Origins of mathematical words: a comprehensive dictionary of Latin, Greek, and Arabic roots

Anthony Lo Bello 

Johns Hopkins University Press | 2013 | 369 páginas | rar - pdf | 1,9 Mb

link (password : matav)

pdf - 3,7 Mb - link

Do you ever wonder about the origins of mathematical terms such as ergodic, biholomorphic, and strophoid? Here Anthony Lo Bello explains the roots of these and better-known words like asymmetric, gradient, and average. He provides Greek, Latin, and Arabic text in its original form to enhance each explanation. This sophisticated, one-of-a-kind reference for mathematicians and word lovers is based on decades of the author's painstaking research and work. Origins of Mathematical Words supplies definitions for words such as conchoids (a shell-shaped curve derived from the Greek noun for "mussel") and zenith (Arabic for "way overhead"), as well as approximation (from the Latin proximus, meaning "nearest"). These and hundreds of other terms wait to be discovered within the pages of this mathematical and etymological treasure chest.

Livro relacionado:

The words of mathematics : an etymological dictionary of mathematical terms used in English por Steven Schwartzman Idioma: Inglês   Editora: Washington, DC : Mathematical Association of America, ©1994.

Circles Disturbed: The Interplay of Mathematics and Narrative

Apostolos Doxiadis e Barry Mazur

Princeton University Press | 2012 | 592 páginas | rar - pdf | 3,75 Mb

link (password: matav)
(novo formato)

epub | 6,7 Mb
link direto
link
link1

mobi - 8 Mb - link

Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier--"Don't disturb my circles"--words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds--stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities.
A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more.
In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier

CONTENTS
Introduction
1 From Voyagers to Martyrs: Toward a Storied History of Mathematics
AMIR ALEXANDER
2 Structure of Crystal, Bucket of Dust
PETER GALISON
3 Deductive Narrative and the Epistemological Function of Belief in Mathematics: On Bombelli and Imaginary Numbers
FEDERICA LA NAVE
4 Hilbert on Theology and Its Discontents: The Origin Myth of Modern Mathematics
COLIN MCLARTY
5 Do Androids Prove Theorems in Their Sleep?
MICHAEL HARRIS
6 Visions, Dreams, and Mathematics
BARRY MAZUR
7 Vividness in Mathematics and Narrative
TIMOTHY GOWERS
8 Mathematics and Narrative: Why Are Stories and Proofs Interesting?
BERNARD TEISSIER
9 Narrative and the Rationality of Mathematical Practice
DAVID CORFIELD
10 A Streetcar Named (among Other Things) Proof: From Storytelling to Geometry, via Poetry and Rhetoric
APOSTOLOS DOXIADIS
11 Mathematics and Narrative: An Aristotelian Perspective
G. E. R. LLOYD
12 Adventures of the Diagonal: Non-Euclidean Mathematics and Narrative
ARKADY PLOTNITSKY
13 Formal Models in Narrative Analysis
DAVID HERMAN
14 Mathematics and Narrative: A Narratological Perspective
URI MARGOLIN
15 Tales of Contingency, Contingencies of Telling: Toward an Algorithm of Narrative Subjectivity
JAN CHRISTOPH MEISTER

Sugestão de tibu

Supporting English language learners in math class, grades 3/5

 Rusty Bresser, Kathy Melanese e Christine Sphar 

 Math Solutions | 2008 | 226 páginas | pdf | 2,4 Mb

link
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This lesson-based series gives teachers the essential tools for simultaneously meeting math content goals and language development goals. Teachers will get a wealth of strategies and activities for modifying their instruction as well as sentence frame structures and dozens of instant-use reproducibles. Grades 3-5

ContentsForeword / vii
Acknowledgments / xi
1 Teaching Math to English Language Learners / 1
2 Identifying and Describing Polygons: A Geometry Lesson / 18
3 Build a Shape, Part 1: A Geometry Lesson / 37
4 Build a Shape, Part 2: A Geometry Lesson / 50
5 Roll Two Dice: A Probability Lesson / 58
6 Building Iguanas with Pattern Blocks: An Algebra Lesson / 81
7 Round Things: A Measurement Lesson / 105
8 Helping English Language Learners Make Sense of Math Word Problems / 130
9 Writing and Solving Multiplication and Division Word Problems / 138
10 How to Modify Math Lessons to Support English Language Learners / 163
11 Frequently Asked Questions / 182
Appendix: Multiple-Meaning Words in Mathematics / 191
Blackline Masters / 193
Identifying and Describing Polygons Cards / 195
Identifying and Describing Polygons Record Sheet / 197
Roll Two Dice Record Sheet / 198
Round Things Record Sheet / 199
Lesson Template / 200
References / 201
Index / 205

