Mathematical reasoning for elementary teachers

 Calvin T. Long, Duane W. DeTemple e Richard S. Millman

Pearson | 2011 -6ª edição |  949 páginas | rar - pdf | 21,5 Mb

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Mathematical Reasoning for Elementary Teachers presents the mathematical knowledge needed for teaching, with an emphasis on whyfuture teachers are learning the content as well as when and how they will use it in the classroom. The Sixth Edition has been streamlined to make it easier to focus on the most important concepts. The authors continue to make the course relevant for future teachers, including the new features like Examining School Book Pages, as well as the hallmark features like Into the Classroom discussions and Responding to Students questions. Activities, classroom videos, and resources for professional development for future teachers are also available at www.pearsonhighered.com/teachingmath

Table of Contents
1. Thinking Critically
1.1 An Introduction to Problem Solving
1.2 Pólya's Problem-Solving Principles
1.3 More Problem-Solving Strategies
1.4 Algebra as a Problem-Solving Strategy
1.5 Additional Problem-Solving Strategies
1.6 Reasoning Mathematically
2. Sets and Whole Numbers
2.1 Sets and Operations on Sets
2.2 Sets, Counting, and the Whole Numbers
2.3 Addition and Subtraction of Whole Numbers
2.4 Multiplication and Division of Whole Numbers
3. Numeration and Computation
3.1 Numeration Systems Past and Present
3.2 Nondecimal Positional Systems
3.3 Algorithms for Adding and Subtracting Whole Numbers
3.4 Algorithms for Multiplication and Division of Whole Numbers
3.5 Mental Arithmetic and Estimation
4. Number Theory
4.1 Divisibility of Natural Numbers
4.2 Tests for Divisibility
4.3 Greatest Common Divisors and Least Common Multiples
5. Integers
5.1 Representations of Integers
5.2 Addition and Subtraction of Integers
5.3 Multiplication and Division of Integers
6. Fractions and Rational Numbers
6.1 The Basic Concepts of Fractions and Rational Numbers
6.2 Addition and Subtraction of Fractions
6.3 Multiplication and Division of Fractions
6.4 The Rational Number System
7. Decimals, Real Numbers, and Proportional Reasoning
7.1 Decimals and Real Numbers
7.2 Computations with Decimals
7.3 Proportional Reasoning
7.4 Percent
8. Algebraic Reasoning and Connections with Geometry
8.1 Algebraic Expressions, Functions, and Equations
8.2 Graphing Points, Lines, and Elementary Functions
8.3 Connections Between Algebra and Geometry
9. Geometric Figures
9.1 Figures in the Plane
9.2 Curves and Polygons in the Plane
9.3 Figures in Space
9.4 Networks
10. Measurement: Length, Area, and Volume
10.1 The Measurement Process
10.2 Area and Perimeter
10.3 The Pythagorean Theorem
10.4 Surface Area and Volume
11. Transformations, Symmetries, and Tilings
11.1 Rigid Motions and Similarity Transformations
11.2 Patterns and Symmetries
11.3 Tilings and Escher-like Designs
12. Congruence, Constructions, and Similarity
12.1 Congruent Triangles
12.2 Constructing Geometric Figures
12.3 Similar Triangles
13. Statistics: The Interpretation of Data
13.1 Organizing and Representing Data
13.2 Measuring the Center and Variation of Data
13.3 Statistical Inference
14. Probability
14.1 Experimental Probability
14.2 Principles of Counting
14.3 Permutations and Combinations
14.4 Theoretical Probability
Appendices
A. Manipulatives in the Mathematics Classroom
B. Getting the Most out of Your Calculator
C. A Brief Guide to the Geometer's Sketchpad
D. Resources

