The Child's Conception of Space

Jean Piaget e Bärbel Inhelder

Routledge | 1998 | 505 páginas | rar - pdf | 8,1 Mb

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“A massive and most important study. . . . All teachers of young children should know the general outline of the work.” —Evelyn Lawrence, British Journal of Educational Studies

The nature of space, whether an innate idea, the outcome of experience in the external world, or an operational construction has long been a source of philosophical and speculative psychological discussion. This book deals with the development of the child’s notions about space.

CONTENTS
PREFACE vii
TRANSLATORS' NOTES ix
SUMMARY xii
PART ONE - TOPOLOGICAL SPACE
Chapter I. PERCEPTUAL SPACE, REPRESENTATIONAL SPACE, AND THE HAPTIC PERCEPTION OF SHAPE 3
1. PERCEPTUAL OR SENSORI-MOTOR SPACE 5
2. THE RECOGNITION OF SHAPES ('HAPTIC PERCEPTION') 17
Chapter II. THE TREATMENT OF ELEMENTARY SPATIAL RELATIONSHIPS IN DRAWING—' PICTORIAL SPACE' 44
1. SPACE IN SPONTANEOUS DRAWINGS 46
2. THE DRAWING OF GEOMETRICAL FIGURES 52
Chapter III. LINEAR AND CIRCULAR ORDER 80
Chapter IV. THE STUDY OF KNOTS AND THE RELATIONSHIP OF 'SURROUNDING' 104
Chapter V. THE IDEA OF POINTS AND THE IDEA OF CONTINUITY 125
PART TWO - PROJECTIVE SPACE
Summary 153
Chapter VI. PROJECTIVE LINES AND PERSPECTIVE 155
1. CONSTRUCTION OF THE PROJECTIVE STRAIGHT LINE 156
2. PERSPECTIVE 171
Chapter VII. THE PROJECTION OF SHADOWS 194
Chapter VIII. THE CO-ORDINATION OF PERSPECTIVES 209
Chapter IX. GEOMETRICAL SECTIONS 247
Chapter X. THE ROTATION AND DEVELOPMENT OF SURFACES 271
PART THREE - THE TRANSITION FROM PROJECTIVE TO EUCLIDEAN SPACE
Summary 301
Chapter XI AFFINITIVE TRANSFORMATIONS OF THE RHOMBUS AND THE CONSERVATION OF PARALLELS 303
Chapter XII. SIMILARITIES AND PROPORTIONS 320
1. SIMILAR TRIANGLES 322
2. THE SIMILARITY OF RECTANGLES 352
Chapter XIII. SYSTEMS OF REFERENCE AND HORIZONTAL- VERTICAL CO-ORDINATES 375
Chapter XIV. DIAGRAMMATIC LAYOUTS AND THE PLAN OF A MODEL VILLAGE 419
Chapter XV. GENERAL CONCLUSIONS. THE' INTUITION' OF SPACE 447
INDEX 487

Outros livros de Piaget:

The child's conception of geometry por Jean Piaget; Bärbel Inhelder; Alina Szeminska Idioma: Inglês   The child's construction of quantities : conservation and atomism por Jean Piaget; Bärbel Inhelder Idioma: Inglês   Editora: London : Routledge and Kegan Paul, 1974, ©1941.

Epistemological Foundations of Mathematical Experience

Leslie P. Steffe

Springer |1991 | 322 páginas | pdf |11,5 Mb

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link1 

This book offers an overview of "constructivism", covers its historical precedents, and goes on to demonstrate that researchers have made substantial progress in understanding the mathematical experiences of children. The author argues that early numerical and other mathematical experiences are always in flux and are as much a function of the adult's as they are of the child's intentions, language and actions. For those in the mathematics education field and for cognitive and developmental psychologists, as well as educational researchers, this book aims to offer fresh concepts and analyses. This monograph on cognitive psychology, developmental psychology and mathematical education is intended for educators and researchers.

Contents
Preface .
Acknowledgments
Contributors 
1 Philosophical and Psychological Aspects of Constructivism.
Clifford Konold and David K. Johnson
2 The Import of Fodor's Anti-Constructivist Argument
Mark H. Bickhard
3 The Learning Paradox: A Plausible Counterexample
Leslie P. Steffe
4 Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and Piaget's Approach
Emst von Glasersfeld
5 A Pre-Logical Model of Rationality.
Mark H. Bickhard
6 Recursion and the Mathematical Experience
Thomas E. Kieren and Susan E.B. Pirie
7 The Role Mathematical Transformations and Practice in Mathematical Development 
Robert G. Coopel Jr.
8 The Concept of Exponential Functions: A Student's Perspective 
Jere Confrey
9 Constructive Aspects of Reflective Abstraction in Advanced Mathematics 
Ed Dubinsky
10 Reflective Abstraction in Humanities Education: Thematic Images and Personal Schemas
Philip Lewin
11 Enhancing School Mathematical Experience Through Constructive Computing Activity 
Lany L. Hatfield
12 To Experience is to Conceptualize: and Mathematical Experience . . .
Patrick W. Thompsom
References . .
Author Index .
Subject Index .

