100 Commonly Asked Questions in Math Class: Answers That Promote Mathematical Understanding, Grades 6-12

Alfred S. (Steven) Posamentier, William L. Farber, Terri L. (Lynn) Germain-Williams e Elaine S. Paris

Corwin | 2013 | 232 páginas | rar - epub | 2,23 Mb

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100 ways to get students hooked on math!

That one question got you stumped? Or maybe you have the answer, but it’s not all that compelling. Al Posamentier and his coauthors to the rescue with this handy reference containing fun answers to students’100 most frequently asked math questions. Even if you already have the answers, Al’s explanations are certain to keep kids hooked.

• Teach to the Common Core’s math content standards

• Promote inquiry and process in mathematical thinking

• Build procedural skills and conceptual understanding

• Encourage flexibility in problem solving

• Emphasize efficient test-taking strategies

Contents
Introduction
Chapter One   General Questions
1. Why do I have to learn mathematics?
2. Is there a language connection between mathematical terms and common English words?
3. How many leaves are on a tree?
4. Why do we have to learn about the history of mathematics?
5. Who introduced the Hindu-Arabic numbers to the Western world, and when?
6. What are the three famous problems of antiquity?
7. What are the Fibonacci numbers?
8. What is the golden ratio?
9. Is there a smallest number, and is there a largest number?
10. Why is infinity not a number?
11. How large is infinity?
12. Is there anything larger than infinity?
13. Can the union of two sets ever be equal to the intersection of the two sets?
14. How can we determine how many subsets a given set has?
15. How can we avoid making an error in a “proof” that leads to a generalization?
16. How does a calculator function?
17. Which is correct—my calculating, the calculator, or the computer?
18. What are conic sections?
19. What is a mathematical group?
20. What is a mathematical ring?
21. What is a mathematical field?
22. What are the three famous laws that Johannes Kepler discovered about planetary motion involving the ellipse?
Notes
Chapter Two   Arithmetic Questions
23. What is the difference between a number and a digit?
24. What are the differences between cardinal, ordinal, and nominal numbers?
25. What are the natural numbers, and does the number zero belong to the natural numbers?
26. How can we remember the order of operations using PEMDAS?
27. What is a fraction?
28. What is a rational number?
29. How can one convert a decimal number to a fraction?
30. What is so special about the Pascal triangle?
31. How can the product of two numbers be smaller than both of its factors?
32. If the temperature rises from 80°F to a temperature of 88°F, why is it wrong to say it became 10% warmer?
33. How do the values of the following differ: abc, (ab)c, (ab)c, abc?
34. Why is division by zero not permissible?
35. Why is x· 0 = 0?
36. What is 0!?
37. What is the largest number that can be represented in the decimal system with three digits (and without using any other symbols)?
38. What is a prime number?
39. Does the number 1 belong to the prime numbers?
40. How many prime numbers are there?
41. What is a palindrome?
42. What are successive percentages?
Notes
Chapter Three   Algebra Questions
43. Why is the product of two negative numbers positive?
44. Why must a and b be positive in order for the following to hold true?
45. Why is it advantageous to rationalize the denominator?
46. What is meant by the “absolute value” of a variable?
47. What is a variable? A term? An expression? An equation?
48. How can we have students realize that the average of rates is not simply the arithmetic mean?
49. Why does 0.99999 . . .= 1?
50. Is a road with a slope of 20% twice as steep as a road with a 10% slope?
51. Is there a number that differs from its reciprocal by 1?
52. What is a determinant, and how can it be used to solve a system of linear equations?
53. How do the arithmetic, geometric, and harmonic means compare in magnitude?
54. What is a function?
55. What is meant by the inverse of a function?
56. Can a function be equal to its inverse?
57. What is a 1–1 onto function?
58. Where does the quadratic formula come from?
59. What is a parabola?
60. How can you find the turning point of a parabola?
61. What is an ellipse?
62. What is a hyperbola?
63. When does one use the Law of Sines?
64. When does one use the Law of Cosines?
65. What is the difference between y= arccos x and y= cos–1 x?
66. What is a vector?
67. Why can a vector not be divided by a vector?
68. What is i?
69. What is e?
Notes
Chapter Four   Geometry Questions
70. Why is the diagonal of a square longer than its side?
71. How can you demonstrate that the circumference of a circle is 2πr?
72. How can you demonstrate that the area of a circle is equal to πr2?
73. Can a triangle contain two right angles?
74. Why must the sum of any two sides of a triangle be greater than the third side?
75. How do the terms “acute angle” and “obtuse angle” relate to the English language?
76. Can trigonometry be used to prove the Pythagorean theorem?
77. How is the distance formula derived?
78. How can the Pythagorean theorem be used to determine if an angle of a triangle is acute or obtuse?
79. What is a Platonic solid?
80. What is a golden rectangle?
81. What is a golden triangle?
82. From which point in a triangle is the sum of the distances to the three vertices smallest?
83. What is the sum of the distances from a point in a triangle to its three sides?
84. What is President James A. Garfield’s proof of the Pythagorean theorem?
85. What is the nine-point circle?
86. How can the Pythagorean theorem be proved by paper folding?
87. How can we prove that the sum of the measures of the angles of any triangle is 180° using paper folding?
88. What figure is created by joining the midpoints of any quadrilateral?
89. How can the concurrency of the medians of a triangle be proved in one step?
Notes
Chapter Five   Probability Questions
90. What is the fundamental principle of counting?
91. What does it mean when the probability of an event is 1? Is 0?
92. What are mutually exclusive events?
93. What is the probability of either or both of two events happening?
94. What is the difference between combinations and permutations?
95. What is the difference between correlation and causation?
96. What is the Pascal triangle?
97. What is binomial probability?
98. What is the birthday problem?
99. How can algebra help us to understand a probability question?
100. What kind of averages are batting averages?

