Unearthing Culturally Responsive Mathematics Teaching: The Legacy of Gloria Jean Merriex

 Emily P. Bonner

Hamilton Books | 2010 | 95 páginas | rar - pdf |1,1 Mb

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Unearthing Culturally Responsive Mathematics Teaching: The Legacy of Gloria Jean Merriex focuses on the theory and practices of a highly successful mathematics teacher of African American children in a high-poverty school. The book aims to contribute to the limited literature base in this area in mathematics education. The discussions in the book center on the ideals of culturally responsive teaching (C.R.T.), and seek to build understanding of this concept in the context of mathematics. Further, the story of Gloria Jean Merriex speaks to the importance of historical influences on teaching practice. Her story is couched in sociopolitical realities of the American educational system, and is discussed as such. Cultural incongruities that exist in classrooms and contribute to the black-white achievement gap, particularly in mathematics, are also discussed.

Contents
Foreword
Preface - They Say I Was Made for Teaching
Acknowledgements
Part I: The Life of a Master Teacher
Chapter I-It Can Be Done
Chapter 2-What I Say Goes
Chapter 3-Making a Difference
Part II: The Classroom-A Research Perspective
Chapter 4-My Teaching Style Is Gonna Be Like That
Part III: The Legacy of Gloria Jean Merriex
Chapter 5-The Biggest Reward
Chapter 6-I'm Going by Reputation
Chapter 7-Orchestrating Greatness - A Tribute to Gloria Jean Merriex
Appendix-Formal Methodology
Notes
Works Cited

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

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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

Reading And Writing The World With Mathematics, Toward a Pedagogy for Social Justice

Eric Gutstein 


Routledge | 2005 | 274 páginas | pdf | 7,2 Mb

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Mathematics education in the United States can reproduce social inequalities whether schools use either "basic-skills" curricula to prepare mainly low-income students of color for low-skilled service jobs or "standards-based" curricula to ready students for knowledge-intensive positions. And working for fundamental social change and rectifying injustice are rarely included in any mathematics curriculum. Reading and Writing the World with Mathematics argues that mathematics education should prepare students to investigate and critique injustice, and to challenge, in words and actions, oppressive structures and acts. Based on teacher-research, the book provides a theoretical framework and practical examples for how mathematics educators can connect schooling to a larger sociopolitical context and concretely teach mathematics for social justice.

Contents
Series Editor’s Introduction ix
Acknowledgments xiii
Chapter 1 Social Justice, Equity, and Mathematics Education 1
Chapter 2 Education for Liberation: Toward a Framework for Teaching Mathematics for Social Justice 21
Chapter 3 Reading the World with Mathematics: Developing Sociopolitical Consciousness 39
Chapter 4 Writing the World with Mathematics: Developing a Sense of Social Agency 71
Chapter 5 The Relationship of Teaching for Social Justice and Mathematics in Context 101
Chapter 6 Co-Creating a Classroom for Social Justice: Possibilities and Challenges 129
Chapter 7 “Lucha Is What My Life Is About”: Students’ Voices on Social Justice Mathematics with Maria Barbosa, Adrián Calderón, Grisel Murillo, and Lizandra Nevárez 165
Chapter 8 “The Real World As We Have Seen It”: Parents’ Voices on Social Justice Mathematics 179
Chapter 9 Conclusion: Revisiting Mathematics Education for a Global Context 199
Notes 223
References 227
Appendix 1: Real-World Projects 237
Appendix 2: Methodology 251
Index 253

The Mathematics Of Sex: How Biology and Society Conspire to Limit Talented Women and Girls

Stephen J. Ceci e Wendy M. Williams

Oxford University Press | 2009 | páginas | rar - pdf |1 Mb

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Nearly half of all physicians and biologists are females, as are the majority of new psychologists, veterinarians, and dentists, suggesting that women have achieved equality with men in the workforce. But the ranks of professionals in math-intensive careers remain lopsidedly male; up to 93% of tenure-track academic positions in some of the most mathematically-oriented fields are held by men.
Three main explanations have been advanced to explain the dearth of women in math-intensive careers, and in The Mathematics of Sex, Stephen J. Ceci and Wendy M. Williams describe and dissect the evidence for each. The first explanation involves innate ability--male brains are physiologically optimized to perform advanced mathematical and spatial operations; the second is that social and cultural biases inhibit females' training and success in mathematical fields; the third alleges that women are less interested in math-intensive careers than are men, preferring people-oriented pursuits. Drawing on research in endocrinology, economics, sociology, education, genetics, and psychology to arrive at their own unique, evidence-based conclusion, the authors argue that the problem is due to certain choices that women (but not men) are compelled to make in our society; that women tend not to favor math-intensive careers for certain reasons, and that sex differences in math and spatial ability cannot adequately explain the scarcity of women in these fields. The Mathematics of Sex represents the first time such a thorough synthesis of data has been carried out to solve the puzzle of women's underrepresentation in math-intensive careers. The result is a readable, engaging account suitable not only for academics in an array of disciplines, but for general readers as well--including educators, science policymakers, parents of daughters, and anyone intellectually curious about a key controversy of our time.

