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

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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.

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

Mathematics Tomorrow

Lynn A. Steen


Springer | 1981 | 244 páginas | pdf |6,9 Mb

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Contents
Introduction ... 1
What Is Mathematics?
Applied Mathematics Is Bad Mathematics
Paul R. Halmos ... 9
Solving Equations Is Not Solving Problems
Jerome Spanier... 21
The Unexpected Art of Mathematics
Jerry P. King .. 29
Redefining the Mathematics Major
Alan Tucker ... 39
Purity in Applications
Tim Poston .... 49
Growth and New Intuitions: Can We Meet the Challenge?
William F. Lucas ... 55
Teaching and Learning Mathematics
A voiding Math Avoidance
Peter J. Hilton. . 73
Learning Mathematics
Anneli Lax and Giuliana Groat 83
Teaching Mathematics
Abe Shenitzer .... 95
Read the Masters!
Harold M. Edwards .... 105
Mathematics as Propaganda
Neal Koblitz .. 111
Mathematicians Love Books
Walter Kaufmann-Buhler, Alice Peters, and Klaus Peters .. 121
A Faculty in Limbo
Donald J. Albers
Junior's All Grown Up Now
George M. Miller..... 135
NSF Support for Mathematics Education
E. P. Miles. Jr... 139
Issues of Equality
The Real Energy Crisis
Eileen L. Poiani ... 155
Women and Mathematics
Alice T. Schafer .... 165
Spatial Separation in Family Life: A Mathematician's Choice
Marian Boykan Pour-EI .... 187
Mathematics for Tomorrow
Applications of Undergraduate Mathematics
Ross L. Finney ... 197
The Decline of Calculus-The Rise of Discrete Mathematics
Anthony Ralston .. 213
Mathematical Software: How to Sell Mathematics
Paul T. Boggs.. 221
Physics and Mathematics
Hartley Rogers. Jr.
Readin', 'Ritin', and Statistics
Tim Robertson and Robert V. Hogg
Mathematization in the Sciences
Maynard Thompson ... 243

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.

Founding Figures and Commentators in Arabic Mathematics: A History of Arabic Sciences and Mathematics - Volume 1

 

Roshdi Rashed e Nader El-Bizri

Routledge |  2011 | 813 páginas | rar - pdf | 4,2 Mb

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In this unique insight into the history and philosophy of mathematics and science in the mediaeval Arab world, the eminent scholar Roshdi Rashed illuminates the various historical, textual and epistemic threads that underpinned the history of Arabic mathematical and scientific knowledge up to the seventeenth century. The first of five wide-ranging and comprehensive volumes, this book provides a detailed exploration of Arabic mathematics and sciences in the ninth and tenth centuries.

Extensive and detailed analyses and annotations support a number of key Arabic texts, which are translated here into English for the first time. In this volume Rashed focuses on the traditions of celebrated polymaths from the ninth and tenth centuries ‘School of Baghdad’ - such as the Banū Mūsā, Thābit ibn Qurra, Ibrāhīm ibn Sinān, Abū Ja´far al-Khāzin, Abū Sahl Wayjan ibn Rustām al-Qūhī - and eleventh-century Andalusian mathematicians like Abū al-Qāsim ibn al-Samh, and al-Mu’taman ibn Hūd. The Archimedean-Apollonian traditions of these polymaths are thematically explored to illustrate the historical and epistemological development of ‘infinitesimal mathematics’ as it became more clearly articulated in the eleventh-century influential legacy of al-Hasan ibn al-Haytham (‘Alhazen’).

Contributing to a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context, this fundamental text will appeal to historians of ideas, epistemologists, mathematicians at the most advanced levels of research.

CONTENTS

Editor’s Foreword .......... xiii

Preface........ xix

Note ......... xxiv

CHAPTER I : BANU MUSA AND THE CALCULATION OF THE VOLUME OF THE SPHERE AND THE CYLINDER

1.1. INTRODUCTION ....... 1

1.1.1. The Banu Musa: dignitaries and learned ..... 1

1.1.2. The mathematical works of the Banu Musa ....... 7

1.1.3. Treatise on the measurement of plane and spherical figures: a Latin translation and a rewritten version by al-Tusî ...... 10

