Ellen Kaplan e Robert Kaplan
Bloomsbury Press | 2014 | 256 páginas | rar - epub | 18,3 Mb
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edição de 2006
Who hasn’t feared the math Minotaur in its labyrinth of abstractions? The subject can seem convoluted and forbidding. Yet to do mathematics is to wrestle with “accessible mysteries”—and Out of the Labyrinth shows how exhilarating the challenge can be. Robert and Ellen Kaplan are founders of the Math Circle, a pioneering learning program begun at Harvard in 1994 and now spreading around the world. In their classrooms students ages six to sixty have discovered mathematics as the highest form of intellectual play, while exploring topics that range from Roman numerals to quantum mechanics.
The Kaplans reveal the secrets of their highly successful approach, leading readers out of the labyrinth and into the joyous embrace of mathematics. Stocked with puzzles, colorful anecdotes, and insights from the authors’ own teaching experience, Out of the Labyrinth is both an engaging and practical guide for parents and educators, and a treasure chest of mathematical discoveries. For any reader who has felt the excitement of mathematical discovery—or tried to convey it to someone else—this volume will be a delightful and valued companion.
Contents
Chapter One: A Glimpse Inside
Chapter Two: Cod Liver Oil
Chapter Three: The Myth of Talent
Chapter Four: Making Your Hats
1. Holding On
Stubbornness
Orneriness
A High Threshold of Frustration
The Jump-Cut Mind
Putting On Hold
2. Taking Apart
Method vs. Approach
Atomizing
Attention Without Tension
Precision
Rotating the Diamond
Breaking Apart
Pursuing the Possible
3. Putting Together
Play
Stubbornness Revisited
The Riddle of the Pygmy Shrew
Analogy
Holding Hypotheses Like Birds
Experimental Fervor
The Architectural Instinct
The Conductor
Chapter Five: The Great Barrier Reef
Language: Symbols
Language: Equations
Language: Third Person Remote
The Buddha, the Bodhisattva, and the Bo
Climbing a Tall Building
Alienation
Diamond Hard
Who Cares?
Chapter Six: How Math Has Been Taught
Behind the Phenomena
The Teaching Wars
Cookbooks, Song-Lines, and Games
Ancestral Voices Calling for Reform
Anticurriculum
The Curate’s Egg
Russian Math Circles
Chapter Seven: How Mathematicians Actually Work
hapter Eight: The Math Circle
Ends
Beginnings
The Students
The Leaders
The Math
Connecting
Intuition Grows
A Proof Takes Shape
Looking Leads to Seeing
Competition
Chapter Nine: Filling in the Details
Where’s the Kit?
Math Itself
Courses
Sample Outline of a Middle Course: Interesting Points in Triangles
Piecemeal Advice
Perilous Turnings and Pivotal Moments
From a Journal
What’s the Way Forward?
The Summer Institute
To Take with You
Acknowledgments
Footnotes
Appendix: Thoughts of a Young Teacher
A Note on Our Pronouns
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