International Handbook of Mathematics Education - Part 1

 (Springer International Handbooks of Education)

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

 Springer | 1997 | 1335 páginas | rar -pdf |53,5 Mb

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This Handbook presents an overview and analysis of the international `state-of-the-field' of mathematics education at the end of the 20th century. The more than 150 authors, editors and chapter reviewers involved in its production come from a range of countries and cultures. They have created a book of 36 original chapters in four sections, surveying the variety of practices, and the range of disciplinary interconnections, which characterise the field today, and providing perspectives on the study of mathematics education for the 21st century. It is first and foremost a reference work, and will appeal to anyone seeking up-to-date knowledge about the main developments in mathematics education. These will include teachers, student teachers and student researchers starting out on a serious study of the subject, as well as experienced researchers, teacher educators, educational policy-makers and curriculum developers who need to be aware of the latest areas of knowledge development.

Table of ContentsIntroduction
Alan 1. Bishop
Curriculum, Goals, Contents, Resources
Jeremy Kilpatrick-Section Editor
Introduction to Section 1
Jeremy Kilpatrick
Chapter 1: Goals of Mathematics Teaching 11
Mogens Niss
Chapter 2: Using and Applying Mathematics in Education 49
Jan de Lange
Chapter 3: Number and Arithmetic 99
Lieven Verschaffel and Erik De Corte
Chapter 4: Designing Curricula for Teaching and Learning Algebra 139
Eugenio Filloy. Rosamund Sutherland
Chapter S: Space and Shape 161
Rina Hershkowitz. Bernard Parzysz. and Joop van Dormolen
Chapter 6: Data Handling 20S
J. Michael Shaughnessy. Joan Garfield and Brian Greer
Chapter 7: Probability 239
M Borovcnik and R. Peard
Chapter 8: Functions and Calculus 289
David Tall
Chapter 9: Assessment 327
David Clarke
Chapter 10: 'This is so': a text on texts 371
Eric Love and David Pimm
Chapter 11: Concrete Materials in tbe Classroom 411
Julianna Szendrei
Chapter 12: Calculators in the Mathematics Curriculum: the Scope of Personal Computational Technology 435
Kenneth Ruthven
Chapter 13: Computer-Based Learning Environments in Mathematics 469
Nicolas BalachejJ and James 1. Kaput
Teaching & Learning Mathematics
Colette Laborde - Section Editor
Introduction to Section 2
Colette Laborde
Chapter 14: Elementary School Practices 511
Jerry P. Becker and Christoph Seiter
Chapter 15: Junior Secondary School Practices 565
Antoine Bodin and Bernard Capponi
Chapter 16: Senior Secondary School Practices 615
Lucia Grugnetti and Franfois Jaquet
Chapter 17: Further Mathematics Education 647
Rudolf Striij3er and Robyn Zevenbergen
Chapter 18: Higher Mathematics Education 675
Guershon Harel and Jana TrgaloVii
Chapter 19: Critical Issues in the Distance Teaching of Mathematics and Mathematics Education 701
Stephen Arnold, Christine Shiu and Nerida Ellerton
Chapter 20: Adults and Mathematics (Adult Numeracy) 755
Gail E. FitzSimons and Helga Jungwirth. Juergen Maaj3 and Wolfgang Schloeglmann
Chapter 21: Popularization: Myths, Massmedia and Modernism 785
Paul Ernest
Perspectives & Interdisciplinary Contexts
Ken Clements - Section Editor
Introduction to Section 3
Ken Clements
Chapter 22: Epistemologies of Mathematics and of Mathematics Education
Anna Sierpinska and Stephen Lerman
Chapter 23: Proof and Proving 877
Gila Hanna and H. Niels Jahnke
Chapter 24: Ethnomathematics and Mathematics Education 909
Paulus Gerdes
Chapter 25: Research and Intervention Programs in Mathematics Education: A Gendered Issue
Gilah C. Leder, Helen J. Forgasz and Claudie Solar
Chapter 26: Language Factors in Matbematics Teacbing and Learning 987
Nerida F. Ellerton and Philip C. Clarkson
Cbapter 27: Anthropological Perspectives on Matbematics and Mathematics Education 1035
Bill Barton
Chapter 28: Tbe Role of Tbeory in Matbematics Education and Researcb
John Mason and Andrew Waywood
Social Conditions & Perspectives on Professional Development
Christine Keitel- Section Editor
Introduction to Section 4
Christine Keitel
Chapter 29: Didactics of Matbematics and tbe Professional Knowledge of Teacbers 1097
Paolo Boero, Carlo Dapueto, and Laura Parenti
Chapter 30: Preparing Teachers to Teacb Mathematics:
A Comparative Perspective 1123
Claude Comiti and Deborah Loewenberg Ball
Cbapter 31: In service Matbematics Teacher Education: The Importance of Listening 1155
Thomas J. Cooney and Konrad Krainer
Cbapter 32: Teacbers as Researchers in Mathematics Education 1187
Kathryn Crawford and Jill Adler
Chapter 33: The Mathematics Teacher and Curriculum Development 1207
Barbara Clarke. Doug Clarke. and Peter Sullivan
Chapter 34: International Co-operation in Mathematics Education 1235
Edward Jacobsen
Chapter 35: Critical Mathematics Education 1257
Ole Skovsmose and Lene Nielsen
Chapter 36: Towards Humanistic Mathematics Education 1289
Stephen I. Brown
Name Index 1323
Subject Index 1347


