Primary Mathematics Curriculum Guide

Harvey Blair e Pat Hughes 

David Fulton Publishers | 2001 | 96 páginas | rar - pdf | 12,33 Mb

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This is a curriculum guide that gives trainee teachers the opportunity to follow a tried and tested primary mathematics curriculum course. The text is easy to follow, up-to-date with good current practice and utilizes materials produced by the DfEE for teachers. It includes interactive tasks to enhance understanding, tasks to consolidate learning at the reader's own level and pace, a full bibliography for further reading, common misconceptions which the reader will find in children's work, and a detailed look at the National Numeracy Strategy (NNS) and the mathematics National Curriculum. The text will provide a firm foundation for teaching mathematics to primary school children and give the reader genuine confidence in their teaching. The text has been piloted by students following a distance learning primary PGCE and revised in line with their comments. The intention of the book is to provide secure subject knowledge for mathematics alongside an understanding of the ways in which children learn mathematics.

ContentsPreface V
Acknowledgements vi
Chapter 1 Introducing the book's objectives 1
Chapter 2 The National Curriculum for mathematics 9
Chapter 3 The National Numeracy Framework 11
Chapter 4 Ma2: Number and algebra 25
Chapter 5 Ma3: Shape, space and measures 45
Chapter 6 Ma4: Handling data 55
Chapter 7 Using and applying mathematics 65
Chapter 8 Planning, assessing, recording and reporting 73
Chapter 9 ICT and mathematics 77
Chapter 10 References and further reading 83
Useful websites 85
Index 87

Enacted Mathematics Curriculum: A Conceptual Framework and Research Needs

Denisse R. Thompson e Zalman Usiskin

 Information Age Publishing | 2013 | páginas | rar - pdf | 4,41 Mb

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This volume is an outgrowth of the Conference on Research on the Enacted Mathematics Curriculum, funded by the National Science Foundation and held in Tampa, Florida in November 2010. The volume has the potential to be useful to a range of researchers, from established veterans in curriculum research to new researchers in this area of mathematics education. The chapters can be used to generate conversation about researching the enacted mathematics curriculum, including similarities and differences in the variables that can and should be studied across various curricula. As such, it might be used by a curriculum project team as it outlines a research agenda for curriculum or program evaluation. It might be used as a text in a university graduate course on curriculum research and design. The chapters in this volume are a natural complement to those in Approaches to Studying the Enacted Mathematics Curriculum (Heck, Chval, Weiss, & Ziebarth, 2012), also published by Information Age Publishing. While the present volume focuses on a range of issues related to researching the enacted mathematics curriculum, including theoretical and conceptual issues, the volume by Heck et al. provides insights into different instrumentations used by groups of researchers to study curriculum enactment

CONTENTS
Acknowledgements . .. vii
Preface. . . . ix
1. The Enacted Curriculum as a Focus of Research
Gabriel Cal and Denisse R. Thompson . . . 1
2. Examining Variations in Enactment of a Grade 7 Mathematics Lesson by a Single Teacher: Implications for Future Research on Mathematics Curriculum Enactment
Mary Ann Huntley and Daniel J. Heck. .. 21
3. Influence of Mathematics Curriculum Enactment on Student Achievement
Patricia D. Hunsader and Denisse R. Thompson . . 47
4. Teachers’ Knowledge and the Enacted Mathematics Curriculum
Ji-Won Son and Sharon L. Senk . . . 75
5. Instruments for Studying the Enacted Mathematics Curriculum
Steven W. Ziebarth, Nicole L. Fonger, and James L. Kratky . .  . 97
6. Conceptualizing the Enacted Curriculum in Mathematics Education
Janine T. Remillard and Daniel J. Heck . . 121
7. Recommendations for Generating and Implementing a Research Agenda for Studying the Enacted Mathematics Curriculum
Kathryn B. Chval, Iris R. Weiss, and Rukiye Didem Taylan. .  . . 149
Postscript

Zalman Usiskin. . . 177

Common Core Mathematics in a PLC at Work, Grades 6-8

Diane J. Briars, Harold Asturias, David Foster e Mardi A. Gale

Solution Tree | 2012 | páginas | rar - epub | Mb

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This teacher guide illustrates how to sustain successful implementation of the CCSS for mathematics for grades 6-8. Discover what students should learn and how they should learn it at each grade level. Acquire strategies for meeting the rigor of the grades 6-8 standards, including the unique content around ratios, proportions, and relationships at grades 6 and 7. Get insight into the new expectations for grades 6-8 assessment as well as the readiness required for the high school standards.

