Epistemological Foundations of Mathematical Experience

Leslie P. Steffe

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

link
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.

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.

A Practical Approach to Using Learning Styles in Math Instruction

Ruby Bostick Midkiff e Rebecca Davis Thomasson 

Charles C Thomas Pub Ltd | 1996 | 132 páginas | rar - pdf | 1,5 Mb

link (password: matav)

CONTENTS
Page
Chapter One INTRODUCTION ....... 3
Chapter Two IMPROVING MATHEMATICS INSTRUCTION ...... 5
Need for Improvement in Math Instruction ..... 5
Why Use Learning Styles? ......... 9
Conclusion ................. 11
Chapter Three LEARNING STYLES IN MATHEMATICS ........... 13
How Can I Implement Learning Styles? ........... 13
Learning Style Models ............ 14
Environmental Stimuli ............. 14
Emotional Stimuli ............ 17
Sociological Stimuli. . .. . . . .. 22
Physical Stimuli .............. 24
Psychological Stimuli. . . . . .. . . . 29
Underachieving Students and Learning Styles .......... 33
Conclusion ............ 34
Chapter Four USE OF MANIPULATIVES FOR INCREASED COMPREHENSION ...... 36
Need for Concrete Experiences. . . .. 36
Manipulatives and Uses ........ 40
Effective Use of Manipulatives ............. 41
Accommodating Learning Style Needs While Using Manipulatives ............ 52
Conclusion ............. 54
Chapter Five DIMINISHING GENDER DIFFERENCES IN MATHEMATICS ACHIEVEMENT .... 55
Physiological Differences. . . .. 56
Societal Expectations ..... 56
Effects of Toys and Games in Achievement of Mathematical Skills ......... 57
Spatial Perception Skills ...... 57
Curriculum and Spatial Reasoning. .  ... 58
Spatial Reasoning Skills. . . .  . . . 60
Accommodating Learning Style Needs While Using Spatial Reasoning Activities. . 73
Conclusion. . .... 74
Chapter Six MATCHING ACTIVITIES AND LEARNING STYLES ....... 75
Auditory, Small, or Large Group Activities ......... 75
Tactual, Visual, Individual, or Small Group Activities ............ 79
Tactual, Visual Activities. . . . . . . . . . .. 82
Kinesthetic, Visual, Mobility, Individual,
or Small Group Activities ...... 86
Small Group Activities ............... 87
Visual, Auditory, Mobility, Whole Group Activities ..... 90
Conclusion .......... 91
Chapter Seven PORTFOLIO ASSESSMENT IN MATHEMATICS..... 92
Need for Change in Assessment.......... 92
An Overview of Portfolio Assessment.. . . . . . . . . .. 93
Portfolio Contents ...... 96
Accommodating Learning Styles Through Portfolios ..... 104
Portfolio Organization ...... 105
Evaluation of Portfolios ..... 105
Parental Involvement. . . . . . . .. 107
Advantages of Portfolio Assessment ........... 107
Conclusion ....... 108
Chapter Eight CONCLUDING REMARKS ............ 110
References . ...... 113
Index . .. 119

Research on mathematical thinking of young children : six empirical studies

Leslie P. Steffe 

 National Council of Teachers of Mathematics | 1975 | 207 páginas | pdf | 3,2 Mb

online: ERIC

This volume includes reports of six studies of the thought processes of children aged four through eight. In the first paper Steffe and Smock outline a model for learning and teaching mathematics. Six reports on empirical studies are then presented in five areas of mathematics learning: (1) equivalence and order relations; (2) classification and seriation; (3) interdependence of classification, seriation, and number concepts; (4) Boolean Algebra; and (5) conservation and measurement. In a final chapter, the main findings of these papers are summarized and implications are discussed, with suggestions for further research.

Table of Contents
Introduction, Leslie P. Sleffe 1
I.On a Model for Learning and Teaching Mathematics, Leslie P. Sleffe and Charles D. Smock 4
II.Learning of Equivalence and Order Relations by Four- and Five-Year-Old Children, Leslie P. Sleffe and Russell L. Carey,19
III.Learning of Equivalence and Order Relations byDisadvantaged Five- and Six-Year-Old Children, Douglas T. Owens 47
IV.Learning of Classification and Seriation by Young Children, R Marlin L. Johnson 73
V.The Generalization of Piagetian Operations as It Relates to the Hypothesized Functional Interdependence between Classification, Seriation, and Number Concepts, Richard A. Lesh 94
VI.Learning of Selected Parts of a Boolean Algebra by Young Children, David C. Johnson 123
VII.The Performance of Mist- and Second -Grade Children on Liquid Conservation and Measurement Problems Employing Equivalence and Order Relations, Thomas P. Carpenter 145
Summary and Implications, Kennelh Lovell 171
References 191

Children's Logical and Mathematical Cognition Progress in Cognitive Development Research

