Early Algebra

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Early Algebra

Carolyn Kieran,JeongSuk Pang,Deborah Schifter,Swee Fong Ng
Early Algebra Book PDF

Author : Carolyn Kieran,JeongSuk Pang,Deborah Schifter,Swee Fong Ng
Publisher : Springer
Page : 48 pages
File Size : 41,7 Mb
Release : 2016-07-11
Category : Education
ISBN : 9783319322582

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Early Algebra by Carolyn Kieran,JeongSuk Pang,Deborah Schifter,Swee Fong Ng Pdf

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.

Algebra in the Early Grades

James J. Kaput,David W. Carraher,Maria L. Blanton
Algebra in the Early Grades Book PDF

Author : James J. Kaput,David W. Carraher,Maria L. Blanton
Publisher : Routledge
Page : 552 pages
File Size : 46,5 Mb
Release : 2017-09-25
Category : Education
ISBN : 9781351577090

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Algebra in the Early Grades by James J. Kaput,David W. Carraher,Maria L. Blanton Pdf

This 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.

Teaching Early Algebra Through Example-Based Problem Solving

Meixia Ding
Teaching Early Algebra Through Example Based Problem Solving Book PDF

Author : Meixia Ding
Publisher : Routledge
Page : 0 pages
File Size : 40,9 Mb
Release : 2023-01-09
Category : Electronic
ISBN : 0367750821

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Teaching Early Algebra Through Example-Based Problem Solving by Meixia Ding Pdf

Drawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-based problem solving" (TEPS). Recognizing young children's particular cognitive and developmental capabilities, this book powerfully argues for the importance of infusing algebraic thinking into early grade mathematics teaching and illustrates how this has been achieved by teachers in U.S. and Chinese contexts. Documenting best practice and students' responses to example-based instruction, the text demonstrates that this TEPS approach - which involves the use of worked examples, representations, and deep questions - helps students learn and master fundamental mathematical ideas, making it highly effective in developing algebraic readiness and mathematical understanding. This text will benefit post-graduate students, researchers, and academics in the fields of mathematics, STEM, and elementary education, as well as algebra research more broadly. Those interested in teacher education, classroom practice, and developmental and cognitive psychology will also find this volume of interest.

Teaching Early Algebra through Example-Based Problem Solving

Meixia Ding
Teaching Early Algebra through Example Based Problem Solving Book PDF

Author : Meixia Ding
Publisher : Routledge
Page : 194 pages
File Size : 48,5 Mb
Release : 2021-04-08
Category : Education
ISBN : 9781000370386

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Teaching Early Algebra through Example-Based Problem Solving by Meixia Ding Pdf

Drawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-based problem solving" (TEPS). Recognizing young children’s particular cognitive and developmental capabilities, this book powerfully argues for the importance of infusing algebraic thinking into early grade mathematics teaching and illustrates how this has been achieved by teachers in U.S. and Chinese contexts. Documenting best practice and students’ responses to example-based instruction, the text demonstrates that this TEPS approach – which involves the use of worked examples, representations, and deep questions – helps students learn and master fundamental mathematical ideas, making it highly effective in developing algebraic readiness and mathematical understanding. This text will benefit post-graduate students, researchers, and academics in the fields of mathematics, STEM, and elementary education, as well as algebra research more broadly. Those interested in teacher education, classroom practice, and developmental and cognitive psychology will also find this volume of interest.

Algebra in the Early Grades

James J. Kaput,David W. Carraher,Maria L. Blanton
Algebra in the Early Grades Book PDF

Author : James J. Kaput,David W. Carraher,Maria L. Blanton
Publisher : Routledge
Page : 526 pages
File Size : 49,8 Mb
Release : 2017-09-25
Category : Education
ISBN : 9781351577083

Get Book

Algebra in the Early Grades by James J. Kaput,David W. Carraher,Maria L. Blanton Pdf

This 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.

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

Carolyn Kieran
Teaching and Learning Algebraic Thinking with 5 to 12 Year Olds Book PDF

Author : Carolyn Kieran
Publisher : Springer
Page : 443 pages
File Size : 46,5 Mb
Release : 2017-12-04
Category : Education
ISBN : 9783319683515

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Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds by Carolyn Kieran Pdf

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.

