Play's the Thing : Mathematical Games for the Classroom and Beyond

 Alan Lipp

Anthem Press | 2011 | 147 páginas | rar - pdf | 238 kb

link (password : matav)

The book presents 18 games and develops the concepts of game analysis and winning strategies. Students are encouraged to play these mathematical games together, collect data developed through their play, and analyze the data to develop a winning strategy. Through the exploration of mathematical games, ‘The Play’s the Thing’ introduces teachers and students to the fun of play and to the mathematics behind the fun.

ContentsAcknowledgments xi
Prologue To the Teacher xiii
Act 0 To the Student xv
Act 1 Blockers 1
Act 1 Exercises 2
Act 2 Nimble 5
Act 2 Exercises 6
Act 3 More Variations 9
Act 3 Exercises 10
Act 4 Take Away 1, 2, 3 13
Looking for a Strategy 13
Act 4 Exercises 14
Act 5 Two Piles: A Hidden Game 17
Act 6 Two Piles 1, 2, 3 21
Act 7 Nim 29
Act 8 Flit 37
Act 8 Exercises 38
Act 9 Mr Flit 41
Act 10 Landis 47
Act 10 Exercises 48
Act 11 Add’em Up 51
Act 11 Exercises 52
Act 12 Connect-the-Dots 55
Act 12 Exercises 55
Act 13 Boxes 59
Act 13 Exercises 60
Act 14 Hold That Line 65
Act 14 Exercises 66
Act 15 The Fifteen Game 69
Act 15 Exercises 70
Act 16 Sliders 73
Act 16 Exercises 75
Act 17 Lynch 76
Act 17 Exercises 78
Act 18 Progression: Down and Up 81
Act 19 Harder Stuff 87
Answers 97

Mathematics Teaching Practice: Guide for University and College Lecturers

John H. Mason

Woodhead Publishing | 2002 | 231 páginas | rar - pdf | 11,6 Mb

link (password: matav)

Mathematics; Clarifying the distinction between mathematical research and mathematics education, this book offers hundreds of suggestions for making small and medium sized changes for lectures, tutorials, task design, or problem solving. Here is guidance and inspiration for effective mathematics teaching in a modern technological environment, directed to teachers who are unhappy with results or experience, or those now in teacher training or new to the profession. Commencing with a range of student behaviours and attitudes that have struck and amazed tutors and lecturers, Proffessor Mason offers a wealth of partial diagnoses, followed by specific advice and suggestions for remedial actions. 

Contents: 
Student difficulties with mathematics; 
Lecturing; 
Tutoring; 
Constructing tasks; 
Marking and commenting; 
Making use of history; 
Issues and concerns in teaching mathematics; 
Appendix A Exploratory tasks; 
Appendix B Convergence case study; 
Bibliography

Puzzles From Penrose the Mathematical Cat

Theoni Pappas

Wide World Publishing, Tetra | 2013 | 158 páginas | rar - pdf | 8,4 Mb

link (password: matav)

The famous mathematical cat Penrose takes us on a trip though puzzleland, while sharing fascinating and challenging puzzles in this uniquely designed mini book. Each page's puzzle is introduced by our star Penrose or one of his quirky friends. Readers are treated to page after page of Penrose antics and problems, while the over 100 mind teasers stimulate and engage its readers gray cells, This book's mini format and fun graphics makes it hard to resist picking up, and its characters and puzzles are sure to entertain both kids or adults.

A Survey of the Almagest: With Annotation and New Commentary by Alexander Jones

Olaf Pedersen e Alexander Jones

Springer | 2011 | 481 páginas 

pdf - 21 Mb
link
link1
djvu - 4,8 Mb
link
link1
link2

The Almagest, by the Greek astronomer and mathematician Ptolemy, is the most important surviving treatise on early mathematical astronomy, offering historians valuable insight into the astronomy and mathematics of the ancient world.Pedersen's 1974 publication, A Survey of the Almagest, is the most recent in a long tradition of companions to the Almagest. Part paraphrase and part commentary, Pedersen's work has earned the universal praise of historians and serves as the definitive introductory text for students interested in studying the Almagest.In this revised edition, Alexander Jones, a distinguished authority on the history of early astronomy, provides supplementary information and commentary to the original text to account for scholarship that has appeared since 1974. This revision also incorporates various corrections to Pedersen's original text that have been identified since its publication.This volume is intended to provide students of the history of astronomy with a self-contained introduction to the Almagest, helping them to understand and appreciate Ptolemy's great and classical work.

