Mathematics of Choice: Or, How to Count Without Counting

(New Mathematical Library)

Ivan Morton Niven

Mathematical Association of America   | 1975 | 202 páginas | rar - PDF - 5,1 Mb

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This text is an engaging, even addictive, introduction to basic combinatorics. Written in a fun and inviting manner, reader interest is amplified by the author’s infectious enthusiasm. This is an excellent introduce to combinations and permutations. First published in 1975, before computers and calculators were assumed to be at hand, the exercises in this book can all be done by hand on paper. Students finishing high school or in their first year of college will find this work an excellent adjunct to textbooks and lectures.

The work is arranged in a logical progression beginning with the definitions and motivations for factorials, combinations, and permutations. From there the reader moves to binomial coefficients, power sets, and Fibonacci numbers. The effect of repetitions on combinations makes a natural prelude in Chapter Four to the Inclusion-Exclusion Principle and the groundwork for basic probability. From partitions of integers the author moves into a brief and basic, yet cogent and enlightening, explanation of generating functions and some applications for them. The book also includes the Pigeonhole Principle, induction, recursion, and allied topics.

Math Misconceptions, PreK-Grade 5: From Misunderstanding to Deep Understanding

Christine Oberdorf, Karren Schultz-Ferrell

Heinemann | 2010 | 200 páginas | mobi | 4,3 Mb

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"In this wonderfully insightful book, Honi, Christine, and Karren not only describe a vast array of perfectly understandable mathematical misconceptions that students have across the elementary curriculum, they also provide numerous practical instructional strategies and activities for helping remediate and "undo" the misconceptions. The classroom vignettes they describe will ring true to everyone who has tried to teach mathematics to young, and not-so-young, children."

-Steven Leinwand

• identifying the most common errors relative to the five NCTM content strands (number and operations, algebra, geometry, measurement, and data analysis and probability)

• investigating the source of these misunderstandings

• proposing ways to avoid as well as "undo" misconceptions.

Children enter school filled with all kinds of ideas about numbers, shapes, measuring tools, time, and money-ideas formed from the expressions they hear...the things they see on television...the computer screen...in children's books...all around them. It's no wonder some children develop very interesting and perhaps incorrect ideas about mathematical concepts.

"How can we connect the informal knowledge that students bring to our classrooms with the mathematics program adopted by our school system? Just as important, how do we ensure that the mathematics we are introducing and reinforcing is accurate and will not need to be re-taught in later years?"

Math Misconceptions answers these questions by:

Using classroom vignettes that highlight common misconceptions in each content area, followed by applicable research about the root causes of the confusion, the authors offer numerous instructional ideas and interventions designed to prevent or correct the misconception.

Untangle your students' math misconceptions. This practical resource will help make it all make sense, and raise math achievement in your classroom.

Contents

Foreword  .v

Acknowledgments . .ix

Introduction . . .xi

CHAPTER 1 Number and Operations ..1

Counting with Number Words 2

Thinking Addition Means “Join Together” and Subtraction Means “Take Away” 7

Renaming and Regrouping When Adding and Subtracting Two-Digit Numbers 13

Misapplying Addition and Subtraction Strategies to Multiplication and Division 20

Multiplying Two-Digit Factors by Two-Digit Factors 24

Understanding the Division Algorithm 29

Understanding Fractions 34

Adding and Subtracting Fractions 40

Representing, Ordering, and Adding/Subtracting Decimals 43

CHAPTER 2 Algebra .. .49

Understanding Patterns 50

Meaning of Equals 55

Identifying Functional Relationships 61

Interpreting Variables 66

Algebraic Representations 71

CHAPTER 3 Geometry . . .78

Categorizing Two-Dimensional Shapes 78

Naming Three-Dimensional Figures 84

Navigating Coordinate Geometry 88

Applying Reflection 95

Solving Spatial Problems 100

CHAPTER 4 Measurement .108

Reading an Analog Clock 108

Determining the Value of Coins 116

Units Versus Numbers 121

Distinguishing Between Area and Perimeter 127

Overgeneralizing Base-Ten Renaming 132

CHAPTER 5 Data Analysis and Probability . . .137

Sorting and Classifying 137

Choosing an Appropriate Display 142

Understanding Terms for Measures of Central Tendency 148

Analyzing Data 152

Probability 158

CHAPTER 6 Assessing Children’s Mathematical Progress . . .164

Assessment: The Received View 164

Assessment from a Better Angle 165

Types of Formative Assessments 166

Why Assess? 170

Final Thoughts 171

References 173

Index ..179

Gödel, Escher, Bach Um entrelaçamento de gênios brilhantes

Douglas R. Hofstadter

Editora UnB; Imprensa Oficial - versão em português (Brasil)| 2001 | 892 páginas | pdf | 19 Mb

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Um verdadeiro best-seller, nos Estados Unidos, onde recebeu os prêmios Pulitzer e American Book Award, em 1980. É uma obra de arte escrita por um cientista, que revela surpreendentes paralelismos entre a música de Johann Sebastian Bach, os desenhos de M. C. Escher e o famoso teorema do matemático Kurt Gödel. É uma leitura fascinante, que não deve atemorizar os não iniciados nos segredos da música clássica, do desenho ou da matemática.