Construction of arithmetical meanings and strategies

 (Recent Research in Psychology) 

 Leslie P. Steffe, Paul Cobb, Hermine Sinclair e Ernst v. Glasersfeld

Springer | 1988 | páginas | rar - pdf | 13,72 Mb

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The studies presented in this book will be of interest to anybody concerned with the teaching of arithmetic to young children or with cognitive development in general. The book provides an extremely detailed account of the different types of counting behavior of half a dozen children over two years. The "teaching experiment" used investigates children's construction of counting schemes, writing operations and their systems, lexical and syntactic meanings of number words and, finally, thinking strategies. The data allowed the authors to reach their main goal: to document the many subtle changes in children's counting and to interpret them theoretically. At the same time, the results of their intensive study lead the authors to affirm that a major shift in the arithmetic curriculum is necessary: they have cogently demonstrated that many of the widespread presuppositions about what young children know and what they do not know are erroneous, and that better insight into how children come to "do mathematics" should greatly improve the the teaching of arithmetic.


Contents
I: On the Construction of the Counting Scheme.
Children's Counting.- The Counting Types.- Perceptual Unit Items.- Figural Unit Items.- Motor Unit Items.- Verbal Unit Items.- Abstract Unit Items.- Ontogenetic Analysis.- Stages.- Adaptation.- Counting as a Scheme.- The First Part of the Counting Scheme.- The Third Part of the Counting Scheme.- Other Sources of Numerosity.- Perceptual Mechanisms.- Spatial Patterns.- Meaning Theory.- Reflection and Abstraction.- II: The Construction of Motor Unit Items: Brenda, Tarus, and James.-
1. Brenda.- The Perceptual Period.- The Motor Period.- Discussion of Brenda's Case Study.- The Perceptual Period.- The Motor Period.-
2. Tarus.- The Perceptual Period.- The Motor Period.- Discusion of Tarus's Case Study.- The Perceptual Period.- The Motor Period.-
3. James.- The Perceptual Period.- The Motor Period.- Discussion of James's Case Study.- The Perceptual Period.- The Motor Period.- Perspectives on the Three Case Studies.- Period Criterion.- The Incorporation and Invariant Sequence Criteria.- The Reorganization Criterion.-
III: The Construction of Verbal Unit Items: Brenda, Tarus, and James.-
1. Brenda.- Discussion of Brenda's Case Study.-
2. Tarus.- Discussion of Tarus's Case Study.-
3. James.- Discussion of James's Case Study.- Perspectives on the Case Studies.- The Verbal Period as a Subperiod in the Figurative Stage.- Counting-on.- IV: The Construction of Abstract Unit Items: Tyrone, Scenetra, and Jason.-
4. Tyrone.- The Motor Period.- The Abstract Period.- Discussion of Tryone's Case Study.-
5. Scenetra.- The Motor Period.- The Verbal Period.- The Abstract Period.- Discussion of Scenetra's Case Study.-
6. Jason.- The Motor Period.- Creating Verbal Unit Items.- The Abstract Period.- Discussion of Jason's Case Study.- Perspectives on the Case Studies.- Stages.- Incorportation Criterion.- Transition to the Abstract Period.- The Reorganization of Counting.-
V: Lexical and Syntactical Meanings: Brenda, Tarus, and James.-
1. Brenda.- The Perceptual Period.- The Motor Period.- The Verbal Period.- Discussion of Brenda's Case Study.- The Perceptual Stage.- The Figurative Stage.-
2. Tarus.- The Perceptual Period.- The Motor Period.- The Verbal Period.- Discussion of Tarus's Case Study.- The Perceptual Stage.- The Figurative Stage.-
3. James.- The Perceptual Period.- The Motor Period.- The Verbal Period.- Discussion of James's Case Study.- The Perceptual Stage.- The Figurative Stage.- Perspectives on the Case Studies.- The Perceptual Stage.- Finger Patterns.- The Figurative Stage.- Mobile Finger Patterns.- Sophisticated Finger Patterns.- Spatio-Auditory Patterns.- Dual Meanings of Number Words.- Counting as the Meaning of Number Words.- Summary of the Types of Preconcepts and Concepts.- Meanings of "Ten".- Ten as an Enactive Concept.- Ten as a Countable Figural Unit.- Ten as a Countable Motor Unit.- Adding Schemes.- The Perceptual Stage.- The Figurative Stage.- Comments on Prenumerical Children.-
VI: Lexical and Syntactical Meanings: Tyrone, Scenetra, and Jason.- Systems of Integration.- Integrations.- Sequential Integration Operations.- Progressive Integration Operations.- Part-Whole Operations.-
4. Tyrone.- The Emergence of the Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- The Period of Part-Whole Operations.- Discussion of Tyrone's Case Study.- The Emergence of the Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- The Period of Part-Whole Operations.- Unit Types of the Unit of Ten.-
5. Scenetra.- Recognition and Re-Presentation of Patterns.- The Emergence of the Integration Operation.- The Period of Sequential Integration operations.- The Period of Progressive Integreation Operations.- Discussion of Scenetra's Case Study.- The Emergence of the Integratoin Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- Unit Types of the Unit of Ten.-
6. Jason.- Recognition and Re-Presentation of Patterns.- The Emergence of The Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive integration Operations.- The Period of Part-Whole Operations.- Discussion of Jason's Case Study.- The Emergence of the Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- The Period of Part-Whole Operations.- Unit Types of the Unit of Ten.- Perspectives on the Case Studies.- The Emergence of the Integration Operation.- Numerical Patterns.- Number Sequences.- Stages in the Construction of the Numerical Counting Scheme.- Piaget's Invariant Sequence and Incorporation Criteria.- The Reorganization Criterion.- Units of One.- The Unit of One in Sequential Integration Operations.- The Unit of One in Progressive Integration Operations.- The Unit of One in Part-Whole Operations.- Units of Ten.- The Stage of Sequential Integration Operations.- The Stage of Progressive Integration Operations.- The Stage of Part-Whole Operations.- Other Perspectives.-
VII: Strategies for Finding Sums and Differences: Brenda, Tarus, and James.- Brenda.- Independent Solutions.- Number Word Coordinations.- Tarus.- Independent Solutions.- Number Word Coordinations.- James.- Independent Solutions.- Number Word Coordinations.- Perspectives on the Case Studies.- Number Facts.-
VIII: Strategies for Finding Sums and Differences: Tyrone, Scenetra, and Jason.- Sequential Integration Operations.- Jason.- Tyrone.- Scenetra.- Discussion: Sequential Integration Operations.- Progressive Integration Operations.- Jason.- Tyrone.- Scenetra.- Discussion: Progressive Integration Operations.- Part-Whole Operations.- Jason.- Tyrone.- Perspective on the Case Studies.- Arithmetical Context.- Thinking Strategies and Integration Operations.- Thinking Strategies and the Basic Facts.- Thinking Strategies and the Construction of Part-Whole Operations.- Goals for Teaching Thinking Strategies.-
IX: Modifications of the Counting Scheme.- Predicting Modifications of the Counting Scheme.- Mathematical Learning.- The Perceptual Stage.- Temporary Modifications.- Procedural Accommodations.- Engendering Accommodations.- Isolated Procedural Accommodations.- The Figurative Stage.- Procedural Accommodations.- Temporary Modifications.- Retrospective Accommodations.- Re-presentation and Review of Prior Activity.- The Figurative Stage: Tyrone, Scenetra, and Jason.- Procedural Engendering Accommodations.- Temporary Modifications.- Metamorphic Accommodations.- Stages in the Construction of Part-Whole Operations.- Sequential Integration Operations.- Procedural Accommodations.- Engendering Accommodations.- Progressive Integration Operations.- Internal Reorganizations.- Part-Whole Operations.- Phylogenetic Perspectives.- Zones of Potential Development in Retrospect.- Figurative Stage.- Sequential Integration Operations.- Progressive Integration Operations.- Part-Whole Operations.-
Final Comments.-
References.