Comprehensive and research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency. You'll also learn how fundamental shifts in collaboration, instruction, curriculum, assessment, and intervention can increase college and career readiness in every one of your students.

Benefits

- Discover the five essential paradigm shifts necessary to implement the CCSS for mathematics.

- Receive guidance on forming and sustaining collaborative teams in a Professional Learning Community at Work culture.
- Develop a 'less is more'; content mind-set: fewer standards will result in the opportunity of time needed for deeper rigor and conceptual understanding work with students.
- Gain helpful formative assessment strategies for development of student proficiency in the Standards for Mathematical Practice.
- Access dozens of tools, activities, examples, resources, and reproducibles to help teachers and teams analyze, interpret, and implement the common core standard expectations for instruction and assessment.
- Examine the research-affirmed foundation of mathematics content and process standards from 1989 to 2010 and deepen your understanding of the common core expectations.

Contents
1. Using high-performing collaborative teams for mathematics
2. Implementing the common core standards for mathematical practice
3. Implementing the common core mathematics content in your curriculum
4. Implementing the teaching-assessing-learning cycle
5. Implementing required response to intervention
Epilogue. Your mathematics professional development model
Appendix A. Standards for mathematical practice
Appendix B. Standards for mathematical content, grade 6
Appendix C. Standards for mathematical content, grade 7
Appendix D. Standards for mathematical content, grade 8.

Focus in Grade 6: Teaching with Curriculum Focal Points

Jane F. Schielack

National Council of Teachers of Mathematics | 2010 | 112 páginas | rar - pdf | 828 kb

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Focus in Grade 6: Teaching with Curriculum Focal Points describes and illustrates learning paths for the mathematical concepts and skills of each grade 6 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate understanding, stimulate productive discussions about mathematical thinking, and provide a foundation for fluency with the core ideas. This book also discusses common student errors and misconceptions, reasons the errors may arise, and teaching methods or visual representations to address the errors. 
Because learning paths cut across grades, related Focal Points for grades 5 and 7 have been included to clarify how prerequisite knowledge in prekindergarten contributes to later understandings. Focus in Grade 6, one in a series of grade-level publications, is designed to support teachers, supervisors, and coordinators as they develop and refine the mathematics curriculum.

ContentsIntroduction
Focusing on multiplication and division of fractions and decimals
Focusing on ratio and rate
Focusing on expressions and equations


Outro livro da mesma série:

Focus in grade 5 : teaching with curriculum focal points

por Karen C Fuson; Sybilla Beckmann; John SanGiovanni; Thomasenia Lott Adams

Idioma: Inglês  

Editora: Reston, VA : NCTM, ©2009.

Mathematics miseducation : the case against a tired tradition

Derek Stolp

ScarecrowEducation | 2005 | 208 páginas | rar - pdf | 17,76 Mb

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Author and veteran teacher Derek Stolp has come to the conclusion that learning mathematics is of no real consequence for the vast majority of our children. This stance flies in the face of the conventional wisdom held among political leaders, business people, teachers, and parents that mathematics is an essential subject for all children to study well into their high school years. In Mathematics Miseducation, Stolp argues that mathematics, as currently taught, does not justify inclusion in the curriculum and he suggests practical changes that can be implemented within a traditional school environment to resuscitate mathematics education. In this book, the author demonstrates that our beliefs about what children need and what motivates them to learn promote practices that are counterproductive, and that these practices ultimately corrupt students' own healthy motivations. Stolp contends that there is too much emphasis upon academics in our schools, and that other important dimensions of education, such as the social, emotional, and moral development of our children, are ignored. Includes: * Progressive and practical alternatives to the traditional methods of teaching * Research and examples citing ways of bringing the discipline to life In seamlessly weaving theory and practice, Derek Stolp provides a narrative that is accessible to any adult concerned about what our children are learning in mathematics.