Women and Mathematics: Balancing the Equation

Susan F. Chipman, Lorelei R. Brush e Donna M. Wilson

Psychology Press | 1985 | 396 páginas | rar - pdf | Mb

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Contents
Foreword
1. Women’s Participation in Mathematics: Outlining the Problem
Susan F. Chipman and Veronica G. Thomas
2. Project TALENT: Mathematics Course Participation in the 1960s and its Career Consequences
Lauress L. Wise
3. A National Assessment of Participation and Achievement of Women in Mathematics
Jane M. Armstrong
4. Self-Perceptions, Task Perceptions, Socializing Influences, and the Decision to Enroll in Mathematics Jacquelynne Eccles (Parsons), Terry F. Adler, Robert Futterman, Susan B. Goff, Caroline M. Kaczala, Judith L. Meece, and Carol Midgley
5. Cognitive and Affective Determinants of Course Preferences and Plans
Lorelei ft. Brush
6. Visual-Spatial Skill: Is it Important for Mathematics? Can it be Taught?
Jane M. Connor and Lisa A. Serbin
7. The Influence of Sex-Role Stereotyping on Women’s
Attitudes and Achievement in Mathematics
Sally L. Boswell
8. School, Classroom, and Home Influences on Women’s Decisions to Enroll in Advanced Mathematics Courses
Jane Stallings
9. Factors Related to Young Women’s Persistence and Achievement in Advanced Placement Mathematics
Patricia L. Casserly and Donald Rock
10. The Impact of Early Intervention Programs Upon Course-Taking and Attitudes in High School
Lynn H. Fox, Linda Brody, and Dianne Tobin
11. Understanding Mathematics Course Enrollment and Mathematics Achievement: A Synthesis of the Research
Susan F. Chipman and Donna M. Wilson
12. Strategies to Increase Mathematics Enrollments
Alma Lantz
References
Author Index
Subject Index 375

The Genius of Archimedes - 23 Centuries of Influence on Mathematics, Science and Engineering:

S. A. Paipetis e Marco Ceccarelli

Springer |2010 | 526 páginas | pdf | 16 MB
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Archimedes is held in high esteem by mathematicians, physicists and engineers as one of the most brilliant scientists of all time. These proceedings contain original, unpublished papers with the primary emphasis on the scientific work of Archimedes and his influence on the fields of mathematics, science, and engineering. There are also papers dealing with archaeological aspects and the myths and legends about Archimedes and about the Archimedes Palimpsest. Papers on the following subjects form part of the book: Hydrostatics (buoyancy, fluid pressure and density, stability of floating bodies); Mechanics (levers, pulleys, centers of gravity, laws of equilibrium); Pycnometry (measurement of volume and density); Integral Calculus (Archimedes as the father of the integral calculus, method of exhaustion, approximation of pi, determination of areas and volumes); Mathematical Physics (Archimedes as the father of mathematical physics, Law of the Lever, Law of Buoyancy, Axiomatization of Physics); History of Mathematics and Mechanics (Archimedes' influence in antiquity, the middle ages, the Renaissance, and modern times; his influence on Leonado da Vinci, Galileo, Newton, and other giants of science and mathematics); Ancient Machines and Mechanisms (catapults, water screws, iron hands, compound pulleys, planetaria, water clocks, celestial globes, the Antikythera Mechanism); Archimedean Solids (their rediscovery in the Rennaisance and their applications in materials science and chemistry); Archimedean Legends (how stories of golden crowns, eureka moments, naked runs, burning mirrors, steam cannons, etc., have influenced us through the ages, whether true or not); The Cattle Problem (how its 18th century rediscovery inspired the study of equations with integer solutions); Teaching the Ideas of Archimedes (how his life and works have influenced the teaching of science, mathematics, and engineering).