1.1.4. Title and date of the  Banu Musa treatise .......... 34

1.2. MATHEMATICAL COMMENTARY .......... 38

1.2.1. Organization and structure of the Banu Musa book ..... 38

1.2.2. The area of the circle ......... 40

1.2.3. The area of the triangle and Hero’s formula ..... 46

1.2.4. The surface area of a sphere and its volume ...... 47

1.2.5. The two-means problem and its mechanical construction ...... 60

1.2.6a. The trisection of angles and Pascal’s Limaçon ........... 66

1.2.6b. Approximating cubic roots ..... 69

1.3. TRANSLATED TEXT: On the Knowledge of the Measurement of Plane and Spherical Figures.... 73

CHAPTER II: THABIT IBN QURRA AND HIS WORKS IN INFINITESIMAL MATHEMATICS

2.1. INTRODUCTION ............ 113

2.1.1. Thabit ibn Qurra: from Harran to Baghdad ............ 113

2.1.2. The works of Thabitibn Qurra in infinitesimal mathematics ....... 122

2.1.3. History of the texts and their translations ....... 124

2.2. MEASURING THE PARABOLA ........ 130

2.2.1. Organization and structure of Ibn Qurra’s treatise ......... 130

2.2.2. Mathematical commentary ....... 133

2.2.2.1. Arithmetical propositions ......... 133

2.2.2.2. Sequence of segments and bounding ...... 142

2.2.2.3. Calculation of the area of a portion of a parabola ......... 154

2.2.3. Translated text: On the Measurement of the Conic Section Called Parabola .. 169

2.3. MEASURING THE PARABOLOID ... 209

2.3.1. Organization and structure of Ibn Qurra’s treatise ... 209

2.3.2. Mathematical commentary ....... 214

2.3.2.1. Arithmetical propositions ..... 214

2.3.2.2. Extension to sequences of segments ...... 218

2.3.2.3. Volumes of cones, rhombuses and other solids ..... 223

2.3.2.4. Property of four segments ........ 230

2.3.2.5. Arithmetical propositions ... 231
2.3.2.6. Sequence of segments and bounding ..... 233
2.3.2.7. Calculation of the volumes of paraboloids ...... 244
2.3.2.8. Parallel between the treatise on the area of the parabola and the treatise on the volume of the paraboloid ....256
2.3.3. Translated text: On the Measurement of the Paraboloids .... 261
2.4. ON THE SECTIONS OF THE CYLINDER AND ITS LATERAL SURFACE .... 333
2.4.1. Introduction ...... 333
2.4.2. Mathematical commentary ........ 337
2.4.2.1. Plane sections of the cylinder . 337
2.4.2.2. Area of an ellipse and elliptical sections . 341
2.4.2.3. Concerning the maximal section of the cylinder and concerning its minimal sections .... 356
2.4.2.4. Concerning the lateral area of the cylinder and the lateral area of portions of the cylinder lying between the plane sections touching all sides ..... 363
2.4.3. Translated text: On the Sections of the Cylinder and its Lateral Surface . 381
CHAPTER III: IBN SINAN, CRITIQUE OF AL-MAHANï: THE AREA OF THE PARABOLA
3.1. INTRODUCTION ................. 459
3.1.1. Ibrahîm ibn Sinan: ‘heir’ and ‘critic’ .... 459
3.1.2. The two versions of The Measurement of the Parabola: texts and translations . 463
3.2. MATHEMATICAL COMMENTARY ....... 466
3.3. TRANSLATED TEXTS
3.3.1. On the Measurement of the Parabola .... 483
3.3.2. On the Measurement of a Portion of the Parabola ......... 495
CHAPTER IV: ABU JA‘FAR AL-KHAZIN: ISOPERIMETRICS AND ISEPIPHANICS
4.1. INTRODUCTION ... 503
4.1.1. Al-Khazin: his name, life and works ...... 503
4.1.2. The treatises of al-Khazin on isoperimeters and isepiphanics... 506
4.2. MATHEMATICAL COMMENTARY ..... 507
4.2.1. Introduction ..... 507
4.2.2. Isoperimetrics ... 509
4.2.3. Isepiphanics ....... 524
4.2.4. The opuscule of al-Sumaysa†î ... 546
4.3. TRANSLATED TEXTS
4.3.1. Commentary on the First Book of the Almagest ..... 551
4.3.2. The Surface of any Circle is Greater than the Surface of any Regular Polygon with the Same Perimeter (al-Sumaysa†î) ... 577
CHAPTER V: AL-QUHï, CRITIQUE OF THABIT: VOLUME OF THE PARABOLOID OF REVOLUTION
5.1. INTRODUCTION ........ 579
5.1.1. The mathematician and the artisan ...... 579
5.1.2. The versions of the volume of a paraboloid... 583
5.2. MATHEMATICAL COMMENTARY ... 588
5.3. TRANSLATION TEXTS
5.3.1. On the Determination of the Volume of a Paraboloid .. 599
5.3.2. On the Volume of a Paraboloid .... 609
CHAPTER VI: IBN AL-SAMÎ: THE PLANE SECTIONS OF A CYLINDER AND THE DETERMINATION OF THEIR AREAS
6.1. INTRODUCTION ...... 615
6.1.1. Ibn al-SamÌ and Ibn Qurra, successors to al-Îasan ibn Musa ..... 615
6.1.2. Serenus of Antinoupolis, al-Îasæn ibn Musa , Thabit ibn Qurra and Ibn al-SamÌ ... 618
6.1.3. The structure of the study by Ibn al-SamÌ ..... 622
6.2. MATHEMATICAL COMMENTARY .. 623
6.2.1. Definitions and accepted results ... 623
6.2.2. The cylinder .... 626
6.2.3. The plane sections of a cylinder ....... 627
6.2.4. The properties of a circle ...... 628
6.2.5. Elliptical sections of a right cylinder .... 632
6.2.6. The ellipse as a plane section of a right cylinder .. 639
6.2.7. The area of an ellipse ......... 645
6.2.8. Chords and sagittas of the ellipse ....... 653
6.3. TRANSLATED TEXT: On the Cylinder and its Plane Section ........... 667
CHAPTER VII: IBN HUD: THE MEASUREMENT OF THE PARABOLA AND THE ISOPERIMETRIC PROBLEM
7.1. INTRODUCTION ...... 721
7.1.1. Kitab al-Istikmal, a mathematical compendium ....... 721
7.1.2. Manuscript transmission of the texts .......... 727
7.2. THE MEASUREMENT OF THE PARABOLA ...... 729
7.2.1. Infinitesimal property or conic property ...... 729
7.2.2. Mathematical commentary on Propositions 18–21 ..... 733
7.2.3. Translation: Kitab al-Istikmal........ 749
7.3. THE ISOPERIMETRIC PROBLEM ........... 755
7.3.1. An extremal property or a geometric property ...... 755
7.3.2. Mathematical commentary on Propositions 16 and 19 ..... 758
7.3.3. Translation: Kitab al-Istikmal...... 764
SUPPLEMENTARY NOTES
The Formula of Hero of Alexandria according to Thæbit ibn Qurra.... 767
Commentary of Ibn Abî Jarræda on The Sections of the Cylinder by Thabit ibn Qurra .767
BIBLIOGRAPHY .............. 779
INDEXES
Index of names .... 793
Subject index ........ 797
Index of works .......... 805