Contents
Preface: Setting the Stage ix
Introduction: Why care about women in science? 3
Chapter 1 A multidimensional problem 16
Chapter 2 Opening arguments: Environment 28
Chapter 3 Opening arguments: Biology 58
Chapter 4 Challenges to the environmental position 79
Chapter 5 Challenges to the biological position 114
Chapter 6 Background and trend data 146
Chapter 7 Comparisons across societies, cultures, and developmental stages 161
Chapter 8 Conclusions and synthesis 179
Chapter 9 What next? Research and policy recommendations 197
Epilogue 219
Notes 223
About the authors 237
References 241
Index 261

Mathematics and Multi-Ethnic Students: Exemplary Practices

Yvelyne Germain- Mc Carthy e  Katharine Owens

Routledge | 2004 | páginas | rar - pdf | 3 Mb

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This book puts a spotlight on the practices of teachers across the nation who have implemented effective mathematics instruction for students of different ethnicities. Among the ethnic groups represented are African Americans, Latinos, Native Americans, Haitians, Arab Americans, and Euro-Americans.

Contents
Acknowledgements
Meet the Authors
Foreword
Introduction
Exemplary Practice: What Does It Look Like
Issues in Multicultural Mathematic Education
Lynn Godfrey: African Americans and The Algebra Project -
Georgine Roldan: Hispanics and Health Issues
Tim Granger: Native Americans and Indirect Measurement
Renote Jean-Francois: Haitians and Technology
Sama Sarmini: Muslims and Inheritance Portions
Diane Christopher: European-Americans and Cultures
Charlene Beckman, et al.: A Three Way School/University Collaboration
Classroom Strategies That Value Multicultural Students
Reform-Based Curriculum Projects
Summary
References

Collaborating to Meet Language Challenges in Indigenous Mathematics Classrooms

 

Tamsin Meaney, Tony Trinick e Uenuku Fairhall

(Mathematics Education Library, 52)

Springer | 2012 | 322 páginas | rar - pdf | 3,85 Mb

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Language can be simultaneously both a support and a hindrance to students’ learning of mathematics. When students have sufficient fluency in the mathematics register so that they can discuss their ideas, they become chiefs who are able to think mathematically. However, learning the mathematics register of an Indigenous language is not a simple exercise and involves many challenges not only for students, but also for their teachers and the wider community. Collaborating to Meet Language Challenges in Indigenous Mathematics Classrooms identifies some of the challenges—political, mathematical, community based, and pedagogical— to the mathematics register, faced by an Indigenous school, in this case a Mäori immersion school. It also details the solutions created by the collaboration of teachers, researchers and community members.

Contents

1 Introduction

pt. 1. Meeting political challenges 

2 The Development of a Mathematics Register in an Indigenous Language
3 The History of Te Kura Kaupapa M¯aori o Te Koutu – The Politicisation of a Local Community
4 It Is Kind of Hard to Develop Ideas When You Can’t Understand the Question: Doing Exams Bilingually
pt. 2. Meeting mathematical challenges 

5 The Resources in Te Reo M¯aori for Students to Think Mathematically
6 Writing to Help Students Think Mathematically
7 The Case of Probability
pt. 3. Meeting community challenges 

8 Using the Mathematics Register Outside the Classroom

9 Teachers as Learners of the Mathematics Register

pt. 4. Meeting pedagogical challenges.

10 “They Don’t Use the Words Unless You Really Teach Them”: Mathematical Register Acquisition Mode
11 “M¯aori were Traditional Explorers”: M¯aori Pedagogical Practices
12 “And That’s What You Want to Happen. You Want the Shift in Classroom Practice”
13 Meeting Challenges

Linguistic and Cultural Influences on Learning Mathematics

(Psychology of Education and Instruction Series)

Rodney R. Cocking e Jose P. Mestre 

Routledge | 1988 | 329 páginas | rar- pdf | 16,1 Mb

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The combined impact of linguistic, cultural, educational and cognitive factors on mathematics learning is considered in this unique book. By uniting the diverse research models and perspectives of these fields, the contributors describe how language and cognitive factors can influence mathematical learning, thinking and problem solving. The authors contend that cognitive skills are heavily dependent upon linguistic skills and both are critical to the representational knowledge intimately linked to school achievement in mathematics.

Contents
Contributors/ ix
Foreword xi
Chapter 1 Introduction: Considerations of Language Mediators of Mathematics Learning
Rodney R. Cocking, Jose P. Mestre
Chapter 2 Conceptual Issues Related to Mathematics Achievement of Language Minority Children 
Rodney R. Cocking, Susan Chipman
Chapter 3 Linking Language with Mathematics Achievement: Problems and Prospects
Geoffrey B. Saxe
Chapter 4 Intention and Convention in Mathematics Instruction: Reflections on the Learning of Deaf Students 63
Joan B. Stone
Chapter 5 Why Should Developmental Psychologists Be Interested in Studying the Acquisition of Arithmetic? 73
Ellin Kofsky Scholnick
Chapter 6 Patterns of Experience and the Language of Mathematics 91
Manon P. Charbonneau, Vera John-Steiner
Chapter 7 Bilingualism, Cognitive Function, and Language Minority Group Membership 101
Edward A. De A vila
Chapter 8 the Mathematics Achievement Characteristics of Asian-American Students 123
Sau-Lim Tsang
Chapter 9 Mexican-American Women and Mathematics: Participation, Aspirations, and Achievement 137
Patricia MacCorquodale
Chapter 10 Assumptions and Strategies Guiding Mathematics Problem Solving by Ute Indian Students 161
William L. Leap
Chapter 11 Opportunity to Learn Mathematics in Eighth-Grade Classrooms in the United States: Some Findings from the Second International Mathematics Study 187
Kenneth J. Travers
Chapter 12 the Role of Language Comprehension in Mathematics and Problem Solving 201
Jose P. Mestre
Chapter 13 Linguistic Features of Mathematical Problem Solving: Insights and Applications 221
George Spanos, Nancy C. Rhodes, Theresa Corasaniti Dale, Joann Crandall
Chapter 14 Bilinguals' Logical Reasoning Aptitude: a Construct Validity Study 241
Richard P. Duran
Chapter 15 Effects of Home Language and Primary Language on Mathematics Achievement: a Model and Results for Secondary Analysis 259
David E. Myers, Ann M. Milne
A Final Note... 294
Epilogue: And Then I Went to School 295
Joseph H. Suina
Author Index 301
Subject Index 309