Pacific CRYSTAL Centre for Science, Mathematics, and Technology Literacy: Lessons Learned

Larry D. Yore, Eileen Van Der Flier-Keller e David W. Blades

Sense Publishers | 2011 | 278 páginas | pdf | 2,2 Mb 

link
link1

The University of Victoria Pacifi c Centre for Scientifi c and Technological Literacy is one of fi ve Centres for Research into Youth, Science Teaching and Learning (CRYSTAL) funded for 5 years (2005-2010) by the Natural Sciences and Engineering Research Council Canada (NSERC). Pacifi c CRYSTAL intended to promote scientifi c, mathematical, and technological literacy for responsible citizenship through research partnerships with university and educational communities. Pacifi c CRYSTAL's functional structure consisted of 3 research and development nodes connected to a leadership and administrative node, which was charged with facilitating the activities of 19 projects and 42 principal investigators, partners, and research associates. Node 1, an incubation centre, involved extracurricular authentic science, mathematics, and technology experiences; Node 2, a classroom testing environment, fi eld-tested instructional ideas and strategies to develop evidence-based practices; and Node 3, lighthouse schools, involved systemic change and leadership opportunities that adapted, demonstrated, and disseminated tested ideas, resources, and strategies to a much broader education community and attempted to infl uence public policy. This book provides descriptions of the target goals, research and development projects, and lessons learned.

TABLE OF CONTENTS
List of Pacific CRYSTAL Project Leaders (2005–2011) ....... vii
Acknowledgements ........ ix
I. Overview, Common Themes, and Theoretical Frameworks
1. Pacific CRYSTAL Centre for Science, Mathematics, and Technology Literacy: Lessons Learned: Overview ......... 3
Larry D. Yore and Eileen Van der Flier-Keller
2. Foundations of Scientific, Mathematical, and Technological Literacies— Common Themes and Theoretical Frameworks ...... 23
Larry D. Yore
II. Authentic Learning—Informal Environments and Extracurricular Science, Mathematics, and Technology Opportunities: Anchoring and Bridging Real-world, Cultural, and School Experiences
3. Adolescents’ Science Career Aspirations Explored through Identity and Possible Selves ....... 47
E. Anne Marshall, Francis L. Guenette, Tanya Ward, Tara Morley, Breanna Lawrence and Kate Fisher
4. Giving Voice to Science from Two Perspectives: A Case Study ......... 67
Nikki Wright, Earl Claxton, Jr., Lewis Williams and Tammy Paul
5. Seaquaria in Schools: Participatory Approaches in the Evaluation of an Exemplary Environmental Education Program......... 83
David B. Zandvliet, Mary Holmes and Matthias Starzner
6. Teaching Problem Solving and Computer Science in the Schools: Concepts and Assessment .......... 99
Sarah Carruthers, Todd M. Milford, Yvonne Coady, Celina Gibbs, Katherine Gunion and Ulrike Stege
7. Outreach Workshops, Applications, and Resources: Helping Teachers to Climb Over the Science, Mathematics, and Technology Threshold by Engaging their Classes ... 113
Leslee Francis Pelton and Timothy W. Pelton
III. Moving Tested Ideas into Classrooms
8. Explicit Literacy Instruction Embedded in Middle School Science Classrooms: A Community-based Professional Development Project to Enhance Scientific Literacy ..... 133
Christine D. Tippett and Robert J. Anthony
9. Enhancing Science Education through an Online Repository of Controversial, Socioscientific News Stories  149
Susan M. Teed, David B. Zandvliet and Carlos Gustavo A. Ormond
10. Promoting Earth Science Teaching and Learning: Inquiry-based Activities and Resources Anchoring Teacher Professional Development and Education ... 165
Eileen Van der Flier-Keller, David W. Blades and Todd M. Milford
IV. Knowledge Transfer, Systemic Implementation, and Building Leadership Capacity
11. Modelling of Large-scale PISA Assessment Data: Science and Mathematics Literacy .. 187
Todd M. Milford, John O. Anderson and Jiesu Luo
12. Time and Teacher Control in Curriculum Adoption: Lessons from the Lighthouse Schools Project ..... 203
David W. Blades
13. The Development of a Place-based Learning Environment at the Bowen Island Community School .... 217
Carlos Gustavo A. Ormond, Susan M. Teed, Laura Piersol and David B. Zandvliet
V. Closing Remarks and Implications for the Future
14. Epilogue of Pacific CRYSTAL—Lessons Learned about Science, Mathematics, and Technology Literacy, Teaching and Learning ..... 237
Larry D. Yore and Eileen Van der Flier-Keller
Appendix: Pacific CRYSTAL Project: Highly Qualified Personnel .... 253
Index .... 265