Smart Shopping Math

(21st Century Lifeskills Mathematics)

 Saddleback Educational Publishing | 2011 - Reprint edition | 115 páginas | rar - pdf | 1,7 Mb


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Smart Shopping Math
Includes: Retail & Wholesale, Reading Ads, Rental Sales, Buying on Layaway, Getting the Best Deal, Online Shopping, Shopping for a Neighbor, Second Time Around
Contents
Unit 1: Retail & Wholesale
Preview . . . 1
Lesson 1: Retail Deals . . . 2
Lesson 2: Visiting the Outlets.  . . 4
Lesson 3: Liquidation and Closeouts  . . 6
Lesson 4: Strategic Purchases  . . 8
Lesson 5: Co-ops & Clubs .. . 10
Review . . . 12
Unit 2: Reading Ads
Preview .. . . 14
Lesson 1: Misleading Data . . . . 15
Lesson 2: Reading the Classifieds  . . 17
Lesson 3: Everyday Ads. . 19
Lesson 4: Reading the Fine Print. . . 21
Lesson 5: Stretching Dollars . . 23
Review . . 25
Unit 3: Rental Sales
Preview  . . 27
Lesson 1: On Vacation. . 28
Lesson 2: Renting Movies  . . 30
Lesson 3: Rented Out!. . . 32
Lesson 4: Temporary Help. . . 34
Lesson 5: Renting Your Home. . . 36
Review . . . 38
Unit 4: Buying on Layaway
Preview . . . 40
Lesson 1: All Sorts of Items to Layaway  . . 41
Lesson 2: Terms & Conditions . . 43
Lesson 3: Return Policies . . 45
Lesson 4: Making Payments . . 47
Lesson 5: Timing Is the Key. . . 49
Review . . 51
Unit 5: Getting the Best Deal
Preview . . . . . 53
Lesson 1: Picking the Time & the Place .. 54
Lesson 2: A Matter of Timing. . 56
Lesson 3: Vacation Deals. . 58
Lesson 4: Trade Show Opportunities . . 60
Lesson 5: Getting an Advantage. . . 62
Review . . 64
Unit 6: On-line Shopping
Preview . . . 66
Lesson 1: Making Comparisons . . 67
Lesson 2: Shopping without Dropping .  . 69
Lesson 3: Searching for Special Items . . 71
Lesson 4: What’s New?.. . 73
Lesson 5: Consulting the Experts. . 75
Review . . . 77
Unit 7: Shopping for a Neighbor
Preview  . . 79
Lesson 1: In Their Shoes  . . 80
Lesson 2: Following Their Lists .. . 82
Lesson 3: Price or Quantity . . 84
Lesson 4: Being a Good Neighbor . . 86
Lesson 5: Match It!.  . 88
Review . . . 90
Unit 8: Second Time Around
Preview . . 92
Lesson 1: Garage Sales . . 93
Lesson 2: Estate & Other Sales . . 95
Lesson 3: What’s the Missing Number? . . 97
Lesson 4: Cars, Clothes, & Books. . 99
Lesson 5: Recycling Trash. . 101
Review  . . 103

Teacher’s Notes and Answer Key . . 105

The exact sciences in antiquity

Otto Neugebauer

Copenhagen | 1957 - 2.ª edição

online: hathitrust.org

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Based on a series of lectures delivered at Cornell University in the fall of 1949, and since revised, this is the standard non-technical coverage of Egyptian and Babylonian mathematics and astronomy, and their transmission to the Hellenistic world. Entirely modern in its data and conclusions, it reveals the surprising sophistication of certain areas of early science, particularly Babylonian mathematics.
After a discussion of the number systems used in the ancient Near East (contrasting the Egyptian method of additive computations with unit fractions and Babylonian place values), Dr. Neugebauer covers Babylonian tables for numerical computation, approximations of the square root of 2 (with implications that the Pythagorean Theorem was known more than a thousand years before Pythagoras), Pythagorean numbers, quadratic equations with two unknowns, special cases of logarithms and various other algebraic and geometric cases. Babylonian strength in algebraic and numerical work reveals a level of mathematical development in many aspects comparable to the mathematics of the early Renaissance in Europe. This is in contrast to the relatively primitive Egyptian mathematics. In the realm of astronomy, too, Dr. Neugebauer describes an unexpected sophistication, which is interpreted less as the result of millennia of observations (as used to be the interpretation) than as a competent mathematical apparatus. The transmission of this early science and its further development in Hellenistic times is also described. An Appendix discusses certain aspects of Greek astronomy and the indebtedness of the Copernican system to Ptolemaic and Islamic methods.
Dr. Neugebauer has long enjoyed an international reputation as one of the foremost workers in the area of premodern science. Many of his discoveries have revolutionized earlier understandings. In this volume he presents a non-technical survey, with much material unique on this level, which can be read with great profit by all interested in the history of science or history of culture. 14 plates. 52 figures.