International Perspectives on Gender and Mathematics Education

Helen J. Forgasz, Joanne Rossi Becker e Kyeong-Hwa Lee

Information Age Publishing | 2010 | 467 páginas | rar - pdf | 2,1 Mb

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A Volume in International Perspectives on Mathematics Education - Cognition, Equity & Society Series Editor Bharath Sriraman, The University of Montana and Lyn English, Queensland University of Technology Why a book on gender issues in mathematics in the 21st century? Several factors have influenced the undertaking of this project by the editors. First, an international volume focusing on gender and mathematics has not appeared since publication of papers emerging from the 1996 International Congress on Mathematical Education (Keitel, 1998). Surely it was time for an updated look at this critical area of mathematics education. Second, we have had lively discussion and working groups on gender issues at conferences of the International Group for the Psychology of Mathematics Education [PME] for the past four years, sessions at which stimulating and ground-breaking research has been discussed by participants from many different countries. Some publication seemed essential to share this new knowledge emerging from a wider variety of countries and from different cultural perspectives. Third, some western countries such as Australia and the USA have experienced in recent years a focus on the "boy problem," with an underlying assumption that issues of females and mathematics have been solved and are no longer worthy of interest. Thus it seemed timely to look more closely at the issue of gender and mathematics internationally. When the idea for this volume first emerged, invitations were issued to those regularly attending the working and discussion groups at PME. Potential authors were charged to focus on gender issues in mathematics and were given wide scope to hone in on the issues that were central to their own research efforts, or were in receipt or in need of close attention in their own national or regional contexts.

Contents
Section I History, Policy, and Non-School Factors
1 International Perspectives on Gender and Mathematics Education: An Overview...1
Joanne Rossi Becker, Helen Forgasz, Olof Bjorg Steinthorsdottir, and Kyeong-Hwa Lee
Section I History, Policy, and Non-School Factors
2 The Ladies’ Diary or Woman’s Almanack, 1704–1841..... 15
Teri Perl
3 Conversations of Parents and Children Working on Mathematics.... 33
Melfried Olson, Judith Olson, Claire Okazaki, and Thuy La
4 Out-of-School-Time (OST) Programs as Mathematics Support for Females.. 55
Lynda R. Wiest
5 Freedom to Choose?: Girls, Mathematics and the Gendered Construction of Mathematical Identity... 87
Fiona Walls
6 Gender Mainstreaming: Maintaining Attention on Gender Equality...111
Colleen Vale
Section II National Focus
7 Studies in Mexico on Gender and Mathematics...... 147
Sonia Ursini, Martha P. Ramírez, and Claudia Rodríguez, María Trigueros, and Ma. Dolores Lozano
8 Gender Differences When Working with Algebraic Variables: A Study with Mexican Secondary School Students.... 173
Carolina Rubí Real Ortega and Sonia Ursini
9 Factors Contributing to Gender Differences in Mathematics Performance of United States High School Students....203
Pamela L. Paek
10 Gender Differences in Mathematics Achievement: Evidence from Regional and International Student Assessments.... 225
Xin Ma
11 Mathematics Achievement in Icelandic Playschools: Examining When Gender Differences Emerge..... 249
Olof Bjorg Steinthorsdottir, Kimberly Dadisman, Dylan L. Robertson, and Kristjana Steinthorsdottir
12 Mathematics Teacher Education and Gender Effects... 263
Sigrid Blömeke and Gabriele Kaiser
Section III High Achievers
13 Discovering the Potential of Gifted Females in Mathematics.... 287
Kyeong-Hwa Lee, Eun-Jung Lee, Seoung-Hey Paik, and HeiSook Lee
14 Gender and High Achievers in Mathematics: Who and What Counts?.... 315
Gilah C. Leder and Helen J. Forgasz
15 What Are High Achieving Young Women’s Perceptions of Mathematics Over Time?.... 341
Amanda Lambertus, Susan Bracken, and Sarah Berenson
Section IV Tertiary Students
16 The Influence of High School and University Experiences on Women’s Pursuit of Undergraduate Mathematics Degrees in Canada......365
Jennifer Hall
17 Try and Catch the Wind: Women Who Do Doctorates at a Mature Stage in Their Lives.... 391
Ansie Harding, Leigh Wood, and Michelle Muchatuta With Barbara Edwards, Lucia Falzon, Sibba Gudlaugsdottir, Belinda Huntley, Jillian Knowles, Barbara Miller-Reilly,and Tobia Steyn
18 Recognizing Gender in Mathematics Relationships: A Relational Counseling Approach Helps Teachers and Students Overcome Damaging Perceptions..... 421
Jillian M. Knowles
Contributors.......451