 C.J. Brainerd

Springer | 2011 - reprint of the original 1st ed. 1982 edition | páginas | pdf | 6,6 Mb

link

Contents
Chapter 1 Conservation - Nonconservation: Alternative Explanations .. 1
Curt Acredolo
Conservation and the Appreciation of an Identity Rule ....
Operational and Nonoperational Conservation .. 2
Nonconservation and the Overreliance on Perceptual Cues .... 4
Pseudononconservation .... 5
Nonoperational Conservation .... 14
Conclusions ....... 21
Future Research: The Development of the Identity Rule ..... 24
Reference Notes ..... 27
References ...... 27
Chapter 2 The Acquisition and Elaboration of the Number Word Sequence .... 33
Karen C. Fuson, John Richards, and Diane J. Briars
Acquisition of the Sequence .... 35
Elaboration of the Sequence ... 55
Conclusion ......... 89
Reference Notes ...... 89
References ..... 91
Chapter 3 Children's Concepts of Chance and Probability
Harry W. Hoemann and Bruce M. Ross
Piagetian Theory ... 94
Subsequent Studies .... 99
Theoretical Implications ... 116
References .... 120
Chapter 4 The Development of Quantity Concepts: Perceptual and Linguistic Factors .. 123
Linda S. Siegel
Linguistic Factors and the Development of Quantity Concepts ..... 123
A Taxonomy of Quantity Concepts .... 124
The Relationship between Language and Thought in the Child .... 128
Study 1: Concept versus Language ....... 129
Study 2: Does Language Training Facilitate Concept Acquisition? ... 132
Study 3: Visual versus Verbal Functions .... 138
Study 4: Training of Cognitive and Language Abilities ...... 140
Study 5: Cognitive Development of Children with Impaired Language Development ... 141
Study 6: The Abstraction of the Concept of Number ....... 144
Conclusion ........ 152
Reference Notes... 153
References ..... 153
Chapter 5 Culture and the Development of Numerical Cognition: Studies among the Oksapmin of Papua New Guinea ... 157
Geoffrey B. Saxe
Methodology and Cross-Cultural Number Research .... 158
The Oksapmin Community ..... 159
Studies on Numerical Cognition among the Oksapmin ... 160
Concluding Remarks
Chapter 6 Children's Concept Learning as Rule-Sampling Systems with Markovian Properties . 177
Charles J. Brainerd
Concept Learning as Rule Sampling ....179
Some Questions about Concept Learning ... 185
Some Experimental Evidence ...192
Remark ......202
Appendix ... 203
References .. 208
Index ..... 213

Windows on Mathematical Meanings: Learning Cultures and Computers

Richard Noss; Celia Hoyles

Mathematics education library, 17.

Springer | 1996 | 287  páginas | pdf | 5,2 Mb

link

link1

This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.

CONTENTS

Visions of the Mathematical

Laying the Foundations

Tools and Technologies

Ratioworld

Webs and Situated Abstractions

Beyond the Individual Learner

Cultures and Change

A Window on Teachers

A Window on Schools

Re-Visioning Mathematical Meanings

Teaching and learning early number

Ian Thompson

Open University Press | 2008 - 2ª edição | 252 páginas | pdf | 1,9 Mb

link
link1

"This richly varied text offers generous support for every aspect of the teacher's role, while constantly reminding us that mathematical activity is not a de-contextualised skill that children possess, but part of their identity, their way of being in the world, engaged with the world, energetically - and playfully - trying to make sense of it."Mary Jane Drummond, formerly of the Faculty of Education, University of Cambridge, UK

Teaching and Learning Early Number is a bestselling guide for all trainee and practising Early Years teachers and classroom assistants. It provides an accessible guide to a wide range of research evidence about the teaching and learning of early number.

Major changes in the primary mathematics curriculum over the last decade - such as the National Numeracy Strategy, the Primary National Strategy, the Early Years Foundation Stage and the Williams Review - have greatly influenced the structure of this new edition. The book includes:

• A new introductory chapter to set the scene

• Six further new chapters - including Mathematics through play, Children's mathematical graphics and Interview-based assessment of early number knowledge

• Six completely re-written chapters and two updated chapters

• A new concluding chapter looking to the future

The chapters can be read in a standalone fashion and many are cross referenced to other parts of the book where specific ideas are dealt with in a different manner. Issues addressed include: new research on the complex process of counting and on children's written mathematical marks; counting in the home environment and play in the school setting; the importance of mathematical representations and of ICT in children's understanding of number; errors and misconceptions and the assessment of children’s number knowledge.

Contents
Notes on contributors ix
Editor’s preface xv
SECTION 1 - Setting the scene for teaching and learning early number 1
1 Still not getting it right from the start? 3
Carol Aubrey and Dondu Durmaz
SECTION 2 - The early stages of number acquisition 17
2 Children’s beliefs about counting 19
Penny Munn
3 Mathematics through play 34
Kate Tucker
4 The family counts 47
Rose Griffiths
SECTION 3 - The place of counting in number development 59
5 Development in oral counting, enumeration, and counting for cardinality 61
John Threlfall
6 Counting: what it is and why it matters 72
Effie Maclellan
7 Compressing the counting process: strength from the flexible interpretation of symbols 82
Eddie Gray
SECTION 4 - Extending counting to calculating 95
8 From counting to deriving number facts 97
Ian Thompson
9 Uses of counting in multiplication and division 110
Julia Anghileri
SECTION 5 - Representation and calculation 123
10 Children’s mathematical graphics: young children calculating for meaning 127
Elizabeth Carruthers and Maulfry Worthington
11 What do young children’s mathematical graphics tell us about the teaching of written calculation? 149
Ian Thompson
12 What’s in a picture? Understanding and representation in early mathematics 160
Tony Harries, Patrick Barmby and Jennifer Suggate
13 Mathematical learning and the use of information and communications technology in the early years 176
Steve Higgins
SECTION 6 - Assessing young children’s progress in number 189
14 Interview-based assessment of early number knowledge 193
Robert J. Wright
15 Addressing errors and misconceptions with young children 205
Ian Thompson
SECTION 7 - Towards an early years mathematics pedagogy 215
16 ‘How do you teach nursery children mathematics?’ In search of a mathematics pedagogy for the early years 217
Sue Gifford