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Third international handbook of mathematics education por M A Clements; et al Idioma: Inglês   Editora: New York : Springer, ©2013

Second international handbook of mathematics education por Alan J Bishop; et al Idioma: Inglês   Editora: Dordrecht ; Boston : Kluwer Academic Publishers, ©2003.

Pluralism in Mathematics: A New Position in Philosophy of Mathematics

Michèle Friend

Springer | 2014 | 297 páginas | rar - pdf | 1,8 Mb

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This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy’s Naturalism, Shapiro’s Structuralism and Formalism.

In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry.

In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a strong warning to treat the word ‘pluralism’ with care.  

Contents
Introduction
Part I. Motivating the Pluralist Position from Familiar Positions
Chapter 1. Introduction. The Journey from Realism to Pluralism
Chapter 2. Motivating Pluralism. Starting from Maddy?s Naturalism
Chapter 3. From Structuralism to Pluralism
Chapter 4. Formalism and Pluralism Co-written with Andrea Pedeferri
Part II. Initial Presentation of Pluralism.-?Chapter 5. Philosophical Presentation of Pluralism
Chapter 6. Using a Formal Theory of Logic Metaphorically
Chapter 7. Rigour in Proof Co-written with Andrea Pedeferri
Chapter 8. Mathematical Fixtures
Part III. Transcendental Presentation of Pluralism
Chapter 9. The Paradoxes of Tolerance and the Transcendental Paradoxes
Chapter 10. Pluralism Towards Pluralism
Part IV. Putting Pluralism to Work. Applications
Chapter 11. A Pluralist Approach to Proof in Mathematics
Chapter 12. Pluralism and Together-Inconsistent Philosophies of Mathematics
Chapter 13. Suggestions for Further Pluralist Enquiry
Conclusion

Oxford Figures. Eight Centuries of the Mathematical Sciences

 

John Fauvel, Raymond Flood e Robin Wilson

OUP Oxford  | 2013 - 2.ª edição | 417 páginas | rar - pdf | 20 Mb

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This is the story of the intellectual and social life of a community, and of its interactions with the wider world. For eight centuries mathematics has been researched and studied at Oxford, and the subject and its teaching have undergone profound changes during that time. This highly readable and beautifully illustrated book reveals the richness and influence of Oxford's mathematical tradition and the fascinating characters that helped to shape it. 
The story begins with the founding of the University of Oxford and the establishing of the medieval curriculum, in which mathematics had an important role. The Black Death, the advent of printing, the Civil War, and the Newtonian revolution all had a great influence on the development of mathematics at Oxford. So too did many well-known figures: Roger Bacon, Henry Savile, Robert Hooke, Christopher Wren, Edmond Halley, Florence Nightingale, Charles Dodgson (Lewis Carroll), and G. H. Hardy, to name but a few. Later chapters bring us to the 20th century, with some entertaining reminiscences by Sir Michael Atiyah of the thirty years he spent as an Oxford mathematician. 
In this second edition the story is brought right up to the opening of the new Mathematical Institute in 2013 with a foreword from Marcus du Sautoy and recent developments from Peter M. Neumann.

