Construction Of Arithmetical Meanings And Strategies

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Construction of Arithmetical Meanings and Strategies

Author : Leslie P. Steffe
Publisher : Springer Science & Business Media
ISBN 13 : 1461238447
Total Pages : 362 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Construction of Arithmetical Meanings and Strategies by : Leslie P. Steffe

Download or read book Construction of Arithmetical Meanings and Strategies written by Leslie P. Steffe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The studies presented in this book should be of interest to anybody concerned with the teaching of arithmetic to young children or with cognitive development in general. The 'eaching experiment· was carried out with half a dozen children entering first grade over two years in biweekly sessions. Methodologically the authors' research is original. It is a longitudinal but not a naturalistic study, since the experimenter-teachers directed their interaction with each individual child with a view to his or her possible progress. It is experimental in the sense that two groups of subjects were selected according to criteria derived from an earlier study (Steffe, von Glasersfeld, Richards & Cobb, 1983) and that the problems proposed were comparable, though far from identical across the subjects; but unlike more rigid and shorter "learning" or ''training" studies it does not include pre-and posttests, or predetermined procedures. Theoretically, the authors subscribe to Piagefs constructivism: numbers are made by children, not found (as they may find some pretty rocks, for example) or accepted from adults (as they may accept and use a toy). The authors interpret changes in the children's counting behaviors in terms of constructivist concepts such as assimilation, accommodation, and reflective abstraction, and certain excerpts from protocols provide on-line examples of such processes at work. They also subscribe to Vygotsky's proposal for teachers '0 utilize the zone of proximal development and to lead the child to what he (can) not yet do· (1965, p. 104).

Construction of Arithmetical Meanings and Strategies

Author : Leslie P. Steffe
Publisher :
ISBN 13 : 9783540966883
Total Pages : 343 pages
Book Rating : 4.9/5 (668 download)

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Book Synopsis Construction of Arithmetical Meanings and Strategies by : Leslie P. Steffe

Download or read book Construction of Arithmetical Meanings and Strategies written by Leslie P. Steffe and published by . This book was released on 1988 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Construction of Arithmetical Meanings and Strategies

Author : Ernst V Glasersfeld
Publisher :
ISBN 13 : 9781461238454
Total Pages : 364 pages
Book Rating : 4.2/5 (384 download)

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Book Synopsis Construction of Arithmetical Meanings and Strategies by : Ernst V Glasersfeld

Download or read book Construction of Arithmetical Meanings and Strategies written by Ernst V Glasersfeld and published by . This book was released on 1987-12-01 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Young Children's Construction of Arithmetical Meanings and Strategies

Author : L. Steffe
Publisher :
ISBN 13 : 9783211966884
Total Pages : pages
Book Rating : 4.9/5 (668 download)

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Book Synopsis Young Children's Construction of Arithmetical Meanings and Strategies by : L. Steffe

Download or read book Young Children's Construction of Arithmetical Meanings and Strategies written by L. Steffe and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Epistemological Foundations of Mathematical Experience

Author : Leslie P. Steffe
Publisher : Springer Science & Business Media
ISBN 13 : 1461231787
Total Pages : 257 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Epistemological Foundations of Mathematical Experience by : Leslie P. Steffe

Download or read book Epistemological Foundations of Mathematical Experience written by Leslie P. Steffe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the 26th, 27th, and 28th of February of 1988, a conference was held on the epistemological foundations of mathematical experience as part of the activities of NSF Grant No. MDR-8550463, Child Generated Multiplying and Dividing Algorithms: A Teaching Experiment. I had just completed work on the book Construction of Arithmetical Meanings and Strategies with Paul Cobb and Ernst von Glasersfeld and felt that substantial progress had been made in understanding the early numerical experiences of the six children who were the subjects of study in that book. While the book was in preparation, I was also engaged in the teaching experiment on mUltiplying and dividing algorithms. My focus in this teaching experiment was on investigating the mathematical experiences of the involved children and on developing a language through which those experiences might be expressed. However, prior to immersing myself in the conceptual analysis of the mathematical experiences of the children, I felt that it was crucial to critically evaluate the progress that we felt we had made in our earlier work. It was toward achieving this goal that I organized the conference. When trying to understand the mathematical experiences of a child, one can do no better than to interact with the child in a mathematical context guided by the intention to specify the child's current knowledge and the progress the child might make.