Supporting English Language Learners in Math Class, Grades K-2

Rusty Bresser, Kathy Melanese e Christine Sphar

Math Solutions | 2008 | 218 páginas | pdf | 3,9 Mb

link direto
link
link1

This lesson-based series gives teachers the essential tools for simultaneously meeting math content goals and language development goals. Teachers will get a wealth of strategies and activities for modifying their instruction as well as sentence frame structures and dozens of instant-use reproducibles. Grades K-2

Contents
Foreword / vii
Acknowledgments / xi
1 Teaching Math to English Language Learners / 1
2 Capture and Double Capture: An Arithmetic Lesson / 18
3 From Rockets to Polygons: A Geometry Lesson / 34
4 Trade Up for a Nickel, Trade Up for a Dime, and Race for a Quarter: Number Sense Lessons About Money / 55
5 Would You Rather . . . ? A Data Analysis Lesson / 73
6 Cubes in a Tube: An Algebra Lesson / 88
7 Junk Sorting: An Algebra Lesson / 112
8 Helping English Language Learners Make Sense of Math Word Problems / 133
9 How to Modify Math Lessons to Support English Language Learners / 160
10 Frequently Asked Questions / 178
Appendix: Multiple-Meaning Words in Mathematics / 187
Blackline Masters / 189
Trade Up for a Nickel Game Board / 190
Trade Up for a Nickel Amount Cards / 191
Trade Up for a Dime Game Board / 192
Trade Up for a Dime Amount Cards / 193
Race for a Quarter Rules / 194
1–100 Chart / 195
References / 197
Index / 201

Using Children’s Literature to Teach Problem Solving in Math: Addressing the Common Core in K–2

Jeanne White

Routledge | 2013 | 111 páginas | rar - pdf | 516 kb

link (password: matav)

Learn how to use children’s literature to engage students in mathematical problem solving. Teaching with children’s literature helps build a positive math environment, encourages students to think abstractly, shows students the real-world purposes of math, builds content-area literacy, and appeals to students with different learning styles and preferences. This practical book provides specific children’s book ideas and standards-based lessons that you can use to bring math alive in your own classroom.

Special Features:

• Step-by-step ideas for using children’s literature to teach lessons based on the Common Core Standards for Mathematical Content in kindergarten, first, and second grade

• Scripting, modeling, and discussion prompts for each lesson

• Information on alignment to the Standards for Mathematical Practice and how to put them into student-friendly language

• Reference to a wide variety of specific children’s literature that can provide a context for young children learning to engage in the standards

• Differentiated activities for students who are early, developing, and advanced problem solvers