Pythagoras His Life, Teaching, and Influence

Christoph Riedweg e Steven Rendall

Cornell University Press | 2011 . 2ª edição | 198 páginas | rar - epub | 1 Mb

link (password: matav)

One of the most important mathematical theorems is named after Pythagoras of Samos, but this semi-mythical Greek sage has more to offer than formulas. He is said to have discovered the numerical nature of the basic consonances and transposed the musical proportions to the cosmos, postulating a "harmony of the spheres." He may have coined the words "cosmos" and "philosophy." He is also believed to have taught the doctrine of transmigration of souls and therefore to have advised a vegetarian diet.

Ancient legends have Pythagoras conversing with dogs, bears, and bulls. A distinctly Pythagorean way of life, including detailed ritual regulations, was observed by his disciples, who were organized as a secret society. Later, Pythagorean and Platonic teachings became fused. In this Platonized form, Pythagoreanism has remained influential through medieval Christianity and the Renaissance down to the present.

Christoph Riedweg's book is an engaging introduction to the fundamental contributions of Pythagoras to the establishment of European culture. To penetrate the intricate maze of lore and ascertain what history can tell us about the philosopher, Riedweg not only examines the written record but also considers Pythagoras within the cultural, intellectual, and spiritual context of his times. The result is a vivid overview of the life and teachings of a crucial Greek thinker and his most important followers.

Contents
Preface
1. Fiction and Truth: Ancient Stories about Pythagoras
Pythagoras’ Appearance
Biographical Information
Pythagoras as a Teacher
2. In Search of the Historical Pythagoras
The Cultural-Historical and Intellectual Environment
The Oldest Testimonies
Guru and Scholar
Did Pythagoras Invent the Word Philosophy?
3. The Pythagorean Secret Society
Were the Pythagoreans an Ancient “Sect”?
The Pythagoreans in the Fifth and Fourth Centuries B.C.E.
4. Thinkers Influenced by Pythagoras and His Pupils
Pre-Platonic Thinkers
Plato and the Old Academy
Hellenistic “Forgeries” and Neo-Pythagoreanism
Pythagoras as an Idea in the Middle Ages and Modernity—A Prospect
Chronology

Martin Gardner in the Twenty-First Century

 Michael Henle e Brian Hopkins

 Mathematical Association of America |  2012 | 312 páginas | rar - pdf | 2,3 Mb

link (password: matav)

Martin Gardner enormously expanded the field of recreational mathematics with the Mathematical Games columns he wrote forScientific American for over 25 years and the more than 70 books he published. He also had a long relationship with the Mathematical Association of America, publishing articles in the MAA journals right up to his death in 2010. This book collects articles Gardner wrote for the MAA in the twenty-first century, together with other articles the MAA published from 1999 to 2012 that spring from and comment on his work. Martin Gardner's interests spanned geometry, number theory, graph theory, and probability, always communicated with engaging exposition often including games and puzzles. Eight works by Gardner himself, published between 1999 and 2010, are collected here and represent the breadth of his work, including his short fiction and lifelong interest in debunking pseudo-science. The remaining 33 chapters were written in response to Gardner's work and include several articles addressing open questions he posed. They come from The American Mathematical Monthly, Mathematics Magazine, The College Mathematics Journal, and Math Horizons and demonstrate how Gardner's influence continues beyond his columns for Scientific American. Although he took no mathematics in college, Martin Gardner inspired many mathematicians, professional and amateur, and his work was informed by frequent correspondence with other mathematics aficionados, both famous and unknown. He was even the basis for a character in a popular novel; his review of that work in included here. This book is a tribute to the deep and lasting impact of this prolific and brilliant writer. It is for anyone who, like Martin Gardner, loves mathematics.