Analysis of Arithmetic for Mathematics Teaching

Author : Gaea Leinhardt
Publisher : Routledge
ISBN 13 : 1135440654
Total Pages : 472 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Analysis of Arithmetic for Mathematics Teaching by : Gaea Leinhardt

Download or read book Analysis of Arithmetic for Mathematics Teaching written by Gaea Leinhardt and published by Routledge. This book was released on 2020-11-25 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume emerges from a partnership between the American Federation of Teachers and the Learning Research and Development Center at the University of Pittsburgh. The partnership brought together researchers and expert teachers for intensive dialogue sessions focusing on what each community knows about effective mathematical learning and instruction. The chapters deal with the research on, and conceptual analysis of, specific arithmetic topics (addition, subtraction, multiplication, division, decimals, and fractions) or with overarching themes that pervade the early curriculum and constitute the links with the more advanced topics of mathematics (intuition, number sense, and estimation). Serving as a link between the communities of cognitive researchers and mathematics educators, the book capitalizes on the recent research successes of cognitive science and reviews the literature of the math education community as well.

Constructing Number

Author : Anderson Norton
Publisher : Springer
ISBN 13 : 3030004910
Total Pages : 377 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Constructing Number by : Anderson Norton

Download or read book Constructing Number written by Anderson Norton and published by Springer. This book was released on 2018-12-17 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book synergizes research on number across two disciplines—mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children’s activity, including mental and physical actions. Subsequent chapters are organized into sections that address specific domains of number: natural numbers, fractions, and integers. Chapters within each section address ways that children build upon biological primitives (e.g., subitizing) and prior constructs (e.g., counting sequences) to construct number. The book relies on co-authored chapters and commentaries at the end of each section to create dialogue between junior faculty and senior researchers, as well as between psychologists and mathematics educators. The final chapter brings this work together around the framework of children’s activity and additional themes that arise in the collective work. The book is aimed to appeal to mathematics educators, mathematics teacher educators, mathematics education researchers, educational psychologists, cognitive psychologists, and developmental psychologists.

Handbook of Academic Learning

Author : Gary D. Phye
Publisher : Elsevier
ISBN 13 : 9780080532936
Total Pages : 607 pages
Book Rating : 4.5/5 (329 download)

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Book Synopsis Handbook of Academic Learning by : Gary D. Phye

Download or read book Handbook of Academic Learning written by Gary D. Phye and published by Elsevier. This book was released on 1997-01-08 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Academic Learning provides a comprehensive resource for educational and cognitive psychologists, as well as educators themselves, on the mechanisms and processes of academic learning. Beginning with general themes that cross subject and age level, the book discusses what motivates students to learn and how knowledge can be made personal for better learning and remembering. Individual chapters identify proven effective teaching methods for the specific domains of math, reading, writing, science, and critical problem solving, how students learn within those domains, and how learning can be accurately assessed for given domains and age levels. The Handbook takes a constructivist perspective to academic learning, emphasizing the construction of personal knowledge of an academic nature. Constructivism within the context of learning theory is viewed as involving an active learner that constructs an academic knowledge base through the development of cognitive strategies and metacognition. The book discusses the development of basic literacy skills that provide the foundation for higher order thinking and problem solving. Constructivism recognizes the social dimension of classroom learning and emphasizes the motivational elements of self-regulation and volition as essential learner characteristics. Written by authors who have first-hand experience with both theory development and the development of authentic classroom instructional techniques, the Handbook empowers educators to develop, implement, and field-test authentic instructional practices at their school site. The book provides a review of the literature, theory, research, and skill techniques for effective teaching and learning. Key Features * Identifies effective teaching with specific techniques * Covers elementary school through high school * Discusses teaching methods for all main subject areas: reading, writing, math, science, and critical thinking * Identifies how students learn to learn * Reviews theory, research, techniques, and assessment * Contains field tested examples for the educational professional at the school site * Provides a resource for staff development

The Emergence of Mathematical Meaning

Author : Paul Cobb
Publisher : Routledge
ISBN 13 : 1136486100
Total Pages : 313 pages
Book Rating : 4.1/5 (364 download)