Third International Handbook of Mathematics Education

M.A. (Ken) Clements, Alan Bishop, Christine Keitel-Kreidt e Jeremy Kilpatrick

Springer | 2013 | 1119 páginas | pdf | 9 Mb

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The four sections in this Third International Handbook are concerned with: (a) social, political and cultural dimensions in mathematics education; (b) mathematics education as a field of study; (c) technology in the mathematics curriculum; and (d) international perspectives on mathematics education. These themes are taken up by 84 internationally-recognized scholars, based in 26 different nations. Each of section is structured on the basis of past, present and future aspects. The first chapter in a section provides historical perspectives (“How did we get to where we are now?”); the middle chapters in a section analyze present-day key issues and themes (“Where are we now, and what recent events have been especially significant?”); and the final chapter in a section reflects on policy matters (“Where are we going, and what should we do?”). Readership: Teachers, mathematics educators, ed.policy makers, mathematicians, graduate students, undergraduate students. Large set of authoritative, international authors.​

Contents
Part I Introduction to Section A: Social, Political and Cultural Dimensions in Mathematics Education .. 1
Christine Keitel
1 From the Few to the Many: Historical Perspectives on Who Should Learn Mathematics... 7
M. A. (Ken) Clements, Christine Keitel, Alan J. Bishop, Jeremy Kilpatrick, and Frederick K. S. Leung
2 Theories for Studying Social, Political and Cultural Dimensions of Mathematics Education ... 41
Eva Jablonka, David Wagner, and Margaret Walshaw
3 Understanding and Overcoming “Disadvantage” in Learning Mathematics.... 69
Lulu Healy and Arthur B. Powell
4 Beyond Deficit Models of Learning Mathematics: Socio-cultural Directions for Change and Research .... 101
Cristina Frade, Nadja Acioly-Régnier, and Li Jun
5 Studying Learners in Intercultural Contexts ... 145
Yoshinori Shimizu and Gaye Williams
6 Learners in Transition Between Contexts.... 169
Tamsin Meaney and Troels Lange
7 Critical Perspectives on Adults’ Mathematics Education ... 203
Jeff Evans, Tine Wedege, and Keiko Yasukawa
8 The Politics of Equity and Access in Teaching and Learning Mathematics..... 243
Neil A. Pateman and Chap Sam Lim
Part II Introduction to Section B: Mathematics Education as a Field of Study ... 265
Alan J. Bishop
9 From Mathematics and Education, to Mathematics Education .... 273
Fulvia Furinghetti, José Manuel Matos, and Marta Menghini
10 Theories in Mathematics Education: Some Developments and Ways Forward .... 303
Bharath Sriraman and Elena Nardi
11 Research Methods in Mathematics Teacher Education ... 327
Uwe Gellert, Rosa Becerra Hernández, and Olive Chapman
12 Linking Research to Practice: Teachers as Key Stakeholders in Mathematics Education Research ..... 361
Carolyn Kieran, Konrad Krainer, and J. Michael Shaughnessy
13 Teachers Learning from Teachers ... 393
Allan Leslie White, Barbara Jaworski, Cecilia Agudelo-Valderrama, and Zahra Gooya
14 Developing Mathematics Educators .... 431
Jarmila Novotná, Claire Margolinas, and Bernard Sarrazy
15 Institutional Contexts for Research in Mathematics Education ...... 459
Tony Brown and David Clarke
16 Policy Implications of Developing Mathematics Education Research .... 485
Celia Hoyles and Joan Ferrini-Mundy
Part III Introduction to Section C: Technology in the Mathematics Curriculum ..... 517
Frederick K. S. Leung
17 From the Slate to the Web: Technology in the Mathematics Curriculum .... 525
David Lindsay Roberts, Allen Yuk Lun Leung, and Abigail Fregni Lins
18 Modelling with Mathematics and Technologies .. 549
Julian Williams and Merrilyn Goos
19 Technology and the Role of Proof: The Case of Dynamic Geometry ... 571
Nathalie Sinclair and Ornella Robutti
20 How Might Computer Algebra Systems Change the Role of Algebra in the School Curriculum?.... 597
M. Kathleen Heid, Michael O. J. Thomas, and Rose Mary Zbiek
21 Technology for Enhancing Statistical Reasoning at the School Level .... 643
Rolf Biehler, Dani Ben-Zvi, Arthur Bakker, and Katie Makar
22 Learning with the Use of the Internet ... 691
Marcelo C. Borba, Philip Clarkson, and George Gadanidis
23 Technology and Assessment in Mathematics .... 721
Kaye Stacey and Dylan Wiliam
24 Technology-Driven Developments and Policy Implications for Mathematics Education .... 753
L. Trouche, P. Drijvers, G. Gueudet, and A. I. Sacristán
Part IV Introduction to Section D: International Perspectives on Mathematics Education .... 791
Jeremy Kilpatrick
25 From the Local to the International in Mathematics Education .... 797
Alexander Karp
26 International Collaborative Studies in Mathematics Education ... 827
Parmjit Singh and Nerida F. Ellerton
27 Influence of International Studies of Student Achievement on Mathematics Teaching and Learning... 861
Vilma Mesa, Pedro Gómez, and Ui Hock Cheah
28 International Organizations in Mathematics Education .... 901
Bernard R. Hodgson, Leo F. Rogers, Stephen Lerman, and Suat Khoh Lim-Teo
29 Toward an International Mathematics Curriculum .... 949
Jinfa Cai and Geoffrey Howson
30 Methods for Studying Mathematics Teaching and Learning Internationally .... 975
Mogens Niss, Jonas Emanuelsson, and Peter Nyström
31 Implications of International Studies for National and Local Policy in Mathematics Education .. 1009
John A. Dossey and Margaret L. Wu
Brief Biographical Details of Authors .... 1043
Names of Reviewers .. 1063

