustrated by lively episodes drawn from the classrooms of collaborating teachers in a wide range of settings. These provide examples of posing problems, engaging students in productive discussion, using representations to develop mathematical arguments, and supporting both students with a wide range of learning profiles. Staff Developers: Available online, the Course Facilitator's Guide provides math leaders with tools and resources for implementing a Connecting Arithmetic to Algebra workshop or preservice course. For information on the PD course offered through Mount Holyoke College, download the flyer.
Author: Carolyn Kieran
Publisher: Springer
Published: 2017-12-04
Total Pages: 443
ISBN-13: 3319683519
DOWNLOAD EBOOKThis 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.
Author: Jinfa Cai
Publisher: Springer Science & Business Media
Published: 2011-02-24
Total Pages: 631
ISBN-13: 3642177352
DOWNLOAD EBOOKIn 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.
Author: Maria L. Blanton
Publisher: Heinemann Educational Books
Published: 2008
Total Pages: 228
ISBN-13:
DOWNLOAD EBOOKAlgebra in the Elementary Classroom provides the support we need as teachers to embed the development of students' algebraic thinking in the teaching of elementary school. - Megan Loef Franke Coauthor of Children's Mathematics and Thinking Mathematically How do you start students down the road to mathematical understanding? By laying the foundation for algebra in the elementary grades. Algebra and the Elementary Classroom shares ideas, tasks, and practices for integrating algebraic thinking into your teaching. Through research-based and classroom-tested strategies, it demonstrates how to use materials you have on hand to prepare students for formal algebra instruction - without adding to your overstuffed curriculum. You'll find ways to: introduce algebraic thinking through familiar arithmetical contexts nurture it by helping students think about, represent, and build arguments for their mathematical ideas develop it by exploring mathematical structures and functional relationships strengthen it by asking students to make algebraic connections across the curriculum reinforce it across the grades through a schoolwide initiative. No matter what your math background is, Algebra and the Elementary Classroom offers strong support for integrating algebraic thinking into your daily teaching. Its clear descriptions show you what algebraic thinking is and how to teach it. Its sample problems deepen your own algebraic thinking. Best of all, it gives you ideas for grade-specific instructional planning. Read Algebra and the Elementary Classroom and prepare your students for a lifetime of mathematical understanding.
Author: National Research Council
Publisher: National Academies Press
Published: 2002-07-31
Total Pages: 53
ISBN-13: 0309131987
DOWNLOAD EBOOKResults 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.
Author: The Early Math Collaborative- Erikson Institute
Publisher: Pearson Higher Ed
Published: 2013-04-25
Total Pages: 209
ISBN-13: 0133259951
DOWNLOAD EBOOKThis is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. Note: This is the bound book only and does not include access to the Enhanced Pearson eText. To order the Enhanced Pearson eText packaged with a bound book, use ISBN 0133548635. In this unique guide, classroom teachers, coaches, curriculum coordinators, college students, and teacher educators get a practical look at the foundational concepts and skills of early mathematics, and see how to implement them in their early childhood classrooms. Big Ideas of Early Mathematics presents the skills educators need to organize for mathematics teaching and learning during the early years. For teachers of children ages three through six, the book provides foundations for further mathematics learning and helps facilitate long-term mathematical understanding. The Enhanced Pearson eText features embedded video. Improve mastery and retention with the Enhanced Pearson eText* The Enhanced Pearson eText provides a rich, interactive learning environment designed to improve student mastery of content. The Enhanced Pearson eText is: Engaging. The new interactive, multimedia learning features were developed by the authors and other subject-matter experts to deepen and enrich the learning experience. Convenient. Enjoy instant online access from your computer or download the Pearson eText App to read on or offline on your iPad® and Android® tablet.* Affordable. Experience the advantages of the Enhanced Pearson eText for 40-65% less than a print bound book. * The Enhanced eText features are only available in the Pearson eText format. They are not available in third-party eTexts or downloads. *The Pearson eText App is available on Google Play and in the App Store. It requires Android OS 3.1-4, a 7” or 10” tablet, or iPad iOS 5.0 or later.
Author: Julie Sarama
Publisher: Routledge
Published: 2009-04-01
Total Pages: 440
ISBN-13: 1135592497
DOWNLOAD EBOOKThis important new book synthesizes relevant research on the learning of mathematics from birth into the primary grades from the full range of these complementary perspectives. At the core of early math experts Julie Sarama and Douglas Clements's theoretical and empirical frameworks are learning trajectories—detailed descriptions of children’s thinking as they learn to achieve specific goals in a mathematical domain, alongside a related set of instructional tasks designed to engender those mental processes and move children through a developmental progression of levels of thinking. Rooted in basic issues of thinking, learning, and teaching, this groundbreaking body of research illuminates foundational topics on the learning of mathematics with practical and theoretical implications for all ages. Those implications are especially important in addressing equity concerns, as understanding the level of thinking of the class and the individuals within it, is key in serving the needs of all children.
Author: Carolyn Kieran
Publisher: Springer
Published: 2016-07-11
Total Pages: 48
ISBN-13: 3319322583
DOWNLOAD EBOOKThis 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.