CONTENTSAcknowledgments
Introduction
PART I THE TRADITIONAL MODEL
Why Do I Need to Know This? The Case Against Traditional Mathematics
2 Whose Knowledge Is It? Experience in the Construction of Knowledge
3 So What's the Alternative? A New Model for Teaching Mathematics
PART II BEYOND THE TRADITION:
A PROGRESSIVE MODEL
4 Why Should I Care About This Stuff? Interest and Autonomy 85
5 How Do We Get These Kids to Learn? The Motivations of Children
6 Academics-Is That All We Should Care About? The Overlooked Intelligences 125
7 So What's the Alternative? A New Model for Teaching 141
8 Who Gets to Choose? Democratic Learning Communities 157
Appendix A: Mathematics Teacher 173
Appendix B: Exercises 177
References 181
Index 189
About the Author 193

Mathematical Enculturation: A Cultural Perspective on Mathematics Education

(Mathematics Education Library, 6)


Alan J Bishop

Springer | 1991 |209 páginas | rar - pdf | 7,9 Mb

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Tony Brown (Manchester Polytechnic), in Mathematics Teaching 
`This book is an informed, extremely rational and objective account of some aspects of enculturation and educational activity in the field of mathematics. I would recommend the book to all interested in mathematics education and curriculum design.' 
Kathryn Crawford (The University of Sydney), in Educational Studies in Mathematics 
`What is unique about Bishop's account is his attempt to specify and describe a universal set of activities that have supported and shaped the development of mathematics throughout the world.' 
J. Stigler, in Journal for Research in Mathematics Education
`Taking a refreshing noneurocentric position which refutes any suggestion that `West is best' as regards the development of mathematical thinking, Bishop sees mathematical development as being a function of the needs of whatever society in which it arises.' 

TABLE OF CONTENTS
PREFACE
ACKNOWLEDGEMENTS
CHAPTER 1- Towards a Way of Knowing
The conflict
My task
Preliminary thoughts on Mathematics education and culture
Technique-oriented curriculum
Impersonal learning
Text teaching
False assumptions
Mathematical education, a social process
What is mathematical about a mathematical education?
Overview
CHAPTER 2- Environmental Activities and Mathematical Culture
Perspectives from cross-cultural studies
The search for mathematical similarities
Counting
Locating
Measuring
Designing
Playing
Explaining
From 'universals' to 'particulars'
Summary
CHAPTER 3- The Values of Mathematical Culture
3.1. Values, ideals and theories of knowledge
3.2. Ideology - rationalism
3.3. Ideology - objectism
3.4. Sentiment - control
3.5. Sentiment - progress
3.6. Sociology - openness

3.7. Sociology - mystery
CHAPTER 4- Mathematical Culture and the Child 82
4.1. Mathematical culture - symbolic technology and values 82
4.2. The culture of a people 84
4.3. The child in relation to the cultural group 87
4.4. Mathematical enculturation 89
CHAPTER 5- Mathematical Enculturation - The Curriculum 92
5.1. The curriculum project 92
5.2. The cultural approach to the Mathematics curriculum - five principles 95
5.2.1. Representativeness 95
5.2.2. Formality 95
5.2.3. Accessibility 96
5.2.4. Explanatory power 96
5.2.5. Broad and elementary 97
5.3. The three components of the enculturation curriculum 98
5.4. The symbolic component: concept-based 99
5.4.1. Counting 100
5.4.2. Locating 100
5.4.3. Measuring 101
5.4.4. Designing 102
5.4.5. Playjng 102
5.4.6. Explaining 103
5.4.7. Concepts throl:lgh activities 103
5.4.8. Connections between concepts 108
5.5. The societal component: project-based 110
5.5.1. Society in the past 111
5.5.2. Society at present 112
5.5.3. Society in the future 113
5.6. The cultural component: investigation-based 114
5.6.1. Investigations in mathematical culture 116
5.6.2. Investigations in Mathematical culture 117
'5.6.3. Investigations and values 117
5.7. Balance in this curriculum 119
5.8. Progress through this curriculum 120
CHAPTER 6- Mathematical Enculturation - The Process 124
6.1. Conceptualising the enculturation process in action 124
6.1.1. What should it involve? 124
6.1.2. Towards a humanistic conception of the process 125