Contents
About the Author ix
Acknowledgments xi
Introduction: Using Children’s Literature to Teach
Problem Solving in Math 1
Types of Problem Solvers 2
Creating a Problem-Solving Community 3
1 Make Sense and Persevere 5
Early Problem Solvers 6
Seven Blind Mice—Decomposing Numbers 6
Developing Problem Solvers 10
MATH-Terpieces: The Art of Problem Solving—Using 2 and 3 Addends to Find a Sum 10
Advanced Problem Solvers 12
Splash!—Representing Addition and Subtraction Problems 12
2 Reason Abstractly 15
Early Problem Solvers 16
Ten Flashing Fireflies—Exploring the Commutative Property of Addition 16
Rooster’s Off to See the World—Exploring the Associative Property of Addition 17
Developing Problem Solvers 19
Each Orange Had 8 Slices—Demonstrating Fluency for Addition 19
Advanced Problem Solvers 21
How Many Mice?—Representing and Solving Problems With Addition and Subtraction 21
3 Construct Arguments 23
Early Problem Solvers 24
How Many Seeds in a Pumpkin?—Skip-Counting and Comparing Three-Digit Numbers 24
Developing Problem Solvers 27
Mall Mania—Adding Two-Digit Numbers Using Various Strategies 27
Advanced Problem Solvers 29
Spaghetti and Meatballs for All!—Creating Composite Shapes 29
4 Create a Model 33
Early Problem Solvers 33
The Doorbell Rang—Representing Addition in Various Ways 33
Developing Problem Solvers 38
Bigger, Better, Best!—Using Addition With Rectangular Arrays 38
Advanced Problem Solvers 42
Alexander, Who Used to be Rich Last Sunday—Solving Word Problems With Money 42
5 Use Mathematical Tools 47
Early Problem Solvers 48
Earth Day-Hooray!—Using Place Value to Add and Subtract 48
Developing Problem Solvers 52
Mummy Math—Recognizing Attributes of 3D Objects 52
Advanced Problem Solvers 54
Measuring Penny—Measuring in Standard and Nonstandard Units 54
6 Attend to Precision 59
Early Problem Solvers 59
If You Were a Quadrilateral—Identifying Quadrilaterals 59
Developing Problem Solvers 62
Lemonade for Sale—Representing and Interpreting Data 62
Advanced Problem Solvers 65
Measuring Penny—Relating Addition and Subtraction to Length 65
7 Look for Structure 69
Early Problem Solvers 69
The Button Box—Identifying Attributes for Sorting 69
Developing Problem Solvers 73
Patterns in Peru—Describing Relative Positions 73
Advanced Problem Solvers 76
The Greedy Triangle—Exploring Attributes of Shapes 76
8 Apply Repeated Reasoning 81
Early Problem Solvers 82
Bunches of Buttons: Counting by Tens—Counting to 100 by Tens 82
Developing Problem Solvers 85
How Big is a Foot?—Iterating Length Units 85
Advanced Problem Solvers 87
The King’s Commissioners—Representing Tens and Ones 87
Next Steps 91
Appendix: Common Addition and Subtraction Situations 93
References 95

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

 C.J. Brainerd

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

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

Mathematics as sign : writing, imagining, counting

Brian Rotman

Stanford University Press | 2000 | 180 páginas | rar - pdf | 4,8 Mb

link (password: matav)

Two features of mathematics stand out: its menagerie of seemingly eternal objects (numbers, spaces, patterns, functions, categories, morphisms, graphs, and so on), and the hieroglyphics of special notations, signs, symbols, and diagrams associated with them. The author challenges the widespread belief in the extra-human origins of these objects and the understanding of mathematics as either a purely mental activity about them or a formal game of manipulating symbols. Instead, he argues that mathematics is a vast and unique man-made imagination machine controlled by writing.

Mathematics as Sign addresses both aspects—mental and linguistic—of this machine. The opening essay, "Toward a Semiotics of Mathematics" (long acknowledged as a seminal contribution to its field), sets out the author's underlying model. According to this model, "doing" mathematics constitutes a kind of waking dream or thought experiment in which a proxy of the self is propelled around imagined worlds that are conjured into intersubjective being through signs.
Other essays explore the status of these signs and the nature of mathematical objects, how mathematical ideograms and diagrams differ from each other and from written words, the probable fate of the real number continuum and calculus in the digital era, the manner in which Platonic and Aristotelean metaphysics are enshrined in the contemporary mathematical infinitude of endless counting, and the possibility of creating a new conception of the sequence of whole numbers based on what the author calls non-Euclidean counting.
Reprising and going beyond the critique of number in Ad Infinitum, the essays in this volume offer an accessible insight into Rotman's project, one that has been called "one of the most original and important recent contributions to the philosophy of mathematics."

CONTENTS
PREFACE: WRITING, IMAGINING, COUNTING IX
1. Toward a Semiotics of Mathematics 1
2. Making Marks on Paper 44
3. How Ideal Are the Reals? 71
4. God Tricks; or, Numbers from the Bottom Up? 106
5. Counting on Non-Euclidean Fingers 125
NOTES 157
WORKS CITED 163
INDEX OF PERSONS 169

English Language Learners and Math: Discourse, Participation, and Community in Reform-Oriented, Middle School Mathematics ClassesEnglish Language Learners and Math: Discourse, Participation, and Community in Reform-Oriented, Middle School Mathematics Classes

Holly Hansen-Thomas 

Information Age Publishing | 2009 | 161 páginas | rar - pdf | 504 kb

link (password: matav)