CONTENTS
INTRODUCTION 1
Eight centuries of mathematical traditions 3
john fauvel
PART I : EARLY DAYS 35
1. Medieval Oxford 37
john north
2. Renaissance Oxford 51
john fauvel and robert goulding
3. Mathematical instruments 75
willem hackmann
PART II : THE 17TH CENTURY 91
4. The first professors 93
allan chapman
5. John Wallis 115
raymond flood and john fauvel
6. Edmond Halley 141
allan chapman
PART III : THE 18TH CENTURY 165
7. Oxford’s Newtonian school 167
allan chapman
8. Georgian Oxford 181
john fauvel
9. Th omas Hornsby and the Radcliff e Observatory 203
allan chapman
PART IV : THE VICTORIAN ERA 221
10. Th e 19th century 223
keith hannabuss
11. Henry Smith 239
keith hannabuss
12. Charles Dodgson 257
robin wilson
13. James Joseph Sylvester 281
john fauvel
PART V : THE MODERN ERA 303
14. Th e 20th century 305
margaret e. rayner
15. Some personal reminiscences 325
sir michael atiyah
EPILOGUE 335
Recent developments 337
peter m. neumann
Appendix: Oxford’s mathematical Chairs 359

Beginning and Intermediate Algebra: The Language & Symbolism of Mathematics

 James Hall e Brian Mercer

McGraw-Hill Science/Engineering/Math | 2010 - 3ª edição | 1137 páginas | pdf | 18 Mb 

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Beginning and Intermediate Algebra: The Language and Symbolism of Mathematics emphasizes what great mathematicians had identified for generations - mathematics is everywhere! Authors James Hall and Brian Mercer believe active student involvement remains the key to learning algebra. Topics in the text are organized by using the principles of the AMATYC standards as a guide, giving strong support to teachers using the text. The book's organization and pedagogy are designed to work for students with a variety of learning styles and for teachers with varied experiences and backgrounds. The inclusion of the "rule of four" or multiple perspectives -- verbal, numerical, algebraic, and graphical -- has proven popular with a broad cross section of students.

A key supplement for the text are the Lecture Guides. This supplement by the authors, with the assistance of Kelly Bails of Parkland College, provides instructors with the framework of day-by-day class activities for each section in the book. Each lecture guide can help instructors make more efficient use of class time and can help keep students focused on active learning. Students who use the lecture guides have the framework of well-organized notes that can be completed with the instructor in class.