Alternative Forms of Knowing (in) Mathematics: Celebrations of Diversity of Mathematical Practices

Swapna Mukhopadhyay e  Wolff-Michael Roth

Sense Publishers |  2012 | 321 páginas | pdf | 24 Mb

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This book grew out of a public lecture series, Alternative forms of knowledge construction in mathematics, conceived and organized by the first editor, and held annually at Portland State University from 2006. Starting from the position that mathematics is a human construction, implying that it cannot be separated from its historical, cultural, social, and political contexts, the purpose of these lectures was to provide a public intellectual space to interrogate conceptions of mathematics and mathematics education, particularly by looking at mathematical practices that are not considered relevant to mainstream mathematics education. One of the main thrusts was to contemplate the fundamental question of whose mathematics is to be valorized in a multicultural world, a world in which, as Paolo Freire said, "The intellectual activity of those without power is always characterized asnon-intellectual". To date, nineteen scholars (including the second editor) have participated in the series. All of the lectures have been streamed for global dissemination at:http://www.media.pdx.edu/dlcmedia/events/AFK/. Most of the speakers contributed a chapter to this book, based either on their original talk or on a related topic. The book is divided into four sections dealing with: • Mathematics and the politics of knowledge • Ethnomathematics • Learning to see mathematically • Mathematics education for social justice.


CONTENTS
Preface vii
Contributors ix
Celebrating Diversity, Realizing Alternatives: An Introduction 1
Brian Greer, Swapna Mukhopadhyay, & Wolff-Michael Roth
PART I: MATHEMATICS AND POLITICS OF KNOWLEDGE 9
Introduction 11
1 Mathematics and Accounting in the Andes before and after the Spanish Conquest 17
Gary Urton
2 Contemporary Indigenous Education: Thoughts for American Indian Education in a 21st-Century World 33
Gregory Cajete
3 Crisis as a Discursive Frame in Mathematics Education Research and Reform: Implications for Educating Black Children
Delaina Washington, Zayoni Torres, Maisie Gholson, & Danny Bernard Martin
4 Whose Language is it? Reflections on Mathematics Education and Language Diversity from Two Contexts 71
Marta Civil & Núria Planas
PART II: ETHNOMATHEMATICS 91
Introduction 93
5 Consulting the Divine: The (Ethno)mathematics of Divination 97
John Kellermeier
6 Map-Making in São Paulo, Southern Brazil: Colonial History, Social Diversity, and Indigenous Peoples’ Rights 115
Mariana Leal Ferreira
7 Developing an Alternative Learning Trajectory for Rational Number Reasoning, Geometry, and Measuring based on Indigenous Knowledge 159
Jerry Lipka, Monica Wong, Dora Andrew-Ihrke, & Evelyn Yanez
8 In Seeking a Holistic Tool for Ethnomathematics: Reflections on Using Ethnomodeling as a Pedagogical Action for Uncovering Ethnomathematical Practices 183
Daniel Clark Orey & Milton Rosa
9 From Ethnomathematics to Ethnocomputing: Indigenous Algorithms in Traditional Context & Contemporary Simulation 205
Bill Babbitt, Dan Lyles, & Ron Eglash
PART III: LEARNING TO SEE MATHEMATICALLY 221
Introduction 223
10 The Work of Seeing Mathematically 227
Wolff-Michael Roth
11 Running the Numbers: A Conversation 247
Chris Jordan
12 To Know How to See: The Realities of Learning and Teaching Mathematics 261
Frank Swetz
PART IV: MATHEMATICS EDUCATION FOR SOCIAL JUSTICE 277
Introduction 279
13 Quantitative Form in Argument 283
Marilyn Frankenstein
14 Connecting Community, Critical, and Classical Knowledge in Teaching Mathematics for Social Justice 299
Rico Gutstein
Epilogue: Why Bother about Diversity of Mathematical Practices? 313

Swapna Mukhopadhyay, Wolff-Michael Roth, & Brian Greer

Mathematical Representation at the Interface of Body and Culture

(International Perspectives on Mathematics Education)