Taking a community of practice perspective that highlights the learner as part of a community, rather than a lone individual responsible for her/his learning, this ethnographically-influenced study investigates how Latina/o English Language Learners (ELLs) in middle school mathematics classes negotiated their learning of mathematics and mathematical discourse. The classes in which the Latina/o students were enrolled used a reform-oriented approach to math learning; the math in these classes was-to varying degrees-taught using a hands-on, discovery approach to learning where group learning was valued, and discussions in and about math were critical. This book presents the stories of how six immigrant and American-born ELLs worked with their three teachers of varied ethnicity, education, experience with second language learners, and training in reform-oriented mathematics curricula to gain a degree of competence in the mathematical discourse they used in class. Identity, participation, situated learning, discourse use by learners of English as a Second Language (ESL), framing in language, and student success in mathematics are all critical notions that are highlighted within this school-based research.

A Handbook of Mathematical Discourse

Charles Wells

Infinity Publishing | 2003 | 300 páginas 

pdf (versão draft - 2002) - online: 
ljk.imag.fr
abstractmath.org

What sort of book is this? It is a dictionary of sorts of all those words and conventions you had questions about as an undergraduate or graduate student but were afraid to ask, for fear of sounding dumb. Nobody, especially not your professors, bothered to explain these words, because they knew them so well and used them so automatically that it never occurred to them that you might not know to use them.
For example, a student might be confused by the many different ways mathematicians use let. This book explains, with illustrative examples, that let can mean assume or suppose, that it can be used to introduce a new symbol when considering successive cases (Let n > 0.... Now let n<0 font="" nbsp="">

to introduce an arbitrary object when proving a for all statement (Let g∈G; we need to prove that…), or
to define a concept (Let an integer be even if it is divisible by 2),
as well as several other meanings. That students are not clear about the use of words like let can be seen from Steve Maurer’s PRIMUS article, “Advice for undergraduates on special aspects of writing mathematics” (Vol. 1, pp. 9–28, 1991).
A student might want to know what a bound variable is — not many transition-to-proof course textbooks cover that very well, if at all. There is a definition here, and it comes with a picture. Whether or not you like the somewhat quirky line drawings, however, depends on your sense of humor: next to the entry for bound variable, one finds an X with lots of rope around its middle. If you know already know the meaning of bound variable, you may be amused by this play on words. However, if you are a student trying to understand its meaning, I doubt it would help.
You can browse the book like a coffee table book (though its size is much smaller at 8 by 8 inches) or like a dictionary, which it resembles. Give it to your favorite math major or beginning graduate student to help enculturate him/her into mathematicians’ sometimes unusual usage of terms and phrases. You might also consider using it as a prize for a math contest or as an addition to your departmental math library.

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

link (password: matav)

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

Problem Solving and Comprehension

Arthur Whimbey, Jack Lochhead, e Ron Narode

 Routledge |  2013 - 7.ª edição | 441 páginas | rar - pdf | 948 kb

link (password: matav)

pdf - 6,8 Mb - link

6.ª edição - 1999

This popular book shows students how to increase their power to analyze problems and comprehend what they read using the Think Aloud Pair Problem Solving [TAPPS] method. First it outlines and illustrates the method that good problem solvers use in attacking complex ideas. Then it provides practice in applying this method to a variety of comprehension and reasoning questions, presented in easy-to-follow steps. As students work through the book they will see a steady improvement in their analytical thinking skills and become smarter, more effective, and more confident problem solvers. Not only can using the TAPPS method assist students in achieving higher scores on tests commonly used for college and job selection, it teaches that problem solving can be fun and social, and that intelligence can be taught.

Changes in the Seventh Edition: New chapter on "open-ended" problem solving that includes inductive and deductive reasoning; extended recommendations to teachers, parents, and tutors about how to use TAPPS instructionally; Companion Website with PowerPoint slides, reading lists with links, and additional problems.