Contents

1 Operations with Real Numbers and a Review of Geome

1.1 Preparing for an Algebra Class 

1.2 The Real Number Line 

1.3 Addition of Real Numbers 

1.4 Subtraction of Real Numbers 

1.5 Multiplication of Real Numbers and Natural Number Exponents 

1.6 Division of Real Numbers 

1.7 Order of Operations 

2 Linear Equations and Patterns 

2.1 The Rectangular Coordinate System and Arithmetic Sequences 

2.2 Function Notation and Linear Functions 

2.3 Graphs of Linear Equations in Two Variables 

2.4 Solving Linear Equations in One Variable by Using the Addition-Subtraction Principle 

2.5 Solving Linear Equations in One Variable by Using the Multiplication-Division Principle 

2.6 Using and Rearranging Formulas 

2.7 Proportions and Direct Variation 

2.8 More Applications of Linear Equations 

3 Lines and Systems of Linear Equations in Two Variables 

3.1 Slope of a Line and Applications of Slope 

3.2 Special Forms of Linear Equations in Two Variables 

3.3 Solving Systems of Linear Equations in Two Variables Graphically and Numerically 

3.4 Solving Systems of Linear Equations in Two Variables by the Substitution Method 

3.5 Solving Systems of Linear Equations in Two Variables by the Addition Method 

3.6 More Applications of Linear Systems

Cumulative Review of Chapters 1-3 

4 Linear Inequalities and Systems of Linear Inequalities 

4.1 Solving Linear Inequalities by Using the Addition-Subtraction Principle

4.2 Solving Linear Inequalities by Using the Multiplication-Divison Principle

4.3 Solving Compound Inequalities 

4.4 Solving Absolute Value Equations and Inequalities 

4.5 Graphing Systems of Linear Inequalities in Two Variables 

5 Exponents and Operations with Polynomials 

5.1 Product and Power Rules for Exponents 

5.2 Quotient Rule and Zero Exponents 

5.3 Negative Exponents and Scientific Notation 

5.4 Adding and Subtracting Polynomials 

5.5 Multiplying Polynomials 

5.6 Special Products of Binomials 

5.7 Dividing Polynomials 

Diagonostic Review of Beginning Algebra 

6 Factoring Polynomials 

6.1 An Introduction to Factoring Polynomials

6.2 Factoring Trinomials of the Form x2 + bxy + cy2 

6.3 Factoring Trinomials of the Form ax2 + bxy + cy2 

6.4 Factoring Special Forms 

6.5 Factoring by Grouping and a General Strategy for Factoring Polynomials 

6.6 Solving Equations by Factoring 

7 Solving Quadratic Equations 

8 Functions: Linear, Absolute Value, and Quadratic

8.1 Functions and Representations of Functions 

8.2 Linear and Absolute Value Functions 

8.3 Linear and Quadratic Functions and Curve Fitting 

8.4 Using the Quadratic Formula to find Real Solutions

8.5 The Vertex of a Parabola and Max-Min Applications 

8.6 More Applications of Quadratic Equations 

8.7 Complex Numbers and Solving Quadratic Equations with Complex Solutions 

9 Rational Functions 

9.1 Graphs of Rational Functions and Reducing Rational Expressions 

9.2 Multiplying and Dividing Rational Expressions 

9.3 Adding and Subtracting Rational Expressions 

9.4 Combining Operations and Simplifying Complex Rational Expressions 

9.5 Solving Equations Containing Rational Expressions 

9.6 Inverse and Joint Variation and Other Applications Yielding Equations with Fractions 

Cumulative Review of Chapters 1-8 

10 Square Root and Cube Root Functions and Rational Exponents

10.1 Evaluating Radical Expressions and Graphs of Square Root and Cube Root Functions 

10.2 Adding and Subtracting Radical Expressions 

10.3 Multiplying and Dividing Radical Expressions 

10.4 Solving Equations Containing Radical Expressions 

10.5 Rational Exponents and Radicals 

11 Exponential and Logarithmic Functions 

11.1 Geometric Sequences Graphs of Exponential Functions

11.2 Inverse Functions 

11.3 Logarithmic Functions 

11.4 Evaluating Logarithms 

11.5 Properties of Logarithms 

11.6 Solving Exponential and Logarithmic Equations 

11.7 Exponential Curve Fitting and Other Applications of Exponential and Logarithmic Equations 

Cumulative Review of Chapters 1-10 

12 A Preview of College Algebra 

12.1 Solving Systems of Linear Equations by Using Augmented Matrices 

12.2 Systems of Linear Equations in Three Variables 

12.3 Horizontal and Vertical Translations of the Graphs of Functions 

12.4 Stretching, Shrinking and Reflecting Graphs of Functions 

12.5 Algebra of Functions 

12.6 Sequences, Series and Summation Notation 

12.7 Conic Sections 

Rhetorical Ways of Thinking: Vygotskian Theory and Mathematical Learning

Lillie R. Albert, Danielle Corea e Vittoria Macadino

Springer | 2012 | páginas |  pdf | 1,2 Mb