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Book Synopsis The Emergence of Mathematical Meaning by : Paul Cobb

Download or read book The Emergence of Mathematical Meaning written by Paul Cobb and published by Routledge. This book was released on 2012-12-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of a five-year collaboration between groups of American and German mathematics educators. The central issue addressed accounting for the messiness and complexity of mathematics learning and teaching as it occurs in classroom situations. The individual chapters are based on the view that psychological and sociological perspectives each tell half of a good story. To unify these concepts requires a combined approach that takes individual students' mathematical activity seriously while simultaneously seeing their activity as necessarily socially situated. Throughout their collaboration, the chapter authors shared a single set of video recordings and transcripts made in an American elementary classroom where instruction was generally compatible with recent reform recommendations. As a consequence, the book is much more than a compendium of loosely related papers. The combined approach taken by the authors draws on interactionism and ethnomethodology. Thus, it constitutes an alternative to Vygotskian and Soviet activity theory approaches. The specific topics discussed in individual chapters include small group collaboration and learning, the teacher's practice and growth, and language, discourse, and argumentation in the mathematics classroom. This collaborative effort is valuable to educators and psychologists interested in situated cognition and the relation between sociocultural processes and individual psychological processes.

Piaget’s Genetic Epistemology for Mathematics Education Research

Author : Paul Christian Dawkins
Publisher : Springer Nature
ISBN 13 : 3031473868
Total Pages : 620 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Piaget’s Genetic Epistemology for Mathematics Education Research by : Paul Christian Dawkins

Download or read book Piaget’s Genetic Epistemology for Mathematics Education Research written by Paul Christian Dawkins and published by Springer Nature. This book was released on 2024-01-22 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an entry point for graduate students and other scholars interested in using the constructs of Piaget’s genetic epistemology in mathematics education research. Constructs comprising genetic epistemology form the basis for some of the most well-developed theoretical frameworks available for characterizing learning, particularly in mathematics. The depth and complexity of Piaget’s work can make it challenging to find adequate entry points for learners, not least because it requires a reorientation regarding the nature of mathematical knowledge itself. This volume gathers leading scholars to help address that challenge. The main section of the book presents key Piagetian constructs for mathematics education research such as schemes and operations, figurative and operative thought, images and meanings, and decentering. The chapters that discuss these constructs include examples from research and address how these constructs can be used in research. There are two chapters on various types of reflective abstraction, because this construct is Piaget’s primary tool for characterizing the advancement of knowledge. The later sections of the book contain commentaries reflecting on the contributions of the body of theory developed in the first section. They connect genetic epistemology to current research domains such as equity and the latest in educational psychology. Finally, the book closes with short chapters portraying how scholars are using these tools in specific arenas of mathematics education research, including in special education, early childhood education, and statistics education.

Radical Constructivism in Mathematics Education

Author : E. Glasersfeld
Publisher : Springer Science & Business Media
ISBN 13 : 0306472015
Total Pages : 264 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Radical Constructivism in Mathematics Education by : E. Glasersfeld

Download or read book Radical Constructivism in Mathematics Education written by E. Glasersfeld and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is the science of acts without things - and through this, of things one can define by acts. 1 Paul Valéry The essays collected in this volume form a mosaik of theory, research, and practice directed at the task of spreading mathematical knowledge. They address questions raised by the recurrent observation that, all too frequently, the present ways and means of teaching mathematics generate in the student a lasting aversion against numbers, rather than an understanding of the useful and sometimes enchanting things one can do with them. Parents, teachers, and researchers in the field of education are well aware of this dismal situation, but their views about what causes the wide-spread failure and what steps should be taken to correct it have so far not come anywhere near a practicable consensus. The authors of the chapters in this book have all had extensive experience in teaching as well as in educational research. They approach the problems they have isolated from their own individual perspectives. Yet, they share both an overall goal and a specific fundamental conviction that characterized the efforts about which they write here. The common goal is to find a better way to teach mathematics. The common conviction is that knowledge cannot simply be transferred ready-made from parent to child or from teacher to student but has to be actively built up by each learner in his or her own mind.