6.2. An asymmetrical process 128
6.2.1. The role of power and influence 128
6.2.2. Legitimate use of power 130
6.2.3. Constructive and collaborative engagement 131
6.2.4. Facilitative influence 132
6.2.5. Metaknowledge and the teacher 135
6.3. An intentional process 135
6.3.1. The choice of activities 135
6.3.2. The concept-environment 139
6.3.3. The project-environment 142
6.3.4. The investigation-environment 147
6.4. An ideational process 151
6.4.1. Social construction of meanings 151
6.4.2. Sharing and contrasting Mathematical ideas 154
6.4.3. The shaping of explanations 157
6.4.4. Explaining and values 159
CHAPTER 7- The Mathematical Enculturators 160
7.I. People are responsible for the process 160
7.2. The preparation of Mathematical enculturators - preliminary thoughts 161
7.3. The criteria for the selection of Mathematical enculturators 164
7.3.I. Ability to personify Mathematical culture 164
7.3.2. Commitment to the Mathematical enculturation process 165
7.3.3. Ability to communicate Mathematical ideas and values 166
7.3.4. Acceptance of accountability to the Mathematical culture 167
7.3.5. Summary of criteria 168
7.4. The principles of the education of Mathematical enculturators 168
7.4.1. Mathematics as a cultural phenomenon 169
7.4.2. The values of Mathematical culture 170
7.4.3. The symbolic technology of Mathematics 171
7.4.4. The technical level of Mathematical culture 172
7.4.5. The meta-concept of Mathematical enculturation 173
7.4.6. Summary of principles 175
7.5. Socialising the future enculturator into the Mathematics Education community 176
7.5.I. The developing Mathematics Education community 176

7.5.2. The critical Mathematics Education community

Interdisciplinarity, Creativity, and Learning: Mathematics with Literature, Paradoxes, History, Technology, and Modeling

(Montana mathematics enthusiast,  7)

Bharath Sriraman, Viktor Freiman e Nicole Lirette-Pitre 

Information Age Publishing | 2009 | 261 páginas | rar - pdf | 2,7 Mb

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A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education Series Editor Bharath Sriraman, The University of Montana Interdisciplinarity is increasingly viewed as a necessary ingredient in the training of future oriented 21st century disciplines that rely on both analytic and synthetic abilities across disciplines. Nearly every curricular document or vision statement of schools and universities include a call for promoting creativity in students. Yet the construct of creativity and giftedness across disciplines remains elusive in the sense that the prototypical examples of such work come from eminent scientists, artists and mathematicians, and little if any work has been conducted with non-eminent individuals. This monograph is an attempt to fill this gap by putting forth the view that interdisciplinarity and creativity are related constructs, and that the cultivation of domain general creativity is possible. Mathematics has historically been anchored to numerous disciplines like theology, natural philosophy, culture and art, allowing for a flexibility of thought that is difficult to cultivate in other disciplines. In this monograph, the numerous chapters from Australia, U.S.A., Canada, Cyprus, Denmark and Japan provide a compelling illustration of the intricate connection of mathematics with literature, paradoxes, history, technology and modeling, thus serving as a conduit for interdisciplinarity, creativity and learning to occur.

ContentsSection I Interdisciplinarity in Mathematics and Literature
1 The Interdisciplinary Nature of Inductive Processes in Forming Generalizations.... 3
Bharath Sriraman and Harry Adrian
2 The Existential Void in Learning: Juxtaposing Mathematics and Literature.... 13
Bharath Sriraman and Harry Adrian
3 Mathematics and Literature: Synonyms, Antonyms or the Perfect Amalgam?...... 31
Bharath Sriraman
4 Mathematics and Literature (The Sequel): Imagination as a Pathway to Advanced Mathematical Ideas and Philosophy..... 41
Bharath Sriraman
Section II Mathematics and Paradoxes 
5 1 or 0?: Cantorian Conundrums in the Contemporary Classroom.... 55
Bharath Sriraman and Libby Knott
6 Understanding Mathematics through Resolution of Paradoxes...... 61
Margo Kondratieva
7 Mathematical Paradoxes as Pathways into Beliefs and Polymathy.... 75
Bharath Sriraman
Section II I Geometry and History
8 Voronoi Diagrams.... 97
Michael Mumm
9 An In-Depth Investigation of the Divine Ratio.... 109
Birch Fett
10 Cyclide Manipulation........ 133
Akihiro Matsuura
Section IV Interdisciplinarity and Modeling
11 Modeling Interdisciplinary Activities Involving Mathematics and Philosophy... 147
Steffen M. Iversen
12 Integrating Engineering Education within the Elementary and Middle School Mathematics Curriculum.... 165
Lyn D. English and Nicholas G. Mousoulides
13 Mathematical Modelling in the Early School Years........... 177
Lyn D. English and James J. Watters
Section V Technology and the NET Generation
14 Connected Giftedness: Mathematical Problem Solving by Means of a Web Technology: Case of the CASMI Project...... 205
Viktor Freiman and Nicole Lirette-Pitre
15 Teaching and Learning for the Net Generation: A Robotic-Based Learning Approach....217
Samuel Blanchard
16 Does Technology Help Building More Creative Mathematical Environments?... 233
Dominic Manuel