Wolff-Michael Roth

Information Age Publishing | 2009 | 369 páginas | rar - pdf | 6,2 Mb

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A Volume in International Perspectives on Mathematics Education - Cognition, Equity & Society Series Editor Bharath Sriraman, The University of Montana and Lyn English, Queensland University of Technology Over the past two decades, the theoretical interests of mathematics educators have changed substantially-as any brief look at the titles and abstracts of articles shows. Largely through the work of Paul Cobb and his various collaborators, mathematics educators came to be attuned to the intricate relationship between individual and the social configuration of which she or he is part. That is, this body of work, running alongside more traditional constructivist and psychological approaches, showed that what happens at the collective level in a classroom both constrains and affords opportunities for what individuals do (their practices). Increasingly, researchers focused on the mediational role of sociomathematical norms and how these emerged from the enacted lessons. A second major shift in mathematical theorizing occurred during the past decade: there is an increasing focus on the embodied and bodily manifestation of mathematical knowing (e.g., Lakoff & Núñez, 2000). Mathematics educators now working from this perspective have come to their position from quite different bodies of literatures: for some, linguistic concerns and mathematics as material praxis lay at the origin for their concerns; others came to their position through the literature on the situated nature of cognition; and yet another line of thinking emerged from the work on embodiment that Humberto Maturana and Francisco Varela advanced. Whatever the historical origins of their thinking, mathematics educators taking an embodiment perspective presuppose that it is of little use to think of mathematical knowing in terms of transcendental concepts somehow recorded in the brain, but rather, that we need to conceptual knowing as mediated by the human body, which, because of its senses, is at the origin of sense. One of the question seldom asked is how the two perspectives, one that focuses on the bodily, embodied nature of mathematical cognition and the other that focuses on its social nature, can be thought together. This edited volume situates itself at the intersection of theoretical and focal concerns of both of these lines of work. In all chapters, the current culture both at the classroom and at the societal level comes to be expressed and provides opportunities for expressing oneself in particular ways; and these expressions always are bodily expressions of body-minds. As a collective, the chapters focus on mathematical knowledge as an aspect or attribute of mathematical performance; that is, mathematical knowing is in the doing rather than attributable to some mental substrate structured in particular ways as conceived by conceptual change theorists or traditional cognitive psychologists. The collection as a whole shows readers important aspects of mathematical cognition that are produced and observable at the interface between the body (both human and those of [inherently material] inscriptions) and culture. Drawing on cultural-historical activity theory, the editor develops an integrative perspective that serves as a background to a narrative that runs through and pulls together the book into an integrated whole.

CONTENTS
Series Preface vii
Preface xi
1. Social Bodies and Mathematical Cognition: An Introduction
Wolff-Michael Roth 1
PART A: MOVING AND TRANSFORMING BODIES IN/AS MATHEMATICAL PRACTICE
Editor’s Section Introduction 19
2. Transformation Geometry from an Embodied Perspective
Laurie D. Edwards 27
3. Signifying Relative Motion: Time, Space and the Semiotics of Cartesian Graphs
Luis Radford 45
4. What Makes a Cube a Cube? Contingency in Abstract, Concrete, Cultural and Bodily Mathematical Knowings
Jean-François Maheux, Jennifer S. Thom, and Wolff-Michael Roth 71
5. Embodied Mathematical Communication and the Visibility of Graphical Features
Wolff-Michael Roth 95
Editor’s Section Commentary 123
PART B: EMERGENCE OF OBJECTS AND UNDERSTANDING
Editor’s Section Introduction 131
6. Supporting Students’ Learning About Data Creation
Paul Cobb and Carrie Tzou 135
7. How Do You Know Which Way the Arrows Go? The Emergence and Brokering of a Classroom Math Practice
Chris Rasmussen, Michelle Zadieh, and Megan Wawro 171
8. Inscription, Narration and Diagram-Based Argumentation: Narrative Accounting Practices in Primary Mathematics Classes
Götz Krummheuer 219
Editor’s Section Commentary 245
PART C: STEPS TOWARD RETHINKING
MATHEMATICS EDUCATION
Editor’s Section Introduction 251
9. And so …?
Brent Davis 257
10. Expressiveness and Mathematics Learning
Ian Whitacre, Charles Hohensee, and Ricardo Nemirovsky 275
11. Gesture, Abstraction, and the Embodied Nature of Mathematics
Rafael E. Núñez 309
Editor’s Section Commentary 329
PART D: EPILOGUE
12. Appreciating the Embodied Social Nature of Mathematical Cognition
Wolff-Michael Roth 335
About the Authors 351

Transnational and Borderland Studies in Mathematics Education

(Studies in Mathematical Thinking and Learning Series)

Richard S. Kitchen e Marta Civil

Routledge | 2010 | 233 páginas | rar - pdf | 1,4 Mb

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Every year, significant numbers of immigrant children from Mexico enter classrooms in the United States. These immigrants comprise a heterogeneous group of students with diverse needs, abilities, and experiences. Transnational and Borderland Studies in Mathematics Educationis the first collection to offer research studies across these communities. Providing invaluable research on both sending and receiving communities in Mexico and the US, this collection considers the multiple aspects of children’s experiences with mathematics, including curriculum, classroom participation structures, mathematical reasoning and discourse – both in and out of school – and parents’ perceptions and beliefs about mathematics instruction. An important treatment of an insufficiently documented subject, this collection brings together researchers on both sides of the border to foster and support an interest in documenting evidence that will set the stage for future studies in mathematics education.