Thinking and Problem Solving

Robert J. Sternberg

Academic Press | 1998 -2ª edição |482 páginas | pdf | 7,2 Mb

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Thinking and Problem-Solving presents a comprehensive and up-to-date review of literature on cognition, reasoning, intelligence, and other formative areas specific to this field. Written for advanced undergraduates, researchers, and academics, this volume is a necessary reference for beginning and established investigators in cognitive and educational psychology. Thinking and Problem-Solving provides insight into questions such as: how do people solve complex problems in mathematics and everyday life? How do we generate new ideas? How do we piece together clues to solve a mystery, categorize novel events, and teach others to do the same? 
Key Features* Provides a comprehensive literature review* Covers both historical and contemporary approaches* Organized for ease of use and reference* Chapters authored by leading scholars

Contents

Contributors xiii
Foreword xv
Preface xvii
1 History of Research on Thinking and Problem Solving
Roger L. Dominowski and Lyle E. Bourne, Jr.
2 Contemporary Approaches to the Study of Thinking and Problem Solving
K. Anders Ericsson and Reid Hastie
3 Knowledge Representation
Timothy P. McNamara
4 Concepts and Categories
Brian H. Ross and Thomas L. Spalding
5 Deduction and Its Cognitive Basis
Lance J. Rips
6 Inductive Reasoning
Jeffery Bisanz, Gay L. Bisanz, and Connie A. Korpan
7 Problem Solving
Earl Hunt
8 Language and Thought
Richard J. Gerrig and Mahzarin R. Banaji
9 Intelligence
Robert J. Sternberg
10 Creativity
Todd I. Lubart
11 Development of Problem Solving
Shari Ellis and Robert S. Siegler
12 Cultural Dimensions of Cognition: A Multiplex, Dynamic System of Constraints and Possibilities
Robert Serpell and A. Wade Boykin
13 The Teaching of Thinking and Problem Solving
Raymond S. Nickerson

Outros livros do mesmo autor:

Understanding and teaching the intuitive mind : student and teacher learning por Bruce Torff; Robert J Sternberg; Idioma: Inglês   Editora: Mahwah, N.J. : Lawrence Erlbaum Associates, 2000.

The nature of mathematical thinking por Robert J Sternberg; Talia Ben-Zeev;   Idioma: Inglês   Editora: Mahwah, NJ : L. Erlbaum Associates, 1996.

The Practice of Mathematics

Yvette Solomon

Routledge | 1989 | 211 páginas | rar - pdf | 6 Mb

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The psychological description and explanation of how children learn to work with numbers is dominated by the theories of Piaget. Yvette Solomon suggests an alternative approach to the child's conception of number.

Contents

Acknowledgements

1. The development of the number concept as a field of psychological investigation

2. Why does Piaget's theory take its particular form? 9

The background to Piaget's explanation: the status and nature of mathematical propositions 10

Mathematics and genetic epistemology: the relation between logic and psychology 18

3. The child's conception of number 28

Piaget's criticisms of intuitionism and logicism 28

Piaget's synthesis of order and class 36

4. Piaget's account of the growth of understanding 43

Piaget's criticisms of empiricism and rationalism 43

Growth as a synthesis of genesis and structure 48

5. Does Piaget give an adequate account of growth? 66

The transition from weaker to stronger logics 67

Reflective abstraction and the growth of knowledge 70

'The individual constructs his world': Piaget's account of objective knowledge 75

6. Do number theorists give adequate accounts of knowing? 79

Piaget's essentialism 80

Bryant's work 89

Gelman and Gallistel' s work 99

7. Can a Piagetian perspective be defended? 109

Socio-cognitive conflict and the growth of knowledge 110

Information-processing theory and Piagetian theory: Case's 'neo-Piagetian' analysis 119

8. Knowing how and when to use numbers 131

Linguistic, non-linguistic and social contexts, and psychological experiments 131

The context of doing arithmetic 147

Understanding the context of doing arithmetic 150

9. 'The development of mathematical thinking ': entering into the social practices of number use 160

Analysing social practices 161

Entering into social practices 179

Notes 188

References 193

Index 200

Outros livros da mesma autora:

Mathematical literacy : developing identities of inclusion por Yvette Solomon Idioma: Inglês   Editora: New York : Routledge, 2009.