From Alexandria, Through Baghdad: Surveys and Studies in the Ancient Greek and Medieval Islamic Mathematical Sciences in Honor of J.L. Berggren

Nathan Sidoli e Glen Van Brummelen

Springer | 2014 | 584 páginas | rar - pdf | 248 Mb

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This book honors the career of historian of mathematics J.L. Berggren, his scholarship, and service to the broader community. The first part, of value to scholars, graduate students, and interested readers, is a survey of scholarship in the mathematical sciences in ancient Greece and medieval Islam. It consists of six articles (three by Berggren himself) covering research from the middle of the 20th century to the present. The remainder of the book contains studies by eminent scholars of the ancient and medieval mathematical sciences. They serve both as examples of the breadth of current approaches and topics, and as tributes to Berggren's interests by his friends and colleagues.

Contents
Part I Surveys
History of Greek Mathematics: A Survey ofRcccnt Research [1984].3
Lennart Berggren
Mathematical Reconstructions Out, Textual Studies In: 30 Years in the Historiography of
Greek Mathematics [1998] . . 17
Ken Saito
Research on Ancient Greek Mathematical Sciences, 1998-2012  . 25
Nathan Sidoti
History of Mathematics in the IsWnic World: The Present State of the Art [1985] . . 51
J. Lennart Berggren
Mathematics and Her Sisters in Medieval Islam: A Selective Review of Work Done from
1985 to 1995 [1997] . 73
 Lennart Berggren
A Survey of Research in the Mathematical Sciences in Medieval Islam from 1996 to 2011. 101
Glen Van Brummelen
Part II Studies
Mechanical Astronomy: A Route to the Ancient Discovery of Epicycles and Eccentrics  . 145
James Evans and Christian Carlos Carman
Some Greek Sundial Meridians . . . . 175
Alexander Jones
An Archimedean Proof of Heron's Fonnula for the Area of a Triangle: Heuristics Reconstructed . 189
Christian Marinus Taisbak
Reading the Lost Folia. of the Archimedean Palimpsest: The Last Proposition of the Method . 199
Ken Saito and Pier Daniele Napolitani
Acts of Geometrical Construction in the Spherics ofTheodosios .  227
Roben Thomas
Archimedes Among the Ottomans: An Updated Survey.. . 239
ihsan Fazlloglu and F. Jamil Ragep
The "Second" Arabic Translation of Theodosius' Spbaerica . . . 255
Richard Lorch
More Archimedean than Archimedes: A New Trace of Abu Sahl al-Kiihi's Work in Latin  . 259
Jan P. Hogendijk
Les mathematiques en Occident musulman (IX-XVIII) : Panorama des travaux realises
entre 1999 et 2011 ... 275
Ahmed Djebbar
Ibn al-Raqqam's al-Zij al-Mustarufi in MS Rabat National Library 2461 ..... 297
Julio Samso
An Ottoman Astrolabe Full of Surprises. . 329
David A. King
Un algebriste arabe : Abu Kamil Suga ibn Aslam .. 343
Add Anbouba avec les commentaires de Jacques Sesiano)
Abu Kamil's Book on Mensuration . . 359
Jacques Sesiano
Hebrew Texts on the Regular Polyhedra  . 409
Tzvi Langermann
A Treatise by al-Biriini on the Rule of Three and its Variations ..... 469
Takanori K.usuba
Safavid Art, Science, and Courtly Education in the Seventeenth Century. .487
Sonja Brentjes
Translating Playir's Geometry into Arabic: Mathematics and Missions . . 503
Gregg De Young
Part III The Story of pi:
The Life of pi: From Archimedes to ENIAC and Beyond  531
Jonathan M. Borwein
Index of Personal Names . 563

Index of Ancient and Medieval Tides  . 577

Reading for Evidence and Interpreting Visualizations in Mathematics and Science Education

Stephen P. Norris 

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

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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