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The Abel Prize: 2003-2007 The First Five Years

Helge Holden e Ragni Piene

Springer | 2010 | 245 páginas | pdf | 2,9 Mb 

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The book presents the winners of the first five Abel Prizes in mathematics: 2003 Jean-Pierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan.

Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize.

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

Eric Gutstein 


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

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

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

Ball of Confusion: Puzzles, Problems and Perplexing Posers

Johnny Ball

Icon Books |  2012 | 254 páginas | rar - epub |2,4 Mb

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From how to cheat in a coin toss to why it is that some parts of a high speed train travelling at 125 mph are actually going backwards, Ball of Confusion is designed to twist your brain into enjoyable knots of empuzzlement—from puzzles solved in a twinkling of an eye to some that will knit your brow for hours.

Contents

How Ball of Confusion was born …

Introduction

1: Kitchen Capers and Domestic Problems

2: ‘I Can Hear You Thinking’ Puzzles

3: Any Number of Puzzles – About Numbers

4: Easy Peasy Puzzles and Catchy Watchy Questions

5: Geometric Shape and Angle Puzzles

6: Dear Old Faves from Days Gone By

7: Even More Thoughtful Thinking Puzzles

8: Party Puzzles and Tricks to Show Off With

Answers

Bibliography

Outros livros do mesmo autor:

Why pi? por Johnny Ball Livro : Público juvenil Idioma: Inglês   Editora: New York, N.Y. : DK Pub., 2009.

Think of a number por Johnny Ball Público juvenil Idioma: Inglês   Editora: London : Dorling Kindersley, 2005.

Pythagoras the Mathemagician

Karim El Koussa


Sunbury Press, Inc. | 2010 | 412 páginas | rar - epub | 417 kb

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Discover who the real Pythagoras was within the pages of this philosophical work of historical fiction. This controversial novel looks at the first philosopher from an unfamiliar perspective to most Western readers and scholars. El Koussa stands in the vanguard of a new generation of writers and thinkers who are bringing the rich and diverse history of the Phoenician culture to a new audience. 

Social Statistics: Managing Data, Conducting Analyses, Presenting Results

Thomas J. Linneman

Routledge | 2014 - 2ª edição | 657 páginas | rar - pdf | 9,3 Mb

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Many fundamentally important decisions about our social life are a function of how well we understand and analyze DATA. This sounds so obvious but it is so misunderstood. Social statisticians struggle with this problem in their teaching constantly. This book and its approach is the ally and support of all instructors who want to accomplish this hugely important teaching goal.

This innovative text for undergraduate social statistics courses is, (as one satisfied instructor put it), a "breath of fresh air." It departs from convention by not covering some techniques and topics that have been in social stat textbooks for 30 years, but that are no longer used by social scientists today. It also includes techniques that conventional wisdom has previously thought to be the province of graduate level courses.