Future Curricular Trends in School Algebra And Geometry

Zalman Usiskin,Kathleen Andersen,Nicole Zotto
Future Curricular Trends in School Algebra And Geometry Book PDF

Author : Zalman Usiskin,Kathleen Andersen,Nicole Zotto
Publisher : IAP
Page : 347 pages
File Size : 48,8 Mb
Release : 2010-06-01
Category : Education
ISBN : 9781617350085

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Future Curricular Trends in School Algebra And Geometry by Zalman Usiskin,Kathleen Andersen,Nicole Zotto Pdf

This volume contains papers from the Second International Curriculum Conference sponsored by the Center for the Study of Mathematics Curriculum (CSMC). The intended audience includes policy makers, curriculum developers, researchers, teachers, teacher trainers, and anyone else interested in school mathematics curricula.

Early Algebra

Carolyn Kieran,JeongSuk Pang,Deborah Schifter,Swee Fong Ng
Early Algebra Book PDF

Author : Carolyn Kieran,JeongSuk Pang,Deborah Schifter,Swee Fong Ng
Publisher : Springer
Page : 42 pages
File Size : 48,8 Mb
Release : 2016-08-12
Category : Education
ISBN : 3319322575

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Early Algebra by Carolyn Kieran,JeongSuk Pang,Deborah Schifter,Swee Fong Ng Pdf

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.

The Future of the Teaching and Learning of Algebra

Kaye Stacey,Helen Chick,Margaret Kendal
The Future of the Teaching and Learning of Algebra Book PDF

Author : Kaye Stacey,Helen Chick,Margaret Kendal
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 53,5 Mb
Release : 2006-04-11
Category : Education
ISBN : 9781402081316

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The Future of the Teaching and Learning of Algebra by Kaye Stacey,Helen Chick,Margaret Kendal Pdf

Kaye Stacey‚ Helen Chick‚ and Margaret Kendal The University of Melbourne‚ Australia Abstract: This section reports on the organisation‚ procedures‚ and publications of the ICMI Study‚ The Future of the Teaching and Learning of Algebra. Key words: Study Conference‚ organisation‚ procedures‚ publications The International Commission on Mathematical Instruction (ICMI) has‚ since the 1980s‚ conducted a series of studies into topics of particular significance to the theory and practice of contemporary mathematics education. Each ICMI Study involves an international seminar‚ the “Study Conference”‚ and culminates in a published volume intended to promote and assist discussion and action at the international‚ national‚ regional‚ and institutional levels. The ICMI Study running from 2000 to 2004 was on The Future of the Teaching and Learning of Algebra‚ and its Study Conference was held at The University of Melbourne‚ Australia fromDecember to 2001. It was the first study held in the Southern Hemisphere. There are several reasons why the future of the teaching and learning of algebra was a timely focus at the beginning of the twenty first century. The strong research base developed over recent decades enabled us to take stock of what has been achieved and also to look forward to what should be done and what might be achieved in the future. In addition‚ trends evident over recent years have intensified. Those particularly affecting school mathematics are the “massification” of education—continuing in some countries whilst beginning in others—and the advance of technology.

Early Algebraization

Jinfa Cai,Eric Knuth
Early Algebraization Book PDF

Author : Jinfa Cai,Eric Knuth
Publisher : Springer Science & Business Media
Page : 631 pages
File Size : 50,7 Mb
Release : 2011-02-24
Category : Education
ISBN : 9783642177354

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Early Algebraization by Jinfa Cai,Eric Knuth Pdf

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.