TABLE OF CONTENTS
Preface v
1. Legacy and Influence in Mathematics 1
An Archimedean Research Theme: The Calculation of the Volume of Cylindrical Groins 3
Nicla Palladino
On Archimedean Roots in Torricelli’s Mechanics 17
Raffaele Pisano and Danilo Capecchi
Rational Mechanics and Science Rationnelle Unique
Johan Gielis, Diego Caratelli, Stefan Haesen and Paolo E. Ricci
Archimedes and Caustics: A Twofold Multimedia and Experimental Approach 45
Assunta Bonanno, Michele Camarca, Peppino Sapia and Annarosa Serpe
Archimedes’ Quadratures 57
Jean Christianidis and Apostolos Demis
On Archimedes’ Pursuit Concerning Geometrical Analysis 69
Philippos Fournarakis and Jean Christianidis
2. Legacy and Influence in Engineering and Mechanisms Design 83
Simon Stevin and the Rise of Archimedean Mechanics in the Renaissance 85
Teun Koetsier
Archimedes’ Cannons Against the Roman Fleet? 113
Cesare Rossi
V-Belt Winding Along Archimedean Spirals During the Variator Speed Ratio Shift 133
Francesco Sorge
Ancient Motors for Siege Towers 149
C. Rossi, S. Pagano and F. Russo
From Archimedean Spirals to Screw Mechanisms – A Short Historical Overview 163
Hanfried Kerle and Klaus Mauersberger
The Mechanics of Archimedes Towards Modern Mechanism Design 177
Marco Ceccarelli
Archimedean Mechanical Knowledge in 17th Century China 189
Zhang Baichun and Tian Miao
Archimedes Arabicus. Assessing Archimedes’ Impact on Arabic
Mechanics and Engineering 207
3. Legacy and Influence in Hydrostatics 213
The Golden Crown: A Discussion 215
Felice Costanti
The Heritage of Archimedes in Ship Hydrostatics: 2000 Years from Theories to Applications 227
Horst Nowacki
Notes on the Syrakosia and on Archimedes’ Approach to the Stability of Floating Bodies 251
Marco Bonino
What Did Archimedes Find at “Eureka” Moment? 265
Kuroki Hidetaka
Floatability and Stability of Ships: 23 Centuries after Archimedes 277
Alberto Francescutto and Apostolos D. Papanikolaou
The “Syrakousia” Ship and the Mechanical Knowledge between Syracuse and Alexandria 289
Giovanni Di Pasquale
4. Legacy and Influence in Philosophy 303
Browsing in a Renaissance Philologist’s Toolbox: Archimedes’ Rule 305
Nadia Ambrosetti
Mathematician, Anti-Platonic and Anti-Aristotelian Philosopher 313
Giuseppe Boscarino
Archimedes to Eratosthenes: “Method for Mechanical Theorems” 323
Roberto Bragastini
Archimedes in Seventeenth Century Philosophy 331
Epaminondas Vampoulis
5. Legacy and Influence in Science and Technology 345
Cross-Fertilisation of Science and Technology in the Time of Archim d s 347
Theodossios P. Tassios
Archimedes in Ancient Roman World 361
Mario Geymonat
Archimedes: Russian Researches 369
Alexander Golovin and Anastasia Golovina
Archimedean Science and the Scientific Revolution 377
Agamenon R.E. Oliveira
Archimedes’ Burning Mirrors: Myth or Reality? 387
Adel Valiullin and Valentin Tarabarin
The Influence of Archimedes in the Machine Books from Renaissance to the 19th Century 397
Francis C. Moon
Archimedes Influence in Science and Engineering 411
Thomas G. Chondros
6. Legacy and Influence in Teaching and History Aspects 427
The Founder-Cult of Hieron II at Akrai: The Rock-Relief from Intagliatella’s latomy 429
Paolo Daniele Scirpo
Archimedes: Russian Editions of Works 439
Alexander Golovin and Anastasia Golovina
Archimedes in Program on History of Mechanics in Lomonosov Moscow St. University 459
Irina Tyulina and Vera Chinenova
Archimedes Discovers and Inventions in the Russian Education 469
Philip Bocharov, Kira Matveeva and Valentin Tarabarin
Archimedes in Secondary Schools: A Teaching Proposal for the Math Curriculum 479
Francesco A. Costabile and Annarosa Serpe
Mechanical Advantage: The Archimedean Tradition of acquiring Geometric Insight form Mechanical Metaphor 493
Vincent De Sapio and Robin De Sapio
The Death of Archimedes: A Reassessment
Cettina Voza

Africa Counts: Number and Pattern in African Cultures

Claudia Zaslavsky 

Chicago Review Press | 1999 - 3ª edição | 369 páginas | rar - pdf | 10 Mb

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This fascinating study of mathematical thinking among sub-Saharan African peoples covers counting in words and in gestures; measuring time, distance, weight, and other quantities; manipulating money and keeping accounts; number systems; patterns in music, poetry, art, and architecture; and number magic and taboos. African games such as mankala and elaborate versions of tic-tac-toe show how complex this thinking can be. An invaluable resource for students, teachers, and others interested in African cultures and multiculturalism, this third edition is updated with an introduction covering two decades of new research in the ethnomathematics of Africa.

CONTENTS
SECTION 1 THE BACKGROUND
1 African Mathematics? 6
2 Historical Background 17
SECTION 2 NUMBERS-WORDS, GESTURES, SIGNIFICANCE 29
3 Construction of Numeration Systems 32
4 How Africans Count 39
5 Taboos and Mysticism 52
SECTION 3 NUMBERS IN DAILY LlEE 59
6 The African Concept of Time 62
7 Numbers and Money 67
8 Those Familiar Weights and Measures! 84
9 Record-Keeping: Sticks and Strings 93
SECTION 4 MATHEMATICAL RECREATIONS 99
10 Games to Grow On 102
11 The Game Played by Kings and Cowherds—and Presidents, Too! 116
12 Magic Squares 137
SECTION 5
13 Geometric Form in Architecture 155
14 Part I: Geometric Form and Pattern in Art 172
15 Part II: Geometric Symmetries in African Art, By D. W. Crowe, with Original Drawings 190
SECTION 6 REGIONAL STUDY: SOUTHWEST NIGERIA
15 History of the Yoruba States and Benin 200
16 Systems of Numeration 204
17 Significant Numbers 213
18 Time-Reckoning 221
19 Markets and Currency 224
SECTION 7 REGIONAL STUDY: EAST AFRICA 231
20 History of East Africa 234
21 Spoken and Gesture Counting 238
22 Number Superstitions 255
23 East African Time 259
24 Wealth Means Cattle—and Other Livestock 266
SECTION 8 PAST AND FUTURE 271
25 Pure Mathematics in Africa 273
26 Update: Twenty-Five Years Later 280