Mathematical relationships in education : identities and participation por Laura Black; Heather Mendick; Yvette Solomon;  Publicação de conferência Idioma: Inglês   Editora: New York : Routledge, 2009.

Soviet studies in the psychology of learning and teaching mathematics - Volumes 7 - 14

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the American mathematics educator have been translated from the Russian and appear in this series for the first time in English. The aim of this series is to acquaint mathematics educators and teachers with directions, ideas, and accomplishments in the psychology of mathematical instruction in the Soviet Union. 

Volume VII - Children's Capacity for Learning Mathematics
Steffe, Leslie P., Ed.; And Others 
1975 | 276 páginas | pdf 
online: ERIC

The work of El'konin, Davydov, and Minskaya reported in this volume represents a start toward the alleviation of the lack of theory-based experimental investigations of mathematics learning and teaching. 
TABLE OF CONTENTS
Introduction, Leslie Steffe
Learning Capacity and Age Level, D. B. El'konin and V. V..Davydov
Primary Schoolchildren's Intellectual Capabilities and the Content of Instruction, D. B. El'konin
Logical and Psychological Problems of Elementary Mathematics as an Academic Subject, V. V. Davydov
The Psychological Characteristics of the "Prenumerical" Period of Mathematics Instruction, V. V. Davydov 
Developing the Concept of Number by Means of the Relationship of Quantities, G. I. Minskaya 

Volume VIII - Methods of Teaching Mathematics
Steffe, Leslie P., Ed.; And Others 
1975 | 290 páginas | pdf 
online: ERIC

This volume contains four articles: Principles, Forms, and Methods of Mathematics Instruction; ; ; and Independent Work for Pupils in Arithmetic Lessons in the Early Grades
TABLE OF CONTENTS 
Introduction, Leslie  P. Steffe
Principles, Forms, and Methods of Mathematics Instruction, I. A. Gibsh 
The Relation Between Mathematics Instruction and Life, G. G. Maslova and. A. D. Semushin 
The Pupil's Activity as a Necessary Condition for Improving the Quality of Instruction, I. A. Gibsh 
Independent Work for Pupils in Arithmetic Lessons in the Early Grades, M. I. More

Volume IX - Problem Solving Processes of Mentally Retarded Children
Clarkson, Sandra P., Ed.; And Others
1975 | 184 páginas | pdf
online: ERIC

The articles in this volume are concerned with the instruction in problem solving of mentally retarded pupils in the auxiliary schools of the Soviet Union. Both articles in this volume describe research in problem solving and also provide concrete suggestions for improving instruction. The literature reviews contained in these articles provide us with much information on the state of research in the Soviet Union on problem solving in mathematics.
TABLE OF CONTENTS
The Solution of Complex Arithmetic Problems in Auxiliary School, K. A. Mikhal'skii 
Basic Difficulties Encountered in Auxiliary School Pupils in Solving Arithmetic Problems, M. I. Ku'mitskaya 

Volume X - Teaching Mathematics to Mentally Retarded Children
Clarkson, Sandra P., Ed.; And Others
1975 | 184 páginas | pdf
online: ERIC

The articles in this volume deal with the instruction in geometry and arithmetic of mentally retarded pupils in the Soviet Union. These pupils attend special schools, called auxiliary schools, where they are trained in content that can later be related to specific job skills. Authors of the articles have attempted to identify the specific knowledge that the pupils possess and to design more effective instructional methods for increasing that knowledge. 
TABLE OF CONTENTS
Introduction
Instructing Auxiliary School Pupils in Visual Geometry, P. G. Tishini
Visual.and Verbal Means in Pregaratory Exercises in Teaching Arithmetic Problem Solving, N. F. Kuimina-Syromyatnikova
Some Features of Elementary Arithmetic Instruction for Auxiliary School Pupils, T. V. Khanutina 

Volume XI - Analysis and Synthesis as Problem Solving Methods
Kantowski, Mary Grace, Ed.; And Others
1975 | 186 páginas | pdf
online: ERIC

This volume differs from the others in the series in that the entire volume records the search for a method of problem-solving instruction based on the analytic-synthetic nature of the problem-solving process. In this work, Kalmykova traces the history of the use of the analytic and synthetic methods in her country, explores elementary classroom situations involving teachers who had various degrees of success in problem-solving instruction, makes hypotheses regarding the use of certain techniques, and concludes with suggestions for "productive" methods to be used in the classroom
TABLE OF CONTENTS
Introduction, Mary C. Kantowski
Chapter I. Overview
Chapter II. Substantiation of the Problem of Analysis end Synthesis
Chapter III. Experimental Investigations of the Use of the Method of Analysis in School 
Chapter IV. Experimental Investigations of Analysis as a Method of Searching for a Solution
Chapter V. Productive Method of Analysis and Synthesis

Volume XII - Problems of Instruction
Wilson, James W., Ed.; And Others
1975 | 185 páginas | pdf
online: ERIC