Focus in Grade 5: Teaching with Curriculum Focal Points

Edited by Sybilla Beckmann Writing Team: Karen C. Fuson, John SanGiovanni, Thomasenia Lott Adams

National Council of Teachers of Mathematics | 2009 | 104 páginas  | pdf 

link direto

rar - pdf - 567 kb

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Focus in Grade 5, one in a series of grade-level publications, is designed to support teachers, supervisors, and coordinators as they begin the discussion of a more focused curriculum across and within prekindergarten through eighth grade, as presented inCurriculum Focal Points. Additionally, teacher educators should find it useful as a vehicle for exploring mathematical ideas and curriculum issues involving the grade 5 mathematics curriculum with their preservice teachers.

This book describes and illustrates learning paths for the mathematical concepts and skills of each fifth-grade Focal Point, including problems for students and powerful representational supports for teaching and learning that can facilitate understanding, stimulate productive discussions about mathematical thinking, and provide a foundation for fluency with the core ideas. Also discussed are common student errors and misconceptions, reasons the errors may arise, and teaching methods or visual representations to address the errors. Because learning paths cut across grades, some discussion of related Focal Points at grades 3 and 4 have been included to describe and clarify prerequisite knowledge and show how the grade 5 understandings build on what went before.

Teachers should find these discussions of the learning paths, representations, problems, and lines of reasoning valuable as they plan activities and discussions for their students and strive to help students achieve the depth of understanding of important mathematical concepts necessary for their future success.

Contents

Preface....... ix

Preface to Curriculum Focal Points for Prekindergarten

through Grade 8........ x

Acknowledgments..... xi

1. Introduction.....1

2. Division........9

3. Addition and Subtraction of Fractions and Decimals..................27
4. Two- and Three-Dimensional Shapes, and Area and Volume........65

Variability is the Rule A Companion Analysis of K-8 State Mathematics Standards

(Research in Mathematics Education) 

John P. Smith III 

Information Age Publishing | 2010 | 234 páginas | rar - pdf |4 Mb

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A volume in the series: Research in Mathematics Education. Series Editor(s): Barbara J. Dougherty, Iowa State University In response to No Child Let Behind, states have developed mathematics curriculum frameworks that outline their intended curriculum for grades K-8. While some have indicated that districts or individual schools may use their framework as a model for specific curricular programs, others have taken a more prescriptive or even mandatory stance. Collectively, these frameworks present a sense of the national mathematics program and what we expect students learn. This volume follows The Intended Curriculum as Represented in State Mathematics Curriculum Standards: Consensus or Confusion? (Reys). While the Reys volume focused on number and operations, algebra and reasoning strands, the Smith volume analyzes geometry, measurement, probability, and statistics strands. It also presents an analysis what verbs used tell us about the cognitive demand of grade level expectations. This volume, even more than the Reys volume, emphasizes the theme of variability in the content, expression, and clarity of grade level expectations across the states. As the nation moves toward implementation of the Common Core Standards, this volume highlights some of the challenges teachers and other school personnel face in interpreting mathematics grade-level standards as goals for classroom teaching. The shift from 50 state standards to one document does not resolve this basic challenge.

CONTENTS
Acknowledgments. . . . . . . . .vii
1. Introduction: An Analysis of State Standards in Two Mathematical Domains
John P. Smith III, Gregory Larnell, and James E. Tarr . .. . . 1
2. An Analysis of K−8 Measurement Grade Level Expectations
Sarah E. Kasten and Jill Newton . . . 13
3. The Treatment of Transformations in K–8 Geometry and Measurement Grade Level Expectations
Sasha Wang and John P. Smith III .. . . 41
4. An Examination of K−8 Geometry State Standards Through the Lens of the van Hiele Levels of Geometric Thinking
Jill Newton . . . .. . . 71
5. Verbs and Cognitive Demand in K–8 Geometry and Measurement Grade Level Expectations
Gregory V. Larnell and John P. Smith III .. . 95
6. The Statistical Process: A View Across K–8 State Standards
Jill Newton, Aladar Horvath, and Leslie Dietiker . . . 119
7. An Analysis of K–8 Probability Standards
Shannon Dingman and James E. Tarr . . . . . 161
8. Major Lessons from the Second Round of Standards Analyses

John P. Smith III, Glenda T. Lappan, and James E. Tarr . . . . 193

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

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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.