Linneman’s text is for those instructors looking for a thoroughly "modern" way to teach quantitative thinking, problem-solving, and statistical analysis to their students…an undergraduate social statistics course that recognizes the increasing ubiquity of analytical tools in our data-driven age and therefore the practical benefit of learning how to "do statistics," to "present results" effectively (to employers as well as instructors), and to "interpret" intelligently the quantitative arguments made by others.

BRIEF CONTENTS

Preface xxix

Acknowledgments xxxvii

Chapter 1: Life in a Data-Laden Age: Finding and Managing Datasets 1

Chapter 2: The Art of Visual Storytelling: Creating Accurate Tables and Graphs 46

Chapter 3: Summarizing Center and Diversity: Basic Descriptive Statistics 92

Chapter 4: Using Sample Crosstabs to Talk about Populations: The Chi-Square Test 141

Chapter 5: Using a Sample Mean or Proportion to Talk about a Population: Confidence Intervals 189

Chapter 6: Using Multiple Sample Means to Talk about Populations: t-Tests and ANOVA 231

Chapter 7: Give Me One Good Reason Why: Bivariate Correlation and Regression 264

Chapter 8: Using Sample Slopes to Talk about Populations: Inference and Regression 303

Chapter 9: It’s All Relative: Dichotomies as Independent Variables in Regression 326

Chapter 10: Above and Beyond: The Logic of Controlling and the Power of Nested Regression Models 348

Chapter 11: Some Slopes Are Bigger than Others: Calculating and Interpreting Beta Coefficients 384

Chapter 12: Different Slopes for Different Folks: Interaction Effects 402

Chapter 13: Explaining Dichotomous Outcomes: Logistic Regression 435

Chapter 14: Visualizing Causal Stories: Path Analysis 467

Chapter 15: Questioning the Greatness of Straightness: Nonlinear Relationships 493

Chapter 16: Problems and Prospects: Regression Diagnostics, Advanced Techniques, and Where to Go Now 532

Appendix A: Variables and Indexes from the Datasets Used in the End-of-Chapter Exercises A-1

Appendix B: 86 Articles That Use Statistics in Less Than Scary Ways B-1

Appendix C: Statistical Tables C-1

Appendix D: Answers to Selected End-of-Chapter Exercises D-1

Bibliography R-1

Glossary/Index I-1

Undiluted Hocus-Pocus: The Autobiography of Martin Gardner

Martin Gardner, James Randi e Persi Diaconis

Princeton University Press | 2013 | 289 páginas | rar - pdf |  2,7 Mb


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Martin Gardner wrote the Mathematical Games column forScientific American for twenty-five years and published more than seventy books on topics as diverse as magic, philosophy, religion, pseudoscience, and Alice in Wonderland. His informal, recreational approach to mathematics delighted countless readers and inspired many to pursue careers in mathematics and the sciences. Gardner's illuminating autobiography is a disarmingly candid self-portrait of the man evolutionary theorist Stephen Jay Gould called our "single brightest beacon" for the defense of rationality and good science against mysticism and anti-intellectualism.Gardner takes readers from his childhood in Oklahoma to his college days at the University of Chicago, his service in the navy, and his varied and wide-ranging professional pursuits. Before becoming a columnist for Scientific American, he was a caseworker in Chicago during the Great Depression, a reporter for the Tulsa Tribune, an editor for Humpty Dumpty, and a short-story writer for Esquire, among other jobs. Gardner shares colorful anecdotes about the many fascinating people he met and mentored, and voices strong opinions on the subjects that matter to him most, from his love of mathematics to his uncompromising stance against pseudoscience. For Gardner, our mathematically structured universe is undiluted hocus-pocus--a marvelous enigma, in other words.

Contents
Foreword: Magic, Mathematics, and Mysterians, by Persi Diaconis xi
Preface xxiii
Prologue: I Am a Mysterian xxv
1 Earliest Memories 1
2 Lee School 10
3 Tulsa Central High, I 21
4 Central High, II 28
5 Hutchins and Adler 40
6 Richard McKeon 47
7 I Lose My Faith 53
8 Chicago, I 62
9 Chicago, II 76
10 I Become a Journalist 88
11 Mother and Dad 98
12 The Navy, I 111
13 The Navy, II 119
PHOTO ESSAY follows page 124
14 Esquire and Humpty 125
15 Scientific American 134
16 Pseudoscience 150
17 Math and Magic Friends 160
18 Charlotte 173
19 Bob and Betty 185
20 God 191
21 My Philosophy 195
Afterword: My Most Elegant Friend . . . , by James Randi 209
Index 215