The seven studies found in this volume are: ;; ;;; ; and Psychological Characteristics of Pupils' Assimilation of the Concept of a Function.
TABLE OF CONTENTS
Introduction
An Experiment in the Psychological Analysis of Algebraic Errors, P. A. Shevarev
Pupils' Comprehension of Geometric Proofs, F. N. Gonoboldn
Elements of the Historical Approach in Teaching Mathematics, I. N. Shevchenko
Overcoming Students' Errors in the Independent Solution of Arithmetic Problems, 0. T. Yochkovskaya
Stimulating Student Activity in the Study of Functional Relationships, Yu. I. Goldberg
Psychological Grounds for Extensive Use of Unsolvable Problems, Ya.  I.  Grudenov
Psychological Characteristics of Pupils' Assimilation of the Concept of a Function, I. A. Marnyanskii

Volume XIII - Analysis of Reasoning Processes
Wilson, James W., Ed.; And Others
1975 | 244 páginas | pdf
online: ERIC

The analysis of reasoning processes in the learning of concepts or the solving of problems is the theme common to the ten articles in this volume. These articles, except for the first one by Ushakova, were published between 1960 and 1967 and were part of the available literature during a revision of the Soviet school mathematics curriculum. The articles are interesting because of the topics they treat and because of the research styles they illustrate
TABLE OF CONTENTS
Introduction, James Wilson and Jeremy Kilpatrick
The Role of Comparison in-the Formation of Concepts do by Third-Grade Pupils,  M. N. Ushakova
On the Formation of an Elementary Concept of Number by the Child, V. V. Davydov
The Generalized Conception in Problem Solving, A. V. Brushlinskii
An Analysis of the Process of Solving Simple Arithmetic Problem, G. P. Shchedrovitskii and S. G. Yak'obson 
An Attempt at an Experimental Investigation of Psychological Regularity in Learning, B. B. Kopov
The Formation of Generalized Operations as a Method for Preparing Pupils to Solve Geometry Problems Independently, E. I. Mashbits
An Experimental Investigation of Problem Solving and Modeling the Thought Processes, D. N.Zavalishin and V. N. Pushkin 
The Composition of Pupils' Geometry Skills, A. K. Artemov
On the Process of Searching for an Unknown-While Solving a Mental Problem,  A. V. Brushlinskii
The Mechanisms of Solving Arithmetic Problems, L. M. Fridman

Volume XIV - Teaching Arithmetic in the Elementary School
Hooten, Joseph R., Ed.; And Others
1975 | 214 páginas | pdf
online: ERIC

The six chapter titles are: 
The Psychological and Didactic Principles of Teaching Arithmetic; 
The Introduction of Numbers, Counting, and the Arithmetical Operations;
Instruction in Mental and Written Calculation; Teaching Problem Solving; 
Geometry in the Primary Grades; 
Different Kinds of Pupils and How to Approach Them in Arithmetic Instruction.

Abstracts of The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia, and India

 Bharath Sriraman, Jinfa Cai e Kyeong-Hwa Lee

Information Age Publishing LLC | 2012 | 270 páginas | rar - pdf | 3 Mb

link (password: matav)

Mathematics and Science education have both grown in fertile directions in different geographic regions. Yet, the mainstream discourse in international handbooks does not lend voice to developments in cognition, curriculum, teacher development, assessment, policy and implementation of mathematics and science in many countries. Paradoxically, in spite of advances in information technology and the "flat earth" syndrome, old distinctions and biases between different groups of researcher's persist. In addition limited accessibility to conferences and journals also contribute to this problem. The International Sourcebooks in Mathematics and Science Education focus on under-represented regions of the world and provides a platform for researchers to showcase their research and development in areas within mathematics and science education. The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India provides the first synthesized treatment of mathematics education that has both developed and is now prominently emerging in the Asian and South Asian world. The book is organized in sections coordinated by leaders in mathematics education in these countries and editorial teams for each country affiliated with them. The purpose of unique sourcebook is to both consolidate and survey the established body of research in these countries with findings that have influenced ongoing research agendas and informed practices in Europe, North America (and other countries) in addition to serving as a platform to showcase existing research that has shaped teacher education, curricula and policy in these Asian countries. The book will serve as a standard reference for mathematics education researchers, policy makers, practitioners and students both in and outside Asia, and complement the Nordic and NCTM perspectives.