Educational Interfaces between Mathematics and Industry: Report on an ICMI-ICIAM-Study

Alain Damlamian, José Francisco Rodrigues e Rudolf Sträßer

New ICMI studies series, v.16.

Springer | 2013 | 451 páginas | rar - pdf | 4 Mb

link (password : matav)

This book is the “Study Book” of ICMI-Study no. 20, which was run in cooperation with the International Congress on Industry and Applied Mathematics (ICIAM). The editors were the co-chairs of the study (Damlamian, Straesser) and the organiser of the Study Conference (Rodrigues). The text contains a comprehensive report on the findings of the Study Conference, original plenary presentations of the Study Conference, reports on the Working Groups and selected papers from all over world. This content was selected by the editors as especially pertinent to the study each individual chapter represents a significant contribution to current research.

Contents

Part I Discussion Document and Study Report

Discussion Document. . . . . . 3

The International Programme Committee

Report on the Study . . .  . . . 17

Alain Damlamian, José Francisco Rodrigues and Rudolf Sträßer

Part II Plenary and Invited Lectures

Getting Math off the Ground: Applied Mathematics at Boeing . . 27

Stephen P. Keeler and Thomas A. Grandine

Mathematics in the Workplace: Issues and Challenges . . . .. . . 43

Celia Hoyles, Richard Noss, Phillip Kent and Arthur Bakker

Mathematical Modeling Education is the Most Important Educational Interface Between Mathematics and Industry . . . 51

Tatsien Li

Models for Industrial Problems: How to Find and How to Use them—in Industry and in Education . . . . . . .  . 59

Helmut Neunzert

Interfacing Education and Research with Mathematics for Industry: The Endeavor in Japan. 77

Masato Wakayama

Part III WG Education/Training with Industry Participation

Education/Training with Industry Participation . . . . 95

Gail FitzSimons and Tom Mitsui

How it is Possible to Make Real-World Mathematics More Visible: Some Results from Two Italian Projects  . . 109

Cinzia Bonotto

The Project ‘‘Ways to More MINT-Graduates’’ of the Bavarian Business Association (vbw) with Focus on the M (=Mathematics) at the University of Augsburg, Germany . . 119

Matthias Brandl

Mathematics in a Safety–Critical Work Context: The Case of Numeracy for Nursing . 127

Diana Coben and Meriel Hutton

Linking Professional Experiences with Academic Knowledge: The Construction of Statistical Concepts by Sale Manager Apprentices . . 137

Corinne Hahn

Learning Conversation in Mathematics Practice School–Industry Partnerships as Arena for Teacher Education . . 147

Gert Monstad Hana, Ragnhild Hansen, Marit Johnsen-Høines, Inger Elin Lilland and Toril Eskeland Rangnes

The Threefold Dilemma of Missing Coherence: Bridging the Artificial Reef Between the Mainland and Some Isolated Islands. . 57

Guenter Törner, Volker Grotensohn and Bettina Roesken

The Project ‘‘Mathe-Meister’’: A Mathematical Self Assessment Centre with Diagnostic Feedback for Vocational Trainees . . . 165

Kathrin Winter

Part IV WG University and Academic Technical/Vocational Education

University and Academic Technical/Vocational Education . . .  . 173

Nilima Nigam and José Francisco Rodrigues

Mathematics for Engineering and Engineering for Mathematics . .185

Miquel Alberti Palmer, Sergio Amat, Sonia Busquier, Pilar Romero and Juan Tejada

Laboratory for Computational Mathematics: An Interface Between Academia and Industry 199

A. Araújo, S. Barbeiro and J. A. Ferreira

Improving the Industrial/Mathematics Interface.. . 205

Jean P. F. Charpin and Stephen B. G. O’Brien

Two Masters on ‘Mathematics for Industry’ at the Universities of Paris and of Pau . 213