Contents
Preface v
I Geometry 1
1 The Asymmetric Propeller 3
Martin Gardner
Gardner, paying tribute to dentist and geometer Leon Bankoff, discusses some of his unpublished results and concludes with an open question.
2 The Asymmetric Propeller Revisited 7
Gillian Saenz, Christopher Jackson, and Ryan Crumley
Three University of Texas students use dynamic geometry software to confirm Bankoff’s results and resolve Gardner’s question.
3 Bracing Regular Polygons As We Race into the Future 11
Greg W. Frederickson
A problem Gardner published in 1963 continues to spur generalizations and improved solutions around the world.
4 A Platonic Sextet for Strings 19
Karl Schaffer
The professor and dance company co-director details string polyhedra constructions for ten participants.
5 Prince Rupert’s Rectangles 25
Richard P. Jerrard and John E. Wetzel
A 17th century puzzle that Gardner posed in higher dimensions is here solved in the case of three-dimensional boxes.
II Number Theory and Graph Theory 35
6 Transcendentals and Early Birds 37
Martin Gardner
Gardnermoves from Liouville to an “innocent but totally useless amusement” that nonetheless captured the attention of Solomon Golomb.
7 Squaring, Cubing, and Cube Rooting 39
Arthur T. Benjamin
The professor and “mathemagician,” inspired as a high school student by Gardner’s tricks for mental calculations, extends some of them here.
8 Carryless ArithmeticMod 10 45
David Applegate, Marc LeBrun, and N. J. A. Sloane
Inspired by the carryless arithmetic of the game Nim, this trio of authors explores the number theory of a South Pacific island.
9 Mad Tea Party Cyclic Partitions 53
Robert Bekes, Jean Pedersen, and Bin Sha
Another playful trio analyzes cyclic arrangements that build from integer partitions in a Lewis Carroll setting.
10 The Continuing Saga of Snarks 65
sarah-marie belcastro
A type of graph, given a fanciful name by Gardner from Lewis Carroll, was the subject of a Branko Grunbaum conjecture for 39 years.
11 The Map-Coloring Game 73
Tomasz Bartnicki, Jaroslaw Grytczuk, H. A. Kierstead, and Xuding Zhu
Daltonism and half-dollar coins are used in this exploration of a Steven Brams game theory approach to the Four Color Theorem.
III Flexagons and Catalan Numbers 85
12 It’s Okay to Be Square If You’re a Flexagon 87
Ethan J. Berkove and Jeffrey P. Dumont
This article details the 1939 origin of flexagons at Princeton University and focuses on the neglected tetraflexagons.
13 The V-flex, Triangle Orientation, and Catalan Numbers in Hexaflexagons 103
Ionut E. Iacob, T. Bruce McLean, and Hua Wang
This trio of Georgia Southern University authors examines a once-illegal variety of flex and makes a connection between “pat classes” and Catalan numbers.
14 From Hexaflexagons to Edge Flexagons to Point Flexagons 109
Les Pook
An engineer and author of two books on flexagons considers the more general edge flexagons and recently discovered point flexagons.
15 Flexagons Lead to a Catalan Number Identity 113
David Callan
Examining the descent permutation statistic on flexagon pats leads the author to full binary trees and a combinatorial proof.
16 Convergence of a Catalan Series 119
Thomas Koshy and Z. Gao
Calculus is brought to bear on the infinite sum of Catalan number reciprocals and related series; and the golden ratio make appearances.
IV Making Things Fit 125
17 L-Tromino Tiling of Mutilated Chessboards 127
Martin Gardner
In his last MAA mathematics article, Gardner moves from classic chessboard domino tiling problems to new results.
18 Polyomino Dissections 135
Tiina Hohn and Andy Liu
The authors introduce a new technique for solving dissection problems, often presented in the context of quilts, leaving several puzzles for the reader.
19 Squaring the Plane 143
Frederick V. Henle and James M. Henle
A father and son team resolve Golomb’s “heterogenous tiling conjecture” and discuss another dozen open questions.
20 Magic Knight’s Tours 153
John Beasley
The author surveys results combining a knight’s tour on the chessboard with magic squares, including a computer-aided solution to a Gardner question.