Pathways To Number

Author : Jacqueline Bideaud
Publisher : Psychology Press
ISBN 13 : 1134762933
Total Pages : 400 pages
Book Rating : 4.1/5 (347 download)

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Book Synopsis Pathways To Number by : Jacqueline Bideaud

Download or read book Pathways To Number written by Jacqueline Bideaud and published by Psychology Press. This book was released on 2013-03-07 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume celebrates the 50th anniversary of the famous and influential work of Jean Piaget and Alina Szeminska, The Child's Conception of Number. It is a tribute to those two authors as well as to the entire Geneva school that pioneered the genetic study of cognitive structures in children. Dealing with the process of the child's construction of the notion of number -- a very important subject for the child as well as for the teacher, the researcher, and the practicing psychologist -- it summarizes the progress that has been made and outlines new research directions in this area. The book is a compilation of the work of the foremost international researchers in this area and includes a wide spectrum of viewpoints and schools of thought. It also introduces several new authors from Europe, including students of Piaget, to the American academic community.

Instructional Strategies for Improving Students' Learning

Author : Jerry Carlson
Publisher : IAP
ISBN 13 : 161735631X
Total Pages : 227 pages
Book Rating : 4.6/5 (173 download)

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Book Synopsis Instructional Strategies for Improving Students' Learning by : Jerry Carlson

Download or read book Instructional Strategies for Improving Students' Learning written by Jerry Carlson and published by IAP. This book was released on 2012-01-01 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twin objectives of the series Psychological Perspectives on Contemporary Educational Issues are: (1) to identify issues in education that are relevant to professional educators and researchers; and (2) to address those issues from research and theory in educational psychology, psychology, and related disciplines. The present volume, consisting of two focal chapters, commentaries, and final responses targets instructional strategies for improving students’ learning in two of the traditional “three R” areas, reading and ?rithmetic (mathematics), in the elementary school grades. The focal chapters in those two skill areas are written by leading contributors to the reading and mathematics research literatures, Cathy Collins Block for the reading section and Douglas Clements and Julie Sarama for the mathematics section. Few would dispute the essentiality of these two curricular domains in laying the foundation for the development of students’ competencies in a vast array of academic disciplines in both the in- and out-of-school years that lie ahead. The present volume is intended for practitioners and researchers who are seeking the latest instructional research-based strategies for improving students’ early reading and mathematics performance.

Learning Mathematics

Author : Paul Cobb
Publisher : Springer Science & Business Media
ISBN 13 : 9401720576
Total Pages : 204 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Learning Mathematics by : Paul Cobb

Download or read book Learning Mathematics written by Paul Cobb and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume emphasizes students' inferred mathematical experiences as the starting point in the theory-building process. The book addresses conceptual constructions, including multiplicative notions, fractions, algebra, and the fundamental theorem of calculus, and theoretical constructs such as the crucial role of language and symbols, and the importance of dynamic imagery.

Handbook of Research Design in Mathematics and Science Education

Author : Anthony Edward Kelly
Publisher : Routledge
ISBN 13 : 1135705828
Total Pages : 984 pages
Book Rating : 4.1/5 (357 download)

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Book Synopsis Handbook of Research Design in Mathematics and Science Education by : Anthony Edward Kelly

Download or read book Handbook of Research Design in Mathematics and Science Education written by Anthony Edward Kelly and published by Routledge. This book was released on 2012-10-12 with total page 984 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Research Design in Mathematics and Science Education is based on results from an NSF-supported project (REC 9450510) aimed at clarifying the nature of principles that govern the effective use of emerging new research designs in mathematics and science education. A primary goal is to describe several of the most important types of research designs that: * have been pioneered recently by mathematics and science educators; * have distinctive characteristics when they are used in projects that focus on mathematics and science education; and * have proven to be especially productive for investigating the kinds of complex, interacting, and adapting systems that underlie the development of mathematics or science students and teachers, or for the development, dissemination, and implementation of innovative programs of mathematics or science instruction. The volume emphasizes research designs that are intended to radically increase the relevance of research to practice, often by involving practitioners in the identification and formulation of the problems to be addressed or in other key roles in the research process. Examples of such research designs include teaching experiments, clinical interviews, analyses of videotapes, action research studies, ethnographic observations, software development studies (or curricula development studies, more generally), and computer modeling studies. This book's second goal is to begin discussions about the nature of appropriate and productive criteria for assessing (and increasing) the quality of research proposals, projects, or publications that are based on the preceding kind of research designs. A final objective is to describe such guidelines in forms that will be useful to graduate students and others who are novices to the fields of mathematics or science education research. The NSF-supported project from which this book developed involved a series of mini conferences in which leading researchers in mathematics and science education developed detailed specifications for the book, and planned and revised chapters to be included. Chapters were also field tested and revised during a series of doctoral research seminars that were sponsored by the University of Wisconsin's OERI-supported National Center for Improving Student Learning and Achievement in Mathematics and Science. In these seminars, computer-based videoconferencing and www-based discussion groups were used to create interactions in which authors of potential chapters served as "guest discussion leaders" responding to questions and comments from doctoral students and faculty members representing more than a dozen leading research universities throughout the USA and abroad. A Web site with additional resource materials related to this book can be found at http://www.soe.purdue.edu/smsc/lesh/ This internet site includes directions for enrolling in seminars, participating in ongoing discussion groups, and submitting or downloading resources which range from videotapes and transcripts, to assessment instruments or theory-based software, to publications or data samples related to the research designs being discussed.