Contents
Preface by Richard S. Kitchen and Marta Civil
1. Ecological Approaches to Transnational Research on Mathematical Reasoning: A Focus on Latino/a Mathematics Learners in the Borderlands by Judit Moschkovich
2. Crossing the Border between Home and School: Dominican Parents' Perspectives on the Teaching and Learning of Mathematics by Mary Q. Foote
3. Impressions of Mexican Immigrant Families on their Early Experiences with School Mathematics in Arizona by Marta Civil & José María Menéndez
4. Becoming a "Liberal" Math Learner: Expanding Secondary School Mathematics to Support Cultural Connections, Multiple Mathematical Identities and Engagement by Lisa M. Jilk
5. Engaging Underprivileged Mexican students in Reform-Oriented Mathematics Instruction by José Luis Cortina
6. Considering Mexican and U.S. Teachers’ Views on the Teaching and Learning of Mathematics Through a Teaching for Diversity Lens by Richard S. Kitchen
7. Teachers’ Task Management Practices in the Context of Routine and Non-Routine Mathematics Problems: A Descriptive Analysis by Guadalupe I. Lozano Terán
8. Teachers’ Conceptions of Mathematics and Mathematics Teaching and Learning: The Case of Two Elementary Teachers in Northern Mexico by Jesús Acosta-Iriqui
9. Looking Forward: Establishing a Research Agenda for Transnational and Borderland Studies in Mathematics Education by Richard S. Kitchen & Marta Civil
Epilogue by Olimpia Figueras

Embracing reason : egalitarian ideals and the teaching of high school mathematics

(Studies in Mathematical Thinking and Learning

Daniel Chazan; Sandra Callis; Michael Lehman

Routledge | 2007 | 396 páginas | rar - pdf | 1,2 Mb

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This book tells a single story, in many voices, about a serious and sustained set of changes in mathematics teaching practice in a high school and how those efforts influenced and were influenced by a local university. It includes the writings and perspectives of high school students, high school teachers, preservice teacher candidates, doctoral students in mathematics education and other fields, mathematics teacher educators, and other education faculty. As a whole, this case study provides an opportunity to reflect on reform visions of mathematics for all students and the challenges inherent in the implementation of these visions in US schools. It challenges us to rethink boundaries between theory and practice and the relative roles of teachers and university faculty in educational endeavors.


Contents
Preface: Mathematics and Egalitarian Ideals
School Mathematics and Egalitarian Ideals: A Focus on Reason(s)
Acknowledgements
1 Introduction to Our Case Study
Our Goals and Our Own Voices
The Importance of Teacher Development
A School-University PDS Two-Way Relationship
The Structure of this Case Study and Its Included Texts
Part I Changes in Classroom Teaching Practice
2 Assessment
Mathematics Performance Assessment
Alternative Formats and A Taxonomy of Tasks
3 Curriculum and Instructional Models
Starting a Functions-Based Approach to Algebra
Perspectives on Holt Algebra 1 from the Department Chair and a Newer Teacher
4 Planning
Teacher as Course-Level Planner
Must Teachers’ Create Curriculum? For Every Class?
5 Interlude A: On-campus Preservice Assignments
TE 804 Reflection and Inquiry in Teaching Practice II
Preservice Teachers as Curriculum Makers
Should Preservice Teachers be Encouraged to Create Curriculum?
6 Instructional Tasks
Finding Mathematics in the World Around Us
Getting Past Lame Justifications!
7 Classroom Roles
One Teacher’s Transformation in Teaching
What Teachers Think is Important!
Part II Student Experience of the Curriculum
8 Lower Track Classes
From an E to an A with the Help of a Graphing Calculator
How Important are Calculators?
9 Standard Track Classes
Students’ views of mathematical conversation
CURRICULUM
PATTERN OF TEACHING/LEARNING
CONCEPTION OF MATHEMATICS
Managing Students’ Participation in Classroom Conversation
10 Advanced Coursework
Developing an Interest in Mathematics
What is "mathematical power"? Related dilemmas of teaching
11 Interlude B: Observation in Classrooms
Field Experience really was the Best Teacher!
Our Contrasting Preservice Field Experiences
12 Interlude C: Student Teaching/Internship
What Kind of Teacher Will I Be?
How Do We Talk with Other Teachers about Our "Holt" Experiences?
Part III Professional Growth and Development
13 Time and Respect
Being Treated (and Treating Ourselves) as Professionals
Thoughts from Latecomers
14 Restructuring Teacher Work
Shared Teaching Assignments
What Do Shared Teaching Assignments Tell Us about Learning while Teaching?
15 Departmental Culture
One Transformed Teacher’s Viewpoint
Elementary Mathematics can be Complex and Interesting!
16 Changing the Math Curriculum
Teaching a Technologically-Supported Approach to School Algebra
Thoughts on Where to Start
17 Learning from Students and Colleagues
Questioning Ourselves and the Authorities
Should We Ever Tell Mathematical White Lies to Our Students?
18 Interlude D: Learning Math from Coursework Conversation
Lines and points
Comments from Some Former "Students"
19 Participation in Teacher Education
Becoming a Professional Teacher; Being a Mentor Teacher
Being a Mentor Teacher is Hard Work!
20 Graduate Study
Theory is Practical!
The Role of Views of Mathematics in Teaching
Part IV Stepping back: The perspective of a local "outsider"
21 A Quiet Revolution? Reflecting on Mathematics Reform at Holt High School

Mathematics Teaching, Learning, and Liberation in the Lives of Black Children

 

(Studies in Mathematical Thinking and Learning Series)

Danny Bernard Martin

Routledge | 2009 |375 páginas | pdf | 2 Mb

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With issues of equity at the forefront of mathematics education research and policy, Mathematics Teaching, Learning, and Liberation in the Lives of Black Children fills the need for authoritative, rigorous scholarship that sheds light on the ways that young black learners experience mathematics in schools and their communities. This timely collection significantly extends the knowledge base on mathematics teaching, learning, participation, and policy for black children and it provides new framings of relevant issues that researchers can use in future work. More importantly, this book helps move the field beyond analyses that continue to focus on and normalize failure by giving primacy to the stories that black learners tell about themselves and to the voices of mathematics educators whose work has demonstrated a commitment to the success of these children.