Outro livro da mesma colecção:

Ibn al-Haytham's theory of conics, geometrical constructions and practical geometry : a history of Arabic sciences and mathematics. Volume 3 por Rushdī Rāshid; Judith Veronica Field Idioma: Inglês   Editora: London : Routledge, 2013.

A History of Ancient Mathematical Astronomy

 (Studies in the History of Mathematics and Physical Sciences) 

O. Neugebauer

Springer | 2013 | reprint of the original 1st ed. 1975 edition | páginas | rar - pdf | 23,8 Mb

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"This monumental work will henceforth be the standard interpretation of ancient mathematical astronomy. It is easy to point out its many virtues: comprehensiveness and common sense are two of the most important. Neugebauer has studied profoundly every relevant text in Akkadian, Egyptian, Greek, and Latin, no matter how fragmentary; [...] With the combination of mathematical rigor and a sober sense of the true nature of the evidence, he has penetrated the astronomical and the historical significance of his material. [...] His work has been and will remain the most admired model for those working with mathematical and astronomical texts.

D. Pingree in Bibliotheca Orientalis, 1977

"... a work that is a landmark, not only for the history of science, but for the history of scholarship. HAMA [History of Ancient Mathematical Astronomy] places the history of ancient Astronomy on a entirely new foundation. We shall not soon see its equal.

N.M. Swerdlow in Historia Mathematica, 1979

Geometry and Algebra in Ancient Civilizations

Bartel L. van der Waerden 

Springer | 2011 - reprint of the original 1st ed. 1983 edition |235 páginas | rar - pdf | 5,3 Mb