Mathematical Puzzles of Sam Loyd

Sam Loyd e Martin Gardner

Dover Publications | 1959 | páginas | djvu | 3,4 Mb

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Bizarre imagination, originality, trickiness, and whimsy characterize puzzles of Sam Loyd, America's greatest puzzler. Present selection from fabulously rare Cyclopedia includes the famous 14–15 puzzles, the Horse of a Different Color, and 115 others in various areas of elementary math. 150 period line drawings.

Contents
Arithmetic and Algebraic Problems 

Probability and Game Theory Problems
Operations Research Problems
Plane Geometry Problems
Geometrical Dissection Problems
Route, Tracing, and Topological Problems
Counter and Sliding Block Problems
Solid Geometry Problems 

Poincaré's prize : the hundred-year quest to solve one of math's greatest puzzles

George Szpiro

Plume | 2007 | 321 páginas | rar - pdf | 1,6 Mb

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The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it

In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.
Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. 

Contents
Chapter 1: Fit for a King 1
Grigori Perelman’s unprecedented refusal of a Fields Medal for solving one of the greatest problems of our age. The king waits in vain.
Chapter 2: What Flies Know and Ants Don’t 8
The importance of dimensions for Christopher Columbus and for bugs.
Chapter 3: The Forensic Engineer 15
The life of Henri Poincaré, in particular his investigation of a tragedy in a coal mine.
Chapter 4: An Oscar for the Best Script 33
Poincaré’s prizewinning theory of the solar system’s stability...and the scandal.
Chapter 5: Geometry Without Euclid 53 Topology; how this mathematical discipline has developed since Euler.
Chapter 6 : From Copenhagen and Hamburg to Black Mountain, North Carolina 75
Poincaré’s first, incorrect attempt to prove the conjecture...and the parts he got right.
Chapter 7 : What the Conjecture Is Really All About 95
Imaging things that are unimaginable.
Chapter 8 : Dead Ends and a Mysterious Disease 112
Around the world with three-dimensional spheres.
Chapter 9 : Voyage to Higher Dimensions 142
A rock-collecting yippie amazes the world.
Chapter 10 : Inquisition—West Coast Style 172
How other hopefuls ended up with egg on their faces.
Chapter 11 : Watching Things Go “Pop” 186
Richard Hamilton gets going with the Ricci flow . . . and then gets stuck.
Chapter 12 : The Cigar Surgeon 205
The proof lands on the Internet. Swooping up Poincaré, Thurston, and Hamilton. History is made.
Chapter 13 : The Gang of Four, plus Two 226
Vetting the proof, a math professor pushes his protégés into the limelight.
Chapter 14 : The Prize 247
The minor matter of a million dollars. Does money motivate math?
Notes 263
Bibliography 285
Acknowledgments 295
Index 297

Outros livros do mesmo autor:

Numbers rule : the vexing mathematics of democracy, from Plato to the present por George Szpiro Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©2010.

The secret life of numbers : 50 easy pieces on how mathematicians work and think por George Szpiro Idioma: Inglês   Editora: Washington, D.C. : Joseph Henry Press, ©2006.

Assessing Children's Mathematical Knowledge: Social Class, Sex and Problem-Solving

Barry Cooper e Máiréad Dunne

Open University Press | 2000 | 233 páginas | pdf | 2,4 Mb

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'this work is highly relevant to the proliferation of accountability measures worldwide' James Scheurich and Douglas Foley In many countries, the lives of teachers and children are increasingly dominated by programmes of national testing of mathematics and other subjects. In England, the majority of the items in such tests have set mathematical tasks in every day situations such as 'shopping'. This requires children to make decisions about whether to use or not their own every day knowledge and experience in their problem-solving. Some children are likely to have a better 'feel for this game' than others. Assessing Children's Mathematical Knowledge draws on the analysis of national curriculum test data from more than 600 children of 10-11 and 13-14 years of age, as well as in-depth interviews with 250 of these as they attempt to solve test problems, in order to explore the nature of the difficulties children experience with 'realistic' items. The book shows, by comparing test and interview data, that many children, as a consequence of their confusion over the requirements of 'realistic' test items, fail in tests to demonstrate mathematical knowledge and understanding that they actually possess. The book also explores whether this problem of invalid measurement is equally spread across children from different social backgrounds, and across the sexes. The book will be of interest to academics and teachers studying for advanced degrees in mathematics education, sociology of education and educational assessment.