The mathematics of sex : how biology and society conspire to limit talented women and girls

 

Stephen J. Ceci e Wendy M. Williams

Oxford University Press | 2010 | 287 | rar - pdf | 1 Mb

link (password: matav)

Nearly half of all physicians and biologists are females, as are the majority of new psychologists, veterinarians, and dentists, suggesting that women have achieved equality with men in the workforce. But the ranks of professionals in math-intensive careers remain lopsidedly male; up to 93% of tenure-track academic positions in some of the most mathematically-oriented fields are held by men.
Three main explanations have been advanced to explain the dearth of women in math-intensive careers, and in The Mathematics of Sex, Stephen J. Ceci and Wendy M. Williams describe and dissect the evidence for each. The first explanation involves innate ability--male brains are physiologically optimized to perform advanced mathematical and spatial operations; the second is that social and cultural biases inhibit females' training and success in mathematical fields; the third alleges that women are less interested in math-intensive careers than are men, preferring people-oriented pursuits. Drawing on research in endocrinology, economics, sociology, education, genetics, and psychology to arrive at their own unique, evidence-based conclusion, the authors argue that the problem is due to certain choices that women (but not men) are compelled to make in our society; that women tend not to favor math-intensive careers for certain reasons, and that sex differences in math and spatial ability cannot adequately explain the scarcity of women in these fields. The Mathematics of Sex represents the first time such a thorough synthesis of data has been carried out to solve the puzzle of women's underrepresentation in math-intensive careers. The result is a readable, engaging account suitable not only for academics in an array of disciplines, but for general readers as well--including educators, science policymakers, parents of daughters, and anyone intellectually curious about a key controversy of our time.

Contents
Preface: Setting the Stage ix
Introduction: Why care about women in science? 3
Chapter 1 A multidimensional problem 16
Chapter 2 Opening arguments: Environment 28
Chapter 3 Opening arguments: Biology 58
Chapter 4 Challenges to the environmental position 79
Chapter 5 Challenges to the biological position 114
Chapter 6 Background and trend data 146
Chapter 7 Comparisons across societies, cultures, and developmental stages 161
Chapter 8 Conclusions and synthesis 179
Chapter 9 What next? Research and policy recommendations 197

Asphalt Children and City Streets: A Life, a City, and a Case Study of History, Culture, and Ethnomathematics in Sao Paulo

Mônica Mesquita, Sal Restivo, Ubiratan D’Ambrosio 

Sense Publishers | 2011 | 172 páginas | pdf | 700 kb

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THIS WORK EXPLORES THE URBAN EXPERIENCES OF STREET CHILDREN IN SAO PAULO, BRAZIL THROUGH THE MATHEMATICAL EPISTEMIC REGIMES AT THE CORE OF THEIR SURVIVAL STRATEGIES. WE ALSO DRAW ATTENTION TO THE SITUATION OF STREET CHILDREN ACROSS TIME, SPACE, CULTURE, AND HISTORY. OUR GOAL IS TO RECOGNIZE, UNDERSTAND, AND VALIDATE FORMS OF MATHEMATICS CONSTRUCTED AND USED OUTSIDE OF THE ESTABLISHED INSTITUTIONS OF MATHEMATICAL PRODUCTION. WE BASE OUR ANALYSIS ON "THE MATHEMATICAL IMAGINATION", WHICH DRAWS TOGETHER SOCIAL CONSTRUCTIONISM AND ETHNOMATHEMATICS. THEORETICALLY, WE DRAW HEAVILY ON THE DURKHEIMIAN TRADITION IN SOCIOLOGY AND ANTHROPOLOGY. WE FOCUS ON A FORM OF PRACTICE THAT LINKS THE FORMAL AND THE INFORMAL IN ORDER TO REALIZE THE FULL POWER OF MATHEMATICAL KNOWLEDGE AS A SOCIAL THING (IN DURKHEIM'S SENSE), A PRODUCT OF THE COLLECTIVE CONSCIOUSNESS THAT EXPRESSES COLLECTIVE REALITIES AND A CATEGORY OF KNOWLEDGE PRESENT IN EVERY CULTURE. THIS IS AS TRUE FOR MATHEMATICS AT THE MARGINS AS IT IS FOR PROFESSIONAL MATHEMATICS. OUR WORK CONTRIBUTES TO AN EMERGING POLITICAL MANIFESTO OF THE MARGINAL THAT DEMONSTRATES THE SOCIAL REALITIES AND SOCIAL POWER OF THEIR MATHEMATICS. THIS BOOK SHOULD BE OF INTEREST TO SOCIAL SCIENTISTS, STUDENTS OF MATHEMATICS AND ETHNOMATHEMATICS, AND EVERYONE INTERESTED IN THE SITUATION OF MARGINALIZED CHILDREN.