Edwige Godlewski, M. Madaune-Tort and S. Dossou-Gbete

Mathematics in Industry and Teachers’ Training . .  223

Matti Heilio

Interfaces Between Mathematics and Industry and the Use of Technology in Mathematics Education in India  . 229

Ajit Kumar

Modeling Modeling: Developing Habits of Mathematical Minds . . 237

John A. Pelesko, Jinfa Cai and Louis F. Rossi

The Evolution of Graduate Applied Math Courses in the Institute of Mathematics, University of the Philippines. . 247

Carlene P. C. Pilar-Arceo and Jose Maria L. Escaner IV

The Vertical Integration of Industrial Mathematics, the WPI Experience  . 253

Bogdan Vernescu

Part V WG Education in Schools

Educational Interfaces Between Mathematics and Industry at School Level . . 263

Gabriele Kaiser, Henk van der Kooij and Geoff Wake

Mathematical Applications, Modelling and Technology as Windows into Industry Based Mathematical Practice .  . 271

Vince Geiger

Mathematics Education and the Information Society . . . 279

Koeno Gravemeijer

Authentic Complex Modelling Problems in Mathematics Education . . 287

Gabriele Kaiser, Martin Bracke, Simone Göttlich and Christine Kaland

Embedding Authentic Real World Tasks into Secondary Mathematics Curricula .. 299

Gloria Stillman and K. E. D. Ng

Drawing on Understanding of Workplace Practice to Inform Design of General Mathematics Curricula .  . 309

Geoff Wake

Part VI WG Mathematics-Industry Communication

Communication and Collaboration. . .. . 319

Solomon Garfunkel, Rolf Jeltsch and Nilima Nigam

Engineering, Mathematics Communication, and Education: Reflections on a Personal Experience . . . 333

Jorge Buescu

A View on Mathematical Discourse in Research and Development . . . 341

Vasco Alexander Schmidt

Using Popular Science in a Mathematical Modeling Course  . . 351

Burt S. Tilley

Part VII WG Technology Issues

Technology Issues . .  . 359

Helmer Aslaksen and Fadil Santosa

Tackling the Challenges of Computational Mathematics Education of Engineers . . 365

France Caron and André Garon

Integrating Computational Modelling in Science, Technology, Engineering, and Mathematics Education.. . 375

Rui Gomes Neves, Jorge Carvalho Silva and Vítor Duarte Teodoro

Incorporating the Ideas and Methods of Mathematical Modeling into Calculus Teaching .385

Qixiao Ye

Part VIII WG the Mathematics-Industry Interface

The Mathematics–Industry Interface . . 397

Jofré Alejandro and Lutz-Westphal Brigitte

Part IX Selected Papers Linked to More than One Working Group 

Inappropriate Use of Spreadsheets in the Finance Industry . . . . 403

Djordje M. Kadijevich

MITACS Accelerate: A Case Study of a Successful Industrial Research Internship Program . . . 413

Sarah Petersen and Marsh Rebeccah

A Meta-analysis by Mathematics Teachers of the GIFT Program Using Success Case Methodology . . . 421

Richard Millman, Meltem Alemdar and Bonnie Harris

Cultivating an Interface Through Collaborative Research Between Engineers in Nippon Steel & Sumitomo Metal and Mathematicians in University . . . 427

Junichi Nakagawa and Masahiro Yamamoto

An Introduction to CUMCM: China/Contemporary Undergraduate Mathematical Contest in Modeling . . 435

Jinxing Xie

Part X Conclusion

Conclusion on Educational Interfaces Between Mathematics and Industry. . . . . 447

Alain Damlamian, José Francisco Rodrigues and Rudolf Sträßer

Index . . . 453

A Decade of Middle School Mathematics Curriculum Implementation: Lessons Learned from the Show-Me Project

(Research in Mathematics Education)

Margaret R Meyer e  Cynthia W Langrall

Information Age Publishing | 2008 | 317 páginas | rar - pdf | 1,88 Mb

link (password : matav)