Contents
CHINA
PART I: CULTURE, TRADITION, AND HISTORY
1. “Zhi Yì Xíng Nán (Knowing Is Easy and Doing Is Difficult)” or Vice Versa?: A Chinese Mathematician’s Observation on History and Pedagogy of Mathematics Activities
Man-Keung Siu . . . . 5
2. The Study on Application of Mathematics History in Mathematics Education in China
Zezhong Yang and Jian Wang . . . 7
3. Cultural Roots, Traditions, and Characteristics of Contemporary Mathematics Education in China
Xuhui Li, Dianzhou Zhang and Shiqi Li . . . 9
PART II: ASSESSMENT AND EVALUATION
4. Factors Affecting Mathematical Literacy Performance of 15-Year-Old Students in Macao: The PISA Perspective
Kwok-Cheung Cheung . . . 13
5. Has Curriculum Reform Made A Difference in the Classroom?: An Evaluation of the New Mathematics
Curriculum in Mainland China
Yujing Ni, Qiong Li, Jinfa Cai, and Kit-Tai Hau . . .  15
6. Effect of Parental Involvement and Investment on Mathematics Learning: What Hong Kong Learned
From PISA
Esther Sui Chu Ho . . . . . . 17PART III: CURRICULUM
7. Early Algebra in Chinese Elementary Mathematics Textbooks: The Case of Inverse Operations
Meixia Ding . . . . . . . 21
8. The Development of Chinese Mathematics Textbooks for Primary and Secondary Schools Since
the Twentieth Century
Shi-hu Lv, Ting Chen, Aihui Peng, and Shangzhi Wang . . . . 23
9. Mathematics Curriculum and Teaching Materials in China from 1950–2000
Jianyue Zhang, Wei Sun, and Arthur B. Powell . . . . . . 2510. Chinese Mathematics Curriculum Reform in the Twenty-first Century: 2000-2010
Jian Liu, Lidong Wang, Ye Sun, and Yiming Cao . . . 27
11. Basic Education Mathematics Curriculum Reform in the Greater Chinese Region: Trends and Lessons Learned
Chi-Chung Lam, Ngai-Ying Wong, Rui Ding, Siu Pang Titus Li, and Yun-Peng Ma . 29
12. Characterizing Chinese Mathematics Curriculum: A Cross-National Comparative Perspective
Larry E. Suter and Jinfa Cai . .  . . . 31
PART IV: MATHEMATICAL COGNITION
13. Promoting Young Children’s Development of Logical- Math Thinking Through Addition, Subtraction,
Multiplication, and Division in Operational Math
Zi-Juan Cheng . . . .. 35
14. Development of Mathematical Cognition in Preschool Children
Qingfen Hu and Jing Zhang . . . 37
15. Chinese Children’s Understanding of Fraction Concepts
Ziqiang Xin and Chunhui Liu . . . . . 39
16. Teaching and Learning of Number Sense in Taiwan
Der-Ching Yang . . . .. . . . . 41
17. Contemporary Chinese Investigations of Cognitive Aspects of Mathematics Learning
Ping Yu, Wenhua Yu, and Yingfang Fu . . . .. . . . 43
18. Chinese Mathematical Processing and Mathematical Brain
Xinlin Zhou, Wei Wei, Chuansheng Chen, and Qi Dong . . . . . . . . . . . . 45
PART V: TEACHING AND TEACHER EDUCATION
19. Comparing Teachers’ Knowledge on Multidigit Division Between the United States and China
Shuhua An and Song A. An . . .. . 49
20. Problem Solving in Chinese Mathematics Education: Research and Practice
Jinfa Cai, Bikai Nie, and Lijun Ye . . . . . .. 51
21. Developing a Coding System for Video Analysis of Classroom Interaction
Yiming Cao, Chen He, and Liping Ding . .. 53
22. Mathematical Discourse in Chinese Classrooms: An Insider’s Perspective
Ida Ah Chee Mok, Xinrong Yang, and Yan Zhu . .. . 55
23. Reviving Teacher Learning: Chinese Mathematics Teacher Professional Development in the Context of Educational Reform
Lynn W. Paine, Yanping Fang, and Heng Jiang .  . . . 57
24. The Status Quo and Prospect of Research on Mathematics Education for Ethnic Minorities in China
Hengjun Tang, Aihui Peng, Bifen Chen, Yu Bo, Yanping Huang, and Naiqing Song . .. . 59
25. Chinese Elementary Teachers’ Mathematics Knowledge for Teaching: Role of Subject Related Training, Mathematic Teaching Experience, and Current Curriculum Study in Shaping Its Quality
Jian Wang . . . 61
26. Why Always Greener on the Other Side?: The Complexity of Chinese and U.S. Mathematics Education
Thomas E. Ricks . .  . . 63
PART VI: TECHNOLOGY
27. A Chinese Software SSP for the Teaching and Learning of Mathematics: Theoretical and Practical Perspectives
Chunlian Jiang, Jingzhong Zhang, and Xicheng Peng . .. . 67
28. E-Learning in Mathematics Education
Siu Cheung Kong . . .. . . 69
KOREA
29. Korean Research in Mathematics Education
Kyeong-Hwa Lee, Jennifer M. Suh, Rae Young Kim, and Bharath Sriraman . . . 73
30. A Review of Philosophical Studies on Mathematics Education
JinYoung Nam . . . . . 77
31. Mathematics Curriculum
Kyungmee Park . . . .  . 79
32. Mathematics Textbooks
JeongSuk Pang . . . . . . . 81
33. Using the History of Mathematics to Teach and Learn Mathematics
Hyewon Chang . . . . . 83
34. Perspectives on Reasoning Instruction in the Mathematics Education
BoMi Shin . . .. . 85
35. Mathematical Modeling
Yeong Ok Chong . .  . . . 87
36. Gender and Mathematics
Eun Jung Lee . . . . . . 89
37. Mathematics Assessment
GwiSoo Na . . . 91
38. Examining Key Issues in Research on Teacher Education
Gooyeon Kim . .. . . . . 93
39. Trends in the Research on Korean Teachers’ Beliefs About Mathematics Education
Dong-Hwan Lee . .  . 95
SINGAPORE
40. A Review of Mathematical Problem-Solving Research Involving Students in Singapore Mathematics Classrooms (2001 to 2011): What’s Done and What More Can be Done
Chan Chun Ming Eric . . . . . . . . 99
41. Research on Singapore Mathematics Curriculum and Textbooks: Searching for Reasons Behind Students’ Outstanding Performance
Yan Zhu and Lianghuo Fan . . . 103
42. Teachers’ Assessment Literacy and Student Learning in Singapore Mathematics Classrooms
Kim Hong Koh .. . . 107
43. A Theoretical Framework for Understanding the Different Attention Resource Demands of Letter-Symbolic Versus Model Method
Swee Fong Ng . .  . . 111
44. A Multidimensional Approach to Understanding in Mathematics Among Grade 8 Students in Singapore
Boey Kok Leong, Shaljan Areepattamannil, and Berinderjeet Kaur . . . 115