CONTENTS

Preface to the Seventh Edition ix

Preface to the Sixth Edition xi

1. Test Your Mind—See How It Works 1

2. Errors in Reasoning 11

3. Problem-Solving Methods 21

4. Verbal Reasoning Problems 43

5. Six Myths About Reading 139

6 Analogies 143

7. Writing Relationship Sentences 157

8. How to Form Analogies 173

9. Analysis of Trends and Patterns 195

10. Deductive and Hypothetical Thinking Through Days of the Week 223

11. Solving Mathematical Word Problems 241

12. Open-Ended Problem Solving 335

13. The Post-WASI Test 356

14. Meeting Academic and Workplace Standards: How This Book Can Help 364

15. How to Use Pair Problem Solving: Advice for Teachers, Parents, Tutors, and Helpers of All Sorts 383

Appendix 1. Answer Key 400

Appendix 2. Compute Your Own IQ 420

References 421

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

link
password: matav

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

Reading for Evidence and Interpreting Visualizations in Mathematics and Science Education

Stephen P. Norris 

Sense Publishers | 2012 | 209 páginas | pdf | 1,2 Mb

link

CRYSTAL-Alberta was established to research ways to improve students' understanding and reasoning in science and mathematics. To accomplish this goal, faculty members in Education, Science, and Engineering, as well as school teachers joined forces to produce a resource bank of innovative and tested instructional materials that are transforming teaching in the K-12 classroom. Many of the instructional materials cross traditional disciplinary boundaries and explore contemporary topics such as global climate change and the spread of the West Nile virus. Combined with an emphasis on the use of visualizations, the instructional materials improve students' engagement with science and mathematics. Participation in the CRYSTAL-Alberta project has changed the way I think about the connection between what I do as a researcher and what I do as a teacher: I have learned how to better translate scientific knowledge into language and activities appropriate for students, thereby transforming my own teaching. I also have learned to make better connections between what students are learning and what is happening in their lives and the world, thereby increasing students' interest in the subject and enriching their learning experience.

TABLE OF CONTENTS
Acknowledgements vii
I. Introduction
1. CRYSTAL—Alberta: A Case of Science-Science Education Research Collaboration 3
Frank Jenkins and Stephen P. Norris
II. Reading for Evidence
2. Reading for Evidence 19
Susan Barker and Heidi Julien
3. Reading for Evidence through Hybrid Adapted Primary Literature 41
Marie-Claire Shanahan
4. Explanatory Reasoning in Junior High Science Textbooks 65
Jerine Pegg and Simon Karuku
5. The Environment as Text: Reading Big Lake 83
Susan Barker and Carole Newton
III. Visualizations in Science and Mathematics
6. Visualizations and Visualization in Mathematics Education 103
John S. Macnab, Linda M. Phillips, and Stephen P. Norris
7. Visualizations and Visualization in Science Education 123
John Braga, Linda M. Phillips, and Stephen P. Norris
8. Curriculum Development to Promote Visualization and
Mathematical Reasoning: Radicals 147
Elaine Simmt, Shannon Sookochoff, Janelle McFeetors, and Ralph T. Mason
9. Introducing Grade Five Students to the Nature of Models 165
Brenda J. Gustafson and Peter G. Mahaffy
10. Using Computer Visualizations to Introduce Grade Five Students to the Particle Nature of Matter 181
Brenda J. Gustafson and Peter G. Mahaffy
Notes on Contributors 203

Index 207

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

link 
password: mat av

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

Student Voice in Mathematics Classrooms around the World

Berinderjeet Kaur, Glenda Anthony e Minoru Ohtani

Sense Publishers | 2013 | 262 páginas | pdf | 3,2 Mb

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TABLE OF CONTENTS

Acknowledgements ix

1 The Learner’s Perspective Study: Attending to Student Voice

Glenda Anthony, Berinderjeet Kaur, Minoru Ohtani and David Clarke

2 Spoken Mathematics as an Instructional Strategy: The Public Discourse of Mathematics Classrooms in Different Countries

David Clarke, Li Hua Xu and May Ee Vivien Wan

3 Students Speaking Mathematics: Practices and Consequences for Mathematics Classrooms in Different Countries

David Clarke, Li Hua Xu and May Ee Vivien Wan

4 Students at the Front: Examples from a Beijing Classroom 53

Yiming Cao, Kan Guo, Liping Ding and Ida Ah Chee Mok

5 Participation of Students in Content-Learning Classroom Discourse: A Study of Two Grade 8 Mathematics Classes in Singapore

Berinderjeet Kaur

6 Martina’s Voice 89

Florenda Gallos Cronberg and Jonas Emanuelsson

7 What o Students Attend to? Students’ Task-Related Attention in Swedish Settings

Rimma Nyman and Jonas Emanuelsson

8 Students and heir Teacher in a Didactical Situation: A Case Study

Jarmila Novotná and Alena Hospešová

9 Developing Mathematical Proficiency and Democratic Agency through Participation – An Analysis of Teacher Student Dialogues in a Norwegian 9th Grade Classroom