Children's Fractional Knowledge

Author : Leslie P. Steffe
Publisher : Springer Science & Business Media
ISBN 13 : 144190591X
Total Pages : 379 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Children's Fractional Knowledge by : Leslie P. Steffe

Download or read book Children's Fractional Knowledge written by Leslie P. Steffe and published by Springer Science & Business Media. This book was released on 2009-12-02 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Children’s Fractional Knowledge elegantly tracks the construction of knowledge, both by children learning new methods of reasoning and by the researchers studying their methods. The book challenges the widely held belief that children’s whole number knowledge is a distraction from their learning of fractions by positing that their fractional learning involves reorganizing—not simply using or building upon—their whole number knowledge. This hypothesis is explained in detail using examples of actual grade-schoolers approaching problems in fractions including the schemes they construct to relate parts to a whole, to produce a fraction as a multiple of a unit part, to transform a fraction into a commensurate fraction, or to combine two fractions multiplicatively or additively. These case studies provide a singular journey into children’s mathematics experience, which often varies greatly from that of adults. Moreover, the authors’ descriptive terms reflect children’s quantitative operations, as opposed to adult mathematical phrases rooted in concepts that do not reflect—and which in the classroom may even suppress—youngsters’ learning experiences. Highlights of the coverage: Toward a formulation of a mathematics of living instead of being Operations that produce numerical counting schemes Case studies: children’s part-whole, partitive, iterative, and other fraction schemes Using the generalized number sequence to produce fraction schemes Redefining school mathematics This fresh perspective is of immediate importance to researchers in mathematics education. With the up-close lens onto mathematical development found in Children’s Fractional Knowledge, readers can work toward creating more effective methods for improving young learners’ quantitative reasoning skills.

Handbook of Research on the Education of Young Children

Author : Bernard Spodek
Publisher : Routledge
ISBN 13 : 1135466130
Total Pages : 887 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Handbook of Research on the Education of Young Children by : Bernard Spodek

Download or read book Handbook of Research on the Education of Young Children written by Bernard Spodek and published by Routledge. This book was released on 2014-01-27 with total page 887 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Research on the Education of Young Children, Second Edition is an essential reference on research in early childhood education not only in the United States but throughout the world. It provides a comprehensive overview of important contemporary issues and the information necessary to make judgments about these issues. The field has changed significantly since the publication of the first edition of this Handbook in 1993, creating a need for an update. The Handbook of Research on the Education of Young Children, Second Edition is thus focused on research conducted over the past decade or so. The volume is organized in four parts: *Early Childhood Education and Child Development. New in this edition: moral development; the development of creativity. *Early Childhood Educational Curriculum. New in this edition: movement or dance education; the education of linguistically and culturally diverse children. *Foundations of Early Childhood Educational Policy. New in this edition: childhood poverty; the education of bilingual children. *Research and Evaluation Strategies for Early Childhood Education. New in this edition: doing historical research in early childhood education; postmodern and feminist orientations. The Handbook of Research on the Education of Young Children, Second Edition makes the expanding knowledge base related to early childhood education readily available and accessible. It is a valuable tool for all who work and study in the field.