MALAYSIA
45. Mathematics Education Research in Malaysia: An Overview
Chap Sam Lim, Parmjit Singh, Liew Kee Kor, and Cheng Meng Chew . . . 121
46. Research Studies in the Learning and Understanding of Mathematics: A Malaysian Context
Parmjit Singh and Sian Hoon Teoh . . . . . . 123
47. Numeracy Studies in Malaysia
Munirah Ghazali and Abdul Razak Othman . . .  . 125
48. Malaysian Research in Geometry
Cheng Meng Chew . .  . . . . 127
49. Research in Mathematical Thinking in Malaysia: Some Issues and Suggestions
Shafia Abdul Rahman  . . . 129
50. Studies About Values in Mathematics Teaching and Learning in Malaysia
Sharifah Norul Akmar Syed Zamri and Mohd Uzi Dollah . .  . . 131
51. Transformation of School Mathematics Assessment
Tee Yong Hwa, Chap Sam Lim, and Ngee Kiong Lau . . . . . . 133
52. Mathematics Incorporating Graphics Calculator Technology in Malaysia
Liew Kee Kor . .  . . . 135
53. Mathematics Teacher Professional Development in Malaysia
Chin Mon Chiew, Chap Sam Lim, and Ui Hock Cheah . . . 137

JAPAN
54. Mathematics Education Research in Japan: An Introduction
Yoshinori Shimizu . . . . . 141
55. A Historical Perspective on Mathematics Education Research in Japan
Naomichi Makinae . . . 143
56. The Development of Mathematics Education as a Research Field in Japan
Yasuhiro Sekiguchi . .  . . . 147
57. Research on Proportional Reasoning in Japanese Context
Keiko Hino . . . .. . 149
58. Japanese Student’s Understanding of School Algebra
Toshiakira Fujii . . . . . . 153
59. Proving as an Explorative Activity in Mathematics Education
Mikio Miyazaki and Taro Fujita .. . 157
60. Developments in Research on Mathematical Problem Solving in Japan
Kazuhiko Nunokawa . .  . . 161
61. Research on Teaching and Learning Mathematics With Information and Communication Technology
Yasuyuki Iijima . . . .. . . . . 165
62. “Inner Teacher”: The Role of Metacognition in Learning Mathematics and Its Implication to Improving Classroom Practice
Keiichi Shigematsu . .  . . 167
63. Cross-Cultural Studies on Mathematics Classroom Practices
Yoshinori Shimizu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
64. Systematic Support of Life-Long Professional Development for Teachers Through Lesson Study
Akihiko Takahashi . . . . . . . 175

INDIA
65. Evolving Concerns Around Mathematics as a School Discipline: Curricular Vision, Classroom Practice and the National Curriculum Framework (2005)
Farida Abdulla Khan . . . . 181
66. Curriculum Development in Primary Mathematics: The School Mathematics Project
Amitabha Mukherjee and Vijaya S. Varma . .. . . . 185
67. Intervening for Number Sense in Primary Mathematics
Usha Menon . . . . . . . 191
68. Some Ethical Concerns in Designing Upper Primary Mathematics Curriculum: A Report From the Field
Jayasree Subramanian, Sunil Verma, and Mohd. Umar . . . . . 199
69. Students’ Understanding of Algebra and Curriculum Reform
Rakhi Banerjee . . . .. . 207
70. Professional Development of In-Service Mathematics Teachers in India
Ruchi S. Kumar, K. Subramaniam, and Shweta Naik . . . . . 213
71. Insights Into Students’ Errors Based on Data From Large-Scale Assessments
Aaloka Kanhere, Anupriya Gupta, and Maulik Shah .  . . 219
72. Assessment of Mathematical Learning: Issues and Challenges
Shailesh Shirali . . . . 227
73. Technology and Mathematics Education: Issues and Challenges 233
Jonaki B. Ghosh . . .  . . 233
74. Mathematics Education in Precolonial and Colonial South India
Senthil Babu D. . . . . .. . . . . 243
75. Representations of Numbers in the Indian Mathematical Tradition of Combinatorial Problems
Raja Sridharan and K. Subramaniam . . .  . . 249

Outros livros sobre o ensino da matemática na região asiática:

Reforms and issues in school mathematics in East Asia : sharing and understanding mathematics education policies and practices por Frederick K S Leung; Yeping Li; Não  disponível em ebook Idioma: Inglês   Editora: Rotterdam ; Boston : Sense Publishers, ©2010. online: cap 1. Sharing and Understanding Mathematics Education Policies and Practices  cap.2 - Mathematics Curriculum Reform in the Chinese Mainland: Changes and Challenges cap. 9 - What can we teach mathematics terachers? Lessons from Hong Kong (versão draft)

Mathematics curriculum in Pacific rim countries--China, Japan, Korea, and Singapore : proceedings of a conference por Zalman Usiskin; Edwin Willmore; Idioma: Inglês   Editora: Charlotte, N.C. : Information Age Pub., ©2008.

Mathematics education in different cultural traditions : a comparative study of East Asia and the West por Frederick K S Leung; Klaus-D Graf; Francis J Lopez-Real; International Commission on Mathematical Instruction.;  Publicação de conferência Idioma: Inglês   Editora: New York : Springer, ©2006.