Encountering Algebra

Cecilia Kilhamn,Roger Säljö
Encountering Algebra Book PDF

Author : Cecilia Kilhamn,Roger Säljö
Publisher : Springer
Page : 263 pages
File Size : 51,9 Mb
Release : 2019-07-03
Category : Education
ISBN : 9783030175771

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Encountering Algebra by Cecilia Kilhamn,Roger Säljö Pdf

The book reports a comparative research project about algebra teaching and learning in four countries. Algebra is a central topic of learning across the world, and it is well-known that it represents a hurdle for many students. The book presents analyses built on extensive video-recordings of classrooms documenting the first introduction to symbolic algebra (students aged 12 to 14). While the content addressed in all classrooms is variables, expressions and equations, the teaching approaches are diverse. The chapters bring the reader into different algebra classrooms, discussing issues such as mathematization and social norms, the role of mediating tools and designed examples, and teacher beliefs. By comparing classrooms, new insights are generated about how students understand the algebraic content, how teachers instruct, and how both parties deal with difficulties in learning elementary algebra. The book also describes a research methodology using video in search of taken-for-granted aspects of algebra lessons.

Taming the Unknown

Victor J. Katz,Karen Hunger Parshall
Taming the Unknown Book PDF

Author : Victor J. Katz,Karen Hunger Parshall
Publisher : Princeton University Press
Page : 502 pages
File Size : 53,7 Mb
Release : 2020-04-07
Category : Mathematics
ISBN : 9780691204079

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Taming the Unknown by Victor J. Katz,Karen Hunger Parshall Pdf

What is algebra? For some, it is an abstract language of x's and y’s. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century. Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era. Taming the Unknown follows algebra’s remarkable growth through different epochs around the globe.

Planting the Seeds of Algebra, PreK–2

Monica Neagoy
Planting the Seeds of Algebra PreK 2 Book PDF

Author : Monica Neagoy
Publisher : Corwin Press
Page : 210 pages
File Size : 45,5 Mb
Release : 2012-04-20
Category : Education
ISBN : 9781452283630

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Planting the Seeds of Algebra, PreK–2 by Monica Neagoy Pdf

Help young minds explore algebraic concepts Algebra is the gateway to higher education, and preparing students to grasp algebraic concepts increases their opportunities to succeed. This book shows teachers how to create a strong foundation in algebra for very young children. Using in-depth math "explorations," the author unpacks—step by step—the hidden connections to higher algebra. Each exploration contains an elegantly simple grade-banded lesson (on addition, subtraction, patterns, and odd and even numbers), followed by a discussion of the algebra connections in the lesson, as well as suggestions for additional problems to explore. Throughout, readers will find: Clear explanations of algebraic connections Specific strategies for teaching the key ideas of algebra Lesson modifications for older or younger students An array of age-appropriate problems, games, and lessons Planting the seeds of Algebra, PreK–2 helps teachers foster mathematical habits of mind in students such as critical thinking, problem solving, adaptability, agility, communication, curiosity, and imagination. Growth in these ways of thinking and doing will transfer to other areas of education and life—raising the bar and challenging students to aspire.

Algebra Structure Sense Development amongst Diverse Learners

Teresa Rojano
Algebra Structure Sense Development amongst Diverse Learners Book PDF

Author : Teresa Rojano
Publisher : Taylor & Francis
Page : 210 pages
File Size : 47,7 Mb
Release : 2022-06-07
Category : Education
ISBN : 9781000591538

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Algebra Structure Sense Development amongst Diverse Learners by Teresa Rojano Pdf

This volume emphasizes the role of effective curriculum design, teaching materials, and pedagogy to foster algebra structure sense at different educational levels. Positing algebra structure sense as fundamental to developing students’ broader mathematical maturity and advanced thinking, this text reviews conceptual, historical, cognitive, and semiotic factors, which influence the acquisition of algebra structure sense. It provides empirical evidence to demonstrate the feasibility of linking algebra structure sense to technological tools and promoting it amongst diverse learners. Didactic approaches include the use of adaptive digital environments, gamification, diagnostic and monitoring tools, as well as exercises and algebraic sequences of varied complexity. Advocating for a focus on both intuitive and formal knowledge, this volume will be of interest to students, scholars, and researchers with an interest in educational research, as well as mathematics education and numeracy.

Planting the Seeds of Algebra, 3-5

Monica Neagoy
Planting the Seeds of Algebra 3 5 Book PDF

Author : Monica Neagoy
Publisher : Corwin Press
Page : 249 pages
File Size : 51,9 Mb
Release : 2014-12-05
Category : Education
ISBN : 9781483379760

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Planting the Seeds of Algebra, 3-5 by Monica Neagoy Pdf

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