A volume in Research in Mathematics Education Series Editor Barbara J. Dougherty, University of Mississippi The purpose of this book is to document the work of the Show-Me Project (1997-2007) and to highlight lessons learned about curriculum implementation. Although the Show-Me Project was charged with promoting the dissemination and implementation of four distinct comprehensive curriculum programs (Connected Mathematics, Mathematics in Context, MathScape, and MathThematics), most of the lessons learned from this work are not curriculum specific. Rather, they cut across the four programs and share commonalities with standards-based curriculum reform at any level. We believe that documenting these lessons learned will be one of the legacies of the Show-Me Project We anticipate that the comprehensive nature of this work will attract readers from multiple audiences that include state and district mathematics supervisors, middle grades mathematics teachers and administrators involved in curriculum reform, as well as mathematics teacher educators. Those about to embark on the review of curriculum materials will appreciate reading about the processes employed by other districts. Readers with interests in a particular curriculum program will be able to trace the curriculum-specific chapters to gain insights into how the design of the curricula relate to professional development, adoption and implementation issues, and teachers' personal experience using the curriculum materials. Individuals who provide professional development at the middle grades level will find chapters that they can use for both general and focused discussions. Teachers at all stages of implementation will recognize their own experiences in reading and reflecting on the stories of teacher change. Mathematics educators will find ideas on how these curricula can be used in the preparation of preservice middle grades teachers.

Contents
Preface..... ix
PART I - Setting the Stage
1 The Road to Reform.... 3
Robert Reys
2 The Genesis of the NSF Curriculum Implementation Centers..... 9
John S. (Spud) Bradley
3 The Show-Me Project: A Decade of Support for Standards-Based Curriculum Implementation... 17
Barbara Reys
PART II - Adoption Case Studies and Implementation Stories
4 Teacher Investment in Curriculum Adoption: The Role of Piloting Materials.... 35
Cary Tuckey
5 Consensus Building: A Key Component of Curriculum Adoption..... 43
Cheryl Rectanus
6 The Critical Work of a Review Committee in Curriculum Adoption....... 55
Leslie E. J. Nielsen
7 Informing a State Adoption Process Through Curriculum Implementation...... 67
Murrel Brewer Hoover
8 Curriculum Implementation Through Teacher Collaboration..... 79
Chip Sharp
9 Curriculum Implementation: Teachers on a Journey.... 87
Carol Den Otter
10 The Role of Teacher Leaders in Curriculum Implementation......... 97
Emily R. Fagan and Rhonda K. Weinstein
11 Supporting Curriculum Implementation Through Its Ups and Downs...... 107
Linda A. Tetley
12 When Things Go Wrong in Curriculum Implementation......... 115
Jane O. Swafford and Cynthia W. Langrall
13 Issues of Implementation: Making Mathematics Accessible to All Learners... 125
Jennifer M. Bay-Williams and Rebecca McGraw
PART III - Professional Development and Teacher Education
14 An Overview of Professional Development......... 141
Elizabeth Phillips, Glenda Lappan, Yvonne Grant, and Fran Arbaugh
15 Key Features of Connected Mathematics for Professional Development... 151
Elizabeth Phillips and Glenda Lappan
16 Key Features of Mathematics in Context for Professional Development..... 161
David C. Webb
17 Key Features of MathScape for Professional Development...... 173
Fred Gross and Emily R. Fagan
18 Key Features of Middle Grades MATHThematics for Professional Development......... 183
Rick Billstein and Jim Williamson
19 Teachers’ Needs at Different Phases of Curriculum Implementation........ 191
Fran Arbaugh
20 Professional Development for Administrators: What They Need to Know to Support Curriculum Adoption and Implementation......... 201
Margaret R. Meyer and Fran Arbaugh
21 A Story of Teacher Growth: Increasing Expectations..... 211
Jane Peterson Porath
22 A Story of Teacher Growth: Teacher as Learner.....217
Barbara Diliegghio
23 A Story of Teacher Growth: Making a Difference..... 225
Kelly Watts
24 A Story of Teacher Growth: From Telling to Facilitating...... 231
Fabienne Anderson
25 Research Mathematician and Mathematics Educator: A Foot in Both Worlds..... 235
Ira J. Papick
26 Using NSF-Funded Mathematics Curricula to Enhance Teacher Preparation........ 245
Jeffrey Frykholm
27 NSF-funded Mathematics Curricula in the Field: A Preservice Teacher’s Opportunity to See Theory in Practice.... 259
Ann Bledsoe
PART IV - What Have We Learned and Where Do We Go from Here?
28 Lessons Learned from the Show-Me Project.......... 269
Barbara Reys
29 Looking into the Future: Curriculum Challenges for the Next Ten Years..... 279
Margaret R. Meyer and Cynthia W. Langrall
References.......291