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Contents
1. Pythagorean Triangles.
A. Written Sources.Fundamental Notions.- The Text Plimpton 322.- A Chinese Method.- Methods Ascribed to Pythagoras and Plato.- Pythagorean Triples in India.- The Hypothesis of a Common Origin.- Geometry and Ritual in Greece and India.- Pythagoras and the Ox. B. Archaeological Evidence.Prehistoric Ages.- Radiocarbon Dating.- Megalithic Monuments in Western Europe.- Pythagorean Triples in Megalithic Monuments.- Megalith Architecture in Egypt.- The Ritual Use of Pythagorean Triangles in India.- C. On Proofs, and on the Origin of Mathematics.Geometrical Proofs.- Euclid’s Proof.- Naber’s Proof.- Astronomical Applications of the Theorem of Pythagoras?.- Why Pythagorean Triangles?.- The Origin of Mathematics.- 
2. Chinese and Babylonian Mathematics 
A. Chinese Mathematics.The Chinese “Nine Chapters”.- The Euclidean Algorithm.- Areas of Plane Figures.- Volumes of Solids.- The Moscow Papyrus.- Similarities Between Ancient Civilizations.- Square Roots and Cube Roots.- Sets of Linear Equations.- Problems on Right-Angled Triangles.- The Broken Bamboo.- Two Geometrical Problems.- Parallel Lines in Triangles. B. Babylonian Mathematics.A Babylonian Problem Text.- Quadratic Equations in Babylonian Texts.- The Method of Elimination.- The “Sum and Difference” Method.C. General Conclusions.Chinese and Babylonian Algebra Compared.- The Historical Development.
3. Greek Algebra
What is Algebra?.- The Role of Geometry in Elementary Algebra.- Three Kinds of Algebra.- On Units of Length, Area, and Volume.- Greek “Geometric Algebra”.- Euclid’s Second Book.- The Application of Areas.- Three Types of Quadratic Equations.- Another Concordance Between the Babylonians and Euclid.- An Application of II, 10 to Sides and Diagonals.- Thales and Pythagoras.- The Geometrization of Algebra.- The Theory of Proportions.- Geometric Algebra in the “Konika” of Apollonios.- The Sum of a Geometrical Progression.- Sums of Squares and Cubes.
4. Diophantos and his Predecessors.
A. The Work of Diophantos.Diophantos’ Algebraic Symbolism.- Determinate and Indeterminate Problems.- From Book A.- From Book B.- The Method of Double Equality.From Book ?.- From Book 4.- From Book 5.- From Book 7.- From Book ?.- From Book E.- B. The Michigan Papyrus 620.- C. Indeterminate Equations in the Heronic Collections.
5. Diophantine Equations.
A. Linear Diophantine Equations.Aryabhata’s Method.- Linear Diophantine Equations in Chinese Mathematics.- The Chinese Remainder Problem.- Astronomical Applications of the Pulverizer.- Aryabhata’s Two Systems.- Brahmagupta’s System.- The Motion of the Apogees and Nodes.- The Motion of the Planets.- The Influence of Hellenistic Ideas.B. PelVs Equation.The Equation x2= 2y2±l.- Periodicity in the Euclidean Algorithm.- Reciprocal Subtraction.- The Equations x2= 3y2 +1 and x2= 3y2— 2.- Archimedes’ Upper and Lower Limits for w3.- Continued Fractions.- The Equation x2= Dy2± 1 for Non-squareD.- Brahmagupta’s Method.- The Cyclic Method.- Comparison Between Greek and Hindu Methods.C. Pythagorean Triples
6. Popular Mathematics
A. General Character of Popular Mathematics.B. Babylonian, Egyptian and Early Greek ProblemsTwo Babylonian Problems.- Egyptian Problems.- The “Bloom of Thymaridas”.C. Greek Arithmetical EpigramsD. Mathematical Papyri from Hellenistic Egypt.Calculations with Fractions.- Problems on Pieces of Cloth.- Problems on Right-Angled Triangles.- Approximation of Square Roots.- Two More Problems of Babylonian Type.- E. Squaring the Circle and Circling the SquareAn Ancient Egyptian Rule for Squaring the Circle.- Circling the Square as a Ritual Problem.- An Egyptian Problem.- Area of the Circumscribed Circle of a Triangle.- Area of the Circumscribed Circle of a Square.- Three Problems Concerning the Circle Segment in a Babylonian Text.- Shen Kua on the Arc of a Circle Segment.F. Heron of Alexandria.The Date of Heron.- Heron’s Commentary to Euclid.- Heron’s Metrika.- Circles and Circle Segments.- Apollonios’ Rapid Method.- Volumes of Solids.- Approximating a Cube RootG. The Mishnat ha-Middot.
7. Liu Hui and Aryabhata.
A. The Geometry of Liu Hui.The “Classic of the Island in the Sea”.- First Problem: The Island in the Sea.- Second Problem: Height of a Tree.- Third Problem: Square Town.- The Evaluation of ?.- The Volume of a Pyramid.- Liu Hui and Euclid.- Liu Hui on the Volume of a Sphere.B. The Mathematics of Aryabhata.Area and Circumference of a Circle.- Aryabhata’s Table of Sines.- On the Origin of Aryabhata’s Trigonometry.- Apollonios and Aryabhata as Astronomers.- On Gnomons and Shadows.- Square Roots and Cube Roots.- Arithmetical Progressions and Quadratic Equations.