Which Way Social Justice in Mathematics Education?

(International Perspectives on Mathematics Education)

Leone Burton

Praeger |  2003  | 344 páginas | PDF | 10,15 Mb

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This contributed volume explores equity and social justice within the field of mathematics education. In part one, Helga Jungwirth's introductory chapter provides a strong theoretical overview that is based in actual classroom behaviors and a typology that classifies the various interpretations found within this volume. Also in part one, Laurie Hart discusses developments in equity research in the United States. Part two focuses on results of studies about social justice and their impact on learning in mathematics classrooms in various parts of the world. For example, in a chapter on Peru, social justice does not just encompass gender, but also inequalities in opportunities to learn, such as problems of resources, living and social conditions, communal demands and language needs. And, part three focuses on computers as a resource to mathematics teaching.

The contributors raise several important social justice issues which have previously remained unresearched. Although there are a number of chapters specifically dealing with gender, many of the authors use one of the following strategies: their gender-specific questions are set in a wider socio-cultural context, they challenge what have threatened to become false orthodoxies, or they raise other important issues. These other issues include the meaning of democratic citizenship for mathematics classrooms, the links between parents and children learning mathematics, and the preconceptions of some teachers of underprivileged students in Australia. Other chapters explore different forms of classroom communication, participation, and assessment. The pieces on computers state that there is still not enough research to conclude whether computers in the mathematics classrooms are supportive of, or detrimental to, the learning of all students. The one thing on which every author in this volume does agree is that social justice in mathematics education has still not been attained, but that we must strive toward it to improve educational practices and society in general.

Mapping Equity and Quality in Mathematics Education

 

Bill Atweh, Mellony Graven, Walter Secada, e Paola Valero

Springer | 2011 | 515 páginas | PDF | 5 Mb

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The issues of equity and quality have been central to international debates on mathematics in research, policy, curriculum and teaching. This book covers a wide variety of topics in the research and practice of mathematics education, demonstrating how equity and quality are inherently political terms whose political bedrock is obscured by them being taken for granted.

Mapping Equity and Quality in Mathematics Education is broken into four parts. Section 1 addresses the constructs of equity and quality from a variety of theoretical perspectives and outlines new directions to approach the question, “What are equity and quality?” Section 2 discusses the complexities in which the discourses of equity and quality move in constant construction and recontextualisation from societal trends to the constitution of subjectivities, passing through policy, the media and pedagogy. Section 3 covers insights and implications from research on the special needs of different “equity groups,” illuminating the way in which a “one-size-fits-all” approach tends to limit quality education to only dominant groups. And Section 4 contains lessons learned by researchers and practitioners who attempted to manage equity and quality within various educational contexts and with a variety of marginalized populations.

Written by teachers, researchers and academics from all over the world, this book represents a powerful response to the international call for quality education of all students in mathematics around the globe.

Street Mathematics and School Mathematics

(Learning in Doing: Social, Cognitive and Computational Perspectives)
Terezinha Nunes, David William Carraher, Analucia Dias Schliemann

Cambridge University Press | 1993 | 180 páginas |  pdf | 23,265 Mb

lib.freescienceengineering.org

Desrição: People who learn to solve problems 'on the job' often have to do it differently from people who learn in theory. Practical knowledge and theoretical knowledge is different in some ways but similar in other ways - or else one would end up with wrong solutions to the problems. Mathematics is also like this. People who learn to calculate, for example, because they are involved in commerce frequently have a more practical way of doing mathematics than the way we are taught at school. This book is about the differences between what we call practical knowledge of mathematics - that is street mathematics - and mathematics learned in school, which is not learned in practice. The authors look at the differences between these two ways of solving mathematical problems and discuss their advantages and disadvantages. They also discuss ways of trying to put theory and practice together in mathematics teaching.

Table of Contents
Preface
Series foreword
1 What is street mathematics? 1
2 Arithmetic in the streets and in schools 13
3 Written and oral arithmetic 28
4 Situational representation in oral and written mathematics 49
5 Situational and mathematical relations: A study on understanding proportions 77
6 Reversibility and transfer in the schema of proportionality 103
7 Reflections on street mathematics in hindsight 127
References 155
Index 161

How Social and Emotional Development Add Up: Getting Results in Math and Science Education

(Social Emotional Learning, 4)
Norris M. Haynes, Michael Ben-Avie, Jacque Ensign, Ed.

Teachers College Press | 2003 | 208 páginas| pdf | 1 Mb

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This landmark volume is essential reading for math and science teachers who are eager to find creative and stimulating ways to engage student's interest and to boost their academic performance. A stellar group of contributors, including both psychologists and teachers, outlines the principles of social emotional learning (SEL) that educators can follow to help "all students to achieve in the math and science classroom. Focusing on inner-city schools and the particular needs of African American students, the text: -Presents a substantial body of empirical research, including findings of the Third International Math and Science Study-Builds on what we already know about social and emotional factors in learning and applies it to the math and science curriculum, shedding new light on ways to help young people succeed academically-Features many examples of successful math and science instruction that teachers can incorporate into their own classrooms-Covers key topics, such as youth development, connecting with students, math-science readiness and policy, developmental pathways to achievement, success for minority students, equity and excellence, preparing students for the future, and corporate partners in the classroom