Early Algebraization

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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.

Early Algebraization

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Author : Jinfa Cai
language : en
Publisher: Springer
Release Date : 2011-03-03

Early Algebraization written by Jinfa Cai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-03 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.

Teaching Early Algebra Through Example Based Problem Solving

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Author : Meixia Ding
language : en
Publisher: Routledge
Release Date : 2021-04-07

Teaching Early Algebra Through Example Based Problem Solving written by Meixia Ding and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-07 with Education categories.

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.

Using Design Research And History To Tackle A Fundamental Problem With School Algebra

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Author : Sinan Kanbir
language : en
Publisher: Springer
Release Date : 2017-10-28

Using Design Research And History To Tackle A Fundamental Problem With School Algebra written by Sinan Kanbir and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-28 with Education categories.

In this well-illustrated book the authors, Sinan Kanbir, Ken Clements, and Nerida Ellerton, tackle a persistent, and universal, problem in school mathematics—why do so many middle-school and secondary-school students find it difficult to learn algebra well? What makes the book important are the unique features which comprise the design-research approach that the authors adopted in seeking a solution to the problem. The first unique feature is that the authors offer an overview of the history of school algebra. Despite the fact that algebra has been an important component of secondary-school mathematics for more than three centuries, there has never been a comprehensive historical analysis of factors influencing the teaching and learning of that component. The authors identify, through historical analysis, six purposes of school algebra: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalized arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of procedures for modeling real-life problems, (e) algebra as an aid to describing structural properties in elementary mathematics, and (f) algebra as a study of variables. They also raise the question whether school algebra represents a unidimensional trait. Kanbir, Clements and Ellerton offer an unusual hybrid theoretical framework for their intervention study (by which seventh-grade students significantly improved their elementary algebra knowledge and skills). Their theoretical frame combined Charles Sanders Peirce’s triadic signifier-interpretant-signified theory, which is in the realm of semiotics, with Johann Friedrich Herbart’s theory of apperception, and Ken Clements’ and Gina Del Campo’s theory relating to the need to expand modes of communications in mathematics classrooms so that students engage in receptive and expressive modes. Practicing classroom teachers formed part of the research team. This book appears in Springer’s series on the “History of Mathematics Education.” Not only does it include an important analysis of the history of school algebra, but it also adopts a theoretical frame which relies more on “theories from the past,” than on contemporary theories in the field of mathematics education. The results of the well-designed classroom intervention are sufficiently impressive that the study might havecreated and illuminated a pathway for future researchers to take.

Advancing Knowledge And Building Capacity For Early Childhood Research

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Author : Sharon Ryan
language : en
Publisher: American Educational Research Association
Release Date : 2021-01-20

Advancing Knowledge And Building Capacity For Early Childhood Research written by Sharon Ryan and has been published by American Educational Research Association this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-20 with Education categories.

This volume employs a multidisciplinary approach to research on a high-profile topic very much on the agenda of state and national policy leaders: early childhood development and education. It aims to reflect how scholarly perspectives shape the contours of knowledge generation, and to illuminate the gaps that prevent productive interchange among scholars who value equity in the opportunities available to young children, their families, and teachers/caregivers. The editors and authors identify and prioritize critical research areas; assess the state of the field in terms of promising research designs and methodologies; and identify capacity-building needs and potential cross-group collaborations.

Proving In The Elementary Mathematics Classroom

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Author : Andreas J. Stylianides
language : en
Publisher: Oxford University Press
Release Date : 2016-07-14

Proving In The Elementary Mathematics Classroom written by Andreas J. Stylianides and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-14 with Mathematics categories.

Although proving is core to mathematics as a sense-making activity, it currently has a marginal place in elementary classrooms internationally. Blending research with practical perspectives, this book addresses what it would take to elevate the place of proving at elementary school. The book uses classroom episodes from two countries to examine different kinds of proving tasks and the proving activity they can generate in the elementary classroom. It examines further the role of teachers in mediating the relationship between proving tasks and proving activity, including major mathematical and pedagogical issues that arise for teachers as they implement each kind of proving task. In addition to its contribution to research knowledge, the book has important implications for teaching, curricular resources, and teacher education.

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.

Handbook Of International Research In Mathematics Education

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Author : Lyn D. English
language : en
Publisher: Routledge
Release Date : 2015-07-30

Handbook Of International Research In Mathematics Education written by Lyn D. English and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-30 with Education categories.

This third edition of the Handbook of International Research in Mathematics Education provides a comprehensive overview of the most recent theoretical and practical developments in the field of mathematics education. Authored by an array of internationally recognized scholars and edited by Lyn English and David Kirshner, this collection brings together overviews and advances in mathematics education research spanning established and emerging topics, diverse workplace and school environments, and globally representative research priorities. New perspectives are presented on a range of critical topics including embodied learning, the theory-practice divide, new developments in the early years, educating future mathematics education professors, problem solving in a 21st century curriculum, culture and mathematics learning, complex systems, critical analysis of design-based research, multimodal technologies, and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Handbook’s original themes for international research in mathematics education and remains in the process a definitive resource for the field.

Encountering Algebra

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Author : Cecilia Kilhamn
language : en
Publisher: Springer
Release Date : 2019-07-03

Encountering Algebra written by Cecilia Kilhamn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-03 with Education categories.

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-grantedaspects of algebra lessons.