Ole Kristian Bergem and Birgit Pepin

10 Matches or Discrepancies: Student Perceptions and Teacher Intentions in Chinese Mathematics Classrooms

Rongjin Huang and Angela T. Barlow

11 What Really Matters to Students? A Comparison between Hong Kong and Singapore Mathematics Lessons

Ida Ah Chee Mok, Berinderjeet Kaur, Yan Zhu and King Woon Yau

12 Student Perceptions of the ‘Good’ Teacher and ‘Good’ Learner in New Zealand Classrooms

Glenda Anthony

Appendix: The LPS Research Design 227

David Clarke

Author Index 243

Subject Index 247

The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip

Keith Devlin

Basic Books| 2001 | 352 Páginas| EPUB | 0,9 Mb

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Why is math so hard? And why, despite this difficulty, are some people so good at it? If there’s some inborn capacity for mathematical thinking—which there must be, otherwise no one could do it —why can’t we all do it well? Keith Devlin has answers to all these difficult questions, and in giving them shows us how mathematical ability evolved, why it’s a part of language ability, and how we can make better use of this innate talent. He also offers a breathtakingly new theory of language development—that language evolved in two stages, and its main purpose was not communication—to show that the ability to think mathematically arose out of the same symbol-manipulating ability that was so crucial to the emergence of true language. Why, then, can’t we do math as well as we can speak? The answer, says Devlin, is that we can and do—we just don’t recognize when we’re using mathematical reasoning.

Outros livros do mesmo autor, disponíveis no blog:

Mathematics: The New Golden Age, Penguin (1988)
Life by the Numbers, John Wiley & Sons (1998)

The Language of Mathematics: Making the Invisible Visible, W.H. Freeman & Company (1998)

Sets, Functions, and Logic: An Introduction to Abstract Mathematics , CRC (2003)
The Numbers Behind NUMB3RS: Solving Crime with Mathematics, Plume (2007)
The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern, Basic Books (2008)
Mathematics Education for a New Era: Video Games as a Medium for Learning, A K Peters (2011)

Reasoning, Communication And Connections In Mathematics

Yearbook 2012, Association of Mathematics Educators

Berinderjeet Kaur (National Institute of Education, Singapore), 

Tin Lam Toh (National Institute of Education, Singapore)

World Scientific Publishing Company | 2012 | 332 páginas | rar - PDF | 3,6 Mb

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Contents:

Reasoning, Communication and Connections in Mathematics: An Introduction (Berinderjeet KAUR and TOH Tin Lam)
The Epistemic Framing of Mathematical Tasks in Secondary Three Mathematics Lessons in Singapore (Ridzuan Abdul RAHIM, David HOGAN and Melvin CHAN)
Modifying Textbook Exercises to Incorporate Reasoning and Communication into the Primary Mathematics Classroom(Denisse R THOMPSON)
Some “What” Strategies that Advance Reasoning and Communication in Primary Mathematics Classrooms (Berinderjeet KAUR)
Reasoning and Justification in the Secondary Mathematics Classroom (Denisse R THOMPSON)
LOGO Project-Based Mathematics Learning for Communication, Reasoning and Connection (Hee-Chan LEW and In-Ok JANG)
Reasoning, Communication and Connections in A-Level Mathematics (TOH Tin Lam)
Visual and Spatial Reasoning: The Changing Form of Mathematics Representation and Communication (Tom LOWRIE)
Understanding Classroom Talk in Secondary Three Mathematics Classes in Singapore (David HOGAN, Ridzuan Abdul RAHIM, Melvin CHAN, Dennis KWEK and Philip TOWNDROW)
Mathematics Classroom Discourse Through Analogical Reasoning (Kyeong-Hwa LEE)
Students' Reasoning Errors in Writing Proof by Mathematical Induction (Alwyn Wai-Kit PANG and Jaguthsing DINDYAL)
Presenting Mathematics as Connected in the Secondary Classroom (LEONG Yew Hoong)
Numeracy: Connecting Mathematics (Barry KISSANE)
Making Connections Between School Mathematics and the Everyday World: The Example of Health (Marian KEMP)
Mathematics, Astronomy and Culture: Helping Students See Connections (Helmer ASLAKSEN)