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Rhetorical Ways of Thinking focuses on how the co-construction of learning models the interpretation of a mathematical situation. It is a comprehensive examination of the role of sociocultural-historical theory developed by Vygotsky. This book puts forward the supposition that the major assumptions of sociocultural-historic theory are essential to understanding the theory’s application to mathematical pedagogy, which explores issues relevant to learning and teaching mathematics-in-context, thus providing a valuable practical tool for general mathematics education research. The most important goal, then, is to exemplify the merging of the theory with practice and the subsequent applications to mathematics teaching and learning. This monograph contains five chapters, including a primer to Vygotsky’s sociocultural historic theory, three comprehensive empirical studies examining:  prospective teachers’ perception of mathematics teaching and learning and the practice of scaffolded instruction to assist practicing teachers in developing their understanding of pedagogical content knowledge. Finally, the book concludes with a contextualization of the theory, linking it to best practices in the classroom.​​

Contents
Introduction
Vygotsky's Sociocultural Historic Theory, A Primer
Images and Drawings: A Study of Prospective Teachers' Perceptions of Teaching and Learning Mathematics
Improving Teachers' Mathematical Content Knowledge Through Scaffolded Instruction
Closing Thoughts and Implications.

The Secrets of Triangles: A Mathematical Journey

Alfred S. Posamentier e Ingmar Lehmann 

Prometheus Books | 2012 | 387 páginas | rar - epub |9,9 Mb

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Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure holds many intriguing "secrets." For example, if a circle is inscribed in any random triangle and then three lines are drawn from the three points of tangency to the opposite vertices of the triangle, these lines will always meet at a common point - no matter what the shape of the triangle. This and many more interesting geometrical properties are revealed in this entertaining and illuminating book about geometry. Flying in the face of the common impression that mathematics is usually dry and intimidating, this book proves that this sometimes-daunting, abstract discipline can be both fun and intellectually stimulating. 
The authors, two veteran math educators, explore the multitude of surprising relationships connected with triangles and show some clever approaches to constructing triangles using a straightedge and a compass. Readers will learn how they can improve their problem-solving skills by performing these triangle constructions. The lines, points, and circles related to triangles harbor countless surprising relationships that are presented here in a very engaging fashion.
Requiring no more than a knowledge of high school mathematics and written in clear and accessible language, this book will give all readers a new insight into some of the most enjoyable and fascinating aspects of geometry. 

Contents
Acknowledgments
Preface
1. Introduction to the Triangle
2. Concurrencies of a Triangle
3. Noteworthy Points in a Triangle
4. Concurrent Circles of a Triangle
5. Special Lines of a Triangle
6. Useful Triangle Theorems
7. Areas of and within Triangles
8. Triangle Constructions
9. Inequalities in a Triangle
10. Triangles and Fractals
Appendix

The Universal History of Computing: From the Abacus to the Quantum Computer

Georges Ifrah

Wiley | 2001 | 413 páginas

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"A fascinating compendium of information about writing systems–both for words and numbers."

"A truly enlightening and fascinating study for the mathematically oriented reader."

"Well researched. . . . This book is a rich resource for those involved in researching the history of computers."

In this brilliant follow-up to his landmark international bestseller, The Universal History of Numbers, Georges Ifrah traces the development of computing from the invention of the abacus to the creation of the binary system three centuries ago to the incredible conceptual, scientific, and technical achievements that made the first modern computers possible. Ifrah takes us along as he visits mathematicians, visionaries, philosophers, and scholars from every corner of the world and every period of history. We learn about the births of the pocket calculator, the adding machine, the cash register, and even automata. We find out how the origins of the computer can be found in the European Renaissance, along with how World War II influenced the development of analytical calculation. And we explore such hot topics as numerical codes and the recent discovery of new kinds of number systems, such as "surreal" numbers.

Adventurous and enthralling, The Universal History of Computing is an astonishing achievement that not only unravels the epic tale of computing, but also tells the compelling story of human intelligence–and how much further we still have to go.