21 Some New Results on Magic Hexagrams 159
Martin Gardner
Here Gardner focuses on three types of puzzles about placing numbers on six-pointed stars, mentioning a “rare mistake” of the British puzzlist Henry Dudeney.
22 Finding All Solutions to theMagic Hexagram 167
Alexander Karabegov and Jason Holland
The authors relate magic hexagrams to magic edge labelings of cubes, using card shuffling to enumerate distinct solutions.
23 Triangular Numbers, Gaussian Integers, and KenKen 173
John J. Watkins
Miyamoto’s contemporary puzzle is expanded to complex numbers where a different unique factorization adds to the challenge.
V Further Puzzles and Games 179
24 Cups and Downs 181
Ian Stewart
One of Gardner’s mathematical successors at Scientific American uses graph theory and linear algebra on two related puzzles.
25 30 Years of Bulgarian Solitaire 187
Brian Hopkins
Some recent math history explains this oddly-named puzzle on integer partitions, visualized with state diagrams and generalized to a new two-player game.
26 Congo Bongo 195
Hsin-Po Wang
A high school student uses state diagrams and Dennis Shasha’s detectives to open a tricky treasure chest.
27 Sam Loyd’s Courier Problem with Diophantus, Pythagoras,
and Martin Gardner 201
Owen O’Shea
A Classroom Capsule extends Gardner’s solution of related Sam Loyd puzzles to other army formations.
28 Retrolife and The Pawns Neighbors 207
Yossi Elran
An inverse version of Conway’s game Life, famously popularized by Gardner, is examined using chessboards.
29 RATWYT 213
Aviezri Fraenkel
The combinatorial game theorist uses the Calkin Wilf tree to devise a rational number version of Wythoff’s Nim.
VI Cards and Probability 219
30 Modeling Mathematics with Playing Cards 221
Martin Gardner
In addition to probability applications, Gardner uses a deck of cards for a discrete version of a fluid mixing puzzle and mentions a correction to W. W. Rouse Ball.
31 The Probability an Amazing Card Trick Is Dull 227
Christopher N. Swanson
Rook polynomials and the principle of inclusion-exclusion help determine the likelihood that the author’s students were underwhelmed.
32 The Monty Hall Problem, Reconsidered 231
Stephen Lucas, Jason Rosenhouse, and Andrew Schepler
These authors remind us of Gardner’s early role in this infamous problem that still “arouses the passions” and examine variations.
33 The Secretary Problem from the Applicant’s Point of View 243
Darren Glass
Changing perspective, the author reconsiders a classic strategy in order to help job seekers choose the best interview slot.
34 LakeWobegon Dice 249
Jorge Moraleda and David G. Stork
Lake Wobegon Dice, named after Garrison Keillor’s Minnesota town, have the property that each is “better than the set average.”
35 Martin Gardner’s Mistake 257
Tanya Khovanova
Another controversial problemabout probability and information is carefully discussed, putting Gardner in the company of Dudeney and Ball.
VII Other Aspects of Martin Gardner 263
36 Against the Odds 265
Martin Gardner
In this short story, a principal recognizes the potential in a student whose unconventional thinking irritates his teacher.
37 A ModularMiracle 271
John Stillwell
Gardner used an obscure result of Hermite and the limitations of 1970’s calculators for an April Fool’s Day prank.
38 The Golden Ratio—A Contrary Viewpoint 273
Clement Falbo
Building on a Gardner article in The Skeptical Inquirer, the author argues that “is not entirely astonishing.”
39 Review of The Mysterious Mr. Ammann by Marjorie Senechal 285
Philip Straffin
ThisMedia Highlight discusses an example of Gardner’s support of an amateurmathematician who independently discovered Penrose tiles.
40 Review of PopCo by Scarlett Thomas 287
Martin Gardner
This popular 2004 novel includes a character based on Gardner, so he was a natural choice to review the book.
41 Superstrings and Thelma 289
Martin Gardner
Gardner’s last MAA submission, a short story about a physics graduate student and a waitress who quips, “How are strings?”
Index 293
About the Editors 297